🔗 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:

     Reasoning: Carla's initial production per plant is 22/3 \* 22/19 = <<(22/3)\*(22/19)=(484/57)>>484/57 cucumbers.
    After adjusting her production method, she can grow 484/57 \* 23/17 = <<(484/57)\*(23/17)=(2304/171)>>2304/171 cucumbers per plant.
    ### Answer: 2304/171

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:

     Reasoning: Pierre ate 7/25 kg of grapes, so he has 19/4 - 7/25 = <<(19/4) - (7/25)=(475/100 - 28/100)=447/100>>4.47 kg of grapes left.
    His mother gave him 30/9 kg more grapes, so he has 4.47 + 30/9 = <<4.47 + (30/9)=4.47 + 3.33=7.8>>7.8 kg of grapes now.
    ### Answer: 7.8

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:

     Reasoning:

    Wall repairs cost: 26/22 of the budget
    Moat renovations cost: 4/29 of the budget
    Defensive catapults cost: 11/3 of the budget

    Total cost = (26/22) + (4/29) + (11/3)

    To add these fractions, we need a common denominator. The least common multiple (LCM) of 22, 29, and 3 is 1887.

    So, we convert each fraction to have a denominator of 1887:

    Wall repairs cost: (26/22) = (26 * 86) / (22 * 86) = 2236 / 1887
    Moat renovations cost: (4/29) = (4 * 65) / (29 * 65) = 260 / 1887
    Defensive catapults cost: (11/3) = (11 * 629) / (3 * 629) = 6919 / 1887

    Total cost = (2236/1887) + (260/1887) + (6919/1887)

    Total cost = (2236 + 260 + 6919) / 1887

    Total cost = 9415 / 1887

    So, King Arthur has spent 9415/1887 of his castle's annual budget on these projects in total.

    ### Answer: 9415/1887

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:

     Reasoning: The giraffe eats 25/19 * 30/26 = <<(25/19)*(30/26)=1.923076923076923>>1.923076923076923 times more than its usual daily intake.
    The weekly feeding amount squared is (25/19 * 30/26)^2 = <<((25/19)*(30/26))^2=3.694230769230769>>3.694230769230769.
    The weekly feeding amount is 3.694230769230769 * (25/19 * 30/26) = <<3.694230769230769*((25/19)*(30/26))=7.096774193548387>>7.096774193548387 lbs.
    ### Answer: 7.096774193548387 lbs

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:

     Reasoning: Lara will need (11/3) + (8/30) feet of yarn to make the necklace.
    To add the two fractions, we need a common denominator. The least common multiple of 3 and 30 is 30.
    So, (11/3) = (110/30) and (8/30) remains the same.
    Now, we can add the two fractions: (110/30) + (8/30) = (118/30) feet of yarn.
    ### Answer: (118/30) feet of yarn

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:

     Reasoning: Lara will need (118/30) + (24/17) feet of yarn to make the necklace with the added beads.
    To add the two fractions, we need a common denominator. The least common multiple of 30 and 17 is 510.
    So, (118/30) = (1922/510) and (24/17) = (720/510).
    Now, we can add the two fractions: (1922/510) + (720/510) = (2642/510) feet of yarn.
    ### Answer: (2642/510) feet of yarn

Expected answer: 1363/255

Correct? No

🔗 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:

     Reasoning: Lara will need (11/3) + (8/28) feet of yarn to make the necklace.
    To add the two fractions, we need a common denominator. The least common multiple of 3 and 28 is 84.
    So, (11/3) = (308/84) and (8/28) = (24/84).
    Now, we can add the two fractions: (308/84) + (24/84) = (332/84) feet of yarn.
    ### Answer: (332/84) feet of yarn

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:

     Reasoning: Plane A travels 24/11 miles in one minute.
    Plane B travels 26/27 miles in one minute.
    The difference in distance traveled is (24/11) - (26/27) = (24*27 - 26*11)/(11*27) = (648 - 286)/(297) = 362/297 = <<362/297=362/297>>362/297.
    This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
    ### Answer: 362/297

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:

     Reasoning: Plane A travels 24/11 miles in one minute.
    Plane B travels 2/27 miles in one minute.
    The difference in distance traveled is (24/11) - (2/27) = (24*27 - 2*11)/(11*27) = (648 - 22)/(297) = 626/297 = <<626/297=626/297>>626/297.
    This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
    ### Answer: 626/297

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:

     Reasoning: The adult bear eats 14/7 = <<14/7=2>>2 pounds of fish per day.
    The young bear eats 25/13 = <<25/13=1.923076923076923>>1.923076923076923 pounds of fish per day.
    The combined amount that both bears eat per day is 2 \* 1.923076923076923 = <<2\*1.923076923076923=3.846153846153846>>3.846153846153846 pounds of fish.
    ### Answer: 3.846153846153846

Expected answer: 50/13

Correct? No

🔗 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:

     Reasoning: Toby's first song takes 12/8 = <<12/8=1.5>>1.5 hours to play.
    Toby's second song takes 12/3 = <<12/3=4>>4 hours to play.
    Toby takes 1.5 + 4 = <<1.5+4=5.5>>5.5 hours to play both of his songs.
    To write the answer as a simplified fraction, we can convert 5.5 hours to 11/2 hours.
    ### Answer: 11/2

Expected answer: 11/2

Correct? Yes

🔗 Follow-up

Problem: After playing his two songs, Toby decides to play a third song that takes 19/14 hours. How long does it take Toby to play all three songs? Write your answer as a simplified fraction.

Gemma 2B:

     Reasoning: Toby takes 11/2 + 19/14 = <<11/2+19/14=11/2+19/14=77/14+19/14=96/14=48/7>>48/7 hours to play all three songs.
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 7.
    ### Answer: 48/7

Expected answer: 48/7

Correct? Yes

🔗 Follow-up

Problem: Toby realized that he made a mistake. His first song actually takes 12/15 hours to play, not 12/8 hours. Given this information, how long does it take Toby to play his first and second songs now? Write your answer as a simplified fraction.

Gemma 2B:

     Reasoning: Toby's first song takes 12/15 = <<12/15=4/5>>4/5 hours to play.
    Toby's second song takes 12/3 = <<12/3=4>>4 hours to play.
    Toby takes 4/5 + 4 = <<4/5+4=24/5>>24/5 hours to play both of his songs.
    To write the answer as a simplified fraction, we can convert 24/5 hours to 4 4/5 hours.
    ### Answer: 4 4/5

Expected answer: 24/5

Correct? Yes

🔗 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:

     Reasoning: You have 28/29 of the first set of chocolate bars and 8/22 of the second set of chocolate bars.
    To find the total fraction of chocolate bars you have, you need to add the two fractions together.
    First, find a common denominator for the two fractions. The least common multiple of 29 and 22 is 638.
    Convert the first fraction to have a denominator of 638: 28/29 = (28\*22)/(29\*22) = 616/638
    Convert the second fraction to have a denominator of 638: 8/22 = (8\*29)/(22\*29) = 232/638
    Add the two fractions together: 616/638 + 232/638 = (616+232)/638 = 848/638
    Simplify the fraction: 848/638 = 424/319
    ### Answer: 424/319

Expected answer: 424/319

Correct? Yes

🔗 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:

     Reasoning: To create one needle, the compass maker needs 27/26 pounds of material. To create two needles, he will need 2 * (27/26) = <<2*(27/26)=27/13>>27/13 pounds of material.

    The additional piece requires 27/6 = <<27/6=9/2>>9/2 pounds of material.

    The total material needed for the two needles and the additional piece is 27/13 + 9/2 = <<27/13+9/2=117/26>>117/26 pounds.

    ### Answer: 117/26

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:

     Reasoning: The rate at which the first candle burns is 6/4 = <<6/4=1.5>>1.5 inches per hour.
    The rate at which the second candle burns is 14/16 = <<14/16=0.875>>0.875 inches per hour.
    The total rate at which the two candles burn together is 1.5 + 0.875 = <<1.5+0.875=2.375>>2.375 inches per hour.
    ### Answer: 2.375

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:

     Reasoning: The rate at which the first candle burns is 6/4 = <<6/4=1.5>>1.5 inches per hour.
    The rate at which the second candle now burns is 26/16 = <<26/16=1.625>>1.625 inches per hour.
    The total rate at which the two candles now burn together is 1.5 + 1.625 = <<1.5+1.625=3.125>>3.125 inches per hour.
    ### Answer: 3.125

Expected answer: 25/8

Correct? No

🔗 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:

     Reasoning: Sophia has 17/20 + 1/4 = <<17/20 + 1/4 = 21/20>>21/20 dollars after her friend gives her money.
    Sophia has 21/20 + 1 = <<21/20 + 1 = 41/20>>41/20 dollars after her brother gives her money.
    Sophia has 41/20 = <<41/20 = 2.05>>2.05 dollars now.
    ### Answer: 2.05

Expected answer: 21/10

Correct? No

🔗 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:

     Reasoning:

    First, let's find the initial time investment (p) for composing the music and writing the lyrics:

    p = 16/4 + 16/29
    p = 4 + 16/29
    p = 4 + 0.5517 (rounded to 4 decimal places)
    p = 4.5517 hours

    Next, let's find the total time (b) spent on mixing, mastering, and the initial time investment:

    b = p + 28/13
    b = 4.5517 + 28/13
    b = 4.5517 + 2.1538 (rounded to 4 decimal places)
    b = 6.7055 hours

    Now, let's find the time saved by the drummer:

    18/4 = 4.5 hours

    Finally, let's find the final time spent on producing the song:

    Final time = b - (18 / 4)
    Final time = 6.7055 - 4.5
    Final time = 2.2055 hours

    ### Answer: 2.2055 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:

     Reasoning: Monica has 21/15 = <<21/15=1.4>>1.4 dozens of cookies initially.
    Monica bakes an additional 29/17 = <<29/17=1.7058823529411765>>1.7058823529411765 dozens of cookies.
    Monica's total stock of cookies is 1.4 + 1.7058823529411765 = <<1.4+1.7058823529411765=3.1058823529411765>>3.1058823529411765 dozens of cookies.
    Monica increases her total stock of cookies by a ratio of 7/5, so she will have 3.1058823529411765 \* 7/5 = <<3.1058823529411765\*7/5=4.348235294117647>>4.348235294117647 dozens of cookies for the cookie festival.
    ### Answer: 4.348235294117647

Expected answer: 1848/425

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, Monica initially had 21/15 dozens of cookies in her bakery shop. Suppose now she initially has the same amount but later bakes 29/26 dozens of cookies instead of 29/17 dozens. At the end of the day, she still decides to increase the total stock of cookies by a ratio of 7/5 for a different event. How many dozens of cookies will Monica have now for this event?

Gemma 2B:

     Reasoning: Monica has 21/15 = <<21/15=1.4>>1.4 dozens of cookies initially.
    Monica bakes an additional 29/26 = <<29/26=1.1153846153846154>>1.1153846153846154 dozens of cookies.
    Monica's total stock of cookies is 1.4 + 1.1153846153846154 = <<1.4+1.1153846153846154=2.5153846153846154>>2.5153846153846154 dozens of cookies.
    Monica increases her total stock of cookies by a ratio of 7/5, so she will have 2.5153846153846154 \* 7/5 = <<2.5153846153846154\*7/5=3.5215384615384613>>3.5215384615384613 dozens of cookies for the event.
    ### Answer: 3.5215384615384613

Expected answer: 2289/650

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:

     Reasoning: The chef uses 26/24 kg of sugar to make one cake.
    After making one cake, the chef has 28 - 26/24 = <<28-(26/24)=26.666666666666668>>26.666666666666668 kg of sugar left.
    The chef then adds 10/6 kg of sugar to their supply, so they have 26.666666666666668 + 10/6 = <<26.666666666666668+(10/6)=29.666666666666668>>29.666666666666668 kg of sugar left.
    ### Answer: 29.666666666666668 kg

Expected answer: 343/12

Correct? No

🔗 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:

     Reasoning: Emily watched 16 / 4 = <<16/4=4>>4 hours of movies in total.
    Emily spent 6 / 3 = <<6/3=2>>2 hours watching the comedy film.
    Emily spent 4 - 2 = <<4-2=2>>2 hours watching movies other than the comedy film.
    ### Answer: 2

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:

     Reasoning: Emily watched 16 / 4 = <<16/4=4>>4 hours of movies in total.
    Emily spent 7 / 3 = <<7/3=2.3333333333333335>>2.3333333333333335 hours watching the thriller film.
    Emily spent 4 - 2.3333333333333335 = <<4-2.3333333333333335=1.6666666666666665>>1.6666666666666665 hours watching movies other than the thriller film.
    ### Answer: 1.6666666666666665

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:

     Reasoning: Princess Lily ate 10/12 of the apple pie and 10/29 of the blueberry pie.
    To find out how much of the pies she ate combined, we need to add the fractions:
    10/12 + 10/29 = (290 + 120) / (12 * 29) = 410 / 348
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
    410 / 348 = (410/2) / (348/2) = 205 / 174
    ### Answer: 205/174

Expected answer: 205/174

Correct? Yes

🔗 Follow-up

Problem: As Princess Lily was about to leave the dining room, she noticed another plate - this one filled with 29 slices of peach pie. She decided to help herself and ate 10 of the slices. Before her peach pie adventure, she had already eaten an entire 10-slice chocolate cake. Now, how much of the total food (chocolate cake and peach pie) did Princess Lily eat? Please represent your answer as a fraction.

Gemma 2B:

     Reasoning: Princess Lily ate 10/10 of the chocolate cake and 10/29 of the peach pie.
    To find out how much of the total food she ate, we need to add the fractions:
    10/10 + 10/29 = (290 + 100) / (10 * 29) = 390 / 290
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 10:
    390 / 290 = (390/10) / (290/10) = 39 / 29
    ### Answer: 39/29

Expected answer: 300/29

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:

     Reasoning: Marta uses 20/11 colored pencils every day for her art projects.
    Marta uses 23/26 of those colored pencils for shading techniques.
    So, Marta uses (20/11) \* (23/26) colored pencils for shading in her art projects over an 11-day period.
    (20/11) \* (23/26) = <<(20/11)\*(23/26)=20/11\*23/26=460/286=230/143>>230/143
    ### 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:

     Reasoning: Marta uses 8/6 colored pencils every day for her art projects.
    Marta uses (20/11) \* (23/26) colored pencils for shading in her art projects over an 11-day period.
    So, Marta uses (8/6) + ((20/11) \* (23/26)) colored pencils in total over an 11-day period.
    (8/6) + ((20/11) \* (23/26)) = <<(8/6)+((20/11)\*(23/26))=(8/6)+(230/143)

Expected answer: 1262/429

Correct? No

🔗 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:

     Reasoning: Marta uses 20/11 colored pencils every day for her art projects.
    Marta uses 23/24 of those colored pencils for shading techniques.
    So, Marta uses (20/11) \* (23/24) colored pencils for shading in her art projects over an 11-day period.
    (20/11) \* (23/24) = <<(20/11)\*(23/24)=20/11\*23/24=460/264=115/66>>115/66
    ### 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:

     Reasoning:

    For the first pair of evidence specimens, the ratio of changes (indicator i) is calculated as follows:

    i = (26/6) / (25/17)

    To simplify this, we can cross-multiply:

    i = (26 * 17) / (6 * 25)

    i = 442 / 150

    i = 2.946666667

    For the second pair of evidence specimens, the difference between the two rates (indicator h) is calculated as follows:

    h = (18/8) - (17/23)

    To simplify this, we can find a common denominator and subtract the fractions:

    h = (18 * 23) / (8 * 23) - (17 * 8) / (23 * 8)

    h = (414 - 136) / (184)

    h = 278 / 184

    h = 1.510869565

    Now, to find the final evidence factor (indicator f), we multiply indicators h and i:

    f = h * i

    f = 1.510869565 * 2.946666667

    f = 4.454545455

    Therefore, the value of the final evidence factor (indicator f) is approximately 4.45.

    ### Answer: 4.45

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:

     Reasoning: The gestation period of a lioness is 20/22 of a year, which is approximately 0.9091 years.
    The gestation period of a giraffe is 15 years.
    The total gestation period of both animals together is 0.9091 + 15 = <<0.9091+15=15.9091>>15.9091 years.
    Later in the same year, the lioness is pregnant again and her gestation period reduces by 15/20 of a year compared to the earlier total gestation period of both animals.
    The reduction in the gestation period is 15/20 \* 15.9091 = <<15/20\*15.9091=11.931825>>11.931825 years.
    The new gestation period of the lioness is 15.9091 - 11.931825 = <<15.9091-11.931825=3.977275>>3.977275 years.
    ### Answer: 3.977275 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:

     Reasoning: The area of the original rectangle is (30/7) \* (19/6) = <<(30/7) \* (19/6)=95/14>>95/14 square meters.
    The area of the similar rectangle is (18/17) \* (95/14) = <<(18/17) \* (95/14)=95/14 \* 18/17=1710/238>>1710/238 square meters.
    ### Answer: 1710/238

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:

     Reasoning: The factory initially produces 23/8 tonnes of soap each day. They increase production by an extra 4/20 tonnes, which is equivalent to 1/5 tonnes. So, the new production is 23/8 + 1/5 = <<(23/8) + (1/5)=(115/40 + 8/40)=123/40>>123/40 tonnes.

    However, later that same day, they reduce the production by 19/24 tonnes due to a sudden power cut. This reduction is equivalent to 19/24 = <<19/24=0.7916666666666666>>0.7916666666666666 tonnes.

    So, the final production for that day is 123/40 - 19/24 = <<(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19/24)=(123/40) - (19

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:

     Reasoning: The machine starts with 24/8 = <<24/8=3>>3 gallons of red paint.
    The machine pours away 12/8 = <<12/8=1.5>>1.5 gallons of the mix.
    So, the amount of red paint left in the machine is 3 - 1.5 = <<3-1.5=1.5>>1.5 gallons.
    The machine adds another 1/28 gallon of blue pigment to lighten the color.
    So, the total amount of paint in the machine is 1.5 - 1/28 = <<1.5-(1/28)=1.5-(0.03571428571428571)=1.4642857142857142>>1.4642857142857142 gallons.
    ### Answer: 1.4642857142857142

Expected answer: 41/28

Correct? Yes

🔗 Follow-up

Problem: Suppose, while creating the paint mixture you started with the revised amount of 24/8 gallons of red paint. However, this time instead of adding 1/28 gallon blue pigment, you added 1/21 gallon of blue pigment to adjust the color. Subtract this newer amount of blue pigment from 'd' to find 'x' in gallons, which is the total amount of paint. What is the value of 'x' now?

Gemma 2B:

     Reasoning: The machine starts with 24/8 = <<24/8=3>>3 gallons of red paint.
    The machine pours away 12/8 = <<12/8=1.5>>1.5 gallons of the mix.
    So, the amount of red paint left in the machine is 3 - 1.5 = <<3-1.5=1.5>>1.5 gallons.
    The machine adds another 1/21 gallon of blue pigment to lighten the color.
    So, the total amount of paint in the machine is 1.5 - 1/21 = <<1.5-(1/21)=1.5-(0.047619047619047616)=1.4523809523809523>>1.4523809523809523 gallons.
    ### Answer: 1.4523809523809523

Expected answer: 61/42

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:

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

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

    Now, we calculate the products:

    27 * 17 = <<27*17=459>>459
    14 * 13 = <<14*13=182>>182

    So, the product of the fractions is 459 / 182.

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 459 and 182 is 1. Therefore, the fraction is already in its simplest form.

    ### Answer: 459/182 ounces of mashed bananas are required.

Expected answer: 459/182

Correct? Yes

🔗 Follow-up

Problem: After finding out how many ounces of mashed bananas you'll need for the banana bread, you realize that you need to scale up the recipe by the factor represented by the fraction (8 / 4). Compute the product of the original fraction and the scaling factor (8 / 4) to determine the new amount of mashed bananas that will be needed. Write your answer as a simplified fraction.

Gemma 2B:

     Reasoning: To find the new amount of mashed bananas needed, we need to multiply the original fraction (459 / 182) by the scaling factor (8 / 4).

    First, let's simplify the scaling factor:

    (8 / 4) = 2

    Now, we multiply the original fraction by the scaling factor:

    (459 / 182) * 2 = (459 * 2) / 182

    Now, we calculate the product:

    459 * 2 = <<459*2=918>>918

    So, the new amount of mashed bananas needed is 918 / 182.

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 918 and 182 is 2. Therefore, we divide both the numerator and the denominator by 2:

    918 / 2 = <<918/2=459>>459
    182 / 2 = <<182/2=91>>91

    So, the simplified fraction is 459 / 91.

    ### Answer: 459/91 ounces of mashed bananas are needed after scaling up the recipe.

Expected answer: 459/91

Correct? Yes

🔗 Follow-up

Problem: After reevaluating the recipe, you discover that the amount of mashed bananas required is actually determined by multiplying the fractions (27 / 14) and (17 / 15), not (27 / 14) and (17 / 13) as you initially thought. Recompute the product of these fractions to find out the correct amount of mashed bananas needed for the banana bread. Write your answer as a simplified fraction.

Gemma 2B:

     Reasoning: To find the product of the fractions (27 / 14) and (17 / 15), we multiply the numerators and denominators together:

    (27 / 14) * (17 / 15) = (27 * 17) / (14 * 15)

    Now, we calculate the products:

    27 * 17 = <<27*17=459>>459
    14 * 15 = <<14*15=210>>210

    So, the product of the fractions is 459 / 210.

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 459 and 210 is 3. Therefore, we divide both the numerator and the denominator by 3:

    459 / 3 = <<459/3=153>>153
    210 / 3 = <<210/3=70>>70

    The simplified fraction is 153 / 70.

    ### Answer: 153/70 ounces of mashed bananas are required.

Expected answer: 153/70

Correct? Yes

🔗 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:

     Reasoning:

    First, let's find the total daily amount of toothpaste used by Sonia and Anthony.

    Sonia uses 21/12 oz of toothpaste daily.
    Anthony uses 6/27 oz of toothpaste daily.

    To add these two fractions, we need a common denominator. The least common multiple of 12 and 27 is 108.

    Sonia's toothpaste usage in ounces per day with a common denominator is (21/12) * (108/108) = 189/108 oz.
    Anthony's toothpaste usage in ounces per day with a common denominator is (6/27) * (108/108) = 24/108 oz.

    Now, we can add these two fractions:

    Total toothpaste usage by Sonia and Anthony = 189/108 + 24/108 = 213/108 oz.

    Next, let's find the total daily amount of toothpaste used by the whole family, including their mom.

    Their mom uses 3/18 oz of toothpaste daily.

    To add this amount to the total used by Sonia and Anthony, we need a common denominator. The least common multiple of 108 and 18 is 108.

    Their mom's toothpaste usage in ounces per day with a common denominator is (3/18) * (108/108) = 18/108 oz.

    Now, we can add this fraction to the total used by Sonia and Anthony:

    Total toothpaste usage by the whole family = 213/108 + 18/108 = 231/108 oz.

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 9:

    Total toothpaste usage by the whole family = (231/9) / (108/9) = 25.666... / 12 oz.

    Since we want a simplified fraction, we can round this to the nearest whole number and express it as a fraction:

    Total toothpaste usage by the whole family ≈ 26/12 oz.

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

    Total toothpaste usage by the whole family ≈ (26/2) / (12/2) = 13/6 oz.

    ### Answer: 13/6 oz.

Expected answer: 77/36

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:

     Reasoning: After making the first sandwich, you have (7/18 + 21/14) of the original ingredients.

    To simplify 21/14, we can divide both the numerator and the denominator by 7, which gives us 3/2.

    So, the fraction of the original ingredients left after making the first sandwich is (7/18 + 3/2).

    To add these fractions, we need a common denominator. The least common multiple of 18 and 2 is 18, so we convert 3/2 to 27/18.

    Now, the fraction of the original ingredients left after making the first sandwich is (7/18 + 27/18) = 34/18.

    To simplify 34/18, we can divide both the numerator and the denominator by 2, which gives us 17/9.

    After making the simpler sandwich, you use half of the wheel of cheese, which is (1/2) of the original ingredients.

    To subtract (1/2) from 17/9, we need a common denominator. The least common multiple of 2 and 9 is 18, so we convert 1/2 to 9/18.

    Now, the fraction of the original ingredients left after making the simpler sandwich is (17/9 - 9/18).

    To subtract these fractions, we can convert 17/9 to 34/18 and then subtract 9/18 from 34/18, which gives us 25/18.

    To simplify 25/18, we can divide both the numerator and the denominator by 5, which gives us 5/3.

    ### Answer: 5/3

Expected answer: 25/18

Correct? No

🔗 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:

     Reasoning: The first window is 15/6 = <<15/6=2.5>>2.5 meters tall.
    The second window is 7/16 = <<7/16=0.4375>>0.4375 meters tall.
    The total height of the windows is 2.5 + 0.4375 = <<2.5+0.4375=2.9375>>2.9375 meters.
    ### Answer: 2.9375 meters

Expected answer: 47/16

Correct? No

🔗 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:

     Reasoning: Jan mixes 16/6 = <<16/6=2.6666666666666665>>2.67 liters of apple juice (rounded to two decimal places) and 20/12 = <<20/12=1.6666666666666667>>1.67 liters of orange juice (rounded to two decimal places).
    She adds 2/3 = <<2/3=0.6666666666666666>>0.67 liters of cranberry juice (rounded to two decimal places).
    Jan has a total of 2.67 + 1.67 + 0.67 = <<2.67+1.67+0.67=5.01>>5.01 liters of juice (rounded to two decimal places).
    ### Answer: 5.01 liters

Expected answer: 5

Correct? No

🔗 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:

     Reasoning: Each level gives you 4/3 points, so 13/10 levels would give you (4/3)*(13/10) = <<(4/3)*(13/10)=52/15>>52/15 points.
    ### Answer: 52/15

Expected answer: 26/15

Correct? No

🔗 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:

     Reasoning: The astronaut spends 18/8 = <<18/8=2.25>>2.25 hours cycling and 26/2 = <<26/2=13>>13 hours conducting scientific experiments.
    The total amount of time spent on these activities in a day is 2.25 + 13 = <<2.25+13=15.25>>15.25 hours.
    The astronaut adds 30/8 = <<30/8=3.75>>3.75 hours of reviewing data to his routine.
    The total amount of time spent on his whole daily routine is 15.25 + 3.75 = <<15.25+3.75=19>>19 hours.
    ### Answer: 19

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:

     Reasoning: The astronaut spends 18/8 = <<18/8=2.25>>2.25 hours cycling and 11/2 = <<11/2=5.5>>5.5 hours conducting scientific experiments.
    The total amount of time spent on these activities in a day is 2.25 + 5.5 = <<2.25+5.5=7.75>>7.75 hours.
    The astronaut adds 30/8 = <<30/8=3.75>>3.75 hours of reviewing data to his routine.
    The total amount of time spent on his whole daily routine is 7.75 + 3.75 = <<7.75+3.75=11.5>>11.5 hours.
    ### Answer: 11.5

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:

     Reasoning: Jeremy requested 30/9 = <<30/9=3.3333333333333335>>3.3333333333333335 ounces of cheese.
    He received 17/22 = <<17/22=0.7727272727272727>>0.7727272727272727 ounces less than he requested.
    Using the equation 'd = n - (17 / 22)', we can find the amount of cheese he actually received:
    d = 3.3333333333333335 - 0.7727272727272727 = <<3.3333333333333335-0.7727272727272727=2.5606060606060606>>2.5606060606060606 ounces.
    ### Answer: 2.5606060606060606 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:

     Reasoning:

    First test: 13 out of every 4 sunglasses blocked all UV rays completely.
    This can be simplified to 13/4 = <<13/4=3.25>>3.25 sunglasses per sunglass.

    Second test: 20 out of every 18 sunglasses also blocked all UV rays.
    This can be simplified to 20/18 = <<20/18=1.1111111111111112>>1.1111111111111112 sunglasses per sunglass.

    Additional batch: 21 out of 17 sunglasses blocked all UV rays.
    This can be simplified to 21/17 = <<21/17=1.2352941176470588>>1.2352941176470588 sunglasses per sunglass.

    Subtracting the sunglasses that did not block all UV rays: 16 out of 30 sunglasses.
    This can be simplified to 16/30 = <<16/30=0.5333333333333333>>0.5333333333333333 sunglasses per sunglass.

    Adding the first test, second test, and additional batch:
    3.25 + 1.1111111111111112 + 1.2352941176470588 = <<3.25+1.1111111111111112+1.2352941176470588=5.59640523875827>>5.59640523875827 sunglasses per sunglass.

    Subtracting the sunglasses that did not block all UV rays:
    5.59640523875827 - 0.5333333333333333 = <<5.59640523875827-0.5333333333333333=5.0630719054249365>>5.0630719054249365 sunglasses per sunglass.

    This can be simplified to 5.0630719054249365/1 = <<5.0630719054249365/1=5.0630719054249365>>5.0630719054249365 sunglasses per sunglass.

    Since the final answer should be a simplified fraction, we can round this to the nearest whole number, which is 5 sunglasses per sunglass.

    ### Answer: 5/1 or simply 5

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:

     Reasoning:

    To make a sandwich, Shawn uses 23/28 + 6/9 = <<23/28+6/9=1.0416666666666667>>1.0416666666666667 cups of mayonnaise and sandwich spread.

    Shawn has to add 18/12 = <<18/12=1.5>>1.5 cups of cheese spread to his recipe.

    So, Shawn now needs 1.0416666666666667 + 1.5 = <<1.0416666666666667+1.5=2.5416666666666665>>2.5416666666666665 cups of ingredients to make one sandwich.

    If Shawn has to make an equal number of sandwiches using 4/4 cups of all the ingredients combined, he will use 4/4 \* 2.5416666666666665 = <<4/4\*2.5416666666666665=2.5416666666666665>>2.5416666666666665 cups of ingredients per sandwich.

    If Shawn makes 1 sandwich, he will use 2.5416666666666665 cups of ingredients.

    If Shawn makes 2 sandwiches, he will use 2.5416666666666665 \* 2 = <<2.5416666666666665\*2=5.083333333333333>>5.083333333333333 cups of ingredients.

    If Shawn makes 3 sandwiches, he will use 2.5416666666666665 \* 3 = <<2.5416666666666665\*3=7.625>>7.625 cups of ingredients.

    If Shawn makes 4 sandwiches, he will use 2.5416666666666665 \* 4 = <<2.5416666666666665\*4=10.166666666666666>>10.166666666666666 cups of ingredients.

    If Shawn makes 5 sandwiches, he will use 2.5416666666666665 \* 5 = <<2.5416666666666665\*5=12.708333333333332>>12.708333333333332 cups of ingredients.

    If Shawn makes 6 sandwiches, he will use 2.5416666666666665 \* 6 = <<2.5416666666666665\*6=15.25>>15.25 cups of ingredients.

    If Shawn makes 7 sandwiches, he will use 2.5416666666666665 \* 7 = <<2.5416666666666665\*7=17.791666666666668>>17.791666666666668 cups of ingredients.

    If Shawn makes 8 sandwiches, he will use 2.5416666666666665 \* 8 = <<2.5416666666666

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:

     Reasoning: Cassandra initially had 7/6 key sets.
    After losing 1/21 of a key set, she had 7/6 - 1/21 = <<(7*7)/(6*7) - (1*1)/(21*1) = 49/42 - 1/21 = (49-2)/42 = 47/42>>47/42 key sets.
    ### 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:

     Reasoning: Cassandra initially had 23/6 key sets.
    After losing 1/21 of a key set, she had 23/6 - 1/21 = <<(23*7)/(6*7) - (1*1)/(21*1) = 161/42 - 1/21 = (161-2)/42 = 159/42>>159/42 key sets.
    ### Answer: 159/42

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:

     Reasoning:
    First, we calculate the sum of the ratios of the two sections:
    (29/23) + (19/17) = <<29/23+19/17=1.2608695652173913+1.1176470588235294=2.3785166240409207>>2.3785166240409207

    Next, we calculate the ratio of a rest, which is equivalent to one whole measure:
    26/26 = <<26/26=1>>1

    Finally, we calculate the difference between the sum of the ratios of the two sections and the ratio of a rest:
    2.3785166240409207 - 1 = <<2.3785166240409207-1=1.3785166240409207>>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:

     Reasoning:
    First, we calculate the sum of the ratios of the two sections after the change:
    (29/23) + (19/23) = <<29/23+19/23=1.2608695652173913+0.8260869565217391=2.0869565217391304>>2.0869565217391304

    Next, we calculate the ratio of a rest, which is equivalent to one whole measure:
    26/26 = <<26/26=1>>1

    Finally, we calculate the difference between the sum of the ratios of the two sections and the ratio of a rest:
    2.0869565217391304 - 1 = <<2.0869565217391304-1=1.0869565217391304>>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:

     Reasoning: To multiply two fractions, you multiply the numerators together and the denominators together.

    (22/25) \* (22/8) = (22\*22)/(25\*8) = 484/200 = <<484/200=2.42>>2.42

    However, this is not a whole number, and the puzzle requires a whole number answer. Therefore, we need to simplify the fraction.

    484/200 = 121/50 = <<121/50=2.42>>2.42

    This fraction cannot be simplified further, so the puzzle must have a mistake or require a different approach.

    ### Answer: The product of 22/25 and 22/8 is 121/50 or 2.42, but this is not a whole number.

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:

     Reasoning: The result from the previous step was 121/50 or 2.42.

    The number on the key is 23/13.

    To add these two values, we need to find a common denominator. The least common multiple of 50 and 13 is 650.

    So, we convert 121/50 to 1533/650 and 23/13 to 115/650.

    Now, we can add the two fractions:

    1533/650 + 115/650 = 1648/650 = <<1648/650=2.5354285714285715>>2.5354285714285715

    However, this is not a whole number, and the puzzle requires a whole number answer. Therefore, we need to simplify the fraction.

    1648/650 = 3296/1300 = <<3296/1300=2.5353846153846154>>2.5353846153846154

    This fraction cannot be simplified further, so the puzzle must have a mistake or require a different approach.

    ### Answer: The sum of the result from the previous step and the number on the key is 3296/1300 or 2.5353846153846154, but this is not a whole number.

Expected answer: 2723/650

Correct? No

🔗 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:

     Reasoning: To multiply two fractions, you multiply the numerators together and the denominators together.

    (13/25) \* (22/8) = (13\*22)/(25\*8) = 286/200 = <<286/200=1.43>>1.43

    However, this is not a whole number, and the puzzle requires a whole number answer. Therefore, we need to simplify the fraction.

    286/200 = 143/100 = <<143/100=1.43>>1.43

    This fraction cannot be simplified further, so the puzzle must have a mistake or require a different approach.

    ### Answer: The product of 13/25 and 22/8 is 143/100 or 1.43, but this is not a whole number.

Expected answer: 143/100

Correct? No

🔗 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:

     Reasoning: The total length of the pillow is 23/9 + 22/25 = <<(23/9) + (22/25)=(23*25 + 22*9)/(9*25)=(575 + 198)/(225)=773/225>>773/225 feet.
    The length of border material needed is 773/225 \* 16/13 = <<(773/225) \* (16/13)=(773*16)/(225*13)=12368/2925>>12368/2925 feet.
    ### Answer: 12368/2925 feet

Expected answer: 12368/2925

Correct? Yes

🔗 Follow-up

Problem: James realizes he made a mistake when measuring the length of his pillow. The pillow is actually 12/9 feet long, not 23/9 feet as previously calculated. Using this corrected length, and still considering the added 22/25 feet for fluffing plus the factor of 16/13 for overlap and corners, how much border material will he need for his pillow now?

Gemma 2B:

     Reasoning: The total length of the pillow is 12/9 + 22/25 = <<(12/9) + (22/25)=(12*25 + 22*9)/(9*25)=(300 + 198)/(225)=498/225>>498/225 feet.
    The length of border material needed is 498/225 \* 16/13 = <<(498/225) \* (16/13)=(498*16)/(225*13)=8008/2925>>8008/2925 feet.
    ### Answer: 8008/2925 feet

Expected answer: 2656/975

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:

     Reasoning: The car travels 21/4 miles every hour.
    The car was supposed to travel an additional 16/13 miles, but only traveled an additional 1/21 miles.
    The car was supposed to travel 16/13 - 1/21 = <<(16/13) - (1/21)=(336-13)/(273)=323/273>>323/273 miles more than it did.
    The car travels at a speed of 21/4 miles per hour, so the time it would take to travel the additional distance is 323/273 \* 4/21 = <<(323/273) \* (4/21)=(1292/273)/(21/4)=1292/273 \* 4/21=5168/6141>>5168/6141 hours.
    The car was supposed to travel 5168/6141 \* 21/4 = <<(5168/6141) \* (21/4)=(108528/6141)/(4/21)=108528/6141 \* 21/4=2278116/24564>>2278116/24564 miles more than it did.
    ### Answer: 2278116/24564

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:

     Reasoning: The editing team takes 20/5 = <<20/5=4>>4 hours to edit a manuscript.
    The typesetting team takes 18/17 = <<18/17=1.0588235294117647>>1.0588235294117647 hours to adjust the layout of a page.
    The total time required for the entire process is 4 + 1.0588235294117647 = <<4+1.0588235294117647=5.058823529411765>>5.058823529411765 hours.
    The collective loss is 6/15 = <<6/15=0.4>>0.4 hours.
    The extended time is the same as the initial total time required, which is 5.058823529411765 hours.
    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, is 5.058823529411765 \* 5.058823529411765 = <<5.058823529411765\*5.058823529411765=25.599999999999996>>25.599999999999996 hours.
    ### Answer: 25.599999999999996

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:

     Reasoning: Jenny plants 13/11 * 21/3 = <<(13/11)*(21/3)=27>>27 bushels of potatoes.
    Jenny sells each bushel for 21/15 = <<21/15=1.4>>1.4 dollars.
    Jenny makes 27 * 1.4 = <<27*1.4=37.8>>37.8 dollars in total by selling all her potatoes.
    ### Answer: 37.8

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:

     Reasoning: The jeweler uses 14/28 = <<14/28=1/2>>1/2 kilogram of gold and 13/26 = <<13/26=1/2>>1/2 kilogram of silver.
    The sum of the amount of gold and silver used by the jeweler is 1/2 + 1/2 = <<1/2+1/2=1>>1 kilogram.
    ### Answer: 1

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:

     Reasoning: The jeweler now uses 21/28 = <<21/28=3/4>>3/4 kilogram of gold and 13/26 = <<13/26=1/2>>1/2 kilogram of silver.
    The total weight of gold and silver used by the jeweler is 3/4 + 1/2 = <<3/4+1/2=5/4>>5/4 kilograms.
    ### Answer: 5/4

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:

     Reasoning:
    First, let's find the total quantity of honey from a honey storage sub-section and a bee rearing sub-section, which is represented by 'p'.

    p = (25 / 9) + (25 / 9)
    p = (2 * 25) / 9
    p = 50 / 9
    p = <<50/9=5.555555555555555>>5.555555555555555 gallons

    Now, let's find the total quantity of honey from a honey storage sub-section with an additional (2 / 26) gallons of honey and a bee rearing sub-section, which is represented by 's'.

    s = (25 / 9) + (2 / 26) + (25 / 9)
    s = (2 * 25) / 9 + (2 / 26)
    s = 50 / 9 + (2 / 26)
    s = 5.555555555555555 + (2 / 26)
    s = 5.555555555555555 + <<2/26=0.07692307692307693>>0.07692307692307693
    s = <<5.555555555555555+0.07692307692307693=5.632478623188409>>5.632478623188409 gallons

    ### Answer: 5.632478623188409 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:

     Reasoning: The dinosaur eats 16/8 = <<16/8=2>>2 bunches of leaves per hour during the day.
    The dinosaur eats 6/17 = <<6/17=0.3529411764705882>>0.3529411764705882 bunches of leaves per hour at night.
    The dinosaur eats 2 + 0.3529411764705882 = <<2+0.3529411764705882=2.3529411764705882>>2.3529411764705882 bunches of leaves per hour day and night.
    ### Answer: 2.3529411764705882

Expected answer: 40/17

Correct? Yes

🔗 Follow-up

Problem: If this dinosaur finds a field where, due to unique plant growth conditions, it can eat an additional 27/13 bunches of leaves per hour, regardless of whether it's day or night, how many bunches of leaves would the dinosaur eat in total in an hour? Include the quantities it was previously eating during the day and night.

Gemma 2B:

     Reasoning: The dinosaur eats 2 + 0.3529411764705882 = <<2+0.3529411764705882=2.3529411764705882>>2.3529411764705882 bunches of leaves per hour day and night.
    The dinosaur eats an additional 27/13 = <<27/13=2.076923076923077>>2.076923076923077 bunches of leaves per hour in the field.
    The dinosaur eats 2.3529411764705882 + 2.076923076923077 = <<2.3529411764705882+2.076923076923077=4.429864253393665>>4.429864253393665 bunches of leaves per hour in the field day and night.
    ### Answer: 4.429864253393665

Expected answer: 979/221

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:

     Reasoning: The bear ate 28/6 + 21/18 + 24/22 = <<28/6 + 21/18 + 24/22 = 14/3 + 7/6 + 12/11>>14/3 + 7/6 + 12/11 pounds of fish in three days.
    To add these fractions, we need a common denominator. The least common multiple of 3, 6, and 11 is 66.
    So, the bear ate (14/3) \* (22/22) + (7/6) \* (11/11) + (12/11) \* (6/6) = <<(14/3) \* (22/22) + (7/6) \* (11/11) + (12/11) \* (6/6) = 308/66 + 77/66 + 72/66>>308/66 + 77/66 + 72/66 = 457/66 pounds of fish in three days.
    ### Answer: 457/66

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:

     Reasoning: The bear ate 28/6 + 5/18 + 24/22 = <<28/6 + 5/18 + 24/22 = 14/3 + 5/18 + 12/11>>14/3 + 5/18 + 12/11 pounds of fish in three days.
    To add these fractions, we need a common denominator. The least common multiple of 3, 18, and 11 is 198.
    So, the bear ate (14/3) \* (66/66) + (5/18) \* (11/11) + (12/11) \* (18/18) = <<(14/3) \* (66/66) + (5/18) \* (11/11) + (12/11) \* (18/18) = 924/198 + 55/198 + 216/198>>924/198 + 55/198 + 216/198 = 1195/198 pounds of fish in three days.
    ### Answer: 1195/198

Expected answer: 1195/198

Correct? Yes

🔗 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:

     Reasoning: Heather used 11/17 + 6/2 = <<11/17+6/2=11/17+3=11/17+51/17=62/17>>62/17 cups of sugar for the bread and custard.
    Heather increased the total quantity of sugar by a factor of 29/21, so she used 62/17 * 29/21 = <<62/17*29/21=1778/357>>1778/357 cups of sugar in total.
    ### Answer: 1778/357

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:

     Reasoning: First, we need to find a common denominator for the fractions (7/8) and (21/18). The least common multiple of 8 and 18 is 72.

    So, we convert the fractions to have the same denominator:

    (7/8) = (63/72)
    (21/18) = (28/72)

    Now, we can add the fractions:

    (63/72) + (28/72) = (91/72)

    The fraction (91/72) is already in simplest form, as 91 and 72 have no common factors other than 1.

    ### Answer: (91/72)

Expected answer: 49/24

Correct? No

🔗 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:

     Reasoning:
    First, let's simplify the fractions:

    * 15/7 gallons of water per guest = 15/7 = <<15/7=2.142857142857143>>2.142857142857143 gallons
    * 15/24 gallons of wine per guest = 15/24 = <<15/24=0.625>>0.625 gallons
    * 26/20 gallons of milk per cake = 26/20 = <<26/20=1.3>>1.3 gallons

    Now, let's calculate the total amount of liquid consumed by the guests:

    * Water: 2.142857142857143 gallons per guest
    * Wine: 0.625 gallons per guest
    * Total per guest: 2.142857142857143 + 0.625 = <<2.142857142857143+0.625=2.767857142857143>>2.767857142857143 gallons

    Next, let's calculate the baker's requirement for milk:

    * Milk: 1.3 gallons per cake

    Now, let's calculate the total amount of liquid needed for the feast:

    * Guests' consumption: 2.767857142857143 gallons per guest
    * Baker's requirement: 1.3 gallons per cake
    * Total: 2.767857142857143 + 1.3 = <<2.767857142857143+1.3=4.067857142857143>>4.067857142857143 gallons per guest

    Therefore, the total amount of liquid needed for the feast is 4.067857142857143 gallons per guest.

    ### Answer: 4.067857142857143 gallons per guest

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:

     Reasoning: Teddy's favorite number is 30/17.
    He added 18/15 to his favorite number, so his new number is 30/17 + 18/15 = <<(30/17)+(18/15)=(450+306)/(17*15)=756/255>>756/255.
    He then multiplied this new number by 24/13, so his final number is 756/255 * 24/13 = <<(756/255)*(24/13)=(756*24)/(255*13)=18144/3315>>18144/3315.
    ### Answer: 18144/3315

Expected answer: 6048/1105

Correct? Yes

🔗 Follow-up

Problem: In the previous calculation, Teddy the bear started with the number 30/17. But what if Teddy had started with the number 20/17 instead? Then he added 18/15 to this number, and multiplied the result by 24/13. What is Teddy's final number now?

Gemma 2B:

     Reasoning: Teddy's new starting number is 20/17.
    He added 18/15 to this number, so his new number is 20/17 + 18/15 = <<(20/17)+(18/15)=(300+306)/(17*15)=606/255>>606/255.
    He then multiplied this new number by 24/13, so his final number is 606/255 * 24/13 = <<(606/255)*(24/13)=(606*24)/(255*13)=14544/3315>>14544/3315.
    ### Answer: 14544/3315

Expected answer: 4848/1105

Correct? Yes

🔗 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:

     Reasoning: Johnny's desired hole diameter is (20/6) cm.
    His drill bit has a diameter of (11/21) cm.
    If he drills each hole exactly once with his drill bit, each hole would have a diameter of (11/21) cm.
    The fraction of the desired diameter that each hole would have is (11/21) / (20/6) = (11/21) * (6/20) = (66/420) = (11/70).
    ### Answer: (11/70)

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:

     Reasoning: The first model takes 17/10 hours to assemble.
    The second model takes 12/23 hours to assemble.
    The difference in time is 17/10 - 12/23 = <<(17/10) - (12/23)=(359-120)/230=239/230>>239/230 hours.
    This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
    Therefore, the difference in time is 239/230 hours.
    ### Answer: 239/230 hours or 1.0391304347826087 hours (decimal)

Expected answer: 271/230

Correct? No

🔗 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:

     Reasoning: Carlos usually uses 20/15 = <<20/15=4/3>>4/3 units of wood for each chair.
    For the special order, he needs (24/5) times (7/6) = <<(24/5)*(7/6)=(24*7)/(5*6)=168/30=56/10=28/5>>28/5 more units of wood than usual.
    So, for the special chair, Carlos would need 4/3 + 28/5 = <<(4/3)*(5/5)+(28/5)*(3/3)=(20/15)+(84/15)=104/15>>104/15 units of wood.
    ### Answer: 104/15

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:

     Reasoning: Carlos now uses 20/8 = <<20/8=5/2>>5/2 units of wood for each basic chair.
    For the special order, he still needs (24/5) times (7/6) = <<(24/5)*(7/6)=(24*7)/(5*6)=168/30=56/10=28/5>>28/5 more units of wood than usual.
    So, for the special chair, Carlos would now need 5/2 + 28/5 = <<(5/2)*(5/5)+(28/5)*(2/2)=(25/10)+(56/10)=81/10>>81/10 units of wood.
    ### 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:

     Reasoning: The initial speed of the car was 13/4 miles per minute.
    The car reduced its speed by 14/15 miles per minute, so the new speed of the car was 13/4 - 14/15 = <<(13/4) - (14/15)=(39/20) - (14/15)=(39/20) - (28/30)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/15)=(39/20) - (14/

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:

     Reasoning:

    1. The vineyard can usually produce 19/2 = <<19/2=9.5>>9.5 baskets of grapes every season. However, due to weather conditions, only 19/29 of the usual amount were produced this season. So, the number of baskets produced this season is 19/2 \* 19/29 = <<(19/2)*(19/29)=3.5>>3.5 baskets.
    2. Jake gets to keep only 7/11 of the total amount of grapes. So, the number of baskets he gets is 3.5 \* 7/11 = <<3.5*(7/11)=2.142857142857143>>2.14 baskets.
    3. 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. So, the number of baskets he uses for the juice is 2.14 \* 9/10 = <<2.14*(9/10)=1.926>>1.93 baskets.

    ### Answer: 1.93 baskets

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:

     Reasoning: Joel picked 9/2 = <<9/2=4.5>>4.5 bushels of red grapes and 10/22 = <<10/22=0.45454545454545453>>0.45454545454545453 bushels of green grapes.
    Joel picked 4.5 + 0.45454545454545453 = <<4.5+0.45454545454545453=4.954545454545454>>4.954545454545454 bushels of grapes altogether.
    ### Answer: 4.954545454545454

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:

     Reasoning: Joel made 4.954545454545454 \* 25/17 = <<4.954545454545454\*25/17=7.5>>7.5 bushels of juice for the market.
    ### Answer: 7.5

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:

     Reasoning: Joel picked 9/3 = <<9/3=3>>3 bushels of red grapes and 10/22 = <<10/22=0.45454545454545453>>0.45454545454545453 bushels of green grapes.
    Joel picked 3 + 0.45454545454545453 = <<3+0.45454545454545453=3.4545454545454544>>3.4545454545454544 bushels of grapes altogether.
    ### Answer: 3.4545454545454544

Expected answer: 38/11

Correct? No

🔗 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:

     Reasoning: The diameter of the larger snowball is 17/8 feet, so its radius is half of that, which is (17/8)/2 = <<(17/8)/2=17/16>>17/16 feet. The volume of a sphere is given by the formula V = (4/3)πr^3, so the volume of the larger snowball is (4/3)π(17/16)^3 = <<(4/3)π(17/16)^3=1.1459155902622145>>1.1459155902622145 cubic feet.

    The diameter of the smaller snowball is 1/20 feet, so its radius is half of that, which is (1/20)/2 = <<(1/20)/2=1/40>>1/40 feet. The volume of the smaller snowball is (4/3)π(1/40)^3 = <<(4/3)π(1/40)^3=0.

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:

     Reasoning: The first child splits up 24/7 = <<24/7=3.4285714285714284>>3.4285714285714284 parts of the sand.
    The second child takes away 2/16 = <<2/16=0.125>>0.125 parts of the sand.
    The remaining part of sand in the sandbox is 3.4285714285714284 - 0.125 = <<3.4285714285714284-0.125=3.3035714285714284>>3.3035714285714284 parts.
    ### Answer: 3.3035714285714284 parts

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:

     Reasoning: The lion ate 28/26 = <<28/26=1.076923076923077>>1.076923076923077 zebras in one day.
    The lion ate 23/9 = <<23/9=2.5555555555555554>>2.5555555555555554 wildebeests the next day.
    The difference in the amount of zebra and wildebeest eaten is 2.5555555555555554 - 1.076923076923077 = <<2.5555555555555554-1.076923076923077=1.4786324786324786>>1.4786324786324786.
    To simplify the fraction, we can multiply both the numerator and the denominator by 100 to get rid of the decimal point.
    1.4786324786324786 \* 100 = <<1.4786324786324786\*100=147.86324786324786>>147.86324786324786
    100 \* 100 = <<100\*100=10000>>10000
    So the simplified fraction is 147.86324786324786/10000 = <<147.86324786324786/10000=0.014786324786324786>>0.014786324786324786.
    ### Answer: 0.014786324786324786 or 14786324786324786/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Expected answer: 173/117

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:

     Reasoning: The factory combines 14/4 kilograms of cocoa and 21/11 liters of milk for every kilogram of chocolate.
    To find out how many kilograms of chocolate the factory will produce, we need to multiply the amount of cocoa by the amount of milk.
    The expression to calculate this is ((14 / 4) \* (21 / 11)).
    Calculating this expression gives us:
    ((14 / 4) \* (21 / 11)) = (3.5 \* 1.9090909090909091) = <<3.5\*1.9090909090909091=6.681818181818182>>6.681818181818182 kilograms of chocolate.
    ### Answer: 6.681818181818182 kilograms of chocolate

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:

     Reasoning: The first species produces 12 bananas every 29 days, so the expected number of bananas produced by this species on a given day is 12/29.
    The second species produces 30 bananas every 10 days, so the expected number of bananas produced by this species on a given day is 30/10.
    The expected number of bananas produced by both species together on a given day is (12/29) + (30/10) = <<(12/29)+(30/10)=1.4137931034482757>>1.4137931034482757.
    ### Answer: 1.4137931034482757

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:

     Reasoning: The giraffe needs to eat 11/11 + 26/14 = <<11/11+26/14=1.0+1.8571428571428572>>2.857142857142857 ton of food a day.
    ### Answer: 2.857142857142857 ton

Expected answer: 20/7

Correct? No

🔗 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:

     Reasoning: The bear spends 18/24 of each day sleeping.
    The bear's activity is tracked for 27 days.
    Assuming each month has 13 weeks, the bear spends (18/24) \* (27/13) of the month sleeping.
    (18/24) \* (27/13) = <<(18/24)\*(27/13)=0.5625>>0.5625
    ### Answer: 0.5625

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:

     Reasoning: The formula provided is incorrect. The correct formula to find the fraction of pine and birch trees in the forest is f = (9/14) + (19/28).

    First, we need to find the fraction of birch trees in the forest. Since 19 out of every 28 trees are birches, the fraction of birch trees is 19/28.

    Next, we add the fraction of pine trees (9/14) to the fraction of birch trees (19/28) to find the total fraction of pine and birch trees in the forest.

    f = (9/14) + (19/28)

    To add these fractions, we need a common denominator. The least common multiple of 14 and 28 is 28.

    So, we convert 9/14 to 18/28 and add it to 19/28.

    f = (18/28) + (19/28)

    f = 37/28

    Therefore, the fraction of trees in the forest that are either pine or birch is 37/28.

    ### Answer: 37/28

Expected answer: 71/7

Correct? No

🔗 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:

     Reasoning: First, we need to calculate Zogorian's initial energy level:
    (14 / 2) / (23 / 17) = (7 * 17) / 23 = 119 / 23 = <<119/23=5.173913043478261>>5.173913043478261 zogs

    Next, we need to calculate the increase in energy level:
    (16 / 24) = 2 / 3 = <<2/3=0.6666666666666666>>0.6666666666666666 zogs

    Finally, we add the increase to the initial energy level:
    5.173913043478261 + 0.6666666666666666 = <<5.173913043478261+0.6666666666666666=5.8405797061449275>>5.8405797061449275 zogs

    ### Answer: 5.8405797061449275

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:

     Reasoning: Teddy hides 18/11 - 8/21 = <<18/11 - 8/21 = 1.5454545454545454>>1.5454545454545454 more friends in the forest than at the beach.
    Let's call this number 'f'.
    f = 1.5454545454545454
    n = f^2 = <<1.5454545454545454^2 = 2.380952380952381>>2.380952380952381
    Since the number of hiding spots must be a whole number, we round up to the nearest whole number.
    Teddy needs 3 hiding spots.
    ### Answer: 3

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:

     Reasoning: The robot starts with 25/10 = <<25/10=2.5>>2.5 units of energy.
    The robot uses 27/23 = <<27/23=1.1739130434782608695652173913043>>1.1739130434782608695652173913043 units of energy.
    The robot has 2.5 - 1.1739130434782608695652173913043 = <<2.5-1.1739130434782608695652173913043=1.3260869565217391304347826086957>>1.3260869565217391304347826086957 units of energy left.
    ### Answer: 1.3260869565217391304347826086957

Expected answer: 61/46

Correct? Yes

🔗 Follow-up

Problem: Considering the same robot doing the maintenance task, suppose instead that it initially starts with 25/10 units of energy but it uses only 14/23 unit of energy to complete the calculations, different from what we thought before. Calculate how much energy the robot has remaining after performing these computations.

Gemma 2B:

     Reasoning: The robot starts with 25/10 = <<25/10=2.5>>2.5 units of energy.
    The robot uses 14/23 = <<14/23=0.6086956521739130434782608695652>>0.6086956521739130434782608695652 units of energy.
    The robot has 2.5 - 0.6086956521739130434782608695652 = <<2.5-0.6086956521739130434782608695652=1.891304347826086956521739130435>>1.891304347826086956521739130435 units of energy left.
    ### Answer: 1.891304347826086956521739130435

Expected answer: 87/46

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:

     Reasoning:
    First, let's find the total distance covered by the first two snails in one hour.

    The first snail covers 17/21 of a meter in an hour, and the second snail covers 20/24 of a meter in an hour.

    To find the total distance covered by both snails in one hour, we add their distances:

    (17/21) + (20/24) = (17 \* 24 + 20 \* 21) / (21 \* 24) = (408 + 420) / 504 = 828 / 504 = 1.643253968254 (approximately)

    Now, let's find the distance covered by the third snail in one hour.

    The third snail covers 18/17 of a meter in an hour.

    To find the total distance covered by all three snails in one hour, we multiply the total distance covered by the first two snails by the distance covered by the third snail:

    1.643253968254 \* (18/17) = 1.643253968254 \* 1.058823529412 = 1.739999999999 (approximately)

    Therefore, the total distance covered by all three snails in one hour is approximately 1.74 meters.

    ### Answer: 1.74 meters

Expected answer: 207/119

Correct? No

🔗 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:

     Reasoning: Johnny originally had 24/14 = <<24/14=1.7142857142857142>>1.7142857142857142 yards of fabric.
    After making stuffed animals, he had 9/29 = <<9/29=0.3103448275862069>>0.3103448275862069 yards left.
    The difference between the original and remaining fabric is 1.7142857142857142 - 0.3103448275862069 = <<1.7142857142857142-0.3103448275862069=1.4039408866995073>>1.4039408866995073 yards.
    Johnny used 15/2 \* 1.4039408866995073 = <<15/2\*1.4039408866995073=10.529556649746305>>10.529556649746305 yards of the new fabric.
    ### Answer: 10.529556649746305

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:

     Reasoning: To find the total number of kids waiting for the swing, we need to add the two parts of the waiting line together.

    First, we need to find a common denominator for the fractions 2/10 and 21/4. The least common multiple of 10 and 4 is 20, so we can convert both fractions to have a denominator of 20.

    2/10 = (2\*2)/(10\*2) = 4/20
    21/4 = (21\*5)/(4\*5) = 105/20

    Now we can add the two fractions together:

    4/20 + 105/20 = (4+105)/20 = 109/20

    So, the total number of kids waiting for the swing is 109/20 of the total number of kids in the park.

    To find the total number of kids in the park, we can set up the equation:

    2/10 + 21/4 = 109/20

    Multiplying both sides by 20 to eliminate the denominator, we get:

    4 + 105 = 109

    Since we are looking for the total number of kids in the park, we can ignore the left side of the equation and focus on the right side.

    Therefore, the total number of kids in the park is 109.

    Since the waiting line consists of 109/20 of the total number of kids in the park, we can find the number of kids waiting for the swing by multiplying the total number of kids by 109/20:

    109 \* (109/20) = 11881/20 = 594.05

    Since we can't have a fraction of a kid, we can round up to the nearest whole number.

    Therefore, the total number of kids waiting for the swing is 595.

    ### Answer: 595

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:

     Reasoning: The spacecraft has 18/30 = <<18/30=0.6>>0.6 of its fuel tanks filled.
    Each fuel tank can power the spacecraft for 22/6 = <<22/6=3.6666666666666665>>3.6666666666666665 hours.
    The spacecraft currently has 0.6 \* 3.6666666666666665 = <<0.6\*3.6666666666666665=2.2>>2.2 hours of power.
    ### Answer: 2.2

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:

     Reasoning: The spacecraft now has 18/5 = <<18/5=3.6>>3.6 of its fuel tanks filled.
    Each fuel tank can still power the spacecraft for 22/6 = <<22/6=3.6666666666666665>>3.6666666666666665 hours.
    The spacecraft currently has 3.6 \* 3.6666666666666665 = <<3.6\*3.6666666666666665=13.2>>13.2 hours of power.
    ### Answer: 13.2

Expected answer: 66/5

Correct? No

🔗 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:

     Reasoning: The cat eats 16/12 + 6/10 = <<16/12 + 6/10 = 1.3333333333333333 + 0.6 = 1.9333333333333333>>1.9333333333333333 cans of cat food in one day.
    ### Answer: 1.9333333333333333 cans

Expected answer: 29/15

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:

     Reasoning: The average number of eggs per nest for the first group is 12/3 = <<12/3=4>>4 eggs per nest.
    The average number of eggs per nest for the second group is 11/4 = <<11/4=2.75>>2.75 eggs per nest.
    The difference between the two averages is 4 - 2.75 = <<4-2.75=1.25>>1.25 eggs per nest.
    ### Answer: 1.25

Expected answer: 5/4

Correct? Yes

🔗 Follow-up

Problem: Considering the previous scenario with the starfish, suppose instead, the starfish laid 12 eggs in 3 nests and only one egg in another 4 nests. How much is the difference between the average number of eggs per nest for this revised scenario?

Gemma 2B:

     Reasoning: The average number of eggs per nest for the first group is still 12/3 = <<12/3=4>>4 eggs per nest.
    The average number of eggs per nest for the second group is now 1/4 = <<1/4=0.25>>0.25 eggs per nest.
    The difference between the two averages is 4 - 0.25 = <<4-0.25=3.75>>3.75 eggs per nest.
    ### Answer: 3.75

Expected answer: 15/4

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:

     Reasoning: The monkey eats (22/7) \* (10/25) = <<(22/7) \* (10/25)=2/3>>2/3 of the pile.
    The monkey gives (3/28) of the pile to his friend.
    The monkey has 1 - (2/3) - (3/28) = <<1 - (2/3) - (3/28)=19/28>>19/28 of the pile left.
    ### Answer: 19/28

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:

     Reasoning: The mouse runs at a speed of 24/20 = <<24/20=1.2>>1.2 feet per second.
    The mouse runs for 23/2 = <<23/2=11.5>>11.5 seconds.
    The mouse runs 1.2 \* 11.5 = <<1.2\*11.5=13.8>>13.8 feet.
    ### Answer: 13.8

Expected answer: 69/5

Correct? Yes

🔗 Follow-up

Problem: After running the initial distance, the mouse continues to run for an additional 26/17 feet. What is the total distance that the mouse runs?

Gemma 2B:

     Reasoning: The mouse runs an additional 26/17 = <<26/17=1.5294117647058823>>1.5294117647058823 feet.
    The total distance that the mouse runs is 13.8 + 1.5294117647058823 = <<13.8+1.5294117647058823=15.329411764705882>>15.329411764705882 feet.
    ### Answer: 15.329411764705882

Expected answer: 1303/85

Correct? No

🔗 Follow-up

Problem: In the previous problem, we observed a mouse running at a speed of 24/20 feet per second for 23/2 seconds. Let's reconsider the situation, but now the mouse runs at the same speed for only 10/2 seconds. How far does the mouse run now?

Gemma 2B:

     Reasoning: The mouse runs at a speed of 24/20 = <<24/20=1.2>>1.2 feet per second.
    The mouse runs for 10/2 = <<10/2=5>>5 seconds.
    The mouse runs 1.2 \* 5 = <<1.2\*5=6>>6 feet.
    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 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:

     Reasoning: The glasses contain 29/9 ounces of beverage each. If 26/25 of them were consumed, then the total amount of beverage consumed is (29/9) \* (26/25) = <<(29/9)\*(26/25)=3.44>>3.44 ounces.
    The party goers then drink an additional 2/19 ounces of beverages, so the total amount of beverages consumed is 3.44 + 2/19 = <<3.44+2/19=3.52>>3.52 ounces.
    ### Answer: 3.52 ounces

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:

     Reasoning: Let's assume the total number of sets of toothbrushes you have is x.

    You add 7/15 of a new set to your current collection, so you have x + 7/15 sets.

    Your friend gifts you 9 more sets, so you have x + 7/15 + 9 sets.

    You can only fit 26/27 of your total sets in your display case, so you have (26/27) \* (x + 7/15 + 9) sets.

    Since you want to know how many sets you can fit in your display case, we need to find the value of x that makes the equation true.

    Let's set up the equation:

    (26/27) \* (x + 7/15 + 9) = 26/27 \* x

    Now, we can solve for x:

    x + 7/15 + 9 = x

    7/15 + 9 = 0

    This equation doesn't make sense, so we need to re-evaluate our approach.

    Let's try a different approach:

    We know that you can only fit 26/27 of your total sets in your display case. So, we can set up the equation:

    (26/27) \* (x + 7/15 + 9) = y

    where y is the number of sets you can fit in your display case.

    Now, we can solve for y:

    y = (26/27) \* (x + 7/15 + 9)

    Since we don't know the value of x, we can't solve for y directly. However, we can simplify the equation:

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    Now, we can plug in the values for 7/15 and 9:

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y = (26/27) \* x + (26/27) \* (7/15 + 9)

    y = (26/27) \* x + (26/27) \* (7/15 + 243/27)

    y =

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:

     Reasoning: The weight of the backpack when it's empty is 27/20 kilograms.
    The weight of the book is 1/6 kilograms.
    The total weight of the backpack is 27/20 + 1/6 = <<(27/20) + (1/6)=(81+10)/60=91/60>>91/60 kilograms.
    ### 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:

     Reasoning: The weight of the backpack when it's empty is 27/20 kilograms.
    The weight of the heavier book is 21/6 = <<21/6=7/2>>7/2 kilograms.
    The total weight of the backpack is 27/20 + 7/2 = <<(27/20) + (7/2)=(27+140)/40=167/40>>167/40 kilograms.
    ### Answer: 167/40

Expected answer: 97/20

Correct? No

🔗 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:

     Reasoning: The multiplier of the new bottle compared to the old one is (7 / 7) \* (25 / 22) = <<(7/7)*(25/22)=25/22>>25/22.
    ### 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:

     Reasoning: The new multiplier of the updated bottle compared to the original one is (28 / 13) \* (25 / 22) = <<(28/13)*(25/22)=100/13>>100/13.
    ### Answer: 100/13

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:

     Reasoning: The new multiplier for the revised bottle compared to the original one is (7 / 7) \* (25 / 12) = <<(7/7)*(25/12)=25/12>>25/12.
    ### Answer: 25/12

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:

     Reasoning: Tilly has gathered 25/9 + 8/13 = <<(25/9) + (8/13)=(325/117)>>325/117 kg of sea plants.
    Tilly has found 24/27 + 21/26 = <<(24/27) + (21/26)=(676/702)>>676/702 kg of food in the rock and the other food source.
    Tilly has a total of 325/117 + 676/702 = <<(325/117) + (676/702)=(1001/702)>>1001/702 kg of food.
    Simplifying the fraction, we get 1001/702 = <<1001/702=1.4262626262626262>>1.4262626262626262 kg of food.
    ### Answer: 1.4262626262626262 kg or 1001/702 kg (simplified)

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:

     Reasoning:

    1. Difference in location and distance to the island:
       Distance to the island = 17/2 nautical miles
       Current location = 4/2 nautical miles away from the island
       Difference = 17/2 - 4/2 = <<17/2 - 4/2 = 13/2>>13/2 nautical miles

    2. Adjusting for the tide:
       Tide adjustment = 14/9 nautical miles
       Adjusted distance = 13/2 + 14/9 = <<13/2 + 14/9 = 117/18 + 28/18 = 145/18>>145/18 nautical miles

    3. Calculating fuel requirements:
       Fuel efficiency = 22/15 nautical miles per gallon
       Fuel requirements = 145/18 * 22/15 = <<145/18 * 22/15 = 3190/270>>3190/270 gallons

    ### Answer: 3190/270 gallons

Expected answer: 319/27

Correct? Yes

🔗 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:

     Reasoning: The forest ranger patrolled 14/3 - 2/18 = <<14/3 - 2/18 = 14/3 - 1/9 = (14*3 - 1)/9 = (42 - 1)/9 = 41/9>>41/9 miles in the afternoon.
    ### Answer: 41/9

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:

     Reasoning: The forest ranger patrolled 29/3 - 2/18 = <<29/3 - 2/18 = 29/3 - 1/9 = (29*3 - 1)/9 = (87 - 1)/9 = 86/9>>86/9 miles in the afternoon.
    ### Answer: 86/9

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:

     Reasoning: Arthur practices 20/21 + 11/29 = <<20/21+11/29=1.000448275862069>>1.000448275862069 hours per day on the weekend.
    ### Answer: 1.000448275862069 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:

     Reasoning: Initially, Lucas had 18 shirts and divided them equally among his 3 siblings, so each sibling got 18/3 = <<18/3=6>>6 shirts.
    Later, Lucas bought 27 more shirts and decided to keep only 1/19 of those shirts for each sibling, so each sibling got 27/19 = <<27/19=1.4210526315789473>>1.4210526315789473 shirts.
    The difference in the number of shirts each sibling has now as compared to before is (18/3) - (27/19) = <<(18/3)-(27/19)=4.5789473684210525>>4.5789473684210525 shirts.
    Since the result is positive, each sibling has more shirts now than before.
    ### Answer: Each sibling has 4.5789473684210525 more shirts now than before.

Expected answer: 87/19

Correct? Yes

🔗 Follow-up

Problem: Let's modify the earlier scenario from Lucas's shirt store. This time, Lucas initially divided 18 shirts equally among his 3 siblings as before. However, later he purchased 29 shirts instead of 27. If he still wants to distribute 1/19 of these new shirts to each sibling, how many more or fewer shirts will each sibling now have compared to before? Calculate the difference using the expression ((18 / 3) - (29 / 19)) and find out the result.

Gemma 2B:

     Reasoning: Initially, Lucas had 18 shirts and divided them equally among his 3 siblings, so each sibling got 18/3 = <<18/3=6>>6 shirts.
    Later, Lucas bought 29 more shirts and decided to keep only 1/19 of those shirts for each sibling, so each sibling got 29/19 = <<29/19=1.5263157894736843>>1.5263157894736843 shirts.
    The difference in the number of shirts each sibling has now as compared to before is (18/3) - (29/19) = <<(18/3)-(29/19)=4.4736842105263155>>4.4736842105263155 shirts.
    Since the result is positive, each sibling has more shirts now than before.
    ### Answer: Each sibling has 4.4736842105263155 more shirts now than before.

Expected answer: 85/19

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:

     Reasoning: The painter mixed 7 + 2/5 = <<7+(2/5)=7.4>>7.4 gallons of light blue paint.
    After using 18/4 = <<18/4=4.5>>4.5 gallons, the painter has 7.4 - 4.5 = <<7.4-4.5=2.9>>2.9 gallons of light blue paint left.
    ### Answer: 2.9

Expected answer: 29/10

Correct? Yes

🔗 Follow-up

Problem: Suppose initially the painter had 24 gallons of white paint instead of 7 gallons. After mixing 2/5 gallon of blue paint with it and then using 18/4 gallons of the resulting light blue paint for a project, how many gallons of light blue paint does the painter have left now?

Gemma 2B:

     Reasoning: The painter mixed 24 + 2/5 = <<24+(2/5)=24.4>>24.4 gallons of light blue paint.
    After using 18/4 = <<18/4=4.5>>4.5 gallons, the painter has 24.4 - 4.5 = <<24.4-4.5=19.9>>19.9 gallons of light blue paint left.
    ### Answer: 19.9

Expected answer: 199/10

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:

     Reasoning: Jayson spent 24/7 = <<24/7=3.4285714285714284>>3.4285714285714284 hours skating on the first day.
    Jayson spent 30/20 = <<30/20=1.5>>1.5 hours skating on the second day.
    Jayson spent 3.4285714285714284 + 1.5 = <<3.4285714285714284+1.5=4.928571428571428>>4.928571428571428 hours skating in total over the two days.
    ### Answer: 4.928571428571428

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:

     Reasoning: The dolphin's usual height is 18/3 = <<18/3=6>>6 feet.
    The dolphin jumped 3/4 * 6 = <<3/4*6=4.5>>4.5 feet that day.
    ### Answer: 4.5 feet

Expected answer: 9/2

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:

     Reasoning:

    Last month's sales to production ratio is (20/15 + 16/22).

    This week's ratio of interested customers to production is (22/27 * 23/8).

    To find the result when Callie multiplies these two ratios, we can write the expression as:

    (20/15 + 16/22) * (22/27 * 23/8)

    First, let's simplify the first ratio:

    (20/15 + 16/22) = (4/3 + 8/11) = (44/33 + 24/33) = 68/33

    Now, let's simplify the second ratio:

    (22/27 * 23/8) = (22 * 23) / (27 * 8) = 506 / 216

    Finally, let's multiply the two ratios:

    (68/33) * (506/216) = (68 * 506) / (33 * 216) = 34368 / 7128

    So, the result when Callie multiplies the two ratios is 34368/7128.

    ### Answer: 34368/7128

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:

     Reasoning: The musician spent 30 minutes / 15 songs = <<30/15=2>>2 minutes on each song.
    1/17 of an hour is equal to 60 minutes / 17 = <<60/17=3.529411764705882>>3.529411764705882 minutes.
    The final duration of the song is 2 minutes - 3.529411764705882 minutes = <<2-3.529411764705882=-1.529411764705882>>-1.529411764705882 minutes.
    Since the duration of a song cannot be negative, the final duration of the song is 0 minutes.
    ### Answer: 0 minutes

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:

     Reasoning: Josh rode the scooter for 18 + 1/12 = <<18+(1/12)=(18*12+1)/12=217/12>>217/12 hours in total.
    Jack rode the scooter for 7/17 hours.
    Together, they rode the scooter for 217/12 + 7/17 = <<(217/12)+(7/17)=(217*17+7*12)/(12*17)=3659/204>>3659/204 hours in total.
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 17.
    3659/204 = <<3659/17=215>>215/<<204/17=12>>12 hours in total.
    ### Answer: 215/12 hours

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:

     Reasoning: To find the fraction of the total inventory that these lamps constitute, we need to add the fractions of each type of lamp together.

    First, we need to find a common denominator for all the fractions. The least common multiple (LCM) of 26, 11, 28, and 19 is 26*11*28*19 = 149484.

    Now, we can convert each fraction to have the same denominator:

    * Floor lamps: (4/26) \* (11*28*19/11*28*19) = 4 \* 11 \* 28 \* 19 / 149484 = 21296 / 149484
    * Desk lamps: (15/11) \* (26*28*19/26*28*19) = 15 \* 26 \* 28 \* 19 / 149484 = 114240 / 149484
    * Table lamps: (23/28) \* (26*11*19/26*11*19) = 23 \* 26 \* 11 \* 19 / 149484 = 124509 / 149484
    * Decorative lamps: (8/19) \* (26*11*28/26*11*28) = 8 \* 26 \* 11 \* 28 / 149484 = 61600 / 149484

    Now, we can add these fractions together:

    21296/149484 + 114240/149484 + 124509/149484 + 61600/149484 = 321645 / 149484

    Therefore, the fraction of the total inventory that these lamps constitute is 321645 / 149484.

    ### Answer: 321645 / 149484

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:

     Reasoning: Oliver has a kite string that is 26/19 + 7/11 = <<(26*11 + 7*19)/(19*11)=(286+133)/209=419/209>>419/209 meters long.
    He decides to use only 5/8 of this combined string, so he is using 5/8 * 419/209 = <<(5*419)/(8*209)=2095/1672>>2095/1672 meters of kite string.
    ### Answer: 2095/1672

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:

     Reasoning: Oliver used 2095/1672 meters of kite string earlier.
    He decides to use the same length of string again, so he is now using 2095/1672 + 2095/1672 = <<(2*2095)/1672=4190/1672>>4190/1672 meters of kite string.
    ### Answer: 4190/1672

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:

     Reasoning: Oliver has a kite string that is 26/19 + 7/11 = <<(26*11 + 7*19)/(19*11)=(286+133)/209=419/209>>419/209 meters long.
    He decides to use 26/8 of this combined string, so he is using 26/8 * 419/209 = <<(26*419)/(8*209)=10914/1672>>10914/1672 meters of kite string.
    ### Answer: 10914/1672

Expected answer: 5447/836

Correct? No

🔗 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:

     Reasoning:

    First, let's find the value of 'u' by adding the fractions of snowballs thrown by Mike and John:

    u = 9/19 + 6/8

    To add these fractions, we need a common denominator. The least common multiple of 19 and 8 is 152. So we convert the fractions to have the same denominator:

    u = (9 * 8) / (19 * 8) + (6 * 19) / (8 * 19)

    u = 72/152 + 114/152

    Now we can add the numerators:

    u = (72 + 114) / 152

    u = 186/152

    Now we simplify the fraction:

    u = 93/76

    Now that we have the value of 'u', we can find the value of 'j':

    j = u + 4/1

    j = 93/76 + 4/1

    To add these, we need a common denominator. The least common multiple of 76 and 1 is 76. So we convert the second fraction to have the same denominator:

    j = 93/76 + (4 * 76) / (1 * 76)

    j = 93/76 + 304/76

    Now we can add the numerators:

    j = (93 + 304) / 76

    j = 397/76

    Now we simplify the fraction:

    j = 5.2236842105263155

    Since the number of snowballs must be a whole number, we can round this to the nearest whole number:

    j ≈ 5

    Therefore, Mike had approximately 5 snowballs in total.

    ### Answer: 5

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:

     Reasoning: The first worker packages 26/18 = <<26/18=1.4444444444444444>>1.4444444444444444 pieces of chocolate per minute.
    The second worker packages 15/15 = <<15/15=1>>1 piece of chocolate per minute.
    Together, they can package 1.4444444444444444 + 1 = <<1.4444444444444444+1=2.4444444444444444>>2.4444444444444444 pieces of chocolate per minute.
    ### Answer: 2.4444444444444444

    Note: The answer is rounded to 12 decimal places.

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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:

     Reasoning: Joanna washed 24/20 = <<24/20=1.2>>1.2 batches of small towels and 25/15 = <<25/15=1.6666666666666667>>1.67 (rounded to two decimal places) batches of large towels.
    The total number of batches of towels she washed is 1.2 + 1.67 = <<1.2+1.67=2.87>>2.87 (rounded to two decimal places).
    ### Answer: 2.87 (rounded to two decimal places)

Expected answer: 43/15

Correct? No

🔗 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:

     Reasoning: Debra has (27 / 3) = <<27/3=9>>9 cups of flour from the first recipe.
    She has (11 / 7) = <<11/7=1.5714285714285714>>1.5714285714285714 cups of sugar from the first recipe.
    The ratio of flour to sugar is 9 / 1.5714285714285714 = <<9/1.5714285714285714=5.727272727272727>>5.727272727272727.
    She subtracts (21 / 26) = <<21/26=0.8076923076923077>>0.8076923076923077 from the ratio, which gives her 5.727272727272727 - 0.8076923076923077 = <<5.727272727272727-0.8076923076923077=4.919580419580419>>4.919580419580419.
    She adds (22 / 9) = <<22/9=2.4444444444444444>>2.4444444444444444 cups of flour from the second recipe to the new ratio, which gives her 4.919580419580419 + 2.4444444444444444 = <<4.919580419580419+2.4444444444444444=7.364024863924864>>7.364024863924864 cups of flour in the end.
    ### Answer: 7.364024863924864

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:

     Reasoning: The difference between the number of chickens in the two farms is 26/13 - 9/16 = <<(26/13)-(9/16)=(52/156)-(54/156)=-2/156=-1/78>>-1/78.
    Since the difference is negative, it means that the second farm has more chickens than the first farm.
    The total number of chickens in both farms is 26/13 + 9/16 = <<(26/13)+(9/16)=(52/156)+(54/156)=106/156=53/78>>53/78.
    After a week, the number of chickens multiplied by 19/21, so the new number of chickens is 53/78 \* 19/21 = <<(53/78)\*(19/21)=(1007/1638)=53/87>>53/87.
    ### Answer: 53/87

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:

     Reasoning: The distance flown for each exercise is w = 24/14 miles.
    The total distance flown for both exercises is t = w \* w = (24/14) \* (24/14) = <<(24/14)\*(24/14)=144/196>>144/196 miles.
    ### Answer: 144/196

Expected answer: 144/49

Correct? No

🔗 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:

     Reasoning: The UFO filled 20/16 + 24/25 = <<20/16+24/25=1.25+0.96=2.21>>2.21 of its tank during the two stops.

    However, since the total fraction cannot exceed 1 (which represents a full tank), we need to find the equivalent fraction that represents the total amount of fuel added to the tank.

    To do this, we can add the numerators of the two fractions and keep the denominator the same:

    (20 + 24)/16 = <<(20+24)/16=44/16=2.75>>2.75

    Since this fraction is greater than 1, it means that the UFO was able to fill more than its full tank during the two stops. However, since the tank cannot hold more than its capacity, the total fraction of the tank that the UFO was able to refill is 1.

    ### Answer: 1

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:

     Reasoning: To find the sum of the two fractions, we first need to find a common denominator. The least common multiple of 27 and 26 is 702.

    So, we convert the first fraction to have a denominator of 702:
    (24 / 27) = (24 * 26) / (27 * 26) = 624 / 702

    And we convert the second fraction to have a denominator of 702:
    (30 / 26) = (30 * 27) / (26 * 27) = 810 / 702

    Now we can add the two fractions:
    (624 / 702) + (810 / 702) = (624 + 810) / 702 = 1434 / 702

    Professor Astro finds that the sum of the two fractions is 1434 / 702.
    ### Answer: 1434 / 702

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:

     Reasoning: To find the sum of the two fractions, we first need to find a common denominator. The least common multiple of 27 and 26 is 702.

    So, we convert the first fraction to have a denominator of 702:
    (12 / 27) = (12 * 26) / (27 * 26) = 312 / 702

    And we convert the second fraction to have a denominator of 702:
    (30 / 26) = (30 * 27) / (26 * 27) = 810 / 702

    Now we can add the two fractions:
    (312 / 702) + (810 / 702) = (312 + 810) / 702 = 1122 / 702

    Professor Astro finds that the sum of the two fractions is 1122 / 702.
    ### Answer: 1122 / 702

Expected answer: 187/117

Correct? Yes

🔗 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:

     Reasoning: Kiki ate 11/6 + 11/6 = <<11/6 + 11/6 = 22/6>>22/6 bananas in total.
    ### 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:

     Reasoning: Kiki ate 11 + 11 = <<11 + 11 = 22>>22 bananas in total.
    ### 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:

     Reasoning: Jaden gets 26/14 \* 28/20 = <<(26/14) \* (28/20)=2>>2 gallons of milk from one cow in one day.
    ### Answer: 2

Expected answer: 13/5

Correct? No