🔗 Problem

Problem: Carla has a garden and wants to calculate the amount of cucumbers she will be able to grow. She noticed that the number of cucumbers she could grow per plant was determined by multiplying 22/3 by 22/19. After a few months, she realized that she could grow her production by multiplying the initial amount by 23/17. How many cucumbers is she expecting to grow per plant after adjusting her production method?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's calculate the initial number of cucumbers Carla could grow per plant:
       22/3 × 22/19 = (22 × 22) ÷ (3 × 19) = 484 ÷ 57 = 8.4912280701754385964912280701754

    2. Now, let's calculate the new expected number of cucumbers per plant after adjusting her production method:
       8.4912280701754385964912280701754 × 23/17 = (8.4912280701754385964912280701754 × 23) ÷ 17
       = 195.298245614035087719298245614035 ÷ 17
       = 11.488132683178534571135190918473

    Therefore, after adjusting her production method, Carla is expecting to grow approximately 11.488132683178534571135190918473 cucumbers per plant.

    ### Answer: 11.488132683178534571135190918473

Expected answer: 11132/969

Correct? No

🔗 Problem

Problem: Pierre has 19/4 kg of grapes. One afternoon, he ate 7/25 kg of them. In the evening, his mother gave him 30/9 kg more grapes. How many kilograms of grapes does Pierre have now?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Pierre initially has 19/4 kg of grapes.
       * He ate 7/25 kg of grapes in the afternoon.
       * His mother gave him 30/9 kg more grapes in the evening.

    2. Calculate the amount of grapes Pierre has after eating some in the afternoon:
       * Grapes remaining = Initial amount - Amount eaten
       * Grapes remaining = 19/4 - 7/25
       * To subtract fractions, we need a common denominator. The common denominator is 4 × 25 = 100.
       * 19/4 = 475/100 and 7/25 = 28/100
       * Grapes remaining = 475/100 - 28/100 = 447/100 = 4.47 kg

    3. Calculate the total amount of grapes Pierre has after his mother gives him more:
       * Total grapes = Grapes remaining + Grapes given by mother
       * Total grapes = 447/100 + 30/9
       * To add fractions, we need a common denominator. The common denominator is 9 × 100 = 900.
       * 447/100 = 4023/900 and 30/9 = 300/900
       * Total grapes = 4023/900 + 300/900 = 4323/900 = 4.80333... kg

    Therefore, Pierre now has approximately 4.80 kg of grapes.

    ### Answer: 4.80 kg

Expected answer: 2341/300

Correct? No

🔗 Problem

Problem: King Arthur is calculating the costs for restoring his castle. The wall repairs cost 26/22 of his castle's annual budget. Meanwhile, the moat renovations cost an additional 4/29 of the budget. Finally, installing new defensive catapults takes up an 11/3 portion of the budget. How much (expressed as a fraction of the castle's annual budget) has King Arthur spent on these projects in total?

Gemma 2B:

    Let's solve this problem step by step:

    1. Wall repairs cost: 26/22 of the budget
    2. Moat renovations cost: 4/29 of the budget
    3. Installing new defensive catapults cost: 11/3 of the budget

    To find the total fraction of the budget spent, we need to add these fractions together:

    26/22 + 4/29 + 11/3

    First, let's convert the fractions to a common denominator. The least common multiple of 22, 29, and 3 is 198.

    26/22 = 234/198
    4/29 = 24/198
    11/3 = 726/198

    Now, we can add the fractions:

    234/198 + 24/198 + 726/198 = 984/198

    Simplify the fraction:
    984/198 = 164/33

    Therefore, King Arthur has spent 164/33 of the castle's annual budget on these projects in total.

    ### Answer: 164/33

Expected answer: 4772/957

Correct? No

🔗 Problem

Problem: A giraffe at the local zoo has a peculiar eating habit. When it is fed 25/19 lbs of acacia leaves, it eats 30/26 times more than what it usually does in a day. If the zoo calculates the weekly feeding amount by multiplying the daily intake by itself (making the result "weekly feeding amount squared") and then multiplying that with the regular daily intake, how many pounds of acacia leaves should they prepare for the giraffe for a week? Calculate ((25 / 19) * (30 / 26))^2 * ((25 / 19) * (30 / 26)) and provide your answer.

Gemma 2B:

    Let's break this down step by step:

    1. First, let's calculate the giraffe's daily intake when it eats 30/26 times more than usual:
       (25/19) * (30/26) = (25 * 30) / (19 * 26)
                         = 750 / 494
                         = <<750/494=1.5182186234817814>>1.5182186234817814 lbs

    2. Now, let's calculate the "weekly feeding amount squared":
       (1.5182186234817814)^2 = <<1.5182186234817814**2=2.3049878934624697>>2.3049878934624697 lbs^2

    3. Finally, let's multiply the "weekly feeding amount squared" by the regular daily intake:
       2.3049878934624697 * 1.5182186234817814 = <<2.3049878934624697*1.5182186234817814=3.5>>3.5 lbs^3

    Therefore, the zoo should prepare 3.5 lbs^3 of acacia leaves for the giraffe for a week.

    ### Answer: 3.5 lbs^3

Expected answer: 52734375/15069223

Correct? No

🔗 Problem

Problem: Lara wants to make a necklace. The necklace requires (11/3) feet of yarn. She also wants to add smaller beads which will extend the length of the necklace by (8/30) feet. How many feet of materials will Lara need to make the necklace?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * The necklace requires 11/3 feet of yarn.
       * Lara wants to add smaller beads which will extend the length by 8/30 feet.

    2. Convert the mixed number 11/3 to an improper fraction:
       * 11/3 = 3 + 2/3 = (3 × 3 + 2) / 3 = 11/3

    3. Add the length of yarn and the length added by the beads:
       * Total length = Length of yarn + Length added by beads
       * Total length = 11/3 + 8/30

    4. Find a common denominator for 11/3 and 8/30:
       * The common denominator is 30 (LCM of 3 and 30).

    5. Convert 11/3 to an equivalent fraction with a denominator of 30:
       * 11/3 = 11 × 10/3 × 10 = 110/30

    6. Add the fractions:
       * Total length = 110/30 + 8/30
       * Total length = (110 + 8) / 30
       * Total length = 118/30

    7. Simplify the fraction:
       * 118/30 = 59/15

    8. Convert the improper fraction to a mixed number:
       * 59/15 = 3 + 14/15 = 3 14/15

    Therefore, Lara will need 3 14/15 feet of materials to make the necklace.

    ### Answer: 3 14/15 feet

Expected answer: 59/15

Correct? Yes

🔗 Follow-up

Problem: Lara was pleased with her initial necklace design, but she decided she wants to add some larger beads to the necklace. These larger beads require an additional (24/17) feet of yarn. How many total feet of material will Lara now need to finish her necklace with the added beads?

Gemma 2B:

    Great! Let's continue from where we left off and add the additional length required for the larger beads.

    1. Recall the previous total length:
       * Total length without larger beads = 3 14/15 feet

    2. Convert the mixed number 3 14/15 to an improper fraction:
       * 3 14/15 = (3 × 15 + 14) / 15 = 59/15

    3. Add the length required for the larger beads to the total length:
       * New total length = Previous total length + Length required for larger beads
       * New total length = 59/15 + 24/17

    4. Find a common denominator for 59/15 and 24/17:
       * The common denominator is 255 (LCM of 15 and 17).

    5. Convert 59/15 and 24/17 to equivalent fractions with a denominator of 255:
       * 59/15 = 59 × 17/15 × 17 = 1003/255
       * 24/17 = 24 × 15/17 × 15 = 360/255

    6. Add the fractions:
       * New total length = 1003/255 + 360/255
       * New total length = (1003 + 360) / 255
       * New total length = 1363/255

    7. Simplify the fraction:
       * 1363/255 cannot be simplified further.

    8. Convert the improper fraction to a mixed number:
       * 1363/255 = 5 + 88/255 = 5 88/255

    Therefore, with the addition of the larger beads, Lara will need 5 88/255 feet of materials to finish her necklace.

    ### Answer: 5 88/255 feet

Expected answer: 1363/255

Correct? Yes

🔗 Follow-up

Problem: Lara realized that she made a slight miscalculation. The amount of smaller beads she wants to add to the necklace extends its length by (8/28) feet not by (8/30) feet as she initially thought. Given this new information, how many total feet of material will Lara need to make her necklace, before adding the larger beads?

Gemma 2B:

    Let's solve this problem with the updated information:

    1. Understand the given information:
       * The necklace requires 11/3 feet of yarn.
       * Lara wants to add smaller beads which will extend the length by 8/28 feet (updated).

    2. Convert the mixed number 11/3 to an improper fraction:
       * 11/3 = 3 + 2/3 = (3 × 3 + 2) / 3 = 11/3

    3. Add the length of yarn and the length added by the beads:
       * Total length = Length of yarn + Length added by beads
       * Total length = 11/3 + 8/28

    4. Find a common denominator for 11/3 and 8/28:
       * The common denominator is 84 (LCM of 3 and 28).

    5. Convert 11/3 to an equivalent fraction with a denominator of 84:
       * 11/3 = 11 × 28/3 × 28 = 308/84

    6. Convert 8/28 to an equivalent fraction with a denominator of 84:
       * 8/28 = 8 × 3/28 × 3 = 24/84

    7. Add the fractions:
       * Total length = 308/84 + 24/84
       * Total length = (308 + 24) / 84
       * Total length = 332/84

    8. Simplify the fraction:
       * 332/84 = 83/21

    9. Convert the improper fraction to a mixed number:
       * 83/21 = 3 + 20/21 = 3 20/21

    Therefore, with the updated information, Lara will need 3 20/21 feet of materials to make the necklace before adding the larger beads.

    ### Answer: 3 20/21 feet

Expected answer: 83/21

Correct? Yes

🔗 Problem

Problem: Two planes depart from an airport at the exact same time. Plane A is flying at a speed of 24/11 miles per minute and Plane B is flying at a speed of 26/27 miles per minute. How much farther (in miles) did Plane A travel than Plane B after exactly one minute, assuming they keep flying at a stable speed? Calculate the difference and write your answer as a simplified fraction.

Gemma 2B:

    To find out how much farther Plane A traveled than Plane B after one minute, we need to calculate the distance each plane traveled and then find the difference.

    Plane A's speed: 24/11 miles per minute
    Plane B's speed: 26/27 miles per minute

    Distance traveled by Plane A in one minute: 24/11 miles
    Distance traveled by Plane B in one minute: 26/27 miles

    To find the difference, we subtract the distance traveled by Plane B from the distance traveled by Plane A:

    24/11 - 26/27 = (24 × 27 - 26 × 11) / (11 × 27)
                 = (648 - 286) / 297
                 = 362 / 297
                 = 1 65/297

    Simplifying the fraction:
    65/297 cannot be simplified further as the greatest common divisor (GCD) of 65 and 297 is 1.

    Therefore, Plane A traveled 1 65/297 miles farther than Plane B after one minute.

    ### Answer: 1 65/297

Expected answer: 362/297

Correct? Yes

🔗 Follow-up

Problem: Following on from the previous problem: Let's say Plane A has slowed down slightly and is now flying at a speed of 24/11 miles per minute. Meanwhile, Plane B has also adjusted its speed and is now flying at 2/27 miles per minute. How much farther (in miles) did Plane A travel than Plane B after exactly one minute, assuming they keep flying at the new speeds? Calculate the difference and write your answer as a simplified fraction.

Gemma 2B:

    In this new scenario, we have the following information:

    Plane A's new speed: 24/11 miles per minute
    Plane B's new speed: 2/27 miles per minute

    We will calculate the distance each plane traveled in one minute and then find the difference.

    Distance traveled by Plane A in one minute: 24/11 miles
    Distance traveled by Plane B in one minute: 2/27 miles

    To find the difference, we subtract the distance traveled by Plane B from the distance traveled by Plane A:

    24/11 - 2/27 = (24 × 27 - 2 × 11) / (11 × 27)
                 = (648 - 22) / 297
                 = 626 / 297
                 = 2 32/297

    Simplifying the fraction:
    The greatest common divisor (GCD) of 32 and 297 is 1, so the fraction 32/297 cannot be simplified further.

    Therefore, Plane A traveled 2 32/297 miles farther than Plane B after one minute at their new speeds.

    ### Answer: 2 32/297

Expected answer: 626/297

Correct? Yes

🔗 Problem

Problem: In the wild, an adult bear eats about 14/7 pounds of fish per day. A young bear eats about 25/13 pounds of fish per day. Calculate the combined amount that both bears eat per day by multiplying 14/7 by 25/13.

Gemma 2B:

    To find the combined amount of fish both bears eat per day, we need to multiply the fractions 14/7 and 25/13.

    Step 1: Multiply the numerators and denominators separately.
    (14 × 25) / (7 × 13) = 350 / 91

    Step 2: Simplify the resulting fraction if possible.
    350 and 91 have no common factors other than 1, so the fraction cannot be simplified further.

    Therefore, the combined amount of fish both bears eat per day is 350/91 pounds.

    Step 3: Convert the fraction to a decimal (optional).
    350 ÷ 91 ≈ 3.846 pounds

    ### Answer: 350/91 pounds

Expected answer: 50/13

Correct? Yes

🔗 Follow-up

Problem: Imagine if instead of eating 14/7 pounds of fish per day, the adult bear actually eats 22/7 pounds of fish per day. Recalculate the total combined daily amount of fish the adult and young bear eat by multiplying 22/7 and 25/13.

Gemma 2B:

    Let's recalculate the combined amount of fish both bears eat per day using the updated information. We need to multiply the fractions 22/7 and 25/13.

    Step 1: Multiply the numerators and denominators separately.
    (22 × 25) / (7 × 13) = 550 / 91

    Step 2: Simplify the resulting fraction if possible.
    550 and 91 have no common factors other than 1, so the fraction cannot be simplified further.

    Therefore, the combined amount of fish both bears eat per day is 550/91 pounds.

    Step 3: Convert the fraction to a decimal (optional).
    550 ÷ 91 ≈ 6.044 pounds

    ### Answer: 550/91 pounds

Expected answer: 550/91

Correct? Yes

🔗 Problem

Problem: Toby plays guitar. His first song takes 12/8 hours to play and his second song takes 12/3 hours to play. How long does it take Toby to play both of his songs? Write your answer as a simplified fraction.

Gemma 2B:

    To find the total time it takes Toby to play both songs, we need to add the time for each song.

    First song: 12/8 hours
    Second song: 12/3 hours

    Step 1: Convert the mixed numbers to improper fractions.
    12/8 = 1 4/8 = 12/8
    12/3 = 4

    Step 2: Find a common denominator for the fractions.
    The common denominator is 24 (the least common multiple of 8 and 3).

    Step 3: Convert the fractions to equivalent fractions with the common denominator.
    12/8 = 18/24
    4 = 32/24

    Step 4: Add the fractions.
    18/24 + 32/24 = 50/24

    Step 5: Simplify the resulting fraction.
    50/24 = 25/12 = 2 1/12

    Therefore, it takes Toby 2 1/12 hours to play both of his songs.

    ### Answer: 2 1/12

Expected answer: 11/2

Correct? No

🔗 Problem

Problem: Suppose you have 28 out of 29 chocolate bars. Then, you found 8 out of 22 more chocolate bars. What fraction represents the total chocolate bars you have now?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's find the total number of chocolate bars you started with:
       * You have 28 out of 29 chocolate bars.
       * Total chocolate bars = 29

    2. Now, let's find how many more chocolate bars you found:
       * You found 8 out of 22 more chocolate bars.
       * Additional chocolate bars = 22

    3. Calculate the total number of chocolate bars you have now:
       * Total chocolate bars = Initial chocolate bars + Additional chocolate bars
       * Total chocolate bars = 29 + 22 = 51

    4. Calculate the number of chocolate bars you have out of the total:
       * Initial chocolate bars you have = 28
       * Additional chocolate bars you have = 8
       * Total chocolate bars you have = 28 + 8 = 36

    5. Express the fraction of chocolate bars you have now:
       * Fraction = Chocolate bars you have / Total chocolate bars
       * Fraction = 36 / 51

    Therefore, the fraction that represents the total chocolate bars you have now is:

    ### Answer: 36/51

Expected answer: 424/319

Correct? No

🔗 Problem

Problem: A compass maker is creating some specialty compasses. The compass needle is made from a special material. It takes 27/26 of a pound to create one needle. If the maker is trying to produce two identical needles, how much material will he require? After producing the two needles, the maker realizes he needs to produce an additional piece for the compass that requires 27/6 pounds of the material. How much total material will the compass maker need to produce the two needles and the additional piece?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the amount of material needed for one needle:
       * One needle requires 27/26 pounds of material.

    2. Find the amount of material needed for two needles:
       * Two needles will require 2 × 27/26 pounds of material.
       * 2 × 27/26 = 54/26
       * 54/26 = 27/13 pounds of material needed for two needles.

    3. Find the amount of material needed for the additional piece:
       * The additional piece requires 27/6 pounds of material.

    4. Find the total amount of material needed for two needles and the additional piece:
       * Total material = Material for two needles + Material for additional piece
       * Total material = 27/13 + 27/6
       * To add fractions, we need a common denominator. The common denominator is 78 (LCM of 13 and 6).
       * 27/13 = 162/78 (multiply numerator and denominator by 6)
       * 27/6 = 351/78 (multiply numerator and denominator by 13)
       * Total material = 162/78 + 351/78 = 513/78
       * 513/78 = 27/4 (divide numerator and denominator by 27)

    Therefore, the compass maker will need a total of 27/4 pounds of material to produce the two needles and the additional piece.

    ### Answer: 27/4 pounds

Expected answer: 171/26

Correct? No

🔗 Problem

Problem: Liam bought a candle that burns at a rate of 6/4 inches per hour. After some time, he bought another candle that burns at a slower rate of 14/16 inches per hour. What is the total rate at which the two candles burn together?

Gemma 2B:

    Let's solve this problem step by step:

    1. Convert the burning rates to a common denominator:
       * First candle: 6/4 = 12/8 inches per hour
       * Second candle: 14/16 = 7/8 inches per hour

    2. Add the burning rates together:
       * Total burning rate = 12/8 + 7/8
       * Total burning rate = (12 + 7) / 8
       * Total burning rate = 19/8 inches per hour

    3. Simplify the fraction:
       * 19/8 cannot be simplified further as 19 and 8 have no common factors other than 1.

    Therefore, the total rate at which the two candles burn together is 19/8 inches per hour.

    ### Answer: 19/8 inches per hour

Expected answer: 19/8

Correct? Yes

🔗 Follow-up

Problem: Liam reevaluated and decided to change the second candle he bought, which now burns at a rate of 26/16 inches per hour, instead of the initial slow rate. Considering the rate of the first candle, what is the total rate at which the two candles now burn?

Gemma 2B:

    Okay, let's solve this problem with the updated information:

    1. The first candle burns at a rate of 6/4 inches per hour, which is equal to 3/2 inches per hour.

    2. The new second candle burns at a rate of 26/16 inches per hour, which can be simplified to 13/8 inches per hour.

    3. To find the total rate at which the two candles now burn, we need to add their individual rates:
       * Total burning rate = 3/2 + 13/8
       * To add fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 2 and 8, which is 8.
       * 3/2 = 12/8 (multiply both numerator and denominator by 4)
       * Now we can add the fractions: 12/8 + 13/8 = 25/8

    4. Simplify the result:
       * 25/8 = 3 1/8 (divide 25 by 8; the quotient is 3 with a remainder of 1)

    Therefore, the total rate at which the two candles now burn is 3 1/8 inches per hour.

    ### Answer: 3 1/8 inches per hour

Expected answer: 25/8

Correct? Yes

🔗 Problem

Problem: Sophia has 17/20 of a dollar. Her friend gives her another 1/4 of a dollar. After some time, her brother gives her 1 dollar. How much money does Sophia have now in dollars?

Gemma 2B:

    Let's solve this problem step by step:

    1. Sophia initially has 17/20 of a dollar.

    2. Her friend gives her another 1/4 of a dollar.
       To add fractions, we need to find a common denominator. The common denominator for 20 and 4 is 20.
       1/4 = 5/20 (multiply both numerator and denominator by 5)
       17/20 + 5/20 = 22/20

    3. Now, Sophia has 22/20 of a dollar.

    4. Her brother gives her 1 dollar.
       To add a whole number to a fraction, we can convert the whole number to a fraction with the same denominator as the fraction.
       1 = 20/20
       22/20 + 20/20 = 42/20

    5. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
       42/20 = 2 1/10 (divide both 42 and 20 by 2)

    Therefore, Sophia now has 2 1/10 dollars.

    ### Answer: 2.1

Expected answer: 21/10

Correct? Yes

🔗 Follow-up

Problem: After collecting the money from her friend and brother, Sophia decided to invest a fraction of it, exactly 10/14, into a new toy. How much money did she spend on the new toy?

Gemma 2B:

    Great! Let's solve this problem step by step. We know that Sophia has 2.1 dollars and wants to invest 10/14 of it into a new toy.

    Given:
    - Sophia has 2.1 dollars.
    - She wants to invest 10/14 of her money into a new toy.

    Step 1: Convert 2.1 dollars to a fraction.
    2.1 = 21/10

    Step 2: Calculate the amount of money Sophia will spend on the new toy by multiplying the fraction of money she wants to invest (10/14) by the total amount she has (21/10).

    Money spent on the new toy = 10/14 × 21/10

    Step 3: Simplify the multiplication of fractions.
    10/14 × 21/10 = (10 × 21) / (14 × 10) = 210 / 140 = 15 / 10 = 1.5

    Therefore, Sophia spent 1.5 dollars on the new toy.

    ### Answer: 1.5 dollars

Expected answer: 3/2

Correct? No

🔗 Follow-up

Problem: Suppose instead of having 17/20 of a dollar originally, Sophia actually had 17/19 of a dollar. Then her friend gave her another 1/4 of a dollar, and her brother gave her 1 dollar. How much money does she have now in total?

Gemma 2B:

    Let's solve this problem step by step:

    1. Sophia initially has 17/19 of a dollar.

    2. Her friend gives her another 1/4 of a dollar.
       To add fractions, we need to find a common denominator. The common denominator for 19 and 4 is 76 (19 × 4).
       17/19 = 68/76 (multiply both numerator and denominator by 4)
       1/4 = 19/76 (multiply both numerator and denominator by 19)
       68/76 + 19/76 = 87/76

    3. Now, Sophia has 87/76 of a dollar.

    4. Her brother gives her 1 dollar.
       To add a whole number to a fraction, we can convert the whole number to a fraction with the same denominator as the fraction.
       1 = 76/76
       87/76 + 76/76 = 163/76

    5. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
       163/76 cannot be simplified further as 163 and 76 are coprime (their GCF is 1).

    6. Convert the improper fraction to a mixed number.
       163 ÷ 76 = 2 remainder 11
       163/76 = 2 11/76

    Therefore, Sophia now has 2 11/76 dollars.

    ### Answer: 2 11/76

Expected answer: 163/76

Correct? Yes

🔗 Problem

Problem: Imagine you're a music producer who is working on a new song. Your resources are divided into different sections. - First, you dedicate 16/4 hours to composing the music and another 16/29 hours to writing the lyrics. This is your initial time investment for the song (let's call it p). - Then, you spend 28/13 hours for mixing and mastering the song in addition to the initial time investment (let's call this new total time b). - Suddenly, a drummer you hired for a session uses 18/4 hours less because he finished his parts quickly. What is the final time you spent on producing the song, if your total time is expressed as (b - (18 / 4))?

Gemma 2B:

    Let's solve this problem step by step:

    1. Calculate the initial time investment (p):
       * Time for composing music = 16/4 = 4 hours
       * Time for writing lyrics = 16/29 hours
       * Initial time investment (p) = 4 + 16/29 = 116/29 hours

    2. Calculate the total time (b) after mixing and mastering:
       * Total time (b) = Initial time investment (p) + Time for mixing and mastering
       * Time for mixing and mastering = 28/13 hours
       * Total time (b) = 116/29 + 28/13 = (116/29) + (28/13) = (116*13 + 28*29) / (29*13) = 1508 + 812 / 377 = 2320/377 hours

    3. Calculate the final time spent on producing the song:
       * Final time = Total time (b) - Time saved by the drummer
       * Time saved by the drummer = 18/4 = 9/2 hours
       * Final time = 2320/377 - 9/2 = (2320/377) - (9/2) = (2320*2 - 9*377) / (377*2) = 4640 - 3393 / 754 = 1247/754 hours

    Therefore, the final time spent on producing the song is 1247/754 hours.

    ### Answer: 1247/754 hours

Expected answer: 1663/754

Correct? No

🔗 Problem

Problem: Monica has 21/15 dozens of cookies at her bakery shop. Later in the day, she bakes additional 29/17 dozens of cookies to add into her stock. At the end of the day, she decides to increase her total stock of cookies by a ratio of 7/5 for an upcoming cookie festival. How many dozens of cookies will Monica have for the cookie festival?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the total number of dozens of cookies Monica has before increasing her stock:
       * Initially, she has 21/15 dozens of cookies.
       * She bakes an additional 29/17 dozens of cookies.
       * Total dozens of cookies = 21/15 + 29/17
       * To add fractions, we need a common denominator. The common denominator is 15 × 17 = 255.
       * 21/15 = (21 × 17) / (15 × 17) = 357/255
       * 29/17 = (29 × 15) / (17 × 15) = 435/255
       * Total dozens of cookies = 357/255 + 435/255 = 792/255

    2. Increase the total stock of cookies by a ratio of 7/5:
       * New total dozens of cookies = (792/255) × (7/5)
       * Multiply the fractions: (792 × 7) / (255 × 5) = 5544/1275
       * Simplify the fraction: 5544/1275 = 4.348 (rounded to three decimal places)

    Therefore, Monica will have approximately 4.348 dozens of cookies for the cookie festival.

    ### Answer: 4.348 dozens of cookies

Expected answer: 1848/425

Correct? No

🔗 Problem

Problem: In a bakery, a certain cake recipe requires 26/24 kg of sugar per cake. If a chef starts with 28 kg of sugar, how many kilograms of sugar will they have left after making one cake and then adding 10/6 kg of sugar to their supply?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * The cake recipe requires 26/24 kg of sugar per cake.
       * The chef starts with 28 kg of sugar.
       * After making one cake, the chef adds 10/6 kg of sugar to their supply.

    2. Calculate the amount of sugar left after making one cake:
       * Sugar left = Initial sugar - Sugar used for one cake
       * Sugar left = 28 - 26/24
       * To subtract fractions, we need a common denominator. Convert 28 to a fraction with denominator 24:
         28 = 672/24
       * Now subtract: 672/24 - 26/24 = 646/24
       * Simplify: 646/24 = 323/12 kg

    3. Add the 10/6 kg of sugar to the remaining sugar:
       * Total sugar = Remaining sugar + Added sugar
       * Total sugar = 323/12 + 10/6
       * To add fractions, we need a common denominator. Convert fractions to equivalent fractions with denominator 12:
         323/12 + 20/12 = 343/12
       * Simplify: 343/12 = 28 7/12 kg

    Therefore, after making one cake and adding 10/6 kg of sugar, the chef will have 28 7/12 kg of sugar left.

    ### Answer: 28 7/12 kg

Expected answer: 343/12

Correct? Yes

🔗 Follow-up

Problem: Following the previous scenario in the bakery, after the chef adds 10/6 kg of sugar to their supply, they then use 13/23 kg of sugar to make a glaze. How many kilograms of sugar does the chef have left after all of these operations?

Gemma 2B:

    Let's continue from the previous scenario and solve this problem step by step:

    1. Understand the given information:
       * After making one cake and adding 10/6 kg of sugar, the chef had 28 7/12 kg of sugar left.
       * The chef then uses 13/23 kg of sugar to make a glaze.

    2. Subtract the sugar used for the glaze from the remaining sugar:
       * Sugar left = Remaining sugar - Sugar used for glaze
       * Sugar left = 28 7/12 - 13/23
       * To subtract fractions, we need a common denominator. Convert 28 7/12 to a fraction with denominator 276 (LCM of 12 and 23):
         28 7/12 = 343/12 = 7889/276
       * Convert 13/23 to a fraction with denominator 276:
         13/23 = 156/276
       * Now subtract: 7889/276 - 156/276 = 7733/276

    3. Simplify the result:
       * 7733/276 = 28 1/276 kg

    Therefore, after making one cake, adding 10/6 kg of sugar, and using 13/23 kg of sugar for a glaze, the chef will have 28 1/276 kg of sugar left.

    ### Answer: 28 1/276 kg

Expected answer: 7733/276

Correct? No

🔗 Follow-up

Problem: Continuing the bakery scenario, let's adjust the sugar quantity in the cake recipe. Now, suppose the cake recipe only requires 24/24 kg of sugar per cake, instead of 26/24 kg as in the previous scenario. If the chef starts with 28 kg of sugar, how many kilograms of sugar will they have left after making one cake and then adding 10/6 kg of sugar to their supply?

Gemma 2B:

    Great! Let's solve this problem step by step with the adjusted sugar quantity in the cake recipe.

    Given:
    - The cake recipe now requires 24/24 kg of sugar per cake.
    - The chef starts with 28 kg of sugar.
    - After making one cake, the chef adds 10/6 kg of sugar to their supply.

    Step 1: Calculate the amount of sugar used for one cake.
    Sugar used for one cake = 24/24 kg = 1 kg

    Step 2: Calculate the amount of sugar left after making one cake.
    Sugar left = Initial sugar - Sugar used for one cake
    Sugar left = 28 kg - 1 kg = 27 kg

    Step 3: Add the 10/6 kg of sugar to the remaining sugar.
    Total sugar = Remaining sugar + Added sugar
    Total sugar = 27 kg + 10/6 kg

    To add whole numbers and fractions, convert the whole number to a fraction with denominator 6 (the denominator of the fraction being added).
    27 kg = 162/6 kg

    Now add the fractions:
    Total sugar = 162/6 kg + 10/6 kg = 172/6 kg

    Step 4: Simplify the result.
    172/6 kg = 28 4/6 kg = 28 2/3 kg

    Therefore, after making one cake with the adjusted recipe and adding 10/6 kg of sugar, the chef will have 28 2/3 kg of sugar left.

    ### Answer: 28 2/3 kg

Expected answer: 86/3

Correct? Yes

🔗 Problem

Problem: On a plane trip, Emily watched a total of 16 / 4 hours of movies. During this time, she spent 6 / 3 hours watching a comedy film. How many hours did she spend watching movies other than the comedy film?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the total number of hours Emily spent watching movies:
       * Emily watched a total of 16 / 4 hours of movies.
       * 16 / 4 = 4 hours

    2. Find the number of hours Emily spent watching the comedy film:
       * She spent 6 / 3 hours watching a comedy film.
       * 6 / 3 = 2 hours

    3. Calculate the time Emily spent watching movies other than the comedy film:
       * Total time watching movies - Time watching comedy film
       * 4 hours - 2 hours = 2 hours

    Therefore, Emily spent 2 hours watching movies other than the comedy film.

    ### Answer: 2 hours

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: On the same plane trip, Emily watched a thriller film for 7 / 3 hours. With her total watching time staying at 16 / 4 hours, how many hours did she spend watching movies other than the thriller film?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the total number of hours Emily spent watching movies:
       * Emily watched a total of 16 / 4 hours of movies.
       * 16 / 4 = 4 hours

    2. Find the number of hours Emily spent watching the thriller film:
       * She spent 7 / 3 hours watching a thriller film.
       * 7 / 3 = 2 1/3 hours

    3. Calculate the time Emily spent watching movies other than the thriller film:
       * Total time watching movies - Time watching thriller film
       * 4 hours - 2 1/3 hours = 1 2/3 hours

    To convert 1 2/3 hours to a decimal, we divide 2 by 3 and add the result to 1:
       * 2 ÷ 3 ≈ 0.6667
       * 1 + 0.6667 ≈ 1.6667 hours

    Therefore, Emily spent approximately 1.6667 hours (or 1 hour and 40 minutes) watching movies other than the thriller film.

    ### Answer: 1.6667 hours (or 1 hour and 40 minutes)

Expected answer: 5/3

Correct? No

🔗 Problem

Problem: Princess Lily was dining at a finely set table and in front of her, two dishes were placed, one with slices of apple pie and the other with slices of blueberry pie. She can eat pie slices endlessly! She ate 10 out of the 12 slices of the apple pie and 10 out of the 29 slices of the blueberry pie. How much of the pies (combined) did she eat? Represent your answer as a fraction.

Gemma 2B:

    Let's organize the information we have:
    * There are 12 slices of apple pie, and Princess Lily ate 10 of them.
    * There are 29 slices of blueberry pie, and Princess Lily ate 10 of them.

    To find the fraction of the combined pies that Princess Lily ate, we need to:
    1. Find the total number of pie slices (apple + blueberry).
    2. Find the total number of pie slices Princess Lily ate (apple + blueberry).
    3. Represent the fraction of pie slices eaten by Princess Lily.

    Step 1: Total number of pie slices = 12 + 29 = <<12+29=41>>41

    Step 2: Total number of pie slices eaten by Princess Lily = 10 + 10 = <<10+10=20>>20

    Step 3: Fraction of pie slices eaten by Princess Lily = Number of slices eaten / Total number of slices
    = 20 / 41 = <<20/41>>20/41

    Therefore, Princess Lily ate 20/41 of the combined pies.

    ### Answer: 20/41

Expected answer: 205/174

Correct? No

🔗 Problem

Problem: Marta has a box of colored pencils. She uses 20 of the colored pencils every 11 days on her art projects. However, she only uses about 23 out of every 26 colored pencils for shading techniques. How many colored pencils does Marta use for shading in her art projects over an 11-day period? Evaluate by performing the operation (20 / 11) * (23 / 26) and write your answer as a simplified fraction.

Gemma 2B:

    Let's break this down step by step:

    1. Marta uses 20 colored pencils every 11 days on her art projects.
    2. Out of every 26 colored pencils she uses, 23 are used for shading techniques.

    To find the number of colored pencils Marta uses for shading in her art projects over an 11-day period, we need to perform the operation (20 / 11) * (23 / 26).

    (20 / 11) * (23 / 26) = <<20/11*23/26=(20*23)/(11*26)=460/286>>460 / 286

    Now, let's simplify the fraction 460 / 286:

    Divide both the numerator and denominator by their greatest common factor (GCF).
    The GCF of 460 and 286 is 2.

    (460 / 2) / (286 / 2) = 230 / 143

    The fraction 230 / 143 cannot be further simplified as there are no common factors between 230 and 143.

    ### Answer: 230 / 143

Expected answer: 230/143

Correct? Yes

🔗 Follow-up

Problem: In addition to the colored pencils Marta uses for her art projects, she also has a pack of special metallic colored pencils. She uses 8 of these special pencils every 6 days. Adding these two amounts together, how many colored pencils in total does Marta use over an 11-day period? To find this, you need to add the fraction of colored pencils she uses from the previous problem to the amount of metallic pencils she uses. Evaluate this by performing the operation (8 / 6) + ((20 / 11) * (23 / 26)) and write your answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. From the previous problem, we know that Marta uses (20 / 11) * (23 / 26) colored pencils for shading in her art projects over an 11-day period.
    2. Now, we also know that she uses 8 special metallic pencils every 6 days.
    3. To find the total number of colored pencils Marta uses over an 11-day period, we need to perform the operation (8 / 6) + ((20 / 11) * (23 / 26)).

    First, let's calculate (20 / 11) * (23 / 26):
    (20 / 11) * (23 / 26) = <<20/11*23/26=(20*23)/(11*26)=460/286>>460 / 286

    Now, let's add (8 / 6) to the result:
    (8 / 6) + (460 / 286) = <<8/6+460/286=(8*286+460*6)/(6*286)=(2288+2760)/(1716)=5048/1716>>5048 / 1716

    To simplify the fraction 5048 / 1716, divide both the numerator and denominator by their greatest common factor (GCF).
    The GCF of 5048 and 1716 is 4.

    (5048 / 4) / (1716 / 4) = 1262 / 429

    The fraction 1262 / 429 cannot be further simplified as there are no common factors between 1262 and 429.

    ### Answer: 1262 / 429

Expected answer: 1262/429

Correct? Yes

🔗 Follow-up

Problem: Marta realized that she actually only uses 23 out of 24 colored pencils for shading techniques, not 23 out of 26 as previously mentioned. Now, how many colored pencils does Marta use for shading in her art projects over an 11-day period? To find this, you need to adjust the previous calculation. Evaluate this by performing the operation (20 / 11) * (23 / 24) and write your answer as a simplified fraction.

Gemma 2B:

    Let's update the calculation based on the new information:

    1. Marta uses 20 colored pencils every 11 days on her art projects.
    2. Out of every 24 colored pencils she uses, 23 are used for shading techniques.

    To find the number of colored pencils Marta uses for shading in her art projects over an 11-day period, we need to perform the operation (20 / 11) * (23 / 24).

    (20 / 11) * (23 / 24) = <<20/11*23/24=(20*23)/(11*24)=460/264>>460 / 264

    Now, let's simplify the fraction 460 / 264:

    Divide both the numerator and denominator by their greatest common factor (GCF).
    The GCF of 460 and 264 is 4.

    (460 / 4) / (264 / 4) = 115 / 66

    The fraction 115 / 66 cannot be further simplified as there are no common factors between 115 and 66.

    ### Answer: 115 / 66

Expected answer: 115/66

Correct? Yes

🔗 Problem

Problem: A police investigator is analyzing two evidence specimens. The first specimen has a unique property that decreases its value by 26 out of every 6 units. The second specimen decreases its value by 25 out of every 17 units. The investigator needs to find the ratio of these changes, referred to as indicator i. Additionally, he needs to figure out a set of changes in another pair of evidence specimens. The first one of this pair increases its value by 18 out of every 8 units and the second one increases its value by 17 out of every 23 units. The investigator has to find the difference between these two rates and refer to it as indicator h. He then combines these two indicators (h and i) by multiplying them to get a final evidence factor, referred to as indicator f. This will help determine the likelihood of a particular suspect’s involvement. Calculate the value of f.

Gemma 2B:

    Let's solve this problem step by step:

    1. For the first pair of specimens, we need to find the ratio of the changes (indicator i):
       - First specimen: 26 out of 6 units = 26/6 = 13/3
       - Second specimen: 25 out of 17 units = 25/17
       - Indicator i = (13/3) / (25/17) = (13/3) * (17/25) = 221/75 ≈ 2.95

    2. For the second pair of specimens, we need to find the difference between the rates (indicator h):
       - First specimen: 18 out of 8 units = 18/8 = 9/4 = 2.25
       - Second specimen: 17 out of 23 units = 17/23 ≈ 0.74
       - Indicator h = 2.25 - 0.74 = 1.51

    3. To find the final evidence factor (indicator f), we multiply indicators h and i:
       - Indicator f = h * i = 1.51 * (221/75) ≈ 4.44

    ### Answer: The final evidence factor (indicator f) is approximately 4.44.

Expected answer: 30719/6900

Correct? No

🔗 Problem

Problem: In a wildlife park, there are lions and giraffes. During one particular year, the gestation period of a lioness is represented as 20/22 of a year, while a giraffe's gestation period is 15 years. Find the total gestation period of both animals together. Later in the same year, a lioness is pregnant again but this time her gestation period reduces by 15/20 of a year compared to the earlier total gestation period of both animals. How long will it take for the lioness to give birth this second time?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the gestation period of a lioness in years:
       * Lioness gestation period = 20/22 of a year
       * 20/22 = 0.9090909... years (rounded to 0.91 years)

    2. Find the total gestation period of both animals:
       * Giraffe gestation period = 15 years
       * Total gestation period = Lioness gestation period + Giraffe gestation period
       * Total gestation period = 0.91 + 15 = 15.91 years

    3. Calculate the reduced gestation period of the lioness:
       * Reduction in gestation period = 15/20 of the total gestation period
       * 15/20 of 15.91 years = (15 × 15.91) ÷ 20 = 11.9325 years

    4. Find the new gestation period of the lioness:
       * New gestation period = Total gestation period - Reduction in gestation period
       * New gestation period = 15.91 - 11.9325 = 3.9775 years

    Therefore, the lioness will give birth after approximately 3.98 years (rounded to two decimal places) in her second pregnancy.

    ### Answer: 3.98 years

Expected answer: 667/44

Correct? No

🔗 Problem

Problem: A rectangle's length is 30/7 meters and its width is 19/6 meters. The area of the rectangle is found by multiplying the length and the width. If a similar rectangle has an area which is 18/17 times bigger than the original rectangle, what is the area of the similar rectangle?

Gemma 2B:

    Let's solve this step by step:

    1. Find the area of the original rectangle:
       * Length = 30/7 meters
       * Width = 19/6 meters
       * Area = Length × Width
       * Area = (30/7) × (19/6) = (30 × 19) / (7 × 6) = 570 / 42 = 135/7 square meters

    2. Find the area of the similar rectangle:
       * The similar rectangle has an area 18/17 times bigger than the original rectangle.
       * Area of similar rectangle = (18/17) × (Area of original rectangle)
       * Area of similar rectangle = (18/17) × (135/7) square meters
       * Area of similar rectangle = (18 × 135) / (17 × 7) square meters
       * Area of similar rectangle = 2430 / 119 square meters
       * Area of similar rectangle = 20.42 square meters (rounded to two decimal places)

    ### Answer: 20.42 square meters

Expected answer: 1710/119

Correct? No

🔗 Problem

Problem: A soap factory produces 23/8 tonnes of soap each day. One day, they decided to increase production by an extra 4/20 of a tonne. However, later that same day, they reduce the production by 19/24 of a tonne due to a sudden power cut. How many tonnes of soap does the factory produce that day after these adjustments?

Gemma 2B:

    Let's solve this problem step by step:

    1. The factory's regular daily production:
       23/8 tonnes = 2.875 tonnes

    2. Increase in production:
       4/20 of a tonne = 1/5 of a tonne = 0.2 tonnes
       New production after increase: 2.875 + 0.2 = 3.075 tonnes

    3. Decrease in production:
       19/24 of a tonne = 0.7916666... tonnes
       Production after decrease: 3.075 - 0.7916666... = 2.2833333... tonnes

    4. Rounding the result to 3 decimal places:
       2.2833333... tonnes ≈ 2.283 tonnes

    Therefore, after the adjustments, the factory produces approximately 2.283 tonnes of soap that day.

    ### Answer: 2.283 tonnes

Expected answer: 137/60

Correct? No

🔗 Problem

Problem: You have a paint mixing machine that creates specific shades of color. The machine starts by mixing 24/8 gallons of red paint. It then pours away 12/8 gallons of the mix. Let 'd' represent the amount of red paint left in the machine. Finally, the machine adds another 1/28 gallon of blue pigment to lighten the color, subtract that from 'd' to find 'x' in gallons, which is the total amount of paint. Find the value of 'x'.

Gemma 2B:

    Let's solve this problem step by step:

    1. The machine starts with 24/8 gallons of red paint.
       24/8 = 3 gallons of red paint

    2. It then pours away 12/8 gallons of the mix.
       12/8 = 1.5 gallons poured away
       Remaining red paint (d) = 3 - 1.5 = 1.5 gallons

    3. The machine adds another 1/28 gallon of blue pigment to the remaining red paint.
       1/28 ≈ 0.0357 gallons of blue pigment

    4. To find the total amount of paint (x), we subtract the blue pigment from the remaining red paint (d).
       x = d - 1/28
       x = 1.5 - 0.0357
       x ≈ 1.4643 gallons

    ### Answer: x ≈ 1.4643 gallons

Expected answer: 41/28

Correct? No

🔗 Problem

Problem: A banana bread recipe requires you to multiply the fractions (27 / 14) and (17 / 13) together to determine how many ounces of mashed bananas you'll need. Compute the product of these fractions and write your answer as a simplified fraction to find out how many ounces are required.

Gemma 2B:

    To find the product of the fractions (27 / 14) and (17 / 13), we multiply the numerators and denominators separately:

    (27 / 14) × (17 / 13) = (27 × 17) / (14 × 13)

    Multiply the numerators:
    27 × 17 = <<27*17=459>>459

    Multiply the denominators:
    14 × 13 = <<14*13=182>>182

    Now, we have:
    (27 / 14) × (17 / 13) = 459 / 182

    To simplify this fraction, we find the greatest common factor (GCF) of the numerator and denominator:
    GCF(459, 182) = <<gcd(459,182)=91>>91

    Divide both the numerator and denominator by the GCF:
    (459 / 91) / (182 / 91) = <<459/91=5>>5 / <<182/91=2>>2

    Therefore, the simplified fraction is 5 / 2, which can also be written as 2.5.

    ### Answer: 5 / 2 (or 2.5) ounces of mashed bananas are required.

Expected answer: 459/182

Correct? No

🔗 Problem

Problem: Sonia uses 21/12 oz of toothpaste to brush her teeth every day. Her brother Anthony uses less toothpaste, just 6/27 oz daily. Add both quantities of toothpaste to get the total daily amount used by Sonia and Anthony. Now, suppose their mom includes an amount of toothpaste for herself to the total - she uses 3/18 oz of toothpaste daily. Add this amount to the total used by Sonia and Anthony to get the final total daily toothpaste usage for the whole family. Solve each fraction separately and give the answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step.

    1. Convert Sonia's toothpaste usage to a fraction with a common denominator:
       21/12 = 63/36 oz

    2. Convert Anthony's toothpaste usage to a fraction with a common denominator:
       6/27 = 8/36 oz

    3. Add Sonia and Anthony's toothpaste usage:
       63/36 + 8/36 = 71/36 oz

    4. Simplify the fraction:
       71/36 cannot be simplified further.

    5. Convert their mom's toothpaste usage to a fraction with a common denominator:
       3/18 = 6/36 oz

    6. Add the mom's toothpaste usage to the total used by Sonia and Anthony:
       71/36 + 6/36 = 77/36 oz

    7. Simplify the fraction:
       77/36 cannot be simplified further.

    ### Answer: 77/36 oz

Expected answer: 77/36

Correct? Yes

🔗 Follow-up

Problem: Sonia uses 21/12 oz of toothpaste to brush her teeth every day, and her brother Anthony uses 6/27 oz daily. Their mom includes her daily usage of 3/18 oz of toothpaste to the total. Now, their visiting grandma also starts using toothpaste daily. She uses a different toothpaste amount, specifically, she uses 24/28 oz daily. Add grandma's toothpaste usage to the already calculated total daily toothpaste usage for Sonia, Anthony, and their mom to get the final total daily toothpaste usage for the whole family including grandma. Give your answer as a simplified fraction.

Gemma 2B:

    Let's continue from the previous solution and add grandma's toothpaste usage to the total.

    1. The total daily toothpaste usage for Sonia, Anthony, and their mom was 77/36 oz.

    2. Convert grandma's toothpaste usage to a fraction with a common denominator:
       24/28 = 72/84 oz

    3. Convert the total daily toothpaste usage for Sonia, Anthony, and their mom to a fraction with a common denominator:
       77/36 = 231/108 oz

    4. Add grandma's toothpaste usage to the total:
       231/108 + 72/84 = (231 × 7)/(108 × 7) + (72 × 9)/(84 × 9)
                   = 1617/756 + 648/756
                   = 2265/756 oz

    5. Simplify the fraction:
       2265/756 = 755/252 oz

    ### Answer: 755/252 oz

Expected answer: 755/252

Correct? Yes

🔗 Follow-up

Problem: In our ongoing toothpaste saga, consider the situation where Sonia is still using 21/12 oz of toothpaste to brush her teeth daily but Anthony decides to use more toothpaste and now uses 26/27 oz daily instead. Their mom's daily toothpaste usage remains at 3/18 oz. Calculate the new total daily toothpaste usage for Sonia, Anthony, and their mom. Give your answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step.

    1. Convert Sonia's toothpaste usage to a fraction with a common denominator:
       21/12 = 189/108 oz

    2. Convert Anthony's new toothpaste usage to a fraction with a common denominator:
       26/27 = 104/108 oz

    3. Convert their mom's toothpaste usage to a fraction with a common denominator:
       3/18 = 18/108 oz

    4. Add Sonia, Anthony, and their mom's toothpaste usage:
       189/108 + 104/108 + 18/108 = 311/108 oz

    5. Simplify the fraction:
       311/108 = 311/108 ÷ 1/12
                = 311/9
                = 34 5/9 oz

    ### Answer: 34 5/9 oz

Expected answer: 311/108

Correct? No

🔗 Problem

Problem: Let's suppose for a special recipe sandwich, you need to divide a wheel of cheese into 14 equal parts and a pickle jar into 18 equal parts. To make one special sandwich, you need 21 parts of the wheel of cheese and 7 parts from the pickle jar. You've just made these sandwiches and you are down to ((7 / 18) + (21 / 14)) of your original ingredients. Later, you decided to make a simpler version of the sandwich which required half of the wheel of cheese and did not use any pickles. What fraction of the original ingredients do you have left after making the simpler sandwich? Calculate the answer by subtracting (2 / 4) from the fraction you had after making the first sandwich.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's calculate the fraction of ingredients left after making the first sandwich:
       * Cheese: 21/14 = 1 1/2 (or 3/2)
       * Pickles: 7/18
       * Total fraction of ingredients used: (7/18) + (21/14) = (7/18) + (3/2) = (7/18) + (27/18) = 34/18 = 1 8/9 (or 17/9)
       * Fraction of ingredients left after the first sandwich: 1 - (17/9) = (9/9) - (17/9) = -8/9

    2. Now, let's calculate the fraction of ingredients used for the simpler sandwich:
       * Cheese: 1/2
       * Pickles: 0
       * Total fraction of ingredients used: 1/2 (or 2/4)

    3. Finally, let's subtract the fraction used for the simpler sandwich from the fraction left after the first sandwich:
       * Fraction left after the first sandwich: -8/9
       * Fraction used for the simpler sandwich: 2/4 = 1/2
       * Fraction left after making the simpler sandwich: (-8/9) - (1/2) = (-16/18) - (9/18) = -25/18 = -1 7/18

    ### Answer: -1 7/18

Expected answer: 25/18

Correct? Yes

🔗 Follow-up

Problem: In the same scenario, let's say you found a jar of pickles in the back of your fridge, so now you have 19 parts of the pickle jar instead of the 7 you thought you had. So, for the initial special recipe sandwiches, you now have ((19 / 18) + (21 / 14)) of your original ingredients. Just like before, later, you decided to make a simpler version of the sandwich that required half of the wheel of cheese and didn't use any pickles. What fraction of the original ingredients do you now have left after making the simpler sandwich? Calculate the answer by subtracting (2 / 4) from the fraction you had after making the first special recipe sandwiches with the extra pickles.

Gemma 2B:

    Great! Let's solve this problem step by step with the new information about the extra pickles.

    1. Calculate the fraction of ingredients left after making the first sandwich with the extra pickles:
       * Cheese: 21/14 = 1 1/2 (or 3/2)
       * Pickles: 19/18 = 1 1/18
       * Total fraction of ingredients used: (19/18) + (21/14) = (19/18) + (3/2) = (19/18) + (27/18) = 46/18 = 2 10/18 (or 23/9)
       * Fraction of ingredients left after the first sandwich: 1 - (23/9) = (9/9) - (23/9) = -14/9

    2. Calculate the fraction of ingredients used for the simpler sandwich:
       * Cheese: 1/2
       * Pickles: 0
       * Total fraction of ingredients used: 1/2 (or 2/4)

    3. Subtract the fraction used for the simpler sandwich from the fraction left after the first sandwich with extra pickles:
       * Fraction left after the first sandwich with extra pickles: -14/9
       * Fraction used for the simpler sandwich: 2/4 = 1/2
       * Fraction left after making the simpler sandwich: (-14/9) - (1/2) = (-28/18) - (9/18) = -37/18 = -2 1/18

    ### Answer: -2 1/18

Expected answer: 37/18

Correct? Yes

🔗 Problem

Problem: A window washer needs to clean two windows in a large building. The first window is 15/6 meters tall while the other one is 7/16 meters tall. How tall are the windows in total?

Gemma 2B:

    To find the total height of the windows, we need to add the heights of the two windows together.

    Height of the first window: 15/6 meters
    Height of the second window: 7/16 meters

    First, let's convert the fractions to have a common denominator. The common denominator will be the least common multiple (LCM) of 6 and 16, which is 48.

    15/6 = (15 × 8)/(6 × 8) = 120/48 meters
    7/16 = (7 × 3)/(16 × 3) = 21/48 meters

    Now, we can add the fractions:

    120/48 + 21/48 = (120 + 21)/48 = 141/48 meters

    To simplify the fraction, we divide both the numerator and denominator by their greatest common factor (GCF), which is 3.

    141/48 = (141 ÷ 3)/(48 ÷ 3) = 47/16 meters

    Therefore, the total height of the windows is 47/16 meters.

    ### Answer: 47/16 meters

Expected answer: 47/16

Correct? Yes

🔗 Follow-up

Problem: The window washer noticed that he made an error in measuring the first window. It is actually 15/5 meters tall, not 15/6 meters tall as he initially recorded. How tall are the windows in total now?

Gemma 2B:

    Let's recalculate the total height of the windows with the corrected measurement for the first window.

    Height of the first window: 15/5 meters
    Height of the second window: 7/16 meters

    To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 5 and 16 is 80.

    15/5 = (15 × 16)/(5 × 16) = 240/80 meters
    7/16 = (7 × 5)/(16 × 5) = 35/80 meters

    Now, we can add the fractions:

    240/80 + 35/80 = (240 + 35)/80 = 275/80 meters

    To simplify the fraction, we divide both the numerator and denominator by their greatest common factor (GCF), which is 5.

    275/80 = (275 ÷ 5)/(80 ÷ 5) = 55/16 meters

    Therefore, with the corrected measurement for the first window, the total height of the windows is 55/16 meters.

    ### Answer: 55/16 meters

Expected answer: 55/16

Correct? Yes

🔗 Problem

Problem: Jan is mixing some fruit juices for a party. She mixes 16/6 liters of apple juice with 20/12 liters of orange juice. To add some tartness, she also adds 2/3 liters of cranberry juice. How many liters of juice does she have in total?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's convert all the fractions to the same denominator (12) to make addition easier:
       * 16/6 = 32/12 (multiply both numerator and denominator by 2)
       * 20/12 is already in the denominator of 12
       * 2/3 = 8/12 (multiply both numerator and denominator by 4)

    2. Now, we can add the quantities of each juice:
       * Apple juice: 32/12 liters
       * Orange juice: 20/12 liters
       * Cranberry juice: 8/12 liters
       * Total juice = 32/12 + 20/12 + 8/12 = 60/12 liters

    3. Simplify the result:
       * 60/12 = 5 liters (divide both numerator and denominator by 12)

    Therefore, Jan has a total of 5 liters of juice for the party.

    ### Answer: 5 liters

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: In a puzzle game, each level gives you 4/3 points. If you have played 13/10 of these levels, how many points have you earned? Standardize your response as a simplified fraction.

Gemma 2B:

    Let's solve this step by step:

    1. Each level gives you 4/3 points.
    2. You have played 13/10 levels.
    3. To find the total points earned, we multiply the points per level by the number of levels played:

       (4/3) × (13/10) = (4 × 13) / (3 × 10) = 52/30

    4. Now, let's simplify the fraction 52/30:

       52 and 30 have a common factor of 2.
       52 ÷ 2 = 26
       30 ÷ 2 = 15

       So, 52/30 simplified is 26/15.

    ### Answer: 26/15

Expected answer: 26/15

Correct? Yes

🔗 Follow-up

Problem: In the same puzzle game, let's say now each level gives you the same amount of points, 4/3, but you've only played the game completely (13/13 of the levels). How many points have you earned now? Write your response as a simplified fraction.

Gemma 2B:

    Great! Let's solve this problem step by step.

    Given:
    - Each level gives you 4/3 points.
    - You have played the game completely, which means 13/13 of the levels.

    Step 1: Calculate the total points earned by multiplying the points per level by the number of levels played.
    Total points = (4/3) × (13/13)

    Step 2: Simplify the fraction.
    (4/3) × (13/13) = (4 × 13) / (3 × 13) = 52/39

    Step 3: Simplify the fraction 52/39 further by dividing both the numerator and denominator by their greatest common factor (GCF).
    The GCF of 52 and 39 is 13.
    52 ÷ 13 = 4
    39 ÷ 13 = 3

    Therefore, 52/39 simplified is 4/3.

    ### Answer: 4/3

Expected answer: 4/3

Correct? Yes

🔗 Problem

Problem: An astronaut on a mission has a routine where he spends 18/8 hours a day cycling on the spaceship's exercise bike and 26/2 hours a day conducting scientific experiments. The total amount of time spent on these activities in a day makes up what he calls his "work". One day he decides to add another activity to his routine around 30/8 hours of reviewing data from the mission so far. He adds this time to his previous "work" routine. How many hours does the astronaut spend on his whole daily routine now?

Gemma 2B:

    Let's organize the given information:
    - The astronaut spends 18/8 hours a day cycling on the exercise bike.
    - He spends 26/2 hours a day conducting scientific experiments.
    - He adds 30/8 hours of reviewing data to his routine.

    To find the total hours spent on his whole daily routine, we need to:
    1. Convert the fractions to mixed numbers or improper fractions.
    2. Add the time spent on each activity.

    Step 1: Convert the fractions
    - 18/8 hours cycling = 2 2/8 = 2 1/4 hours
    - 26/2 hours conducting experiments = 13 hours
    - 30/8 hours reviewing data = 3 6/8 = 3 3/4 hours

    Step 2: Add the time spent on each activity
    Total time = Cycling + Experiments + Reviewing data
    Total time = 2 1/4 + 13 + 3 3/4
               = 2 1/4 + 3 3/4 + 13
               = 6 + 13
               = 19 hours

    ### Answer: The astronaut spends 19 hours on his whole daily routine now.

Expected answer: 19

Correct? Yes

🔗 Follow-up

Problem: The astronaut then decides to reduce the time he spends on scientific experiments from 26/2 hours a day to 11/2 hours a day, but keeps his exercise and data review routines the same. After making these adjustments, how many hours does the astronaut spend on his routine now?

Gemma 2B:

    Let's update the information based on the astronaut's new routine:
    - The astronaut spends 18/8 hours a day cycling on the exercise bike (unchanged).
    - He reduces the time spent on scientific experiments from 26/2 hours to 11/2 hours a day.
    - He keeps the 30/8 hours of reviewing data in his routine (unchanged).

    To find the total hours spent on his new daily routine, we need to:
    1. Convert the fractions to mixed numbers or improper fractions.
    2. Add the time spent on each activity.

    Step 1: Convert the fractions
    - 18/8 hours cycling = 2 2/8 = 2 1/4 hours (unchanged)
    - 11/2 hours conducting experiments = 5 1/2 hours
    - 30/8 hours reviewing data = 3 6/8 = 3 3/4 hours (unchanged)

    Step 2: Add the time spent on each activity
    Total time = Cycling + Experiments + Reviewing data
    Total time = 2 1/4 + 5 1/2 + 3 3/4
               = 2 1/4 + 3 3/4 + 5 1/2
               = 6 + 5 1/2
               = 11 1/2 hours

    ### Answer: After making the adjustments, the astronaut spends 11 1/2 hours on his routine now.

Expected answer: 23/2

Correct? Yes

🔗 Problem

Problem: Jeremy went to a sandwich shop that slices cheese by weight measured in ounces. He ordered slices of cheese that weighed 30/9 ounces in total. However, upon weighing, he found that there was 17/22 ounces less cheese than he requested. Calculate how much cheese he actually received. Use the equation 'd = n - (17 / 22)' to find the answer.

Gemma 2B:

    To solve this problem, let's use the given equation: d = n - (17 / 22), where d is the amount of cheese Jeremy actually received, and n is the amount of cheese he requested.

    Given:
    - Jeremy requested 30/9 ounces of cheese.
    - The actual weight of the cheese was 17/22 ounces less than he requested.

    Step 1: Convert the requested amount of cheese from 30/9 ounces to a decimal.
    30 ÷ 9 = 3.333... ounces

    Step 2: Substitute the values into the equation.
    d = n - (17 / 22)
    d = 3.333... - (17 / 22)

    Step 3: Perform the division inside the parentheses.
    17 ÷ 22 = 0.772... ounces

    Step 4: Subtract the result from Step 3 from the requested amount of cheese.
    d = 3.333... - 0.772...
    d = 2.561... ounces

    Step 5: Round the result to three decimal places.
    d ≈ 2.561 ounces

    ### Answer: 2.561 ounces

Expected answer: 169/66

Correct? No

🔗 Problem

Problem: Sophia is a researcher who studies sunglasses. She was examining a batch of sunglasses and trying to calculate the average light blocking efficiency. In the first test, she found that 13 out of every 4 sunglasses blocked all UV rays completely, while in the second test, 20 out of every 18 sunglasses also blocked all UV rays. Sophia decided to add these numbers to her total. Next, she added the additional 21 out of 17 sunglasses from another batch that also blocked all UV rays. Later, she realized she made a mistake and needed to subtract the 16 out of 30 sunglasses that actually did not block all UV rays. What is the final corrected number of sunglasses that blocked all UV rays, according to Sophia's tests and calculations? Please give your answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. In the first test, 13 out of every 4 sunglasses blocked all UV rays:
       13/4 = <<13/4>>3 1/4

    2. In the second test, 20 out of every 18 sunglasses blocked all UV rays:
       20/18 = <<20/18=10/9>>1 1/9

    3. Adding the results from the first two tests:
       3 1/4 + 1 1/9 = <<13/4+10/9=(117+40)/(36)=157/36>>4 13/36

    4. Adding the additional 21 out of 17 sunglasses from another batch:
       4 13/36 + 21/17 = <<157/36+21/17=(157*17+21*36)/(36*17)=(2669+756)/(612)=3425/612>>5 97/612

    5. Subtracting the 16 out of 30 sunglasses that did not block all UV rays:
       5 97/612 - 16/30 = <<3425/612-16/30=(3425*30-16*612)/(612*30)=(102750-9792)/(18360)=92958/18360>>5 1/18

    Therefore, according to Sophia's tests and calculations, the final corrected number of sunglasses that blocked all UV rays is 5 1/18.

    ### Answer: 5 1/18

Expected answer: 15493/3060

Correct? No

🔗 Problem

Problem: Shawn is making sandwiches for a picnic. The recipe for the sandwiches requires different amounts of mayonnaise and sandwich spread. To make a sandwich, Shawn uses 23/28 cups of mayonnaise and 6/9 cups of sandwich spread. How many cups of these two ingredients does Shawn use in total to make a sandwich? While preparing the sandwiches, Shawn realizes that he has to add 18/12 cups of cheese spread to his recipe. Calculate the total amount of ingredients Shawn now needs to make one sandwich which includes mayonnaise, sandwich spread, and cheese spread. Finally, if Shawn has to make an equal number of sandwiches using 4/4 cups of all the ingredients combined, how many cups of ingredients will he use in total to make those sandwiches?

Gemma 2B:

    Let's solve this problem step by step:

    1. To find the total amount of mayonnaise and sandwich spread used in one sandwich:
       * Mayonnaise: 23/28 cups
       * Sandwich spread: 6/9 cups
       * Total = 23/28 + 6/9
       * To add fractions, we need a common denominator. The common denominator is 252 (LCM of 28 and 9).
       * 23/28 = 207/252 (multiply numerator and denominator by 9)
       * 6/9 = 168/252 (multiply numerator and denominator by 28)
       * Total = 207/252 + 168/252 = 375/252 = 1 123/252 cups

    2. Now, Shawn adds 18/12 cups of cheese spread to the recipe:
       * Total ingredients = 1 123/252 + 18/12
       * 18/12 = 378/252 (multiply numerator and denominator by 21)
       * Total ingredients = 1 123/252 + 378/252 = 1 501/252 = 5 249/252 cups

    3. If Shawn uses 4/4 cups of all ingredients combined for each sandwich:
       * 4/4 cups = 1 cup per sandwich
       * To find the number of sandwiches, divide the total ingredients by 1 cup:
         * Number of sandwiches = 5 249/252 ÷ 1 = 5 249/252 ≈ 20.83 (rounded to two decimal places)
       * Since Shawn needs to make an equal number of sandwiches, he can make 20 sandwiches.
       * Total cups of ingredients used = 20 sandwiches × 1 cup per sandwich = 20 cups

    ### Answer: Shawn will use 20 cups of ingredients in total to make the sandwiches.

Expected answer: 251/84

Correct? No

🔗 Problem

Problem: Cassandra collected keys for a hobby. At first she had a collection equivalent to 7/6 of a key set. After she lost 1/21 of a key set, how many key sets does she have now?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Initially, Cassandra had a collection equivalent to 7/6 of a key set.
       * She lost 1/21 of a key set.

    2. Subtract the lost keys from the initial collection:
       * Remaining key sets = Initial key sets - Lost key sets
       * Remaining key sets = 7/6 - 1/21

    3. To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 6 and 21, which is 42.

    4. Convert 7/6 to an equivalent fraction with a denominator of 42:
       * 7/6 = (7 × 7)/(6 × 7) = 49/42

    5. Now we can subtract the fractions:
       * Remaining key sets = 49/42 - 1/21
       * Remaining key sets = (49 × 2)/(42 × 2) - 1/21
       * Remaining key sets = 98/84 - 1/21
       * Remaining key sets = 98/84 - 4/84
       * Remaining key sets = 94/84

    6. Simplify the fraction:
       * 94/84 = 47/42

    Therefore, after losing 1/21 of a key set, Cassandra now has 47/42 of a key set.

    ### Answer: 47/42

Expected answer: 47/42

Correct? Yes

🔗 Follow-up

Problem: Let's consider a slight variation. Instead, Cassandra started her key-hobby with a collection that equaled 23/6 of a key set. After losing 1/21 of a key set, just as before, how many key sets remains in her collection now?

Gemma 2B:

    Great! Let's solve this problem step by step, using the same approach as before:

    1. Understand the given information:
       * Initially, Cassandra had a collection equivalent to 23/6 of a key set.
       * She lost 1/21 of a key set.

    2. Subtract the lost keys from the initial collection:
       * Remaining key sets = Initial key sets - Lost key sets
       * Remaining key sets = 23/6 - 1/21

    3. To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 6 and 21, which is 42.

    4. Convert 23/6 to an equivalent fraction with a denominator of 42:
       * 23/6 = (23 × 7)/(6 × 7) = 161/42

    5. Now we can subtract the fractions:
       * Remaining key sets = 161/42 - 1/21
       * Remaining key sets = (161 × 2)/(42 × 2) - 1/21
       * Remaining key sets = 322/84 - 1/21
       * Remaining key sets = 322/84 - 4/84
       * Remaining key sets = 318/84

    6. Simplify the fraction:
       * 318/84 = 53/14

    Therefore, after losing 1/21 of a key set, Cassandra now has 53/14 of a key set in her collection.

    ### Answer: 53/14

Expected answer: 53/14

Correct? Yes

🔗 Problem

Problem: A songwriter is composing a new piece. In the first section, he uses a ratio of 29 notes every 23 measures. In the second section, he uses a ratio of 19 notes every 17 measures. Calculate the difference between the sum of the ratios of the two sections ((29 / 23) + (19 / 17)) and the ratio of a rest, which is equivalent to one whole measure (26/26), used in the third section of his composition.

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the ratio of notes to measures in the first section:
       * 29 notes / 23 measures = 1.2608695652173913

    2. Find the ratio of notes to measures in the second section:
       * 19 notes / 17 measures = 1.1176470588235294

    3. Find the sum of the ratios of the two sections:
       * 1.2608695652173913 + 1.1176470588235294 = 2.3785166240409207

    4. Find the ratio of a rest in the third section:
       * 26 / 26 = 1

    5. Calculate the difference between the sum of the ratios of the two sections and the ratio of a rest:
       * 2.3785166240409207 - 1 = 1.3785166240409207

    ### Answer: 1.3785166240409207

Expected answer: 539/391

Correct? Yes

🔗 Follow-up

Problem: In the same song composition, the songwriter decided to revise the second section. Instead of having a ratio of 19 notes every 17 measures, he decided to keep it consistent with the first section and have a ratio of 19 notes every 23 measures just like in the first section. Calculate the difference between the sum of the ratios of the two sections ((29 / 23) + (19 / 23)) and the ratio of a rest, which is equivalent to one whole measure (26/26), used in the third section of his composition after this change.

Gemma 2B:

    Great! Let's solve this problem step by step with the revised ratio for the second section.

    1. Find the ratio of notes to measures in the first section (unchanged):
       * 29 notes / 23 measures = 1.2608695652173913

    2. Find the ratio of notes to measures in the revised second section:
       * 19 notes / 23 measures = 0.8260869565217391

    3. Find the sum of the ratios of the two sections:
       * 1.2608695652173913 + 0.8260869565217391 = 2.0869565217391304

    4. Find the ratio of a rest in the third section (unchanged):
       * 26 / 26 = 1

    5. Calculate the difference between the sum of the ratios of the two sections and the ratio of a rest:
       * 2.0869565217391304 - 1 = 1.0869565217391304

    ### Answer: 1.0869565217391304

Expected answer: 25/23

Correct? No

🔗 Problem

Problem: You're trying to solve a puzzle that requires you to multiply two fractions together. The fractions are 22/25 and 22/8. Calculate the product to get the answer you need to advance in the puzzle.

Gemma 2B:

    To multiply two fractions, we multiply the numerators together and multiply the denominators together. Then, we simplify the resulting fraction if possible.

    Given fractions: 22/25 and 22/8

    Multiplying the numerators: 22 × 22 = 484
    Multiplying the denominators: 25 × 8 = 200

    The resulting fraction is 484/200. Let's simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

    The GCF of 484 and 200 is 4.

    Dividing the numerator by 4: 484 ÷ 4 = 121
    Dividing the denominator by 4: 200 ÷ 4 = 50

    The simplified fraction is 121/50.

    ### Answer: 121/50

Expected answer: 121/50

Correct? Yes

🔗 Follow-up

Problem: You solved the first part of the puzzle with the result from multiplying the fractions 22/25 and 22/8. Now, you've come across a key with the number 23/13 etched on it. To open the next door, you need to add the result from the step you just completed to the number on the key. What is the sum of these two values?

Gemma 2B:

    In the previous step, we found that the product of 22/25 and 22/8 is 121/50.

    Now, we need to add this result to the number on the key, which is 23/13.

    To add fractions with different denominators, we first need to find a common denominator. We can do this by multiplying the denominators together.

    Common denominator: 50 × 13 = 650

    Now, we need to adjust the numerators accordingly:
    121/50 = (121 × 13) / (50 × 13) = 1573/650
    23/13 = (23 × 50) / (13 × 50) = 1150/650

    Adding the numerators:
    1573/650 + 1150/650 = (1573 + 1150) / 650 = 2723/650

    Simplifying the resulting fraction by dividing both the numerator and denominator by their greatest common factor (GCF):

    The GCF of 2723 and 650 is 1, so the fraction cannot be simplified further.

    Therefore, the sum of 121/50 and 23/13 is 2723/650.

    ### Answer: 2723/650

Expected answer: 2723/650

Correct? Yes

🔗 Follow-up

Problem: Previously, you multiplied fractions 22/25 and 22/8 in the first part of the puzzle. Suppose instead of the 22/25 that you initially saw, the actual fraction in the text was 13/25. Now, you wonder how this change in information might affect your product. Recalculate the result using the correct fractions, which are now 13/25 and 22/8. What is the new product of these fractions?

Gemma 2B:

    Let's recalculate the product using the correct fractions, 13/25 and 22/8.

    To multiply fractions, we multiply the numerators together and multiply the denominators together. Then, we simplify the resulting fraction if possible.

    Given fractions: 13/25 and 22/8

    Multiplying the numerators: 13 × 22 = 286
    Multiplying the denominators: 25 × 8 = 200

    The resulting fraction is 286/200. Let's simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

    The GCF of 286 and 200 is 2.

    Dividing the numerator by 2: 286 ÷ 2 = 143
    Dividing the denominator by 2: 200 ÷ 2 = 100

    The simplified fraction is 143/100.

    ### Answer: 143/100

Expected answer: 143/100

Correct? Yes

🔗 Problem

Problem: James is making a decorative pillow and would like to add a matching border. He needs to calculate the length of border material he will need. The pillow is 23/9 feet long. He had an additional 22/25 feet of length due to the fluffing of the pillow. The total length is then multiplied by 16/13 to account for overlap and corners. Calculate the length of border material James will need for his pillow.

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the length of the pillow:
       * The pillow is 23/9 feet long.
       * 23/9 = 2.555... feet (rounded to 3 decimal places)

    2. Add the additional length due to fluffing:
       * The additional length is 22/25 feet.
       * 22/25 = 0.88 feet
       * Total length = 2.555... + 0.88 = 3.435... feet

    3. Multiply the total length by 16/13 to account for overlap and corners:
       * 3.435... × 16/13 = 4.223... feet

    Therefore, the length of border material James will need for his pillow is approximately 4.223 feet.

    ### Answer: 4.223 feet

Expected answer: 12368/2925

Correct? No

🔗 Problem

Problem: A car travels 21/4 miles every hour. One day, the car was needed to travel an extra 16/13 miles, but due to a detour, it only traveled an additional 1/21 miles. How many more miles was the car supposed to travel in total that day, given that it ran continuously at the same speed? Calculate by multiplying the additional distance needed by the average miles the car travels in an hour.

Gemma 2B:

    Let's break this down step by step:

    1. The car travels 21/4 miles every hour.
    2. The car was supposed to travel an extra 16/13 miles.
    3. Due to a detour, it only traveled an additional 1/21 miles.
    4. We need to find the difference between the extra miles the car was supposed to travel and the additional miles it actually traveled.

    Extra miles needed = 16/13 miles
    Additional miles traveled = 1/21 miles

    Difference in miles = Extra miles needed - Additional miles traveled
                        = 16/13 - 1/21
                        = (16 × 21 - 1 × 13) / (13 × 21)
                        = (336 - 13) / 273
                        = 323 / 273
                        = 1 50/273 miles

    Now, we multiply this difference by the average miles the car travels in an hour:

    Additional miles the car was supposed to travel = Difference in miles × Miles per hour
                                                    = 1 50/273 × 21/4
                                                    = (1 50/273 × 21) / 4
                                                    = (1 50/273 × 21) / 4
                                                    = (1 × 21 + 50/273 × 21) / 4
                                                    = (21 + 1050/273) / 4
                                                    = (21 + 3 217/273) / 4
                                                    = 24 217/273 / 4
                                                    = 6 54/273 miles

    ### Answer: 6 54/273 miles

Expected answer: 323/52

Correct? No

🔗 Problem

Problem: In a book publishing company, the manager has to look after various departments. The editing team takes 20/5 hours to edit a manuscript of a book, while the typesetting team needs 18/17 hours to adjust the layout of a page. Some break delay happens that results in a collective loss of 6/15 hours. After these delays and losses, the manager, to compensate, extended the working hours by the same amount of time as the initial time span of the process. On a particular day, they continue to work. What's the total extended time in hours, if you multiply the time required for the entire process and the extended time after the reduction of the lost hours with the initial total time required?

Gemma 2B:

    Let's organize the given information:
    - Editing a manuscript takes 20/5 hours
    - Typesetting a page takes 18/17 hours
    - Break delay results in a loss of 6/15 hours
    - The manager extends the working hours by the same amount of time as the initial time span of the process

    Step 1: Calculate the initial total time required for the process.
    Editing time + Typesetting time = 20/5 + 18/17
    = <<20/5=4>>4 + <<18/17≈1.06>>1.06 (rounded to 2 decimal places)
    = <<4+1.06=5.06>>5.06 hours

    Step 2: Calculate the total time after considering the break delay.
    Total time - Break delay = 5.06 - 6/15
    = 5.06 - <<6/15=0.4>>0.4
    = <<5.06-0.4=4.66>>4.66 hours

    Step 3: Calculate the extended time.
    Extended time = Initial total time = 5.06 hours

    Step 4: Multiply the time required for the entire process (after the reduction of lost hours) with the extended time.
    Time required for the entire process × Extended time = 4.66 × 5.06
    = <<4.66*5.06≈23.58>>23.58 hours (rounded to 2 decimal places)

    ### Answer: 23.58 hours

Expected answer: 34056/1445

Correct? No

🔗 Problem

Problem: Jenny plants 13/11 rows of potatoes in her garden. Each row yields approximately 21/3 bushels. If Jenny sells her yield at the farmer's market where each bushel earns her 21/15 dollars, how many dollars will she make in total by selling all her potatoes?

Gemma 2B:

    Let's break down the problem and solve it step by step:

    1. Find the total number of rows Jenny plants:
       - Jenny plants 13/11 rows of potatoes.

    2. Calculate the total yield of potatoes:
       - Each row yields approximately 21/3 bushels.
       - Total yield = Number of rows × Yield per row
       - Total yield = 13/11 × 21/3
       - Total yield = (13 × 21) / (11 × 3) = 273 / 33 = 8 9/33 bushels

    3. Calculate the total earnings from selling the potatoes:
       - Each bushel earns Jenny 21/15 dollars.
       - Total earnings = Total yield × Earnings per bushel
       - Total earnings = 8 9/33 × 21/15
       - Total earnings = (8 9/33 × 21) / 15
       - Total earnings = (189/33 × 21) / 15
       - Total earnings = 3969 / 495 = 8 14/495 dollars

    Therefore, Jenny will make a total of 8 14/495 dollars by selling all her potatoes.

    ### Answer: 8 14/495 dollars

Expected answer: 637/55

Correct? No

🔗 Problem

Problem: A jeweler uses 14/28 of a kilogram of gold to craft a certain type of rings. Additionally, he uses 13/26 of a kilogram of silver to design another type of rings. What is the sum of the amount of gold and silver used by the jeweler in kilograms?

Gemma 2B:

    Let's solve this problem step by step:

    1. Simplify the fraction of gold used:
       14/28 = 1/2 kilogram of gold

    2. Simplify the fraction of silver used:
       13/26 = 1/2 kilogram of silver

    3. Add the amount of gold and silver used:
       1/2 + 1/2 = 2/2 = 1 kilogram

    Therefore, the sum of the amount of gold and silver used by the jeweler is 1 kilogram.

    ### Answer: 1 kilogram

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: The jeweler decided to use a more expensive gold making process for his rings, which requires a slightly larger amount of gold, specifically 21/28 of a kilogram instead of the original 14/28. Taking this into account, now how much total weight of gold and silver is he using to craft his rings?

Gemma 2B:

    Great! Let's solve this problem step by step with the updated information.

    Given:
    - The jeweler now uses 21/28 of a kilogram of gold instead of 14/28.
    - He still uses 13/26 of a kilogram of silver.

    Step 1: Simplify the fraction of silver used.
    13/26 = 1/2 kilogram of silver

    Step 2: Add the amount of gold and silver used.
    21/28 + 1/2

    To add these fractions, we need to find a common denominator. The least common multiple of 28 and 2 is 28.

    21/28 + 14/28 = (21 + 14)/28 = 35/28

    Step 3: Convert the improper fraction to a mixed number.
    35/28 = 1 7/28

    Therefore, with the updated gold amount, the jeweler is now using a total of 1 7/28 kilograms of gold and silver to craft his rings.

    ### Answer: 1 7/28 kilograms

Expected answer: 5/4

Correct? Yes

🔗 Problem

Problem: In a beehive, there are sections for honey storage and bee rearing. Each section is classified into many sub-sections. One day, the beekeeper discovered that each honey storage sub-section had (25 / 9) gallons of honey. He also found the same amount of honey in each bee rearing sub-section. If he combined the honey from both a honey storage sub-section and a bee rearing sub-section, the beekeeper would have a total quantity represented by 'p'. However, one honey storage sub-section had an additional (2 / 26) gallons of honey. So, if the beekeeper was calculating the total amount from this sub-section plus a bee rearing sub-section, the total amount of honey would be defined as 's'. What quantity of honey ('s') would the beekeeper have in total from this scenario?

Gemma 2B:

    Let's solve this problem step by step:

    1. Each honey storage sub-section and bee rearing sub-section has (25 / 9) gallons of honey.
    2. If the beekeeper combines honey from one honey storage sub-section and one bee rearing sub-section, the total quantity is represented by 'p'.
       * p = (25 / 9) + (25 / 9)
       * p = (50 / 9) gallons

    3. One honey storage sub-section has an additional (2 / 26) gallons of honey.
    4. If the beekeeper calculates the total amount from this sub-section plus a bee rearing sub-section, the total amount of honey would be defined as 's'.
       * s = (25 / 9) + (2 / 26) + (25 / 9)
       * s = (50 / 9) + (2 / 26)
       * s = (1300 / 234) + (18 / 234)
       * s = (1318 / 234)
       * s = 5.632478632 gallons (rounded to 9 decimal places)

    ### Answer: 5.632478632 gallons

Expected answer: 659/117

Correct? No

🔗 Problem

Problem: In prehistoric times, a herbivorous dinosaur eats 16/8 bunches of leaves per hour during the day. But at night, it only eats 6/17 bunches of leaves every hour because of reduced visibility. Calculate the total bunches of leaves the dinosaur eats in an hour if it is eating day and night.

Gemma 2B:

    Let's solve this problem step by step:

    1. Simplify the fraction of bunches of leaves the dinosaur eats during the day:
       16/8 = 2 bunches of leaves per hour during the day

    2. Simplify the fraction of bunches of leaves the dinosaur eats at night:
       6/17 bunches of leaves per hour at night

    3. To find the total bunches of leaves the dinosaur eats in an hour if it is eating day and night, we need to add the two fractions:
       2 + 6/17

    4. To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 17:
       2 = 34/17 (multiply both numerator and denominator by 17)

       Now we can add the fractions:
       34/17 + 6/17 = 40/17

    5. Simplify the result:
       40/17 ≈ 2.35 (rounded to two decimal places)

    Therefore, the dinosaur eats approximately 2.35 bunches of leaves in an hour if it is eating day and night.

    ### Answer: 2.35 bunches of leaves

Expected answer: 40/17

Correct? No

🔗 Problem

Problem: A bear ate 28/6 pounds of fish one day and 21/18 pounds the next day. On the third day, the bear ate 24/22 pounds of fish. How many total pounds of fish did the bear eat in these three days, written as a fraction?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's convert all the fractions to a common denominator. The least common multiple of 6, 18, and 22 is 198.

    2. Day 1: 28/6 pounds of fish
       28/6 = (28 × 33)/(6 × 33) = 924/198 pounds of fish

    3. Day 2: 21/18 pounds of fish
       21/18 = (21 × 11)/(18 × 11) = 231/198 pounds of fish

    4. Day 3: 24/22 pounds of fish
       24/22 = (24 × 9)/(22 × 9) = 216/198 pounds of fish

    5. Now, let's add the fractions together:
       924/198 + 231/198 + 216/198 = (924 + 231 + 216)/198 = 1371/198 pounds of fish

    Therefore, the bear ate a total of 1371/198 pounds of fish over the three days.

    ### Answer: 1371/198

Expected answer: 457/66

Correct? Yes

🔗 Follow-up

Problem: In the previously mentioned problem, suppose on the second day, the bear ate only 5/18 pounds of fish rather than 21/18 pounds. With this change, how many total pounds of fish did the bear eat in those three days? Write your answer as a simplified fraction.

Gemma 2B:

    Okay, let's solve this problem with the updated information:

    1. The common denominator remains 198.

    2. Day 1: 28/6 pounds of fish
       28/6 = (28 × 33)/(6 × 33) = 924/198 pounds of fish

    3. Day 2 (updated): 5/18 pounds of fish
       5/18 = (5 × 11)/(18 × 11) = 55/198 pounds of fish

    4. Day 3: 24/22 pounds of fish
       24/22 = (24 × 9)/(22 × 9) = 216/198 pounds of fish

    5. Now, let's add the fractions together:
       924/198 + 55/198 + 216/198 = (924 + 55 + 216)/198 = 1195/198 pounds of fish

    6. Simplify the fraction:
       1195/198 = (1195 ÷ 11)/(198 ÷ 11) = 1195/18 ÷ 11 = 665/18

    Therefore, with the updated information, the bear ate a total of 665/18 pounds of fish over the three days.

    ### Answer: 665/18

Expected answer: 1195/198

Correct? No

🔗 Problem

Problem: Heather was preparing a special three-course dinner for her family. For the first course, she had a bread recipe that required 11/17 of a cup of sugar. In addition, she baked a custard for dessert that required another 6/2 cups of sugar. As her family loves sweet dishes, she decided to increase the total quantity of sugar by a factor of 29/21. How many cups of sugar did Heather use in total?

Gemma 2B:

    Let's break down the problem and solve it step by step:

    1. Calculate the total amount of sugar used in the original recipes:
       * Bread recipe: 11/17 cups of sugar
       * Custard recipe: 6/2 = 3 cups of sugar
       * Total sugar: 11/17 + 3 = (11/17) + (51/17) = 62/17 cups of sugar

    2. Increase the total quantity of sugar by a factor of 29/21:
       * Increased sugar: (62/17) × (29/21) = (62 × 29) / (17 × 21)
       * Simplify: 1798 / 357 = 5 1/357 cups of sugar

    Therefore, Heather used a total of 5 1/357 cups of sugar in her special three-course dinner.

    ### Answer: 5 1/357 cups of sugar

Expected answer: 1798/357

Correct? No

🔗 Problem

Problem: Ms. Parker, a math teacher, was grading papers and noticed that a student did the calculation ((7 / 8) + (21 / 18)), but she didn't write down the final answer. What is the result of this calculation as a simplified fraction?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's add the fractions (7 / 8) and (21 / 18).
    2. To add fractions with different denominators, we need to find the least common denominator (LCD).
       - The LCD of 8 and 18 is 72 (the least common multiple of 8 and 18).
    3. Now, we convert each fraction to an equivalent fraction with the LCD as the denominator:
       - (7 / 8) = (7 × 9) / (8 × 9) = 63 / 72
       - (21 / 18) = (21 × 4) / (18 × 4) = 84 / 72
    4. Add the numerators of the equivalent fractions:
       - (63 / 72) + (84 / 72) = (63 + 84) / 72 = 147 / 72
    5. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF):
       - The GCF of 147 and 72 is 3.
       - (147 / 72) = (147 ÷ 3) / (72 ÷ 3) = 49 / 24

    Therefore, the simplified result of ((7 / 8) + (21 / 18)) is 49 / 24.

    ### Answer: 49 / 24

Expected answer: 49/24

Correct? Yes

🔗 Follow-up

Problem: In the previous exercise, the student was initially solving the problem ((7 / 8) + (21 / 18)). However, upon double-checking their work, they realised that the second part of their calculation had been wrong, it wasn't (21 / 18), but instead (25 / 18). What would be the answer to ((7 / 8) + (25 / 18)) as a simplified fraction?

Gemma 2B:

    Let's solve the updated problem ((7 / 8) + (25 / 18)) step by step:

    1. Add the fractions (7 / 8) and (25 / 18).
    2. Find the least common denominator (LCD) of 8 and 18.
       - The LCD is 72 (the least common multiple of 8 and 18).
    3. Convert each fraction to an equivalent fraction with the LCD as the denominator:
       - (7 / 8) = (7 × 9) / (8 × 9) = 63 / 72
       - (25 / 18) = (25 × 4) / (18 × 4) = 100 / 72
    4. Add the numerators of the equivalent fractions:
       - (63 / 72) + (100 / 72) = (63 + 100) / 72 = 163 / 72
    5. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF):
       - The GCF of 163 and 72 is 1 (163 and 72 are relatively prime).
       - (163 / 72) cannot be simplified further.

    Therefore, the simplified result of ((7 / 8) + (25 / 18)) is 163 / 72.

    ### Answer: 163 / 72

Expected answer: 163/72

Correct? Yes

🔗 Problem

Problem: King Arthur is planning a grand feast at his castle. He estimates that each guest will consume 15/7 gallons of water and 15/24 gallons of wine. On the other hand, the royal baker needs 26/20 gallons of milk for each of the cakes he's baking. Calculate the total amount of liquid (v) that will be consumed if the baker's requirement is multiplied by the guests' consumption (i), and then add this to the guests' consumption (v) to find the total amount of liquid (x) needed for the feast.

Gemma 2B:

    To solve this problem, let's break it down into steps:

    1. Find the total amount of liquid each guest will consume:
       * Water per guest = 15/7 gallons
       * Wine per guest = 15/24 gallons
       * Total liquid per guest = 15/7 + 15/24
         * 15/7 + 15/24 = (15 × 24 + 15 × 7) / (7 × 24) = (360 + 105) / 168 = 465/168 gallons

    2. Find the amount of milk needed for each cake:
       * Milk per cake = 26/20 gallons

    3. Multiply the baker's requirement by the guests' consumption:
       * i = (26/20) × (465/168) = (26 × 465) / (20 × 168) = 12090 / 3360 = 3.6 gallons

    4. Add the result from step 3 to the guests' consumption to find the total amount of liquid needed:
       * x = 3.6 + 465/168 = (3.6 × 168 + 465) / 168 = (604.8 + 465) / 168 = 1069.8 / 168 = 6.369047619 gallons

    ### Answer: 6.369047619 gallons

Expected answer: 713/112

Correct? No

🔗 Problem

Problem: Teddy is a bear who loves to play with numbers. One day, Teddy was playing with his favorite number, which just so happened to be 30/17. While playing, he saw another number, 18/15, and decided to add it to his favorite number. With this new number in mind, he then saw another, 24/13, and decided to multiply it by his new number. What is Teddy's final number?

Gemma 2B:

    Let's solve this problem step by step to find Teddy's final number.

    Given:
    - Teddy's favorite number is 30/17.
    - He adds 18/15 to his favorite number.
    - He then multiplies the result by 24/13.

    Step 1: Add Teddy's favorite number (30/17) to 18/15.
    (30/17) + (18/15) = (30 × 15 + 18 × 17) / (17 × 15)
                      = (450 + 306) / 255
                      = 756 / 255
                      = <<756/255=2.96>>2.96

    Step 2: Multiply the result from Step 1 by 24/13.
    (756/255) × (24/13) = (756 × 24) / (255 × 13)
                        = 18,144 / 3,315
                        = <<18144/3315=5.47>>5.47

    Therefore, Teddy's final number is 5.47.

    ### Answer: 5.47

Expected answer: 6048/1105

Correct? No

🔗 Problem

Problem: Johnny is building a scooter from scratch. He needs to drill holes into the scooter deck to attach the wheels. The size of each hole should be approximately (20/6) cm in diameter. Unfortunately, his drill bit only has a diameter of (11/21) cm. If he uses his current drill bit, he needs to drill a hole, move it over and drill again to achieve the diameter he needs. If he drills each hole exactly once with his drill bit, calculate what fraction of the desired diameter would each hole have? Don't simplify the fraction, keep as (20/6) * (11 / 21).

Gemma 2B:

    Let's approach this step by step:

    1) The desired diameter of each hole is (20/6) cm.

    2) The diameter of Johnny's drill bit is (11/21) cm.

    3) If Johnny drills each hole exactly once with his drill bit, the actual diameter of each hole will be (11/21) cm.

    4) To find what fraction of the desired diameter each hole will have, we need to divide the actual diameter by the desired diameter:

       (Actual diameter) / (Desired diameter) = (11/21) / (20/6)

    5) To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

       (11/21) * (6/20) = (11*6) / (21*20) = 66 / 420

    Therefore, if Johnny drills each hole exactly once with his current drill bit, each hole will have (66/420) of the desired diameter.

    ### Answer: (66/420)

Expected answer: 110/63

Correct? No

🔗 Problem

Problem: Aaron has a small model car collection. His favorite car model takes exactly 17/10 hours to assemble. He started assembling a new car model and realized that it was simpler, taking only 12/23 hours to complete. How much less time, in hours, will the second model take than the first one? Write your answer as a simplified fraction or decimal.

Gemma 2B:

    To find the difference in time between the two model cars, we need to subtract the time taken for the second model from the time taken for the first model.

    Time taken for the first model = 17/10 hours
    Time taken for the second model = 12/23 hours

    Difference in time = 17/10 - 12/23

    To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators.

    LCM of 10 and 23 = 230

    Now, we can convert both fractions to equivalent fractions with the common denominator:

    17/10 = 17 × 23/10 × 23 = 391/230
    12/23 = 12 × 10/23 × 10 = 120/230

    Difference in time = 391/230 - 120/230 = 271/230

    To simplify the fraction 271/230, we find the greatest common factor (GCF) of 271 and 230.

    GCF of 271 and 230 = 1

    Since the GCF is 1, the fraction 271/230 is already in its simplest form.

    ### Answer: 271/230 hours (or approximately 1.18 hours)

Expected answer: 271/230

Correct? Yes

🔗 Follow-up

Problem: Aaron realized he had made a mistake in his timekeeping. Assembling his favorite car model actually took 18/10 hours, not 17/10 hours as he initially thought. How much less time, in hours, will it now take to assemble the second model as compared to the new time for the first model? Write your answer as a simplified fraction or decimal.

Gemma 2B:

    Let's update the problem with the new information and solve it again.

    Time taken for the first model = 18/10 hours
    Time taken for the second model = 12/23 hours

    Difference in time = 18/10 - 12/23

    To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators.

    LCM of 10 and 23 = 230

    Now, we can convert both fractions to equivalent fractions with the common denominator:

    18/10 = 18 × 23/10 × 23 = 414/230
    12/23 = 12 × 10/23 × 10 = 120/230

    Difference in time = 414/230 - 120/230 = 294/230

    To simplify the fraction 294/230, we find the greatest common factor (GCF) of 294 and 230.

    GCF of 294 and 230 = 2

    Simplifying the fraction: 294/230 ÷ 2/2 = 147/115

    ### Answer: 147/115 hours (or approximately 1.28 hours)

Expected answer: 147/115

Correct? Yes

🔗 Problem

Problem: Carlos is very handy, and he decided to start a business making and selling chairs. He usually makes each chair using 20/15 units of wood. For a special order, he decided to design a larger, sturdier chair that uses (24/5) times (7/6) units more wood than usual. In total, how many units of wood would Carlos need to make one of these special chairs? Please give your answer in simplest form.

Gemma 2B:

    Let's break this down step by step:

    1) First, let's calculate how many units of wood Carlos usually uses for a chair:

       20/15 = 4/3 units of wood

    2) Now, let's calculate how many more units of wood the special chair requires:

       (24/5) * (7/6) = 168/30 = 28/5 = 5 3/5 units of wood

    3) So, for the special chair, Carlos needs the usual amount of wood plus the additional amount:

       4/3 + 5 3/5 = 4/3 + 28/5

       To add these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15. So, let's convert both fractions to fifteenths:

       4/3 = 20/15
       28/5 = 84/15

       Now we can add:

       20/15 + 84/15 = 104/15 = 6 14/15

    Therefore, Carlos needs 6 14/15 units of wood to make one special chair.

    ### Answer: 6 14/15

Expected answer: 104/15

Correct? Yes

🔗 Follow-up

Problem: Carlos realized he could be using a more efficient design for his chairs. Instead of using 20/15 units of wood as he was previously, he can now use only 20/8 units for the basic chair design. The larger design with the special feature still requires (24/5) times (7/6) units more wood than the basic chair. With this more efficient design for the basic chair, how many units of wood would Carlos now need in total to make one of these larger special design chairs? Please express your answer as a simplified fraction.

Gemma 2B:

    Okay, let's solve this problem step by step with the new information:

    1) First, let's calculate how many units of wood Carlos now uses for the basic chair:

       20/8 = 5/2 units of wood

    2) The additional units of wood required for the special chair remains the same:

       (24/5) * (7/6) = 168/30 = 28/5 = 5 3/5 units of wood

    3) Now, for the special chair, Carlos needs the new basic amount of wood plus the additional amount:

       5/2 + 5 3/5 = 5/2 + 28/5

       To add these fractions, we need a common denominator. The least common multiple of 2 and 5 is 10. So, let's convert both fractions to tenths:

       5/2 = 25/10
       28/5 = 56/10

       Now we can add:

       25/10 + 56/10 = 81/10

    4) Let's simplify this fraction:

       81/10 = 8 1/10

    Therefore, with the more efficient design, Carlos would need 8 1/10 units of wood to make one special chair.

    ### Answer: 81/10

Expected answer: 81/10

Correct? Yes

🔗 Problem

Problem: Officer Davis was monitoring traffic for speeders. He was measuring the speed of cars passing by him using a radar gun. The gun showed one car was going 13/4 miles per minute. Suddenly, the car slows down and reduces his speed by 14/15 miles per minute. Officer Davis noted down the new speed of the car. Suddenly, the car increased its speed again by 30/15 miles per minute. What was the final speed of the car according to Officer Davis's radar gun?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, we need to find the initial speed of the car in miles per minute:
       * Initial speed = 13/4 miles per minute
       * 13/4 = 3.25 miles per minute

    2. Next, the car reduces its speed by 14/15 miles per minute:
       * Speed reduction = 14/15 miles per minute
       * New speed = Initial speed - Speed reduction
       * New speed = 3.25 - 14/15
       * New speed = 3.25 - 0.93 (rounded to 2 decimal places)
       * New speed = 2.32 miles per minute

    3. Finally, the car increases its speed by 30/15 miles per minute:
       * Speed increase = 30/15 miles per minute = 2 miles per minute
       * Final speed = New speed + Speed increase
       * Final speed = 2.32 + 2
       * Final speed = 4.32 miles per minute

    Therefore, according to Officer Davis's radar gun, the final speed of the car is 4.32 miles per minute.

    ### Answer: 4.32 miles per minute

Expected answer: 259/60

Correct? No

🔗 Problem

Problem: Jake is trying to figure out how many grapes he can get from a certain vineyard. - The vineyard can usually produce 19/2 baskets of grapes every season. However, due to weather conditions, only 19/29 of the usual amount were produced this season. How many baskets of grapes were produced this season? - But Jake isn't the only one interested in these grapes. He has to share the grapes with others. He gets to keep only 7/11 of the total amount of grapes. How many baskets of grapes does he get? - Out of the grapes that he got, Jake wants to make some grape juice. But he only uses 9/10 of his grapes to make the juice. How many baskets of grapes does he use for the juice?

Gemma 2B:

    Let's solve this problem step by step:

    1. Calculating the number of baskets produced this season:
       * The vineyard usually produces 19/2 baskets of grapes.
       * This season, only 19/29 of the usual amount was produced.
       * Baskets produced this season = 19/2 × 19/29
       * 19/2 × 19/29 = 361/58 = <<361/58=6.224137931034483>>6.224137931034483 baskets

    2. Calculating Jake's share of the grapes:
       * Jake gets to keep 7/11 of the total amount of grapes.
       * Jake's share = 6.224137931034483 × 7/11
       * 6.224137931034483 × 7/11 = 43.568965517241379/11 = <<43.568965517241379/11=3.961724137931034>>3.961724137931034 baskets

    3. Calculating the number of baskets Jake uses for grape juice:
       * Jake uses 9/10 of his grapes to make juice.
       * Baskets used for juice = 3.961724137931034 × 9/10
       * 3.961724137931034 × 9/10 = 35.655517241379309/10 = <<35.655517241379309/10=3.5655517241379309>>3.5655517241379309 baskets

    ### Answer: Jake uses 3.5655517241379309 baskets of grapes to make grape juice.

Expected answer: 22743/6380

Correct? No

🔗 Problem

Problem: Joel has a grape farm. One day, he picked 9/2 bushels of red grapes and 10/22 bushels of green grapes from his farm. Calculate the total number of bushels of grapes Joel picked that day.

Gemma 2B:

    To solve this problem, we need to add the number of bushels of red grapes and green grapes that Joel picked.

    Given:
    - Joel picked 9/2 bushels of red grapes.
    - Joel picked 10/22 bushels of green grapes.

    Step 1: Convert the fractions to a common denominator.
    The common denominator is the least common multiple (LCM) of 2 and 22, which is 22.

    Red grapes: 9/2 = (9 × 11) / (2 × 11) = 99/22
    Green grapes: 10/22 (already has a denominator of 22)

    Step 2: Add the fractions with the common denominator.
    Total bushels = Red grapes + Green grapes
    Total bushels = 99/22 + 10/22 = (99 + 10) / 22 = 109/22

    Step 3: Simplify the fraction if possible.
    109/22 cannot be simplified further as there are no common factors between 109 and 22.

    Therefore, Joel picked a total of 109/22 bushels of grapes that day.

    ### Answer: 109/22 bushels

Expected answer: 109/22

Correct? Yes

🔗 Follow-up

Problem: Joel then sold a unique juice blend at a farmer's market. He used a ratio of 25/17 bushels of juice per bushel of grapes. Calculate how many bushels of juice Joel made for the market using the total number of bushels of grapes he picked.

Gemma 2B:

    To find out how many bushels of juice Joel made, we need to multiply the total number of bushels of grapes he picked by the ratio of bushels of juice per bushel of grapes.

    Given:
    - Joel picked a total of 109/22 bushels of grapes.
    - The ratio of bushels of juice per bushel of grapes is 25/17.

    Step 1: Multiply the total bushels of grapes by the ratio of bushels of juice per bushel of grapes.
    Bushels of juice = Total bushels of grapes × Ratio of bushels of juice per bushel of grapes
    Bushels of juice = 109/22 × 25/17

    Step 2: Multiply the fractions.
    Bushels of juice = (109 × 25) / (22 × 17)
    Bushels of juice = 2725 / 374

    Step 3: Simplify the fraction if possible.
    2725 and 374 have a common factor of 11.
    Bushels of juice = (2725 ÷ 11) / (374 ÷ 11)
    Bushels of juice = 275 / 34

    Therefore, Joel made 275/34 bushels of juice for the farmer's market.

    ### Answer: 275/34 bushels

Expected answer: 2725/374

Correct? No

🔗 Follow-up

Problem: Suppose Joel made an error and actually only picked 9/3 bushels of red grapes instead of 9/2 bushels. He still picked 10/22 bushels of green grapes. Calculate the corrected total number of bushels of grapes Joel picked.

Gemma 2B:

    Let's solve this problem with the corrected information. We need to add the number of bushels of red grapes and green grapes that Joel picked.

    Given:
    - Joel picked 9/3 bushels of red grapes (corrected from 9/2).
    - Joel picked 10/22 bushels of green grapes.

    Step 1: Convert the fractions to a common denominator.
    The common denominator is the least common multiple (LCM) of 3 and 22, which is 66.

    Red grapes: 9/3 = (9 × 22) / (3 × 22) = 198/66 = 3/1
    Green grapes: 10/22 = (10 × 3) / (22 × 3) = 30/66 = 5/11

    Step 2: Add the fractions with the common denominator.
    Total bushels = Red grapes + Green grapes
    Total bushels = 3/1 + 5/11 = (3 × 11) / (1 × 11) + 5/11 = 33/11 + 5/11 = 38/11

    Step 3: Simplify the fraction if possible.
    38/11 cannot be simplified further as there are no common factors between 38 and 11.

    Therefore, with the corrected information, Joel picked a total of 38/11 bushels of grapes that day.

    ### Answer: 38/11 bushels

Expected answer: 38/11

Correct? Yes

🔗 Problem

Problem: A snowman is constructed by stacking two different sized snowballs on top of each other. The larger snowball at the bottom has a diameter of 17/8 feet, and the smaller snowball on top has a diameter of 1/20 feet. What is the total height of the snowman in feet when these two snowballs are stacked on top of each other?

Gemma 2B:

    To find the total height of the snowman, we need to add the diameters of the two snowballs.

    1. Convert the fractions to decimals:
       * Larger snowball diameter: 17/8 = 2.125 feet
       * Smaller snowball diameter: 1/20 = 0.05 feet

    2. Add the diameters:
       * Total height = Larger snowball diameter + Smaller snowball diameter
       * Total height = 2.125 feet + 0.05 feet
       * Total height = 2.175 feet

    3. Convert the decimal back to a mixed number:
       * 2.175 = 2 + 0.175
       * 0.175 × 8 = 1.4
       * 1.4/8 = 7/5
       * Total height = 2 7/5 feet

    ### Answer: 2 7/5 feet

Expected answer: 87/40

Correct? No

🔗 Problem

Problem: In a sandbox, a child splits up 24/7 parts of the sand in a fair way. Later on, another child takes away 2/16 part of the sand. Calculate the remaining part of sand in the sandbox.

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Initially, the sandbox had 1 whole part of sand (which can be represented as 1 or 24/24).
       * The first child split up 24/7 parts of the sand fairly.
       * The second child took away 2/16 part of the sand.

    2. Calculate the part of sand remaining after the first child split it up:
       * Remaining sand = 1 - 24/7
       * To subtract fractions, we need a common denominator. The common denominator is 7.
       * 1 = 7/7
       * Remaining sand = 7/7 - 24/7 = -17/7

    3. Calculate the part of sand remaining after the second child took away 2/16:
       * Remaining sand = -17/7 - 2/16
       * To subtract fractions, we need a common denominator. The common denominator is 112 (7 × 16).
       * -17/7 = -272/112
       * 2/16 = 14/112
       * Remaining sand = -272/112 - 14/112 = -286/112
       * Simplify the fraction: -286/112 = -143/56

    Therefore, the remaining part of sand in the sandbox is -143/56.

    ### Answer: -143/56

Expected answer: 185/56

Correct? No

🔗 Problem

Problem: In the jungle, a lion ate 28/26 of a zebra in one day and 23/9 of a wildebeest the next day. How much less of the zebra did the lion eat compared with the wildebeest? Calculate your answer as a simplified fraction.

Gemma 2B:

    To solve this problem, let's follow these steps:

    1. Convert the fractions to a common denominator:
       * 28/26 = 14/13 (multiply both numerator and denominator by 2)
       * 23/9 = 23/9 (already simplified)

    2. Find the common denominator of 13 and 9:
       * The common denominator is 13 × 9 = 117

    3. Convert both fractions to the common denominator of 117:
       * 14/13 = (14 × 9)/(13 × 9) = 126/117
       * 23/9 = (23 × 13)/(9 × 13) = 299/117

    4. Subtract the fraction of the zebra from the fraction of the wildebeest:
       * 299/117 - 126/117 = 173/117

    5. Simplify the resulting fraction:
       * 173/117 cannot be simplified further as 173 and 117 have no common factors other than 1.

    Therefore, the lion ate 173/117 less of the zebra compared with the wildebeest.

    ### Answer: 173/117

Expected answer: 173/117

Correct? Yes

🔗 Follow-up

Problem: In the jungle, a lion ate 28/26 of a zebra in one day and 23/9 of a wildebeest the next day. The lion realized it was still hungry, so it ate 21/4 as much as the difference between the wildebeest and the zebra the next day. How much did the lion eat the next day? Please express your answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the difference between the amount of wildebeest and zebra the lion ate:
       * 28/26 = 14/13 (multiply both numerator and denominator by 2)
       * 23/9 - 14/13 = (23 × 13 - 14 × 9) / (9 × 13) = 173/117

    2. Calculate 21/4 times the difference:
       * 21/4 × 173/117 = (21 × 173) / (4 × 117) = 3633/468

    3. Simplify the fraction:
       * 3633/468 = 7 139/468 (divide both numerator and denominator by 9)
       * 139/468 cannot be simplified further as 139 and 468 have no common factors other than 1.

    Therefore, the lion ate 7 139/468 the next day.

    ### Answer: 7 139/468

Expected answer: 1211/156

Correct? No

🔗 Problem

Problem: A chocolate factory makes a batch of chocolate by combining 14/4 kilograms of cocoa and 21/11 liters of milk for every kilogram. How many kilograms of chocolate will the factory produce by combining these ingredients? Calculate your answer to the following expression, ((14 / 4) * (21 / 11)).

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * The factory combines 14/4 kilograms of cocoa and 21/11 liters of milk for every kilogram of chocolate.
       * We need to calculate ((14 / 4) * (21 / 11)) to find the number of kilograms of chocolate produced.

    2. Simplify 14/4:
       * 14 ÷ 4 = 3.5
       * So, 14/4 = 3.5

    3. Simplify 21/11:
       * 21 ÷ 11 = 1.909090...
       * So, 21/11 ≈ 1.91 (rounded to two decimal places)

    4. Multiply the simplified fractions:
       * (14 / 4) * (21 / 11) = 3.5 * 1.91
       * 3.5 * 1.91 = 6.685

    Therefore, by combining 14/4 kilograms of cocoa and 21/11 liters of milk, the factory will produce approximately 6.685 kilograms of chocolate.

    ### Answer: 6.685 kilograms

Expected answer: 147/22

Correct? No

🔗 Problem

Problem: In the tropical rainforest, there are two different species of banana trees. One species produces 12 bananas every 29 days, while another species produces 30 bananas every 10 days. If a day is chosen at random, what is the expected number of bananas that the two species together will have produced on that day? Use the formula ((12 / 29) + (30 / 10)) to calculate the answer.

Gemma 2B:

    Let's break this down step by step:

    1. The first species produces 12 bananas every 29 days. This means that on an average day, it produces 12/29 bananas.

    2. The second species produces 30 bananas every 10 days. This means that on an average day, it produces 30/10 = 3 bananas.

    3. To find the expected number of bananas produced by both species together on a randomly chosen day, we add their individual daily averages:

       ((12 / 29) + (30 / 10))

    4. Let's calculate this:

       12 / 29 ≈ 0.4138
       30 / 10 = 3

       0.4138 + 3 = 3.4138

    Therefore, on a randomly chosen day, the expected number of bananas produced by both species together is approximately 3.4138.

    ### Answer: 3.4138

Expected answer: 99/29

Correct? No

🔗 Problem

Problem: A giraffe needs to eat a total of 11/11 ton of acacia leaves plus 26/14 ton of grasses a day. Calculate the total ton of food the giraffe needs to eat in a day.

Gemma 2B:

    To find the total amount of food the giraffe needs to eat in a day, we need to add the amount of acacia leaves and grasses.

    Given:
    - The giraffe needs to eat 11/11 ton of acacia leaves a day.
    - The giraffe needs to eat 26/14 ton of grasses a day.

    Step 1: Convert the mixed numbers to improper fractions.
    Acacia leaves: 11/11 ton = 1 ton
    Grasses: 26/14 ton = 13/7 ton

    Step 2: Add the fractions.
    Total food = 1 ton + 13/7 ton
               = 7/7 ton + 13/7 ton
               = (7 + 13) / 7 ton
               = 20/7 ton

    Step 3: Convert the improper fraction to a mixed number.
    20/7 ton = 2 6/7 tons

    Therefore, the giraffe needs to eat a total of 2 6/7 tons of food in a day.

    ### Answer: 2 6/7 tons

Expected answer: 20/7

Correct? Yes

🔗 Follow-up

Problem: In addition to the acacia leaves and grasses, the giraffe also drinks 10/30 ton of water per day. What is the total weight of food and water that the giraffe consumes in a day?

Gemma 2B:

    Let's add the amount of water to the total amount of food the giraffe consumes in a day.

    Given:
    - The giraffe needs to eat a total of 2 6/7 tons of food (acacia leaves and grasses) a day.
    - The giraffe drinks 10/30 ton of water per day.

    Step 1: Convert the mixed number to an improper fraction.
    2 6/7 tons = (2 × 7 + 6) / 7 tons = 20/7 tons

    Step 2: Simplify the fraction of water consumed.
    10/30 ton = 1/3 ton

    Step 3: Add the fractions of food and water.
    Total weight of food and water = 20/7 tons + 1/3 ton
                                    = 60/21 tons + 7/21 ton
                                    = (60 + 7) / 21 tons
                                    = 67/21 tons

    Step 4: Convert the improper fraction to a mixed number.
    67/21 tons = 3 4/21 tons

    Therefore, the giraffe consumes a total weight of 3 4/21 tons of food and water in a day.

    ### Answer: 3 4/21 tons

Expected answer: 67/21

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, suppose the giraffe ate 24/14 ton of grasses, instead of 26/14 ton. How much total food does the giraffe eat per day now?

Gemma 2B:

    Let's solve this problem using the given information and the same steps as before.

    Given:
    - The giraffe needs to eat 11/11 ton of acacia leaves a day.
    - The giraffe now eats 24/14 ton of grasses a day.

    Step 1: Convert the mixed numbers to improper fractions.
    Acacia leaves: 11/11 ton = 1 ton
    Grasses: 24/14 ton = 12/7 ton

    Step 2: Add the fractions.
    Total food = 1 ton + 12/7 ton
               = 7/7 ton + 12/7 ton
               = (7 + 12) / 7 ton
               = 19/7 ton

    Step 3: Convert the improper fraction to a mixed number.
    19/7 ton = 2 5/7 tons

    Therefore, with the updated amount of grasses, the giraffe now eats a total of 2 5/7 tons of food per day.

    ### Answer: 2 5/7 tons

Expected answer: 19/7

Correct? Yes

🔗 Problem

Problem: A bear spends 18 hours of the day sleeping. Given that each day has 24 hours, this bear spends 18/24th of each day asleep. For 27 days of the month, the bear's activity is tracked. Assume that the bear has a regular sleeping pattern. Calculate the fraction of time the bear has spent sleeping over the 27 days assuming each month has 13 weeks. Your answer should be the result of (18 / 24) * (27 / 13). Write your answer as a decimal.

Gemma 2B:

    Let's break this down step by step:

    1. The bear spends 18 hours out of 24 hours sleeping each day.
       Fraction of the day spent sleeping = 18 / 24 = 0.75

    2. The bear's activity is tracked for 27 days out of a month.
       The month is assumed to have 13 weeks.
       Number of days in the month = 13 * 7 = 91 days

    3. Fraction of the month tracked = 27 / 91

    4. To find the fraction of time the bear spent sleeping over the 27 days, we multiply the fraction of each day spent sleeping by the fraction of the month tracked:
       (18 / 24) * (27 / 91) = 0.75 * (27 / 91) = 0.75 * 0.2967032967032967 = 0.2225274725274725

    Therefore, the fraction of time the bear spent sleeping over the 27 days is 0.2225274725274725.

    ### Answer: 0.2225274725274725

Expected answer: 81/52

Correct? No

🔗 Problem

Problem: In a beautiful forest, the park rangers recorded that 9 out of every 14 trees were pine trees. They also noticed an exceptional occurrence where 19 out of every 2 trees were birches. If you count all the pine trees and birch trees together, what fraction of the trees in the forest are either pine or birch? Use the formula f = ((9 / 14) + (19 / 2)) to solve this.

Gemma 2B:

    Let's solve this problem step by step using the given formula: f = ((9 / 14) + (19 / 2))

    Step 1: Simplify the fractions inside the parentheses.
    (9 / 14) cannot be simplified further.
    (19 / 2) = 9.5

    Step 2: Add the fractions inside the parentheses.
    f = ((9 / 14) + 9.5)

    To add fractions with different denominators, we need to find a common denominator. In this case, we need to convert 9.5 to a fraction with a denominator of 14.

    9.5 = (9.5 × 14) / 14 = 133 / 14

    Now, we can add the fractions:
    f = ((9 / 14) + (133 / 14))
    f = (9 + 133) / 14
    f = 142 / 14

    Step 3: Simplify the resulting fraction.
    142 / 14 = 71 / 7

    Therefore, the fraction of trees in the forest that are either pine or birch is 71/7.

    ### Answer: 71/7

Expected answer: 71/7

Correct? Yes

🔗 Follow-up

Problem: In the same forest, the park rangers conducted another seasonal survey. This time, they found that the number of pine trees made up 9 out of every 14 trees. In an unexpected turn of events, the number of birch trees significantly increased to 30 out of every 2 trees. Given these new numbers, what fraction of the trees in the forest are either pine or birch now? Use the updated formula f = ((9 / 14) + (30 / 2)) to solve this.

Gemma 2B:

    Let's solve this problem step by step using the updated formula: f = ((9 / 14) + (30 / 2))

    Step 1: Simplify the fractions inside the parentheses.
    (9 / 14) cannot be simplified further.
    (30 / 2) = 15

    Step 2: Add the fractions inside the parentheses.
    f = ((9 / 14) + 15)

    To add fractions with different denominators, we need to find a common denominator. In this case, we need to convert 15 to a fraction with a denominator of 14.

    15 = (15 × 14) / 14 = 210 / 14

    Now, we can add the fractions:
    f = ((9 / 14) + (210 / 14))
    f = (9 + 210) / 14
    f = 219 / 14

    Step 3: Simplify the resulting fraction.
    The fraction 219 / 14 is an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator:

    219 ÷ 14 = 15 remainder 9
    15 9/14

    Therefore, the fraction of trees in the forest that are either pine or birch is 15 9/14.

    ### Answer: 15 9/14

Expected answer: 219/14

Correct? Yes

🔗 Problem

Problem: On planet Zog, aliens use an interesting system to track their energy levels. At the beginning of the day, Zogorian calculates his energy level to be (14 / 2) / (23 / 17) zogs. Later in the day, after harnessing energy from their primary star, his energy level increases by (16 / 24) zogs. Calculate the Zogorian's energy level after the increase.

Gemma 2B:

    Let's solve this problem step by step:

    1. Calculate Zogorian's initial energy level:
       (14 / 2) / (23 / 17) = 7 / (23 / 17)
                            = 7 / 1.3529411764705883
                            = 5.1764705882352935 zogs

    2. Calculate the increase in energy level:
       16 / 24 = 0.6666666666666666 zogs

    3. Add the increase to the initial energy level:
       5.1764705882352935 + 0.6666666666666666 = 5.843137254901961 zogs

    Therefore, Zogorian's energy level after the increase is 5.843137254901961 zogs.

    ### Answer: 5.843137254901961 zogs

Expected answer: 403/69

Correct? No

🔗 Problem

Problem: Teddy, the bear, loves to play hide and seek with his friends. One day, he decided to play a game where he hides some number of his stuffed animal friends. Teddy hides 18/11 of his friends in the forest and 8/21 of his friends at the beach. First calculate how many more friends Teddy hides in the forest than at the beach. Let's call this number 'f'. Then square 'f' to find 'n', the total number of hiding spots Teddy needs. How many hiding spots does Teddy need?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the difference between the fraction of friends Teddy hides in the forest and at the beach:
       18/11 - 8/21 = (18 × 21 - 8 × 11) / (11 × 21)
                   = (378 - 88) / 231
                   = 290 / 231
                   = 10/7

       So, f = 10/7

    2. Square the value of f to find n:
       n = (10/7)^2
         = 100/49
         = <<100/49=2.0408163265306123>>2 2/49

    Therefore, Teddy needs 2 2/49 hiding spots.

    ### Answer: 2 2/49

Expected answer: 84100/53361

Correct? No

🔗 Problem

Problem: A robot is performing a maintenance task. It starts with 25/10 units of energy. However, it quickly uses 27/23 units of energy to complete a series of complex computations. Calculate how much energy it has left.

Gemma 2B:

    Okay, let's solve this problem step by step:

    1. The robot starts with 25/10 units of energy.
       To convert this to a decimal, we divide 25 by 10:
       25 ÷ 10 = 2.5 units of energy

    2. The robot uses 27/23 units of energy for computations.
       Again, we convert this to a decimal:
       27 ÷ 23 ≈ 1.1739 units of energy

    3. To find the remaining energy, we subtract the energy used from the initial energy:
       2.5 - 1.1739 ≈ 1.3261 units of energy

    4. To express the remaining energy as a fraction, we can approximate:
       1.3261 ≈ 1 17/50

       To get this, we first write 1.3261 as 1 + 0.3261.
       Then, we convert 0.3261 to a fraction by multiplying both numerator and denominator by 10000:
       0.3261 = 3261/10000 ≈ 17/50 (after simplifying)

    Therefore, the energy the robot has left is approximately 1 17/50 units.

    ### Answer: 1 17/50 units of energy (or approximately 1.3261 units)

Expected answer: 61/46

Correct? No

🔗 Problem

Problem: During rainy weather, a small snail moves at a snail-pace covering 17/21 of a meter in an hour. Another slightly faster snail covers 20/24 of a meter in the same time during such weather. One rainy day, the first snail started an hour earlier than the second. At the time when the second snail began, a third snail that covers 18/17 of a meter per hour also started moving. What is their total distance in meters 1 hour after all three have started moving? Compute the result using the operation ((17 / 21) + (20 / 24)) for the first two snails' distance, and multiply this result by (18 / 17) for the total distance , including the third snail.

Gemma 2B:

    Let's solve this problem step by step:

    1. Distance covered by the first snail in 2 hours:
       17/21 × 2 = 34/21 meters

    2. Distance covered by the second snail in 1 hour:
       20/24 = 5/6 meters

    3. Distance covered by the first two snails in 1 hour after both have started moving:
       (17/21) + (20/24) = (17/21) + (5/6)
                         = (17/21) + (35/42)
                         = (714 + 735) / 882
                         = 1449/882 meters

    4. Distance covered by the third snail in 1 hour:
       18/17 meters

    5. Total distance covered by all three snails 1 hour after all have started moving:
       (1449/882) × (18/17) = 1449/833 meters

    Therefore, the total distance covered by all three snails 1 hour after all have started moving is 1449/833 meters.

    ### Answer: 1449/833 meters

Expected answer: 207/119

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous snail problem, after the hour was up, an ultra-fast snail appeared and traveled a distance of 25/23 meters in just half an hour. What is the total distance in meters covered by all four snails 1.5 hours after the third snail had started moving? To compute this, take the total distance covered by the first three snails, represented as ((17 / 21) + (20 / 24)) * (18 / 17), and then add to this the ultra-fast snail's distance of 25/23 meters.

Gemma 2B:

    Okay, let's continue from the previous problem and add the ultra-fast snail's distance:

    1. Total distance covered by the first three snails 1 hour after all have started moving (from the previous problem):
       ((17/21) + (20/24)) × (18/17) = 1449/833 meters

    2. Distance covered by the ultra-fast snail in 0.5 hours:
       25/23 meters

    3. Total distance covered by all four snails 1.5 hours after the third snail had started moving:
       ((17/21) + (20/24)) × (18/17) + (25/23)
       = (1449/833) + (25/23)
       = (1449/833) + (908/833)
       = (1449 + 908) / 833
       = 2357/833 meters

    Therefore, the total distance covered by all four snails 1.5 hours after the third snail had started moving is 2357/833 meters.

    ### Answer: 2357/833 meters

Expected answer: 7736/2737

Correct? No

🔗 Follow-up

Problem: In the first scenario, we determined the total distance covered by the snails in an hour. But now, let's revise our story a little bit and adjust the distance that one of our snails covers. The second snail, instead of covering 20/24 of a meter in an hour during rainy weather, now can only cover 18/24 of a meter. Given this new information, can you recalculate the total distance covered by the first three snails in the hour after they all start moving? Use the following structure: ((17 / 21) + (18 / 24)) * (18 / 17).

Gemma 2B:

    Certainly! Let's solve this problem with the updated information:

    1. Distance covered by the first snail in 2 hours:
       17/21 × 2 = 34/21 meters

    2. Distance covered by the second snail in 1 hour (updated):
       18/24 = 3/4 meters

    3. Distance covered by the first two snails in 1 hour after both have started moving:
       (17/21) + (18/24) = (17/21) + (3/4)
                         = (68 + 63) / 84
                         = 131/84 meters

    4. Distance covered by the third snail in 1 hour:
       18/17 meters

    5. Total distance covered by all three snails 1 hour after all have started moving:
       ((17/21) + (18/24)) × (18/17) = (131/84) × (18/17)
                                      = (131 × 18) / (84 × 17)
                                      = 2358 / 1428
                                      = 1179/714 meters

    Therefore, with the updated information, the total distance covered by all three snails 1 hour after all have started moving is 1179/714 meters.

    ### Answer: 1179/714 meters

Expected answer: 393/238

Correct? Yes

🔗 Problem

Problem: Johnny had 24/14 of a yard of fabric that he used to make stuffed animals. After creating a few, he found he only had 9/29 of a yard left. He then got a new type of fabric and used 15/2 times the difference of the original and remaining fabric to make more stuffed animals. How many yards of the new fabric did Johnny use?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the amount of fabric Johnny used for the first few stuffed animals:
       * Original fabric = 24/14 yards
       * Remaining fabric = 9/29 yards
       * Fabric used = Original fabric - Remaining fabric
       * Fabric used = 24/14 - 9/29 = (24 × 29 - 9 × 14) / (14 × 29) = 570 / 406 = 285/203 yards

    2. Calculate the amount of new fabric Johnny used:
       * New fabric used = 15/2 × (Original fabric - Remaining fabric)
       * New fabric used = 15/2 × 285/203 = 4275/406 = 10.5246305418719 yards

    Therefore, Johnny used approximately 10.52 yards of the new fabric.

    ### Answer: 10.52 yards

Expected answer: 4275/406

Correct? No

🔗 Problem

Problem: In a park, there are some kids lining up for the swings. Part of the waiting line consists of 2/10 of the total number of kids in the park, while another part is made up of 21/4 kids. What is the total number of kids waiting for the swing? Add together 2/10 and 21/4 to find your answer.

Gemma 2B:

    To solve this problem, we need to add the fractions 2/10 and 21/4.

    Step 1: Convert the mixed number 21/4 to an improper fraction.
    21/4 = 2 × 4 + 1 = 9/4

    Step 2: Find the common denominator of 2/10 and 9/4.
    The common denominator is the least common multiple (LCM) of 10 and 4, which is 20.

    Step 3: Convert 2/10 and 9/4 to equivalent fractions with the common denominator of 20.
    2/10 = 2 × 2/10 × 2 = 4/20
    9/4 = 9 × 5/4 × 5 = 45/20

    Step 4: Add the fractions.
    4/20 + 45/20 = 49/20

    Step 5: Convert the improper fraction 49/20 to a mixed number.
    49/20 = 2 × 20 + 9 = 29/20 = 2 9/20

    Therefore, the total number of kids waiting for the swing is 2 9/20.

    ### Answer: 2 9/20

Expected answer: 109/20

Correct? No

🔗 Problem

Problem: An alien spacecraft has 18 fuel tanks out of a total of 30 fuel tanks filled. Each fuel tank can power the spacecraft for 22/6 hours. How many hours of power does the spacecraft currently have? Calculate (18 / 30) * (22 / 6) to find out.

Gemma 2B:

    Okay, let's break this down step by step:

    1. The spacecraft has 18 out of 30 fuel tanks filled. This can be represented as a fraction: 18/30.

    2. Each fuel tank can power the spacecraft for 22/6 hours.

    3. To find the total hours of power the spacecraft currently has, we need to multiply the fraction of filled tanks by the hours each tank provides:

       (18/30) * (22/6)

    4. First, let's simplify 22/6:
       22/6 = 11/3 = 3 2/3

    5. Now, let's multiply the fractions:
       (18/30) * (11/3) = (18 * 11) / (30 * 3) = 198/90

    6. Simplify the fraction:
       198/90 = 22/10 = 2 2/10 = 2 1/5

    So, (18/30) * (22/6) = 2 1/5 hours.

    ### Answer: The spacecraft currently has 2 1/5 hours of power.

Expected answer: 11/5

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we found out how many hours of power the alien spacecraft has when there were 18 fuel tanks filled out of 30. Now suppose a mechanism cleaned the fuel tanks in the spacecraft, enabling 18 out of 5 tanks to be filled instead. If each fuel tank can still power the spacecraft for 22/6 hours, how many hours of power does the spacecraft currently have? Just as before, calculate ((18 / 5) * (22 / 6)) to find out.

Gemma 2B:

    In this problem, we have a different fraction of fuel tanks filled: 18 out of 5. Let's solve this step by step:

    1. The spacecraft now has 18 out of 5 fuel tanks filled. This can be represented as a fraction: 18/5.

    2. Each fuel tank can still power the spacecraft for 22/6 hours.

    3. To find the total hours of power the spacecraft currently has, we need to multiply the fraction of filled tanks by the hours each tank provides:

       (18/5) * (22/6)

    4. First, let's simplify 22/6:
       22/6 = 11/3

    5. Now, let's multiply the fractions:
       (18/5) * (11/3) = (18 * 11) / (5 * 3) = 198/15

    6. Simplify the fraction:
       198/15 = 13 3/15 = 13 1/5

    So, (18/5) * (22/6) = 13 1/5 hours.

    ### Answer: The spacecraft currently has 13 1/5 hours of power.

Expected answer: 66/5

Correct? Yes

🔗 Problem

Problem: A cat is fed twice a day. In the morning, it eats 16/12 of a can of cat food. in the evening, it eats 6/10 of a can. How much of a can in total does the cat eat in one day?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * The cat is fed twice a day.
       * In the morning, it eats 16/12 of a can of cat food.
       * In the evening, it eats 6/10 of a can of cat food.

    2. Convert the fractions to have a common denominator:
       * 16/12 = 4/3 (divide both numerator and denominator by 4)
       * 6/10 = 3/5 (divide both numerator and denominator by 2)

    3. Add the fractions to find the total amount of cat food eaten in one day:
       * 4/3 + 3/5
       * To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
       * LCM of 3 and 5 is 15.
       * 4/3 = 20/15 (multiply both numerator and denominator by 5)
       * 3/5 = 9/15 (multiply both numerator and denominator by 3)
       * 20/15 + 9/15 = 29/15

    4. Simplify the result:
       * 29/15 = 1 14/15 (divide 29 by 15 to get the whole number and the remaining fraction)

    Therefore, the cat eats 1 14/15 cans of cat food in total in one day.

    ### Answer: 1 14/15 cans

Expected answer: 29/15

Correct? Yes

🔗 Follow-up

Problem: Continuing from the original problem, suppose the morning serving size changes and the cat now eats 16/21 of a can of cat food in the morning rather than the original 16/12 of a can. Maintaining the same evening portion of 6/10 of a can, how much does the cat eat in total in one day with the new morning serving size?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the updated information:
       * The cat is fed twice a day.
       * In the morning, it now eats 16/21 of a can of cat food (updated from 16/12).
       * In the evening, it still eats 6/10 of a can of cat food.

    2. Convert the fractions to have a common denominator:
       * 16/21 (no simplification needed)
       * 6/10 = 3/5 (divide both numerator and denominator by 2)

    3. Add the fractions to find the total amount of cat food eaten in one day:
       * 16/21 + 3/5
       * To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
       * LCM of 21 and 5 is 105.
       * 16/21 = 80/105 (multiply both numerator and denominator by 5)
       * 3/5 = 63/105 (multiply both numerator and denominator by 21)
       * 80/105 + 63/105 = 143/105

    4. Simplify the result:
       * 143/105 = 1 38/105 (divide 143 by 105 to get the whole number and the remaining fraction)
       * 38/105 can be further simplified by dividing both numerator and denominator by 2.
       * 38/105 = 19/105 = 19/35 (divide both numerator and denominator by 3)

    Therefore, with the new morning serving size of 16/21 of a can and maintaining the evening portion of 6/10 of a can, the cat eats 1 19/35 cans of cat food in total in one day.

    ### Answer: 1 19/35 cans

Expected answer: 143/105

Correct? No

🔗 Problem

Problem: A starfish laid 12 eggs in 3 nests and 11 eggs in 4 other nests. How much is the difference between the average number of eggs per nest for these two groups of nests?

Gemma 2B:

    Let's solve this step by step:

    1. Find the total number of eggs in the first group of nests:
       * There are 3 nests with 12 eggs each.
       * Total eggs in the first group = 12 × 3 = 36 eggs

    2. Find the average number of eggs per nest in the first group:
       * Average eggs per nest in the first group = 36 eggs ÷ 3 nests = 12 eggs per nest

    3. Find the total number of eggs in the second group of nests:
       * There are 4 nests with 11 eggs each.
       * Total eggs in the second group = 11 × 4 = 44 eggs

    4. Find the average number of eggs per nest in the second group:
       * Average eggs per nest in the second group = 44 eggs ÷ 4 nests = 11 eggs per nest

    5. Calculate the difference between the average number of eggs per nest for the two groups:
       * Difference = Average eggs per nest in the first group - Average eggs per nest in the second group
       * Difference = 12 - 11 = 1 egg per nest

    ### Answer: 1 egg per nest

Expected answer: 5/4

Correct? No

🔗 Problem

Problem: A monkey finds a pile of bananas and ends up eating (22 / 7) times (10 / 25) of the pile. Later, he gives (3 / 28) of the pile to his friend. How much of the pile does the monkey have left?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's calculate the fraction of the pile the monkey ate:
       (22 / 7) × (10 / 25) = (22 × 10) / (7 × 25) = 220 / 175 = 44 / 35 = 1.257142857...
       This means the monkey ate approximately 1.26 times the pile, which is not possible. Let's assume the monkey ate (10 / 25) of the pile, which is a proper fraction.

    2. So, after eating, the monkey has:
       1 - (10 / 25) = (25 - 10) / 25 = 15 / 25 = 3 / 5 of the pile left.

    3. Now, the monkey gives (3 / 28) of the original pile to his friend. To find out how much of the remaining pile this is, we divide:
       (3 / 28) ÷ (3 / 5) = (3 / 28) × (5 / 3) = 5 / 28 = 5 / 28

    4. So, the monkey gives 5 / 28 of the remaining pile to his friend. To find out how much of the pile the monkey has left, we subtract:
       (3 / 5) - (5 / 28) = (84 - 25) / 140 = 59 / 140

    Therefore, the monkey has 59 / 140 of the original pile left.

    ### Answer: 59 / 140

Expected answer: 23/20

Correct? No

🔗 Problem

Problem: A mouse runs at a speed of 24/20 feet per second. If the mouse runs for 23/2 seconds, how many feet does the mouse run?

Gemma 2B:

    To solve this problem, we need to find the distance the mouse runs. We can use the formula: Distance = Speed × Time.

    Given:
    - The mouse runs at a speed of 24/20 feet per second.
    - The mouse runs for 23/2 seconds.

    Step 1: Convert the mixed fraction 23/2 to an improper fraction.
    23/2 = 2 × 2 + 3 = 7/2

    Step 2: Calculate the distance using the formula Distance = Speed × Time.
    Distance = 24/20 × 7/2
    Distance = (24 × 7) ÷ (20 × 2)
    Distance = 168 ÷ 40
    Distance = 21/5 feet

    Therefore, the mouse runs 21/5 feet.

    ### Answer: 21/5 feet

Expected answer: 69/5

Correct? No

🔗 Problem

Problem: At a party, the drinks are served in glasses that contain 29/9 ounces of beverage each. If 26/25 of them were consumed, how many ounces of beverage were consumed? Now imagine that the party goers then drink an additional 2/19 ounces of beverages. How many total ounces of beverages were consumed at the party in total?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the number of ounces in each glass:
       * Each glass contains 29/9 ounces of beverage.
       * 29/9 ounces = 3 2/9 ounces (or approximately 3.22 ounces)

    2. Find the number of ounces consumed initially:
       * 26/25 of the glasses were consumed.
       * (26/25) × (29/9) = (26 × 29) / (25 × 9) = 754 / 225 ounces
       * 754 / 225 ounces = 3 79/225 ounces (or approximately 3.35 ounces)

    3. Find the total number of ounces consumed after drinking an additional 2/19 ounces:
       * Total ounces consumed = (754 / 225) + (2/19)
       * (754 / 225) + (2/19) = (754 × 19 + 2 × 225) / (225 × 19)
       * (14326 + 450) / 4275 = 14776 / 4275 ounces
       * 14776 / 4275 ounces = 3 1501/4275 ounces (or approximately 3.46 ounces)

    ### Answer: The party goers consumed a total of 3 1501/4275 ounces (or approximately 3.46 ounces) of beverages.

Expected answer: 14776/4275

Correct? No

🔗 Problem

Problem: You decide to start a toothbrush collection and you add 7/15 of a new set of toothbrushes to your current collection. Suddenly, a friend gifts you 9 more sets. After grouping everything, you realized you can only fit 26/27 of them in your display case. How many sets of toothbrushes can you fit in your display case?

Gemma 2B:

    Let's solve this problem step by step:

    1. We don't know how many sets of toothbrushes you had initially, so let's call that number x.

    2. You added 7/15 of a new set to your collection. So now you have:
       x + 7/15 sets of toothbrushes

    3. Your friend gifted you 9 more sets. So the total number of sets you have now is:
       x + 7/15 + 9 sets of toothbrushes

    4. You can fit 26/27 of your total sets in the display case. This means:
       26/27 * (x + 7/15 + 9) sets of toothbrushes fit in the display case

    5. To find the number of sets that fit, we need to calculate the value of the expression:
       26/27 * (x + 7/15 + 9)

       However, we don't know the value of x. But since the question doesn't ask about the initial number of sets, we can assume it's not necessary for the solution.

    6. Let's simplify the expression:
       26/27 * (x + 7/15 + 9)
       = 26/27 * (x + 16/15)
       = 26/27 * x + 26/27 * 16/15
       = 26/27 * x + 832/405
       = 26/27 * x + 2.0543...

       The result is a fractional number of sets, which doesn't make sense in the context of the problem. We need a whole number of sets.

    7. Therefore, we can conclude that the maximum number of whole sets that can fit in the display case is the integer part of the result, which is 2.

    ### Answer: 2

Expected answer: 3692/405

Correct? No

🔗 Problem

Problem: Joan has a backpack which weighs 27/20 kilograms when it's empty. She adds a book which weighs 1/6 kilograms. Calculate the total weight of the backpack in kilograms now. Please write the answer as a simplified fraction.

Gemma 2B:

    To find the total weight of the backpack, we need to add the weight of the empty backpack and the weight of the book.

    Weight of the empty backpack: 27/20 kilograms
    Weight of the book: 1/6 kilograms

    Adding the weights:
    27/20 + 1/6 = (27 × 3)/(20 × 3) + (1 × 20)/(6 × 20)
               = 81/60 + 20/120
               = 81/60 + 1/6
               = (81 + 10)/60
               = 91/60

    Simplifying the fraction:
    91/60 cannot be simplified further as 91 and 60 have no common factors other than 1.

    ### Answer: 91/60

Expected answer: 91/60

Correct? Yes

🔗 Follow-up

Problem: Let's revise our original situation. This time, Joan's backpack weighs 27/20 kilograms when it's empty. She then adds a heavier book which weighs 21/6 kilograms. What's the total weight of her backpack now? Please write your answer as a simplified fraction.

Gemma 2B:

    Alright, let's solve this problem step by step.

    Given:
    - The empty backpack weighs 27/20 kilograms.
    - Joan adds a book that weighs 21/6 kilograms.

    Step 1: Add the weight of the empty backpack and the weight of the book.
    Total weight = Weight of empty backpack + Weight of book
                 = 27/20 + 21/6

    Step 2: Find a common denominator for the fractions.
    The least common multiple of 20 and 6 is 60.

    Step 3: Convert the fractions to equivalent fractions with the common denominator.
    27/20 = (27 × 3)/(20 × 3) = 81/60
    21/6 = (21 × 10)/(6 × 10) = 210/60

    Step 4: Add the fractions.
    Total weight = 81/60 + 210/60
                 = (81 + 210)/60
                 = 291/60

    Step 5: Simplify the fraction.
    291/60 cannot be simplified further as 291 and 60 have no common factors other than 1.

    ### Answer: 291/60

Expected answer: 97/20

Correct? Yes

🔗 Problem

Problem: A soda company is changing its bottle design. The new design will change the volume of the bottles so that they become (7 / 7) * (25 / 22) times larger. What will be the multiplier of the new bottle compared to the old one?

Gemma 2B:

    To find the multiplier of the new bottle compared to the old one, we need to calculate the product of the given fractions:

    (7 / 7) * (25 / 22)

    Step 1: Simplify the first fraction (7 / 7).
    7 / 7 = 1

    Step 2: Multiply the simplified first fraction by the second fraction (25 / 22).
    1 * (25 / 22) = 25 / 22

    Step 3: Simplify the resulting fraction if possible.
    25 and 22 have no common factors other than 1, so the fraction cannot be simplified further.

    Therefore, the new bottle will be 25 / 22 times larger than the old one.

    ### Answer: 25 / 22

Expected answer: 25/22

Correct? Yes

🔗 Follow-up

Problem: The soda company decided to further increase the size of the new bottle design. Now the bottles will be enlarged by a multiplier of (28 / 13) times the previous size change. What will be the new multiplier of the updated bottle compared to the original one?

Gemma 2B:

    In the previous problem, we found that the new bottle size was 25 / 22 times the original size. Now, the company wants to increase the size further by a multiplier of 28 / 13.

    To find the updated multiplier, we need to multiply the previous size change by the new size change:

    (25 / 22) * (28 / 13)

    Step 1: Multiply the numerators and denominators separately.
    Numerator: 25 * 28 = 700
    Denominator: 22 * 13 = 286

    Step 2: Write the result as a fraction.
    700 / 286

    Step 3: Simplify the fraction if possible.
    700 and 286 have a common factor of 14.
    700 ÷ 14 = 50
    286 ÷ 14 = 22

    Simplified fraction: 50 / 22

    Therefore, the updated bottle size will be 50 / 22 times the original size.

    ### Answer: 50 / 22

Expected answer: 350/143

Correct? No

🔗 Follow-up

Problem: The soda company revises their decision and decides to slightly reduce the increase in the size of the new bottle design. Now, the bottles will be (7 / 7) * (25 / 12) times larger than the original design. What will be the new multiplier for the revised bottle compared to the origianl one?

Gemma 2B:

    To find the new multiplier for the revised bottle compared to the original one, we need to calculate the product of the given fractions:

    (7 / 7) * (25 / 12)

    Step 1: Simplify the first fraction (7 / 7).
    7 / 7 = 1

    Step 2: Multiply the simplified first fraction by the second fraction (25 / 12).
    1 * (25 / 12) = 25 / 12

    Step 3: Simplify the resulting fraction if possible.
    25 and 12 have a common factor of 1, so we can divide both the numerator and denominator by 1 to simplify the fraction.
    25 ÷ 1 = 25
    12 ÷ 1 = 12
    Therefore, the fraction cannot be simplified further.

    Step 4: Convert the fraction to a mixed number or decimal if desired.
    25 ÷ 12 ≈ 2.0833333...
    Or, as a mixed number: 2 1/12

    Therefore, the revised bottle will be 25 / 12 (or approximately 2.08 times) larger than the original one.

    ### Answer: 25 / 12 (or approximately 2.08)

Expected answer: 25/12

Correct? Yes

🔗 Problem

Problem: Turtle Tilly is collecting food for the winter. She has gathered 25/9 kg of sea plants, and she then finds 8/13 kg more. In a close-by rock, she spots another food stash weighing 24/27 kg. After gobbling up these finds, Tilly stumbles upon yet another food source weighing 21/26 kg. If Tilly combines all her found food, how many kilograms does she now have in total? Answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. Tilly starts with 25/9 kg of sea plants.

    2. She then finds 8/13 kg more.
       25/9 + 8/13 = (25 × 13 + 8 × 9) / (9 × 13) = 397/117

    3. Tilly spots another food stash weighing 24/27 kg.
       397/117 + 24/27 = (397 × 27 + 24 × 117) / (117 × 27) = 13533/3159

    4. Finally, Tilly finds another food source weighing 21/26 kg.
       13533/3159 + 21/26 = (13533 × 26 + 21 × 3159) / (3159 × 26) = 418491/82134

    5. Simplify the fraction:
       418491/82134 = 5097/1001

    Therefore, Tilly now has a total of 5097/1001 kg of food.

    ### Answer: 5097/1001

Expected answer: 397/78

Correct? No

🔗 Problem

Problem: Captain Alf undertakes multi-step calculations to ensure the safe navigation of his boat. First, he calculates the difference in his current location and the distance of a nearby island. The distance to the island is 17/2 nautical miles, and his boat is currently 4/2 nautical miles away from the island. Next, Captain Alf adjusts for the tide, which he has estimated to push his boat off course by 14/9 nautical miles. He adds this to his previous calculations. Finally, when considering his fuel efficiency rated at 22/15 nautical miles per gallon, Captain Alf multiplies his adjusted distance by this rate to figure out his fuel requirements. What does Captain Alf’s final calculation come to? Use these steps and corresponding fractions to find your answer.

Gemma 2B:

    Let's solve this problem step by step:

    Step 1: Calculate the distance between Captain Alf's current location and the island.
    Distance to the island = 17/2 nautical miles
    Current distance from the island = 4/2 nautical miles
    Difference = 17/2 - 4/2 = 13/2 nautical miles

    Step 2: Adjust the distance for the tide.
    Tide adjustment = 14/9 nautical miles
    Adjusted distance = 13/2 + 14/9 nautical miles
    To add these fractions, we need a common denominator. The common denominator is 18.
    Adjusted distance = (13 × 9)/(2 × 9) + (14 × 2)/(9 × 2) = 117/18 + 28/18 = 145/18 nautical miles

    Step 3: Calculate the fuel requirements.
    Fuel efficiency = 22/15 nautical miles per gallon
    Fuel requirements = Adjusted distance × Fuel efficiency
    Fuel requirements = (145/18) × (22/15) nautical miles
    To multiply these fractions, multiply the numerators and denominators separately.
    Fuel requirements = (145 × 22)/(18 × 15) = 3190/270 = 11.8148 gallons (rounded to 4 decimal places)

    ### Answer: 11.8148 gallons

Expected answer: 319/27

Correct? No

🔗 Problem

Problem: A forest ranger patrolled 14/3 miles of trails in the morning. In the afternoon, he patrolled 2/18 mile less than what he walked in the morning. How many miles did the forest ranger patrol in the afternoon?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's find out how many miles the forest ranger patrolled in the morning:
       * The forest ranger patrolled 14/3 miles in the morning.
       * 14/3 = 4 2/3 miles

    2. Now, let's calculate how many miles the forest ranger patrolled in the afternoon:
       * In the afternoon, he patrolled 2/18 mile less than what he walked in the morning.
       * 2/18 = 1/9 mile
       * So, in the afternoon, he patrolled: 4 2/3 - 1/9 miles
       * To subtract fractions, we need to find a common denominator. The common denominator is 9.
       * 4 2/3 = 4 6/9
       * 4 6/9 - 1/9 = 4 5/9 miles

    Therefore, the forest ranger patrolled 4 5/9 miles in the afternoon.

    ### Answer: 4 5/9 miles

Expected answer: 41/9

Correct? Yes

🔗 Follow-up

Problem: Instead of the 14/3 miles, suppose the forest ranger actually patrolled 29/3 miles of trails in the morning. Considering he covered 2/18 mile less in the afternoon, how many miles did he patrol in the afternoon now?

Gemma 2B:

    Okay, let's solve this problem with the updated information:

    1. The forest ranger patrolled 29/3 miles in the morning.
       * 29/3 = 9 2/3 miles

    2. In the afternoon, he patrolled 2/18 mile less than what he walked in the morning.
       * 2/18 = 1/9 mile
       * So, in the afternoon, he patrolled: 9 2/3 - 1/9 miles
       * To subtract fractions, we need to find a common denominator. The common denominator is 9.
       * 9 2/3 = 9 6/9
       * 9 6/9 - 1/9 = 9 5/9 miles

    Therefore, with the updated morning patrol distance of 29/3 miles, the forest ranger patrolled 9 5/9 miles in the afternoon.

    ### Answer: 9 5/9 miles

Expected answer: 86/9

Correct? Yes

🔗 Problem

Problem: Arthur practices piano for 20/21 of an hour every day. On weekends, he practices an additional 11/29 of an hour per day. How many hours in total does Arthur spend practicing the piano each day on the weekend?

Gemma 2B:

    Let's solve this problem step by step:

    1. Arthur practices piano for 20/21 of an hour every day.
    2. On weekends, he practices an additional 11/29 of an hour per day.
    3. To find the total hours he practices on weekends, we need to add the regular practice time and the additional weekend practice time.

    First, let's convert 20/21 and 11/29 to decimals to make the addition easier:
    * 20/21 ≈ 0.9524 hours
    * 11/29 ≈ 0.3793 hours

    Now, let's add the regular practice time and the additional weekend practice time:
    * Total weekend practice time = 0.9524 + 0.3793
    * Total weekend practice time ≈ 1.3317 hours

    To convert 1.3317 hours to hours and minutes:
    * 0.3317 hours = 0.3317 × 60 minutes ≈ 19.9 minutes

    Therefore, on weekends, Arthur practices piano for approximately 1 hour and 20 minutes each day.

    ### Answer: 1 hour and 20 minutes (or 1.3317 hours)

Expected answer: 811/609

Correct? No

🔗 Problem

Problem: Lucas has a shirt store. Initially, he had 18 shirts which he divided equally among his 3 siblings. Later, he bought 27 more shirts but wanted to sell them at a higher price, so he decided to keep only 1/19 of those shirts for each sibling. How many more or fewer shirts does each sibling now have as compared to before? Calculate the difference using the expression ((18 / 3) - (27 / 19)) and find out the result.

Gemma 2B:

    Let's solve this problem step by step:

    1. Initially, Lucas divided 18 shirts equally among his 3 siblings:
       * Number of shirts each sibling got = 18 ÷ 3 = 6 shirts

    2. Later, Lucas bought 27 more shirts and decided to keep only 1/19 of those shirts for each sibling:
       * Number of new shirts each sibling got = 27 ÷ 19 = 1.42 shirts (rounded to 2 decimal places)

    3. To find the difference in the number of shirts each sibling has now compared to before, we use the given expression:
       * Difference = (18 ÷ 3) - (27 ÷ 19)
       * Difference = 6 - 1.42
       * Difference = 4.58 shirts

    4. Since the difference is positive, each sibling now has 4.58 fewer shirts than before.

    ### Answer: Each sibling now has 4.58 fewer shirts than before.

Expected answer: 87/19

Correct? No

🔗 Problem

Problem: A painter mixed 7 gallons of white paint with 2/5 gallon of blue paint to make a light blue paint. After using 18/4 gallons of the light blue paint for a project, how many gallons does the painter have left?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the total amount of light blue paint the painter made:
       * White paint: 7 gallons
       * Blue paint: 2/5 gallon
       * Total light blue paint = 7 + 2/5 = 35/5 + 2/5 = 37/5 = 7.4 gallons

    2. Find the amount of light blue paint used for the project:
       * Paint used = 18/4 gallons
       * 18/4 = 4.5 gallons

    3. Calculate the remaining amount of light blue paint:
       * Remaining paint = Total light blue paint - Paint used
       * Remaining paint = 7.4 - 4.5 = 2.9 gallons

    Therefore, the painter has 2.9 gallons of light blue paint left.

    ### Answer: 2.9 gallons

Expected answer: 29/10

Correct? No

🔗 Problem

Problem: Jayson went to the roller rink and spent 24/7 hours skating on the first day. On the second day, he decided to skate for an additional 30/20 hours. How many hours in total did Jayson spend skate skating over the two days?

Gemma 2B:

    To solve this problem, we need to add the time Jayson spent skating on the first day and the second day.

    1. Convert the fractions to decimals:
       * First day: 24/7 = 3.428571... ≈ 3.43 hours
       * Second day: 30/20 = 1.5 hours

    2. Add the skating time for both days:
       * Total skating time = First day + Second day
       * Total skating time = 3.43 + 1.5 = 4.93 hours

    Therefore, Jayson spent approximately 4.93 hours skating over the two days.

    ### Answer: 4.93 hours

Expected answer: 69/14

Correct? No

🔗 Problem

Problem: Dolphins can leap approximately 18/3 feet out of the water. If a dolphin only manages to jump 3/4 of his usual height one day, how high did the dolphin jump?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Dolphins can usually leap 18/3 feet out of the water.
       * On a particular day, a dolphin only managed to jump 3/4 of its usual height.

    2. Calculate the dolphin's usual leaping height in feet:
       * Usual height = 18/3 feet
       * 18/3 = 6 feet

    3. Calculate the height the dolphin jumped on that day:
       * Jumped height = 3/4 of the usual height
       * Jumped height = 3/4 × 6 feet
       * Jumped height = (3 × 6) / 4 feet
       * Jumped height = 18/4 feet
       * Jumped height = 4.5 feet

    ### Answer: The dolphin jumped 4.5 feet out of the water on that day.

Expected answer: 9/2

Correct? Yes

🔗 Follow-up

Problem: After observing that the dolphin managed to only jump 3/4 of his usual 18/3 feet out of the water, the trainer noted a reduction in his jumping height by 14/25 feet the next day. How high did the dolphin jump this time?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Dolphins can usually leap 18/3 feet out of the water.
       * On the first day, the dolphin only managed to jump 3/4 of its usual height.
       * On the next day, the trainer noted a further reduction in the dolphin's jumping height by 14/25 feet.

    2. Calculate the dolphin's usual leaping height in feet:
       * Usual height = 18/3 feet
       * 18/3 = 6 feet

    3. Calculate the height the dolphin jumped on the first day:
       * First day height = 3/4 of the usual height
       * First day height = 3/4 × 6 feet
       * First day height = (3 × 6) / 4 feet
       * First day height = 18/4 feet
       * First day height = 4.5 feet

    4. Calculate the height the dolphin jumped on the next day:
       * Next day height = First day height - 14/25 feet
       * Next day height = 4.5 feet - 14/25 feet
       * Next day height = (4.5 × 25 - 14) / 25 feet
       * Next day height = (112.5 - 14) / 25 feet
       * Next day height = 98.5 / 25 feet
       * Next day height = 3.94 feet

    ### Answer: The dolphin jumped 3.94 feet out of the water on the next day.

Expected answer: 197/50

Correct? No

🔗 Follow-up

Problem: Previously, we measured the dolphin's jump when it managed to reach 3/4 of his usual height of 18/3 feet. Now let's consider a day when the dolphin jumps to an unusually high 19/4 of his normal height. If the dolphin's usual jump is 18/3 feet, how high does the dolphin jump on this particular day?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the information from the previous problem to find the dolphin's jump height on this particular day.

    Given:
    - The dolphin's usual jump height is 18/3 feet.
    - On this particular day, the dolphin jumps 19/4 times its normal height.

    Step 1: Express the dolphin's usual jump height as a decimal.
    Usual jump height = 18/3 feet = 6 feet

    Step 2: Calculate the dolphin's jump height on this particular day.
    Unusually high jump height = 19/4 × Usual jump height
    Unusually high jump height = 19/4 × 6 feet
    Unusually high jump height = (19 × 6) / 4 feet
    Unusually high jump height = 114 / 4 feet
    Unusually high jump height = 28.5 feet

    ### Answer: On this particular day, the dolphin jumps 28.5 feet high, which is 19/4 times its usual jump height of 18/3 feet (6 feet).

Expected answer: 57/2

Correct? No

🔗 Problem

Problem: Callie owns a pen business. Last month, she sold 20 pens for every 15 she produced. At the same time, she sold an additional 16 pens for every 22 she put out for sale. Meanwhile, she found that for every 22 pens she advertised, 27 were interested customers. For each 23 pens she produced this week, she was able to sell 8. What is the result when she multiplies the ratio of last month's sales to production (20/15 + 16/22) and this week's figure for the ratio of interested customers to production (22/27 * 23/8)? Leave your answer as an unsimplified fraction.

Gemma 2B:

    Let's break this down step by step:

    1. Last month's sales to production ratio:
       - She sold 20 pens for every 15 she produced: 20/15
       - She also sold 16 pens for every 22 she put out for sale: 16/22
       - Total ratio of last month's sales to production: 20/15 + 16/22

    2. This week's ratio of interested customers to production:
       - For every 22 pens she advertised, 27 were interested customers: 22/27
       - For each 23 pens she produced this week, she was able to sell 8: 23/8
       - Ratio of interested customers to production: 22/27 * 23/8

    3. Multiplying the two ratios:
       (20/15 + 16/22) * (22/27 * 23/8)
       = (4/3 + 8/11) * (11/27 * 23/8)
       = (44/33 + 88/121) * (253/216)
       = (5324/3993 + 19184/29403) * (253/216)
       = (5324/3993 + 19184/29403) * 253/216
       = (1346972/855144 + 4853552/6310443) * 1
       = 1346972/855144 + 4853552/6310443
       = 8503495728/5410059432 + 4853552/6310443
       = (8503495728/5410059432 + 4853552/6310443)

    Therefore, the result when she multiplies the ratio of last month's sales to production and this week's figure for the ratio of interested customers to production is:

    ### Answer: (8503495728/5410059432 + 4853552/6310443)

Expected answer: 391/81

Correct? No

🔗 Problem

Problem: Consider a band practice session in which a musician played a song for exactly 30 minutes. After dividing this time equally between 15 songs, how much time did they spend on each song? From this average time per song, the band reduced the time spent on a particular song by 1/17 of an hour. Can you calculate the final duration of that song?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the average time spent on each song:
       * Total time = 30 minutes
       * Number of songs = 15
       * Average time per song = 30 minutes ÷ 15
       * Average time per song = 2 minutes

    2. Convert the average time per song from minutes to hours:
       * 2 minutes = 2 ÷ 60 hours
       * 2 minutes = 1/30 hours

    3. Calculate the reduction in time for the particular song:
       * Reduction = 1/17 of an hour

    4. Calculate the final duration of the particular song:
       * Final duration = Average time per song - Reduction
       * Final duration = 1/30 hours - 1/17 hours
       * Final duration = (1/30 - 1/17) hours
       * Final duration = (17 - 30) ÷ (30 × 17) hours
       * Final duration = -13 ÷ 510 hours
       * Final duration = -1/510 hours

    5. Convert the final duration from hours to minutes:
       * Final duration in minutes = -1/510 hours × 60 minutes/hour
       * Final duration in minutes = -6/51 minutes
       * Final duration in minutes ≈ -0.1176 minutes (rounded to 4 decimal places)

    ### Answer: The final duration of the particular song is approximately -0.1176 minutes or -7.06 seconds.

Expected answer: 33/17

Correct? No

🔗 Problem

Problem: Josh rented a scooter for a day. He rode the scooter for a total of 18 hours during the first day. The next day, he rode the scooter for an additional 1/12 of an hour. Later that afternoon, his friend Jack also rented a scooter and rode it for 7/17 of an hour. How many hours did they both ride scooters in total (expressed as a fraction)? Combine the hours they both rode and simplify the fraction to get the answer.

Gemma 2B:

    Let's break this down step by step:

    1. Josh's total riding time:
       * First day: 18 hours
       * Second day: 1/12 of an hour
       * Josh's total: 18 + 1/12 = 216/12 + 1/12 = 217/12 hours

    2. Jack's riding time:
       * 7/17 of an hour

    3. Total riding time for both Josh and Jack:
       * Total = Josh's total + Jack's total
       * Total = 217/12 + 7/17 hours

    4. To add these fractions, we need a common denominator. The least common multiple of 12 and 17 is 204.
       * 217/12 = 217 × 17/12 × 17 = 3689/204
       * 7/17 = 7 × 12/17 × 12 = 84/204

    5. Now we can add the fractions:
       * Total = 3689/204 + 84/204 = 3773/204

    6. Simplify the fraction:
       * 3773 and 204 have a greatest common factor of 17.
       * 3773/17 = 222
       * 204/17 = 12
       * Simplified total = 222/12 = 37/2 hours

    ### Answer: 37/2

Expected answer: 3773/204

Correct? No

🔗 Problem

Problem: A lamp store owner is doing inventory of all the lamps in his store. He found that he has 4/26 of lamps that are floor lamps, 15/11 that are desk lamps, he also discovered he has 23/28 of table lamps and finally 8/19 of lamps that are decorative. What fraction of his total inventory do these lamps constitute?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, we need to add all the fractions of different types of lamps to find the total fraction of the inventory these lamps constitute.

       4/26 + 15/11 + 23/28 + 8/19

    2. To add fractions, we need to find the least common multiple (LCM) of the denominators.

       LCM(26, 11, 28, 19) = 11,438

    3. Now, we convert each fraction to an equivalent fraction with the denominator 11,438.

       4/26 = 1,760/11,438
       15/11 = 15,580/11,438
       23/28 = 9,405/11,438
       8/19 = 4,810/11,438

    4. Add the numerators of the equivalent fractions:

       1,760/11,438 + 15,580/11,438 + 9,405/11,438 + 4,810/11,438
       = (1,760 + 15,580 + 9,405 + 4,810)/11,438
       = 31,555/11,438

    5. Simplify the fraction:

       31,555/11,438 = 2.759 (rounded to three decimal places)

    Therefore, the floor lamps, desk lamps, table lamps, and decorative lamps constitute 2.759 of the total inventory.

    ### Answer: 2.759

Expected answer: 209967/76076

Correct? No

🔗 Problem

Problem: Oliver has a kite string that is 26/19 meters long and another kite string that is 7/11 meters long. He decides to add these two strings to create an even longer kite string. Later on, he decides to use only 5/8 of this combined string. How long is the kite string that he is using now? Do not simplify your fractions within your calculation.

Gemma 2B:

    Okay, let's solve this problem step by step:

    1. Find the total length of the combined kite string:
       * First string length = 26/19 meters
       * Second string length = 7/11 meters
       * Total length = 26/19 + 7/11 meters
       * Total length = (26 × 11 + 7 × 19) / (19 × 11) meters
       * Total length = (286 + 133) / 209 meters
       * Total length = 419/209 meters

    2. Find the length of the string Oliver is using now:
       * Oliver is using 5/8 of the total length
       * Length of the string being used = 5/8 × 419/209 meters
       * Length of the string being used = (5 × 419) / (8 × 209) meters
       * Length of the string being used = 2095/1672 meters

    Therefore, the kite string that Oliver is using now is 2095/1672 meters long.

    ### Answer: 2095/1672 meters

Expected answer: 2095/1672

Correct? Yes

🔗 Follow-up

Problem: After using the combined kite string, Oliver realizes he needs a similar length of string for another kite. He decides to use the same length of string that he used earlier, effectively doubling his previous length. What is the total length of the kite string Oliver is now using? Note: Do not simplify your fractions within your calculation.

Gemma 2B:

    Great! Let's continue from where we left off in the previous problem.

    Given:
    - Oliver is now using twice the length of the string he used earlier.
    - The length of the string he used earlier was 2095/1672 meters.

    Step 1: Calculate the new total length of the kite string Oliver is using.
    New total length = 2 × Previous length
    New total length = 2 × 2095/1672 meters
    New total length = (2 × 2095) / 1672 meters
    New total length = 4190/1672 meters

    Therefore, the total length of the kite string Oliver is now using is 4190/1672 meters.

    ### Answer: 4190/1672 meters

Expected answer: 2095/836

Correct? Yes

🔗 Follow-up

Problem: Previously, Oliver used a string that was 5/8 of the combined total. However, now, he decides to use 26/8 of the same combined total length (26/19 meters and 7/11 meters) for a larger kite. What would be the length of the string that he is using now? Note: Do not simplify your fractions within your calculation.

Gemma 2B:

    Great! Let's solve this problem step by step:

    1. Find the total length of the combined kite string (same as before):
       * First string length = 26/19 meters
       * Second string length = 7/11 meters
       * Total length = 26/19 + 7/11 meters
       * Total length = (26 × 11 + 7 × 19) / (19 × 11) meters
       * Total length = (286 + 133) / 209 meters
       * Total length = 419/209 meters

    2. Find the length of the string Oliver is using now:
       * Oliver is now using 26/8 of the total length
       * Length of the string being used = 26/8 × 419/209 meters
       * Length of the string being used = (26 × 419) / (8 × 209) meters
       * Length of the string being used = 10894/1672 meters

    Therefore, the kite string that Oliver is using now is 10894/1672 meters long.

    ### Answer: 10894/1672 meters

Expected answer: 5447/836

Correct? Yes

🔗 Problem

Problem: In a snow fight, Mike threw 9/19 of his snowballs and his friend, John threw 6/8 of his snowballs. After a while, Mike found 4 more snowballs to throw. The question is, if 'u' represents the number of snowballs thrown by both Mike and John and 'j' is the total number of snowballs Mike had after finding more, how many snowballs did Mike have in total? Solve the following equations to find the variable 'j': u = 9/19 + 6/8 j = u + 4/1

Gemma 2B:

    Let's solve this problem step by step:

    1. First, we need to find the value of 'u' by solving the equation:
       u = 9/19 + 6/8

       To add fractions, we need to find a common denominator. The common denominator is 19 * 8 = 152.

       9/19 = (9 * 8)/(19 * 8) = 72/152
       6/8 = (6 * 19)/(8 * 19) = 114/152

       Now, we can add the fractions:
       u = 72/152 + 114/152 = 186/152

       Simplify the fraction:
       u = 31/38

    2. Now that we have the value of 'u', we can solve the equation for 'j':
       j = u + 4/1

       Substitute the value of 'u':
       j = 31/38 + 4/1

       To add fractions, we need to find a common denominator. The common denominator is 38 * 1 = 38.

       31/38 = 31/38
       4/1 = (4 * 38)/(1 * 38) = 152/38

       Now, we can add the fractions:
       j = 31/38 + 152/38 = 183/38

       Simplify the fraction:
       j = 4 + 19/38 = 4 19/38

    Therefore, Mike had a total of 4 19/38 snowballs.

    ### Answer: Mike had a total of 4 19/38 snowballs.

Expected answer: 397/76

Correct? No

🔗 Problem

Problem: In a chocolate factory, one worker packages 26 pieces of chocolate in 18 minutes, while another worker can package 15 pieces of chocolate every 15 minutes. Find out the total amount of chocolate they can package in one minute.

Gemma 2B:

    To solve this problem, let's break it down into steps:

    1. Find the number of chocolates the first worker packages per minute:
       * The first worker packages 26 pieces of chocolate in 18 minutes.
       * Chocolates per minute for the first worker = 26 ÷ 18 = <<26/18=1.4444444444444444>>1.444 (rounded to 3 decimal places)

    2. Find the number of chocolates the second worker packages per minute:
       * The second worker packages 15 pieces of chocolate in 15 minutes.
       * Chocolates per minute for the second worker = 15 ÷ 15 = <<15/15=1>>1

    3. Calculate the total amount of chocolate they can package in one minute:
       * Total chocolates per minute = Chocolates per minute for the first worker + Chocolates per minute for the second worker
       * Total chocolates per minute = 1.444 + 1 = <<1.4444444444444444+1=2.4444444444444444>>2.444 (rounded to 3 decimal places)

    ### Answer: 2.444

Expected answer: 22/9

Correct? No

🔗 Problem

Problem: Yesterday, Joanna washed 24/20 batches of small towels and 25/15 batches of large towels. Find the total number of batches of towels she washed.

Gemma 2B:

    To find the total number of batches of towels Joanna washed, we need to add the number of batches of small towels and large towels.

    Given:
    - Joanna washed 24/20 batches of small towels.
    - Joanna washed 25/15 batches of large towels.

    Step 1: Convert the mixed numbers to improper fractions.
    Small towels: 24/20 = 1 4/20 = (1 × 20 + 4) / 20 = 24/20
    Large towels: 25/15 = 1 10/15 = (1 × 15 + 10) / 15 = 25/15

    Step 2: Find a common denominator for the fractions.
    The common denominator is the least common multiple (LCM) of 20 and 15, which is 60.

    Step 3: Convert the fractions to equivalent fractions with the common denominator.
    Small towels: 24/20 = 24 × 3/20 × 3 = 72/60
    Large towels: 25/15 = 25 × 4/15 × 4 = 100/60

    Step 4: Add the fractions.
    Total batches = 72/60 + 100/60 = 172/60

    Step 5: Convert the result to a mixed number.
    172/60 = 2 52/60 = 2 26/30 = 2 13/15

    ### Answer: 2 13/15

Expected answer: 43/15

Correct? Yes

🔗 Follow-up

Problem: Joanna originally thought she washed 25/15 batches of large towels. However, she realized that she had actually washed 25/7 batches. Taking this into account, with the 24/20 batches of small towels she washed, how many total batches of towels did Joanna wash?

Gemma 2B:

    Let's solve this problem step by step, using the corrected information that Joanna washed 25/7 batches of large towels instead of 25/15.

    Given:
    - Joanna washed 24/20 batches of small towels.
    - Joanna washed 25/7 batches of large towels.

    Step 1: Convert the mixed numbers to improper fractions.
    Small towels: 24/20 = 1 4/20 = (1 × 20 + 4) / 20 = 24/20
    Large towels: 25/7 = 3 4/7 = (3 × 7 + 4) / 7 = 25/7

    Step 2: Find a common denominator for the fractions.
    The common denominator is the least common multiple (LCM) of 20 and 7, which is 140.

    Step 3: Convert the fractions to equivalent fractions with the common denominator.
    Small towels: 24/20 = 24 × 7/20 × 7 = 168/140
    Large towels: 25/7 = 25 × 20/7 × 20 = 500/140

    Step 4: Add the fractions.
    Total batches = 168/140 + 500/140 = 668/140

    Step 5: Convert the result to a mixed number.
    668/140 = 4 108/140 = 4 54/70 = 4 27/35

    ### Answer: 4 27/35

Expected answer: 167/35

Correct? Yes

🔗 Problem

Problem: Debra is baking cookies and she realizes she has two different recipes for the same type of cookie. She's wondering if she combines the ingredients from both, if she will end up with even more cookies or not. The first recipe requires (27 / 3) cups flour and (11 / 7) cups sugar. She determines the ratio of flour to sugar by dividing the amount of flour by the amount of sugar. She then subtracts (21 / 26) from this ratio because that's how many cups of sugar her friend says makes the cookies too sweet. After that, she adds (22 / 9) cups of flour from the second recipe to the new ratio to see how many total cups of flour she will need. How many cups of flour will she have in the end?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the ratio of flour to sugar in the first recipe:
       * Flour: 27 / 3 = 9 cups
       * Sugar: 11 / 7 cups
       * Ratio = (27 / 3) / (11 / 7) = 9 / (11 / 7) = 9 * (7 / 11) = 63 / 11 ≈ 5.73

    2. Subtract (21 / 26) from the ratio:
       * New ratio = (63 / 11) - (21 / 26) = (1638 / 286) - (21 / 26) = (1638 * 26 - 21 * 286) / (286 * 26) = 36036 / 7436 ≈ 4.85

    3. Add (22 / 9) cups of flour from the second recipe to the new ratio:
       * Total flour = (36036 / 7436) + (22 / 9) = (36036 / 7436) + (1958 / 7436) = 37994 / 7436 ≈ 5.11 cups

    Therefore, Debra will have approximately 5.11 cups of flour in the end.

    ### Answer: 5.11 cups

Expected answer: 18955/2574

Correct? No

🔗 Problem

Problem: There are 26/13 chickens in one farm and 9/16 chickens in another farm. Farmer John calculated the difference between the number of chickens in the two farms. After a week, the number of chickens multiplied by 19/21 due to new chickens born. How many chickens are there now in Farmer John's farm?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the number of chickens in the first farm:
       * There are 26/13 chickens in the first farm.
       * 26/13 = 2 chickens

    2. Find the number of chickens in the second farm:
       * There are 9/16 chickens in the second farm.
       * 9/16 = 0.5625 chickens (we'll consider this as 1 chicken since there can't be a fraction of a chicken)

    3. Calculate the difference between the number of chickens in the two farms:
       * Difference = Chickens in first farm - Chickens in second farm
       * Difference = 2 - 1 = 1 chicken

    4. After a week, the number of chickens multiplied by 19/21:
       * New number of chickens = 1 × 19/21
       * New number of chickens = 19/21 ≈ 0.9048 chickens (we'll consider this as 1 chicken)

    Therefore, after a week, there is 1 chicken in Farmer John's farm.

    ### Answer: 1

Expected answer: 437/336

Correct? No

🔗 Problem

Problem: A helicopter traveled a distance of 24/14 miles for a training exercise. During a second exercise, the helicopter flew the same distance. If we let 'w' be the distance flown for each exercise and 't' be the total distance flown for both exercises represented as the product of 'w' times 'w', what is the value of 't'?

Gemma 2B:

    Let's solve this step by step:

    1. The helicopter traveled a distance of 24/14 miles for each exercise.
       So, w = 24/14

    2. To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2.
       w = (24/2) / (14/2) = 12/7

    3. The total distance flown for both exercises is represented as the product of 'w' times 'w'.
       t = w * w

    4. Substituting the value of 'w':
       t = (12/7) * (12/7)

    5. Multiplying fractions:
       t = (12 * 12) / (7 * 7)
       t = 144 / 49

    6. Simplifying the fraction:
       t = 144/49

    Therefore, the value of 't' is 144/49.

    ### Answer: 144/49

Expected answer: 144/49

Correct? Yes

🔗 Follow-up

Problem: Let's consider a modification in our previous problem. Instead of initially flying a distance of 24/14 miles for each exercise, the helicopter now travels a distance of 17/14 miles for each exercise. If we still let 'w' be the distance flown for each exercise and 't' be the total distance flown for both exercises, which is represented as the product of 'w' times 'w', what is the new value of 't'?

Gemma 2B:

    Okay, let's solve this modified problem step by step:

    1. The helicopter now travels a distance of 17/14 miles for each exercise.
       So, w = 17/14

    2. Unlike the previous problem, 17 and 14 do not have any common factors other than 1, so we cannot simplify this fraction further.

    3. The total distance flown for both exercises is still represented as the product of 'w' times 'w'.
       t = w * w

    4. Substituting the value of 'w':
       t = (17/14) * (17/14)

    5. Multiplying fractions:
       t = (17 * 17) / (14 * 14)
       t = 289 / 196

    6. 289 and 196 do not have any common factors other than 1, so we cannot simplify this fraction further.

    Therefore, the new value of 't' is 289/196.

    ### Answer: 289/196

Expected answer: 289/196

Correct? Yes

🔗 Problem

Problem: A UFO has made two fuel stops. During the first refuel, the UFO was able to fill 20/16 of its fuel tank. At the second fuel stop, the UFO filled another 24/25 of its tank. Calculate the total fraction of the tank that the UFO was able to refill during these two stops.

Gemma 2B:

    Let's solve this step by step:

    1. In the first refuel, the UFO filled 20/16 of its tank.
       To convert this to a mixed number: 20 ÷ 16 = 1 with a remainder of 4.
       So, 20/16 = 1 4/16 = 1 1/4 (simplifying the fraction)

    2. In the second refuel, the UFO filled 24/25 of its tank.

    3. Now, we need to add these two fractions:
       1 1/4 + 24/25

    4. To add fractions, we need a common denominator. The common denominator is 100 (4 * 25).
       1 1/4 = 1 25/100
       24/25 = 96/100

    5. Now, we can add:
       1 25/100 + 96/100 = 1 121/100

    6. Converting the improper fraction to a mixed number:
       121 ÷ 100 = 1 with a remainder of 21
       So, 1 121/100 = 2 21/100 = 2 1/5 (simplifying the fraction)

    Therefore, the UFO was able to refill 2 1/5 of its tank during these two stops.

    ### Answer: 2 1/5

Expected answer: 221/100

Correct? No

🔗 Problem

Problem: Professor Astro is working on his telescope. He believes the power of his telescope is directly proportional to the sum of two fractions. The first fraction is the light gathering power of the lens, which is 24 out of 27. The second fraction is the zooming potential, which is 30 out of 26. So, Professor Astro calculates the sum of these two fractions ((24 / 27) + (30 / 26)). What does he find?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's calculate the light gathering power of the lens:
       24 / 27 = 0.8888888888888888

    2. Next, let's calculate the zooming potential:
       30 / 26 = 1.1538461538461537

    3. Now, we need to add these two fractions:
       (24 / 27) + (30 / 26) = 0.8888888888888888 + 1.1538461538461537
                             = 2.0427350427350425

    Therefore, Professor Astro finds that the sum of the two fractions is 2.0427350427350425.

    ### Answer: 2.0427350427350425

Expected answer: 239/117

Correct? Yes

🔗 Follow-up

Problem: Upon recalculating his telescope's potential with more accurate data, Professor Astro realizes that the light gathering power of his lens is actually 12 out of 27, not 24 out of 27 as previously calculated. Professor Astro recalculates the sum of these two fractions ((12 / 27) + (30 / 26)). What is the resulting sum now?

Gemma 2B:

    Let's solve this problem step by step with the updated information:

    1. The light gathering power of the lens is now:
       12 / 27 = 0.4444444444444444

    2. The zooming potential remains the same:
       30 / 26 = 1.1538461538461537

    3. Now, let's add these two fractions with the updated light gathering power:
       (12 / 27) + (30 / 26) = 0.4444444444444444 + 1.1538461538461537
                             = 1.5982905982905981

    Therefore, with the updated light gathering power, Professor Astro finds that the sum of the two fractions is now 1.5982905982905981.

    ### Answer: 1.5982905982905981

Expected answer: 187/117

Correct? No

🔗 Problem

Problem: Kiki is a lively little monkey. She loves eating bananas. She ate 11/6 bananas in the morning and the same amount in the afternoon. How many bananas did she eat in total? Express your answer as an improper fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. Kiki ate 11/6 bananas in the morning.
    2. She ate the same amount, 11/6 bananas, in the afternoon.
    3. To find the total number of bananas Kiki ate, we need to add the number of bananas she ate in the morning and afternoon.

    Total bananas = Morning bananas + Afternoon bananas
    Total bananas = 11/6 + 11/6

    4. To add fractions with the same denominator, we simply add the numerators and keep the denominator the same.

    Total bananas = (11 + 11) / 6
    Total bananas = 22 / 6

    Therefore, Kiki ate a total of 22/6 bananas.

    ### Answer: 22/6

Expected answer: 11/3

Correct? Yes

🔗 Follow-up

Problem: Kiki realized that she miscounted the amount of bananas she ate. Instead of eating 11/6 bananas in the morning, she actually ate 11 whole bananas in the morning and another 11 in the afternoon. Given this new information, how many bananas did Kiki eat in total?

Gemma 2B:

    Okay, let's update our problem with the new information:

    1. Kiki ate 11 whole bananas in the morning.
    2. She ate another 11 whole bananas in the afternoon.
    3. To find the total number of bananas Kiki ate, we need to add the number of bananas she ate in the morning and afternoon.

    Total bananas = Morning bananas + Afternoon bananas
    Total bananas = 11 + 11

    4. Adding whole numbers is straightforward:

    Total bananas = 11 + 11 = 22

    Therefore, with the updated information, Kiki ate a total of 22 whole bananas.

    ### Answer: 22

Expected answer: 22

Correct? Yes

🔗 Problem

Problem: Jaden is a dairy farmer who milks his cows twice a day. In the morning, his cows give him 26/14 gallons of milk per cow, and in the evening, they give 28/20 gallons of milk per cow. If he multiplies these two fractions together, how much milk is he getting from one cow in one day?

Gemma 2B:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Jaden milks his cows twice a day.
       * In the morning, each cow gives 26/14 gallons of milk.
       * In the evening, each cow gives 28/20 gallons of milk.
       * We need to multiply these two fractions to find the total milk from one cow in a day.

    2. Multiply the fractions:
       * (26/14) × (28/20) = (26 × 28) / (14 × 20)
       * <<26*28=728>>26 × 28 = 728
       * <<14*20=280>>14 × 20 = 280
       * (26/14) × (28/20) = 728 / 280

    3. Simplify the resulting fraction:
       * 728 and 280 have a common factor of 28.
       * <<728/28=26>>728 ÷ 28 = 26
       * <<280/28=10>>280 ÷ 28 = 10
       * (26/14) × (28/20) = 26 / 10
       * <<26/10=13/5>>26 / 10 = 13 / 5 (dividing both numerator and denominator by 2)

    Therefore, by multiplying the two fractions together, we find that Jaden is getting 13/5 gallons of milk from one cow in one day.

    ### Answer: 13/5 gallons

Expected answer: 13/5

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, let's consider that Jaden has made some changes on his farm that affected the milk production in the evening. Now, his cows give him 28/10 gallons of milk per cow in the evening instead of the previous 28/20 gallons. If we still take the morning milk production as 26/14 gallons per cow, how much milk is he getting from one cow in one day now?

Gemma 2B:

    Great! Let's solve this problem step by step, using the new information about the evening milk production.

    1. Understand the updated information:
       * Jaden's cows now give 28/10 gallons of milk per cow in the evening, instead of 28/20 gallons.
       * The morning milk production remains the same at 26/14 gallons per cow.
       * We need to multiply these two fractions to find the total milk from one cow in a day.

    2. Multiply the fractions:
       * (26/14) × (28/10) = (26 × 28) / (14 × 10)
       * <<26*28=728>>26 × 28 = 728
       * <<14*10=140>>14 × 10 = 140
       * (26/14) × (28/10) = 728 / 140

    3. Simplify the resulting fraction:
       * 728 and 140 have a common factor of 28.
       * <<728/28=26>>728 ÷ 28 = 26
       * <<140/28=5>>140 ÷ 28 = 5
       * (26/14) × (28/10) = 26 / 5

    4. Convert the improper fraction to a mixed number:
       * 26 ÷ 5 = 5 remainder 1
       * 26 / 5 = 5 1/5

    Therefore, with the changes in evening milk production, Jaden is now getting 5 1/5 gallons of milk from one cow in one day.

    ### Answer: 5 1/5 gallons

Expected answer: 26/5

Correct? Yes