🔗 Problem

Problem: In their game, Kyle threw a ball for a distance of 18/4 yards, while Lisa threw the same ball for a distance of 19/9 yards. How many yards did the ball travel in total?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distances thrown by Kyle and Lisa.

    First, let's simplify the fractions:
    Kyle threw the ball for 18/4 yards, which is equal to 9/2 yards (since 18 ÷ 2 = 9 and 4 ÷ 2 = 2).
    Lisa threw the ball for 19/9 yards, which is equal to 2 1/9 yards (since 19 ÷ 9 = 2 with a remainder of 1).

    Now, let's convert the mixed number to an improper fraction:
    2 1/9 = (2 × 9 + 1) / 9 = 19/9.

    Now we can add the distances:
    (9/2) + (19/9) = (81/18) + (38/18) = 119/18.

    To convert the improper fraction back to a mixed number, we can divide the numerator by the denominator:
    119 ÷ 18 = 6 with a remainder of 11, so the mixed number is 6 11/18.

    ### Answer: 6 11/18 yards.

Expected answer: 119/18

Correct? Yes

🔗 Follow-up

Problem: After both Kyle and Lisa's throws, the ball bounced an additional 3/13 yards. Subtract this distance from the total distance the ball traveled when Kyle and Lisa threw it. What is the remaining distance?

Gemma 2B:

    Reasoning: We already found the total distance the ball traveled when Kyle and Lisa threw it: 6 11/18 yards.

    To subtract the additional distance the ball bounced, we need to convert both distances to improper fractions:

    6 11/18 = (6 × 18 + 11) / 18 = 119/18 yards (which we already found)

    3/13 yards is already an improper fraction.

    Now, let's subtract the distances:

    (119/18) - (3/13) = (1691/234) - (54/234) = 1637/234

    To convert the improper fraction back to a mixed number, we can divide the numerator by the denominator:

    1637 ÷ 234 = 7 with a remainder of 13, so the mixed number is 7 13/234.

    ### Answer: 7 13/234 yards.

Expected answer: 1493/234

Correct? No

🔗 Follow-up

Problem: In their game, suppose that Kyle actually threw the ball for a distance of 15/4 yards, while Lisa still threw the ball for 19/9 yards. How many yards did the ball travel in total now?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distances thrown by Kyle and Lisa.

    First, let's simplify the fractions:
    Kyle threw the ball for 15/4 yards, which is equal to 15/4 yards (no simplification needed).
    Lisa threw the ball for 19/9 yards, which is equal to 2 1/9 yards (since 19 ÷ 9 = 2 with a remainder of 1).

    Now, let's convert the mixed number to an improper fraction:
    2 1/9 = (2 × 9 + 1) / 9 = 19/9.

    Now we can add the distances:
    (15/4) + (19/9) = (135/36) + (76/36) = 211/36.

    To convert the improper fraction back to a mixed number, we can divide the numerator by the denominator:
    211 ÷ 36 = 5 with a remainder of 31, so the mixed number is 5 31/36.

    ### Answer: 5 31/36 yards.

Expected answer: 211/36

Correct? Yes

🔗 Problem

Problem: Johnnie the monkey was given 18/7 bananas by the zookeeper in the morning, and 12/14 bananas in the afternoon. In total, how many bananas were given to Johnnie the monkey?

Gemma 2B:

    Reasoning: To find the total number of bananas given to Johnnie, we need to add the number of bananas given in the morning and afternoon. To do this, we need to find a common denominator for the two fractions. The least common multiple of 7 and 14 is 14. So, we can convert 18/7 to an equivalent fraction with a denominator of 14:

    18/7 = (18 × 2)/(7 × 2) = 36/14

    Now we can add the two fractions:

    36/14 + 12/14 = (36 + 12)/14 = 48/14

    We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

    48/14 = (48 ÷ 2)/(14 ÷ 2) = 24/7

    So, Johnnie the monkey was given 24/7 bananas in total.
    ### Answer: 24/7

Expected answer: 24/7

Correct? Yes

🔗 Follow-up

Problem: In addition to the bananas given to Johnnie the monkey in the morning and afternoon, the zookeeper decides to give Johnnie the same total amount of bananas the next day. How many bananas in total did Johnnie the monkey receive over these two days?

Gemma 2B:

    Reasoning: We already found that Johnnie received 24/7 bananas on the first day. Since the zookeeper gives Johnnie the same total amount of bananas the next day, Johnnie will receive another 24/7 bananas.

    To find the total number of bananas Johnnie received over the two days, we can add the number of bananas received on each day:

    24/7 + 24/7 = (24 + 24)/7 = 48/7

    So, Johnnie the monkey received a total of 48/7 bananas over the two days.
    ### Answer: 48/7

Expected answer: 48/7

Correct? Yes

🔗 Problem

Problem: The bottom of a door measures 4/19 inches from the floor, and the top of the door measures 9/10 inches from the ceiling. What is the total distance of the bottom and top of the door from the floor and ceiling, respectively?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distance from the floor to the bottom of the door and the distance from the ceiling to the top of the door.

    The distance from the floor to the bottom of the door is 4/19 inches.
    The distance from the ceiling to the top of the door is 1 - 9/10 = 1/10 inches (since the top of the door is 9/10 inches from the ceiling, the distance from the ceiling to the top of the door is 1 - 9/10).

    Now, we add the two distances: 4/19 + 1/10 = (4*10 + 1*19) / (19*10) = (40 + 19) / 190 = 59 / 190 inches.

    ### Answer: 59/190 inches.

Expected answer: 211/190

Correct? No

🔗 Problem

Problem: Ralph's juice recipe requires 17/3 liters of apple juice. However, he only uses 15/11 liters of it. How many liters of apple juice are left unused?

Gemma 2B:

    Reasoning: To find the amount of apple juice left unused, we need to subtract the amount used from the total amount required.

    First, we need to find a common denominator for the two fractions. The least common multiple of 3 and 11 is 33. So, we can convert both fractions to have a denominator of 33:

    17/3 = (17 × 11) / (3 × 11) = 187/33
    15/11 = (15 × 3) / (11 × 3) = 45/33

    Now, we can subtract the amount used from the total amount required:

    187/33 - 45/33 = (187 - 45) / 33 = 142/33

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. So, the fraction remains the same:

    142/33

    ### Answer: 142/33

Expected answer: 142/33

Correct? Yes

🔗 Follow-up

Problem: After finishing his juice recipe, Ralph decides to add an additional 3/18 liters of apple juice to the mix. How many liters of unused apple juice are left now?

Gemma 2B:

    Reasoning: We already found that 142/33 liters of apple juice were left unused initially. Now, Ralph adds 3/18 liters of apple juice to the mix. To find the new amount of unused apple juice, we need to subtract the additional amount from the initial amount.

    First, we need to find a common denominator for the two fractions. The least common multiple of 33 and 18 is 198. So, we can convert both fractions to have a denominator of 198:

    142/33 = (142 × 6) / (33 × 6) = 852/198
    3/18 = (3 × 11) / (18 × 11) = 33/198

    Now, we can subtract the additional amount from the initial amount:

    852/198 - 33/198 = (852 - 33) / 198 = 819/198

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3. So, we get:

    819 ÷ 3 = 273
    198 ÷ 3 = 66

    ### Answer: 273/66

Expected answer: 91/22

Correct? Yes

🔗 Follow-up

Problem: If Ralph had initially started with 17/3 liters of apple juice but had only used 14/11 liters, how many liters of apple juice would he have left unused then?

Gemma 2B:

    Reasoning: To find the amount of apple juice left unused, we need to subtract the amount used from the total amount required.

    First, we need to find a common denominator for the two fractions. The least common multiple of 3 and 11 is 33. So, we can convert both fractions to have a denominator of 33:

    17/3 = (17 × 11) / (3 × 11) = 187/33
    14/11 = (14 × 3) / (11 × 3) = 42/33

    Now, we can subtract the amount used from the total amount required:

    187/33 - 42/33 = (187 - 42) / 33 = 145/33

    ### Answer: 145/33

Expected answer: 145/33

Correct? Yes

🔗 Problem

Problem: Billy is trying to roller skate in an empty parking lot. He initially travels 4 miles, but rolls back for 17/20 of a mile after spotting a pothole. How many miles did he ultimately travel forward?

Gemma 2B:

    Reasoning: Billy initially travels 4 miles forward.
    He then rolls back 17/20 of a mile, which is equivalent to 0.85 miles (since 17/20 = 0.85).
    So, the total distance he travels forward is 4 - 0.85 = 3.15 miles.
    ### Answer: 3.15 miles

Expected answer: 63/20

Correct? No

🔗 Problem

Problem: A rocket was launched into orbit. On the first day, it traveled 15/3 light years. On the second day, it traveled an additional 2/7 light years. How far has the rocket traveled in total?

Gemma 2B:

    Reasoning: To find the total distance traveled, we need to add the distances traveled on each day.

    On the first day, the rocket traveled 15/3 light years. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3. This gives us 5 light years.

    On the second day, the rocket traveled 2/7 light years.

    To add these distances, we need to find a common denominator, which is 7. So, we can convert 5 light years to 35/7 light years.

    Now, we can add the distances: 35/7 + 2/7 = 37/7 light years.

    ### Answer: 37/7

Expected answer: 37/7

Correct? Yes

🔗 Follow-up

Problem: In a change of earlier data, it was discovered that the rocket only traveled 15/3 light years on the first day. However, on the second day, it actually covered 18/7 light years instead of 2/7 light years. With this new information, how far has the rocket traveled in total?

Gemma 2B:

    Reasoning: To find the total distance traveled, we need to add the distances traveled on each day.

    On the first day, the rocket traveled 15/3 light years. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3. This gives us 5 light years.

    On the second day, the rocket traveled 18/7 light years.

    To add these distances, we need to find a common denominator, which is 7. So, we can convert 5 light years to 35/7 light years.

    Now, we can add the distances: 35/7 + 18/7 = 53/7 light years.

    ### Answer: 53/7

Expected answer: 53/7

Correct? Yes

🔗 Problem

Problem: Captain Silverbeard found 10/13 of a treasure map at one shipwreck site and 16/19 of the same treasure map at another site. What is the total portion of the treasure map that he found?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 13 and 19 is 247. So, we can convert both fractions to have a denominator of 247:

    10/13 = (10*19)/(13*19) = 190/247
    16/19 = (16*13)/(19*13) = 208/247

    Now we can add:

    190/247 + 208/247 = (190+208)/247 = 398/247

    So, Captain Silverbeard found a total of 398/247 of the treasure map.

    ### Answer: 398/247

Expected answer: 398/247

Correct? Yes

🔗 Follow-up

Problem: After Captain Silverbeard finds the portions of the treasure map, he discovers another piece on a third site which is 15/17 of the total map. What is the total portion of the treasure map that Captain Silverbeard has now?

Gemma 2B:

    Reasoning: We already know that Captain Silverbeard found 398/247 of the treasure map from the first two sites. Now, he finds another piece that is 15/17 of the total map. To add this to the previous portion, we need to convert 15/17 to a fraction with a denominator of 247:

    15/17 = (15*247)/(17*247) = 3715/4199

    Now, we can add the two fractions:

    398/247 + 3715/4199

    To add these fractions, we need to find a common denominator. The least common multiple of 247 and 4199 is 1038083. So, we can convert both fractions to have a denominator of 1038083:

    398/247 = (398*4199)/(247*4199) = 1669202/1038083
    3715/4199 = (3715*247)/(4199*247) = 918155/1038083

    Now we can add:

    1669202/1038083 + 918155/1038083 = (1669202+918155)/1038083 = 2587357/1038083

    So, Captain Silverbeard now has a total of 2587357/1038083 of the treasure map.

    ### Answer: 2587357/1038083

Expected answer: 10471/4199

Correct? No

🔗 Follow-up

Problem: Suppose instead of finding 10/13 of the treasure map at the first shipwreck site, Captain Silverbeard found a larger piece which was 10/9 of the total map. Keeping the second portion from the other shipwreck site the same at 16/19, what is the total portion of the treasure map that he found now?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 9 and 19 is 171. So, we can convert both fractions to have a denominator of 171:

    10/9 = (10*19)/(9*19) = 190/171
    16/19 = (16*9)/(19*9) = 144/171

    Now we can add:

    190/171 + 144/171 = (190+144)/171 = 334/171

    So, Captain Silverbeard found a total of 334/171 of the treasure map.

    ### Answer: 334/171

Expected answer: 334/171

Correct? Yes

🔗 Problem

Problem: A hiker decides to walk 9/6 miles North before walking 2/16 miles East. How many miles has the hiker traveled in total?

Gemma 2B:

    Reasoning: To find the total distance traveled, we need to add the distances traveled in each direction. However, we need to make sure the units are the same. Let's convert both fractions to have a common denominator, which is 48.

    9/6 = (9*8)/(6*8) = 72/48
    2/16 = (2*3)/(16*3) = 6/48

    Now we can add the distances:
    72/48 + 6/48 = 78/48

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 6:
    78 ÷ 6 = 13
    48 ÷ 6 = 8

    So, the total distance traveled is 13/8 miles.

    ### Answer: 13/8 miles

Expected answer: 13/8

Correct? Yes

🔗 Follow-up

Problem: In continuation to the previous question, after walking 9/6 miles North and 2/16 miles East, the hiker then decides to continue his journey and walks an additional 8/14 miles South. How many miles has the hiker now traveled in total?

Gemma 2B:

    Reasoning: We already found the total distance traveled by the hiker before walking South: 13/8 miles.

    Now, let's convert the additional distance walked South to have a common denominator with 13/8, which is 8:
    8/14 = (8*4)/(14*4) = 32/56
    To make it easier to add, we can convert 13/8 to have a denominator of 56:
    13/8 = (13*7)/(8*7) = 91/56

    Now we can add the distances:
    91/56 + (-32/56) = 59/56

    The negative sign is used because the hiker walked South, which is opposite to walking North.

    So, the total distance traveled by the hiker now is 59/56 miles.

    ### Answer: 59/56 miles

Expected answer: 123/56

Correct? No

🔗 Follow-up

Problem: In opinion to the previous case, imagine if the hiker had initially decided to walk 10/6 miles North instead of 9/6 miles, while keeping the distance walked East unchanged at 2/16 miles. How many miles would the hiker have then traveled in total?

Gemma 2B:

    Reasoning: Let's convert both fractions to have a common denominator, which is 48.

    10/6 = (10*8)/(6*8) = 80/48
    2/16 = (2*3)/(16*3) = 6/48

    Now we can add the distances:
    80/48 + 6/48 = 86/48

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 2:
    86 ÷ 2 = 43
    48 ÷ 2 = 24

    So, the total distance traveled is 43/24 miles.

    ### Answer: 43/24 miles

Expected answer: 43/24

Correct? Yes

🔗 Problem

Problem: In Jessica's sandbox, she has a pile of sand that is 16/9 cubic feet. She then removes 4/13 cubic feet of sand from the sandbox. How much sand does she have left in her sandbox?

Gemma 2B:

    Reasoning: To find the amount of sand left, we need to subtract the amount of sand removed from the initial amount of sand.

    Initial amount of sand = 16/9 cubic feet
    Amount of sand removed = 4/13 cubic feet

    To subtract these fractions, we need to find a common denominator, which is 117. So, we can convert both fractions to have a denominator of 117:

    Initial amount of sand = (16/9) × (13/13) = 208/117 cubic feet
    Amount of sand removed = (4/13) × (9/9) = 36/117 cubic feet

    Now, we can subtract:

    Amount of sand left = 208/117 - 36/117 = 172/117 cubic feet

    ### Answer: 172/117

Expected answer: 172/117

Correct? Yes

🔗 Follow-up

Problem: Jessica decided to add more sand to her sandbox. She adds an extra 19/15 cubic feet of sand to it. After this, how much sand does she now have in her sandbox?

Gemma 2B:

    Reasoning: We already found the amount of sand Jessica had left in her sandbox after removing some sand: 172/117 cubic feet.

    Now, she adds 19/15 cubic feet of sand to it. To add these fractions, we need to find a common denominator, which is 117 × 15 = 1755. So, we can convert both fractions to have a denominator of 1755:

    Amount of sand left = (172/117) × (15/15) = 2580/1755 cubic feet
    Amount of sand added = (19/15) × (117/117) = 2233/1755 cubic feet

    Now, we can add:

    Total amount of sand = 2580/1755 + 2233/1755 = 4813/1755 cubic feet

    ### Answer: 4813/1755

Expected answer: 1601/585

Correct? No

🔗 Follow-up

Problem: In our previous scenario, let's say that Jessica initially had a smaller pile of sand that was 16/9 cubic feet. If she still removed 4/8 cubic feet of sand as before, how much sand does she now have left in her sandbox?

Gemma 2B:

    Reasoning: To find the amount of sand left, we need to subtract the amount of sand removed from the initial amount of sand.

    Initial amount of sand = 16/9 cubic feet
    Amount of sand removed = 4/8 cubic feet

    To subtract these fractions, we need to find a common denominator, which is 72. So, we can convert both fractions to have a denominator of 72:

    Initial amount of sand = (16/9) × (8/8) = 128/72 cubic feet
    Amount of sand removed = (4/8) × (9/9) = 36/72 cubic feet

    Now, we can subtract:

    Amount of sand left = 128/72 - 36/72 = 92/72 cubic feet

    We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 4:

    Amount of sand left = (92 ÷ 4) / (72 ÷ 4) = 23/18 cubic feet

    ### Answer: 23/18

Expected answer: 23/18

Correct? Yes

🔗 Problem

Problem: Jacob has a piece of rope that is 15/12 meters long and he adds a piece that is 17/17 meters long to it. What is the total length of the rope now?

Gemma 2B:

    Reasoning: To add the lengths of the two pieces of rope, we need to have the same denominator. The least common multiple of 12 and 17 is 204. So, we can convert both fractions to have a denominator of 204:

    15/12 = (15*17)/(12*17) = 255/204
    17/17 = (17*12)/(17*12) = 204/204

    Now we can add the two lengths:

    255/204 + 204/204 = 459/204

    So, the total length of the rope is 459/204 meters.

    ### Answer: 459/204 meters.

Expected answer: 9/4

Correct? Yes

🔗 Follow-up

Problem: Jacob now wants to double the total length of the rope he has. If Jacob starts with the rope that is ((15 / 12) + (17 / 17)) meters long, and then adds another piece of the same length to it, what will be the total length of the combined ropes?

Gemma 2B:

    Reasoning: We already found the total length of the rope Jacob has, which is 459/204 meters. To double the length, we can add another rope of the same length:

    459/204 + 459/204 = 918/204

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

    918 ÷ 6 = 153
    204 ÷ 6 = 34

    So, the total length of the combined ropes is:

    153/34 meters

    ### Answer: 153/34 meters.

Expected answer: 9/2

Correct? Yes

🔗 Follow-up

Problem: Now, suppose Jacob starts with a piece of rope that is 7/12 meters long instead of 15/12 meters. If he still adds the rope piece that is 17/17 meters long to it, what is the total length of the rope now?

Gemma 2B:

    Reasoning: Again, we need to have the same denominator to add the lengths of the two pieces of rope. The least common multiple of 12 and 17 is 204. So, we can convert both fractions to have a denominator of 204:

    7/12 = (7*17)/(12*17) = 119/204
    17/17 = (17*12)/(17*12) = 204/204

    Now we can add the two lengths:

    119/204 + 204/204 = 323/204

    So, the total length of the rope is 323/204 meters.

    ### Answer: 323/204 meters.

Expected answer: 19/12

Correct? Yes

🔗 Problem

Problem: Mark has 1 full pair of pants and another 13/4 pairs from various incomplete sets. How many pairs of pants does he have in total?

Gemma 2B:

    Reasoning: Mark has 1 full pair of pants, which is equivalent to 4/4 pairs.
    He also has 13/4 pairs from various incomplete sets.
    To find the total number of pairs, we add the two amounts together: 4/4 + 13/4 = 17/4.
    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. So, the fraction remains 17/4.
    Since 4 is the denominator, we can convert the fraction to a mixed number by dividing 17 by 4: 17 ÷ 4 = 4 with a remainder of 1. So, the mixed number is 4 1/4.
    ### Answer: 4 1/4.

Expected answer: 17/4

Correct? Yes

🔗 Follow-up

Problem: Mark already had 1 full pair of pants and another 13/4 pairs from various incomplete sets. If he goes shopping and buys an additional 13/3 pairs of pants, how many pairs of pants does he have in total now?

Gemma 2B:

    Reasoning: Mark already had 1 full pair of pants, which is equivalent to 4/4 pairs.
    He also had 13/4 pairs from various incomplete sets.
    To find the total number of pairs he had initially, we add the two amounts together: 4/4 + 13/4 = 17/4.
    Now, he buys an additional 13/3 pairs of pants. To add this to his initial total, we need to find a common denominator between 4 and 3, which is 12. So, we convert both fractions to have a denominator of 12:
    17/4 = (17 × 3)/(4 × 3) = 51/12
    13/3 = (13 × 4)/(3 × 4) = 52/12
    Now, we can add the two amounts together: 51/12 + 52/12 = 103/12.
    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. So, the fraction remains 103/12.
    Since 12 is the denominator, we can convert the fraction to a mixed number by dividing 103 by 12: 103 ÷ 12 = 8 with a remainder of 7. So, the mixed number is 8 7/12.
    ### Answer: 8 7/12.

Expected answer: 103/12

Correct? Yes

🔗 Follow-up

Problem: Instead of starting with 1 full pair of pants and another 13/4 pairs, let's say Mark originally had 1 full pair of pants and 9/4 pairs from various incomplete sets. How many pairs of pants would he then have in total?

Gemma 2B:

    Reasoning: Mark has 1 full pair of pants, which is equivalent to 4/4 pairs.
    He also has 9/4 pairs from various incomplete sets.
    To find the total number of pairs, we add the two amounts together: 4/4 + 9/4 = 13/4.
    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. So, the fraction remains 13/4.
    Since 4 is the denominator, we can convert the fraction to a mixed number by dividing 13 by 4: 13 ÷ 4 = 3 with a remainder of 1. So, the mixed number is 3 1/4.
    ### Answer: 3 1/4.

Expected answer: 13/4

Correct? Yes

🔗 Problem

Problem: Miss Jenny stayed after school to grade papers. She spent 8/8 hours on one subject and an additional 20/19 hours on another subject. How long did she spend grading papers in total?

Gemma 2B:

    Reasoning: Since 8/8 is equal to 1, Miss Jenny spent 1 hour grading one subject.
    To add the hours, we need to find a common denominator for 1 and 20/19.
    The least common multiple of 1 and 19 is 19.
    So, we can rewrite 1 as 19/19.
    Now, we can add the hours: 19/19 + 20/19 = 39/19.
    To simplify, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.
    So, 39/19 is already in simplest form.
    ### Answer: 39/19

Expected answer: 39/19

Correct? Yes

🔗 Follow-up

Problem: After grading papers, Miss Jenny spends an additional 1/12 hours organizing her lesson plans. How long did she spend in total between grading papers and organizing her lesson plans?

Gemma 2B:

    Reasoning: We already found that Miss Jenny spent 39/19 hours grading papers.
    To add the hours, we need to find a common denominator for 39/19 and 1/12.
    The least common multiple of 19 and 12 is 228.
    So, we can rewrite 39/19 as (39*12)/(19*12) = 468/228 and 1/12 as (1*19)/(12*19) = 19/228.
    Now, we can add the hours: 468/228 + 19/228 = 487/228.
    To simplify, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.
    So, 487/228 is already in simplest form.
    ### Answer: 487/228

Expected answer: 487/228

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of spending 20/19 hours on the second subject, Miss Jenny had actually spent 20/13 hours. How long did she spend grading papers in total then?

Gemma 2B:

    Reasoning: Since 8/8 is equal to 1, Miss Jenny spent 1 hour grading one subject.
    To add the hours, we need to find a common denominator for 1 and 20/13.
    The least common multiple of 1 and 13 is 13.
    So, we can rewrite 1 as 13/13.
    Now, we can add the hours: 13/13 + 20/13 = 33/13.
    To simplify, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.
    So, 33/13 is already in simplest form.
    ### Answer: 33/13

Expected answer: 33/13

Correct? Yes

🔗 Problem

Problem: A cloud was observed at a height of 12/3 kms, it later ascended by 15/12 kms. What was the resultant height of the cloud from the ground?

Gemma 2B:

    Reasoning: To find the initial height of the cloud, we need to simplify the fraction 12/3. We can divide both the numerator and the denominator by their greatest common divisor, which is 3. So, 12/3 = 4.

    The cloud ascended by 15/12 kms. To add this to the initial height, we need to find a common denominator, which is 12. So, we can rewrite 4 as 48/12.

    Now, we can add the initial height and the ascended height: 48/12 + 15/12 = 63/12.

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, 63/12 = 21/4 = 5.25.

    ### Answer: 5.25 kms.

Expected answer: 21/4

Correct? No

🔗 Problem

Problem: Jack rides his scooter 3/9 of a mile to the library. After leaving, he scoots another 17/15 of a mile to his grandparents' house. How many miles does Jack ride his scooter in total?

Gemma 2B:

    Reasoning: To find the total distance Jack rode his scooter, we need to add the distances he traveled to the library and to his grandparents' house.

    First, we need to convert both fractions to have a common denominator, which is 45. So, we can rewrite the fractions as:

    3/9 = 15/45
    17/15 = 51/45

    Now, we can add the distances:

    15/45 + 51/45 = 66/45

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    66 ÷ 3 = 22
    45 ÷ 3 = 15

    So, the simplified fraction is:

    22/15

    To convert this to a mixed number, we can divide the numerator by the denominator:

    22 ÷ 15 = 1 with a remainder of 7

    So, the mixed number is:

    1 7/15

    ### Answer: 1 7/15 miles

Expected answer: 22/15

Correct? Yes

🔗 Follow-up

Problem: After visiting his grandparents' house, Jack decides to ride his scooter to the park, which is another 20/12 of mile from his grandparents' house. How many miles does Jack ride his scooter in total now?

Gemma 2B:

    Reasoning: We already found that Jack rode his scooter a total distance of 1 7/15 miles to the library and his grandparents' house. Now, we need to add the distance from his grandparents' house to the park.

    First, we can simplify the fraction 20/12 by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

    20 ÷ 4 = 5
    12 ÷ 4 = 3

    So, the simplified fraction is:

    5/3

    To convert this to a mixed number, we can divide the numerator by the denominator:

    5 ÷ 3 = 1 with a remainder of 2

    So, the mixed number is:

    1 2/3

    Now, we can add this distance to the total distance Jack rode his scooter:

    1 7/15 + 1 2/3

    To add these mixed numbers, we need to convert them to improper fractions:

    1 7/15 = 22/15
    1 2/3 = 5/3

    Now, we can add the fractions:

    22/15 + 5/3

    To add these fractions, we need to find a common denominator, which is 15. So, we can rewrite the fractions as:

    22/15 + 25/15

    Now, we can add the fractions:

    22/15 + 25/15 = 47/15

    To convert this to a mixed number, we can divide the numerator by the denominator:

    47 ÷ 15 = 3 with a remainder of 2

    So, the mixed number is:

    3 2/15

    ### Answer: 3 2/15 miles

Expected answer: 47/15

Correct? Yes

🔗 Follow-up

Problem: Suppose after revisiting the route, Jack realizes the distance from his home to the library is actually 3/9 of a mile instead of 5/9. The distance from the library to his grandparents' house still remains 17/20 of a mile. How many miles does Jack ride his scooter in total then?

Gemma 2B:

    Reasoning: To find the total distance Jack rode his scooter, we need to add the distances he traveled to the library and to his grandparents' house.

    First, we need to convert both fractions to have a common denominator, which is 180. So, we can rewrite the fractions as:

    3/9 = 60/180
    17/20 = 153/180

    Now, we can add the distances:

    60/180 + 153/180 = 213/180

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    213 ÷ 3 = 71
    180 ÷ 3 = 60

    So, the simplified fraction is:

    71/60

    To convert this to a mixed number, we can divide the numerator by the denominator:

    71 ÷ 60 = 1 with a remainder of 11

    So, the mixed number is:

    1 11/60

    ### Answer: 1 11/60 miles

Expected answer: 71/60

Correct? Yes

🔗 Problem

Problem: There are 4 logs in a pile that each burn for 1/16 of an hour. The fire burns out and Tom brings 16 twigs, each of which burns for 1/12 of an hour. What is the total burn time for the logs and twigs?

Gemma 2B:

    Reasoning: The total burn time for the logs is 4 x 1/16 = 1/4 of an hour.
    The total burn time for the twigs is 16 x 1/12 = 4/3 of an hour.
    To add these times, we need to find a common denominator, which is 12. So, we can convert 1/4 to 3/12.
    The total burn time is 3/12 + 4/3 = 3/12 + 16/12 = 19/12 of an hour.
    ### Answer: 19/12 of an hour.

Expected answer: 19/12

Correct? Yes

🔗 Follow-up

Problem: After the logs and twigs burn out, Tom adds 8 pieces of charcoal, each of which burns for 1/5 of an hour. What is the total burn time for the logs, twigs, and charcoal?

Gemma 2B:

    Reasoning: We already found the total burn time for the logs and twigs, which is 19/12 of an hour.
    The total burn time for the charcoal is 8 x 1/5 = 8/5 of an hour.
    To add these times, we need to find a common denominator, which is 60. So, we can convert 19/12 to 95/60 and 8/5 to 48/60.
    The total burn time is 95/60 + 48/60 = 143/60 of an hour.
    ### Answer: 143/60 of an hour.

Expected answer: 191/60

Correct? No

🔗 Follow-up

Problem: In the original scenario, consider that there were actually 4 logs that each burn for 1/16 of an hour, but Tom only added 15 twigs that each burn for 1/12 of an hour instead. What would be the total burn time for the logs and twigs in this situation?

Gemma 2B:

    Reasoning: The total burn time for the logs is still 4 x 1/16 = 1/4 of an hour.
    The total burn time for the twigs is 15 x 1/12 = 15/12 = 5/4 of an hour.
    To add these times, we need to find a common denominator, which is 12. So, we can convert 1/4 to 3/12.
    The total burn time is 3/12 + 5/4 = 3/12 + 15/12 = 18/12 of an hour.
    ### Answer: 18/12 of an hour or 1 1/2 hours.

Expected answer: 3/2

Correct? Yes

🔗 Problem

Problem: If a ring maker uses 12/16 ounces of a silver for the base of the ring and 16/2 ounces to make the rest of the ring, how many ounces of silver did the ring maker use in total?

Gemma 2B:

    Reasoning: To find the total amount of silver used, we need to add the amount used for the base of the ring and the amount used for the rest of the ring.

    First, let's simplify the fractions:
    12/16 = 3/4 ounces (base of the ring)
    16/2 = 8 ounces (rest of the ring)

    Now, add the two amounts:
    3/4 + 8 = 3/4 + 32/4 = 35/4 = 8 3/4 ounces

    ### Answer: 8 3/4 ounces

Expected answer: 35/4

Correct? Yes

🔗 Follow-up

Problem: The ring maker decides to add an ornamental filigree to the ring, which requires an additional 18/20 ounces of silver. How many total ounces of silver did the ring maker use including the filigree?

Gemma 2B:

    Reasoning: We already found the total amount of silver used for the ring: 8 3/4 ounces.

    To add the amount of silver needed for the filigree, we need to convert the mixed number to an improper fraction:
    8 3/4 = 35/4 ounces

    Now, let's simplify the fraction for the filigree:
    18/20 = 9/10 ounces

    Add the two amounts:
    35/4 + 9/10 = 35/4 + 9/10 = 175/20 + 36/20 = 211/20 = 10 11/20 ounces

    ### Answer: 10 11/20 ounces

Expected answer: 193/20

Correct? No

🔗 Follow-up

Problem: If initially, the ring maker used 10/16 ounces of a silver for the base of the ring instead of 12/16 ounces, while still using 16/2 ounces to make the rest of the ring, how many total ounces of silver did the ring maker use then?

Gemma 2B:

    Reasoning: To find the total amount of silver used, we need to add the amount used for the base of the ring and the amount used for the rest of the ring.

    First, let's simplify the fractions:
    10/16 = 5/8 ounces (base of the ring)
    16/2 = 8 ounces (rest of the ring)

    Now, add the two amounts:
    5/8 + 8 = 5/8 + 64/8 = 69/8 = 8 5/8 ounces

    ### Answer: 8 5/8 ounces

Expected answer: 69/8

Correct? Yes

🔗 Problem

Problem: A farmer has an apple tree that produced 10/11 bushels of apples in the morning and 17/11 bushels in the afternoon. How many bushels of apples did the tree produce in total?

Gemma 2B:

    Reasoning: To find the total number of bushels of apples produced, we need to add the number of bushels produced in the morning and afternoon.

    In the morning, the tree produced 10/11 bushels of apples.
    In the afternoon, the tree produced 17/11 bushels of apples.

    To add these fractions, we need to have the same denominator, which is 11 in this case. So, we can add the numerators (10 and 17) and keep the same denominator:

    (10 + 17)/11 = 27/11

    So, the tree produced 27/11 bushels of apples in total.

    ### Answer: 27/11

Expected answer: 27/11

Correct? Yes

🔗 Follow-up

Problem: Now assume the farmer's first apple tree produced 10/9 bushels instead of 10/11 bushels in the morning. With the same amount of apples in the afternoon, how many bushels of apples did this tree produce in one day?

Gemma 2B:

    Reasoning: To find the total number of bushels of apples produced, we need to add the number of bushels produced in the morning and afternoon.

    In the morning, the tree produced 10/9 bushels of apples.
    In the afternoon, the tree produced 17/11 bushels of apples.

    To add these fractions, we need to find the least common multiple (LCM) of 9 and 11, which is 99. So, we can convert both fractions to have a denominator of 99:

    (10/9) × (11/11) = 110/99
    (17/11) × (9/9) = 153/99

    Now we can add the fractions:

    (110 + 153)/99 = 263/99

    So, the tree produced 263/99 bushels of apples in one day.

    ### Answer: 263/99

Expected answer: 263/99

Correct? Yes

🔗 Problem

Problem: If Sam's binoculars increase his range of sight by 3/14 of a mile and Joe's binoculars increase his range of sight by exactly 1 mile (16/16), what is their combined range increase when they use the binoculars one after the other?

Gemma 2B:

    Reasoning: To find the combined range increase, we need to add the range increases of Sam's and Joe's binoculars.

    Sam's binoculars increase his range of sight by 3/14 of a mile.
    Joe's binoculars increase his range of sight by 16/16 = 1 mile.

    To add these fractions, we need to find a common denominator, which is 14. So, we can convert 1 mile to 14/14 miles.

    Now, we can add the fractions:
    3/14 + 14/14 = 17/14

    To simplify this fraction, we can convert it to a mixed number:
    17/14 = 1 3/14

    So, the combined range increase when they use the binoculars one after the other is 1 3/14 miles.

    ### Answer: 1 3/14 miles

Expected answer: 17/14

Correct? Yes

🔗 Follow-up

Problem: If Sam's binoculars instead increased his range of sight by 4/14 of a mile, while Joe's binoculars still increase his range of sight by exactly 1 mile, how much would their combined range increase be when they use the binoculars one after the other?

Gemma 2B:

    Reasoning: To find the combined range increase, we need to add the range increases of Sam's and Joe's binoculars.

    Sam's binoculars increase his range of sight by 4/14 of a mile.
    Joe's binoculars increase his range of sight by 14/14 = 1 mile.

    To add these fractions, we can add the numerators (4 + 14) and keep the same denominator (14):
    (4 + 14)/14 = 18/14

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
    18/14 = 9/7

    So, the combined range increase when they use the binoculars one after the other is 9/7 miles.

    ### Answer: 9/7 miles

Expected answer: 9/7

Correct? Yes

🔗 Problem

Problem: Maria uses 15/10 yards of fabric for a section of a blanket and 9/18 more yards for another section. What is the total length of fabric Maria uses for these two sections?

Gemma 2B:

    Reasoning: To find the total length of fabric Maria uses, we need to add the lengths of fabric used for both sections.

    For the first section, Maria uses 15/10 yards of fabric. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

    15 ÷ 5 = 3
    10 ÷ 5 = 2

    So, Maria uses 3/2 yards of fabric for the first section.

    For the second section, Maria uses 9/18 more yards of fabric. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9:

    9 ÷ 9 = 1
    18 ÷ 9 = 2

    So, Maria uses 1/2 yards of fabric for the second section.

    To find the total length of fabric, we add the lengths of fabric used for both sections:

    3/2 + 1/2 = 4/2

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

    4 ÷ 2 = 2
    2 ÷ 2 = 1

    So, Maria uses 2 yards of fabric for both sections.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: After reviewing her measurements, Maria realizes that she actually used a smaller piece of fabric for the second section of the blanket. Instead of the 9/18 yards she originally thought, she actually used only 6/18 yards of fabric. What is the total length of fabric that Maria used for these two sections of the blanket now?

Gemma 2B:

    Reasoning: We already know that Maria used 3/2 yards of fabric for the first section. For the second section, she used 6/18 yards of fabric. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

    6 ÷ 6 = 1
    18 ÷ 6 = 3

    So, Maria used 1/3 yards of fabric for the second section.

    To find the total length of fabric, we add the lengths of fabric used for both sections:

    3/2 + 1/3

    To add these fractions, we need to find a common denominator, which is 6. We can convert both fractions to have a denominator of 6:

    3/2 = 9/6
    1/3 = 2/6

    Now we can add:

    9/6 + 2/6 = 11/6

    So, Maria used a total of 11/6 yards of fabric for both sections.

    ### Answer: 11/6

Expected answer: 11/6

Correct? Yes

🔗 Problem

Problem: A turtle walks 10/5 miles forward, then walks backward 5/16 mile. How many miles has the turtle actually covered from its starting point?

Gemma 2B:

    Reasoning: The turtle walks 10/5 = 2 miles forward.
    Then, it walks 5/16 miles backward.
    To find the distance from the starting point, subtract the distance walked backward from the distance walked forward: 2 - 5/16 = 2 - 0.3125 = 1.6875 miles.
    ### Answer: 1.6875 miles.

Expected answer: 27/16

Correct? No

🔗 Problem

Problem: A painter uses 18/11 liters of blue paint and 1/8 liters of white paint to mix a shade of sky blue. How much paint in liters did he use in total?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 11 and 8 is 88. So, we can convert both fractions to have a denominator of 88:

    (18/11) = (144/88)
    (1/8) = (11/88)

    Now we can add:

    (144/88) + (11/88) = (155/88)

    To convert this back to a mixed number, we can divide the numerator by the denominator:

    155 ÷ 88 = 1 with a remainder of 77

    So, the total amount of paint used is 1 77/88 liters.

    ### Answer: 1 77/88 liters.

Expected answer: 155/88

Correct? No

🔗 Problem

Problem: A computer program executed 8 tasks in 4 minutes and then executed another 20 tasks in 14 minutes. What is the total number of tasks it executed per minute?

Gemma 2B:

    Reasoning: The program executed 8 tasks in 4 minutes, so it executed 8/4 = 2 tasks per minute.
    Then, it executed 20 tasks in 14 minutes, so it executed 20/14 = 10/7 tasks per minute.
    The total number of tasks it executed per minute is 2 + 10/7 = (14 + 10)/7 = 24/7 tasks per minute.
    ### Answer: 24/7

Expected answer: 24/7

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, let's say that instead of executing 20 tasks in 14 minutes, the computer program executed 20 tasks in 6 minutes. What would be the total number of tasks that the program would execute per minute then?

Gemma 2B:

    Reasoning: The program executed 8 tasks in 4 minutes, so it executed 8/4 = 2 tasks per minute.
    Then, it executed 20 tasks in 6 minutes, so it executed 20/6 = 10/3 tasks per minute.
    The total number of tasks it executed per minute is 2 + 10/3 = (6 + 10)/3 = 16/3 tasks per minute.
    ### Answer: 16/3

Expected answer: 16/3

Correct? Yes

🔗 Problem

Problem: At the end of a rainbow, there are pots filled with magical gold coins. One pot contains 12/13 of a pound of gold coins while another contains 3/2 pounds of gold coins. How much gold is there in total?

Gemma 2B:

    Reasoning: To find the total amount of gold, we need to add the amount of gold in both pots. However, the amounts are given in different units, so we need to convert them to the same unit. Let's convert both amounts to pounds.

    The first pot contains 12/13 of a pound, which is already in pounds.

    The second pot contains 3/2 pounds, which is already in pounds.

    Now, we can add the amounts:

    12/13 + 3/2 = ?

    To add these fractions, we need to find a common denominator, which is 26. So, we can convert both fractions to have a denominator of 26:

    12/13 = 24/26
    3/2 = 39/26

    Now, we can add:

    24/26 + 39/26 = 63/26

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 13:

    63 ÷ 13 = 4.85
    26 ÷ 13 = 2

    So, the total amount of gold is 4.85/2 pounds.

    ### Answer: 4.85/2 pounds or 2.425 pounds.

Expected answer: 63/26

Correct? No

🔗 Problem

Problem: In space, an alien named Zorg receives a video message from earth that is divided into parts. The first part of the message is 4/4 hours long, and the second part is 11/1 hour long. How long in total is the message Zorg received?

Gemma 2B:

    Reasoning: To find the total length of the message, we need to add the lengths of the two parts.

    The first part is 4/4 hours long, which is equal to 1 hour (since 4/4 = 1).

    The second part is 11/1 hours long, which is equal to 11 hours.

    To find the total length, we add the lengths of the two parts: 1 hour + 11 hours = 12 hours.

    ### Answer: 12 hours

Expected answer: 12

Correct? Yes

🔗 Follow-up

Problem: After watching the original message, Zorg receives an additional part of the message from earth that is 7/8 hours long. What is the total length of all parts of the message that Zorg received?

Gemma 2B:

    Reasoning: We already know that the total length of the original message is 12 hours.

    The additional part of the message is 7/8 hours long. To add this to the total length, we need to convert the fraction to a decimal: 7/8 = 0.875 hours.

    Now, we add the length of the additional part to the total length of the original message: 12 hours + 0.875 hours = 12.875 hours.

    ### Answer: 12.875 hours

Expected answer: 103/8

Correct? No

🔗 Follow-up

Problem: Upon reviewing the original video message, Zorg realised that the first part of the video message was actually half as long at 4/8 hours instead of 4/4. The second part of the message still remains 11/1 hour long. What is the total length of the message that Zorg has corrected?

Gemma 2B:

    Reasoning: Since the first part is now 4/8 hours long, we can simplify it by dividing both numerator and denominator by 2, which gives us 2/4 hours. This is equal to 1/2 hour or 0.5 hours.

    The second part remains 11/1 hours long, which is equal to 11 hours.

    To find the total length, we add the lengths of the two parts: 0.5 hours + 11 hours = 11.5 hours.

    ### Answer: 11.5 hours

Expected answer: 23/2

Correct? No

🔗 Problem

Problem: In a park, 10 ducks are equally distributed among 5 ponds, implying each pond has 10 / 5 ducks. In the same park, 8 fish are distributed among 10 small pools, with each pool having 8 / 10 fish. How many animals are there in each pond and pool combined?

Gemma 2B:

    Reasoning: Each pond has 10 / 5 = 2 ducks.
    Each pool has 8 / 10 = 0.8 fish.
    In each pond and pool combined, there are 2 + 0.8 = 2.8 animals.
    ### Answer: 2.8

Expected answer: 14/5

Correct? Yes

🔗 Follow-up

Problem: In the same park, there are also 12 frogs evenly distributed across 4 lily pads, meaning each lily pad has 12 / 4 frogs. Adding this to the previous sum of animals in each pond and pool, what is the total number of animals on each respective setting (pond, pool, lily pad) combined?

Gemma 2B:

    Reasoning: Each lily pad has 12 / 4 = 3 frogs.
    In each pond and pool combined, there are 2.8 animals (from previous problem).
    In each lily pad, there are 3 frogs.
    In each pond, pool, and lily pad combined, there are 2.8 + 3 = 5.8 animals.
    ### Answer: 5.8

Expected answer: 29/5

Correct? No

🔗 Follow-up

Problem: In the same park, let's consider a different scenario. Suppose there are now only 2 ducks equally distributed among 5 ponds. Given that each pond will have 2 / 5 ducks and each small pool still has 8 / 10 fish, what will be the total number of animals across each pond and pool in this new scenario?

Gemma 2B:

    Reasoning: Each pond has 2 / 5 = 0.4 ducks.
    Each pool has 8 / 10 = 0.8 fish.
    In each pond and pool combined, there are 0.4 + 0.8 = 1.2 animals.
    ### Answer: 1.2

Expected answer: 6/5

Correct? No

🔗 Problem

Problem: On a map, 15/11 inches represents the distance between Town A and Town B, and 16/15 inches represents the distance between Town B and Town C. What is the total distance between Town A and Town C on the map?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distances between Town A and Town B, and Town B and Town C. However, we need to have a common denominator to add these fractions. The least common multiple of 11 and 15 is 165. So, we can convert both fractions to have a denominator of 165:

    15/11 = (15*15)/(11*15) = 225/165
    16/15 = (16*11)/(15*11) = 176/165

    Now we can add the distances:

    225/165 + 176/165 = (225 + 176)/165 = 401/165

    ### Answer: 401/165

Expected answer: 401/165

Correct? Yes

🔗 Follow-up

Problem: On a map, 15/11 inches represents the distance between Town A and Town B, and 16/15 inches represents the distance between Town B and Town C. After measuring the distance between Town C and Town D, which was found to be 20/5 inches. What is the total distance between Town A and Town D on the map?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distances between Town A and Town B, Town B and Town C, and Town C and Town D. However, we need to have a common denominator to add these fractions. The least common multiple of 11, 15, and 5 is 165. So, we can convert all fractions to have a denominator of 165:

    15/11 = (15*15)/(11*15) = 225/165
    16/15 = (16*11)/(15*11) = 176/165
    20/5 = (20*33)/(5*33) = 660/165

    Now we can add the distances:

    225/165 + 176/165 + 660/165 = (225 + 176 + 660)/165 = 1061/165

    ### Answer: 1061/165

Expected answer: 1061/165

Correct? Yes

🔗 Follow-up

Problem: On the same map, suppose the distance between Town A and Town B is not 15/11 but 15/11 inches, and 16/7 inches represents the distance between Town B and Town C. Now, what would be the total distance on the map from Town A to Town C?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distances between Town A and Town B, and Town B and Town C. We are given that the distance between Town A and Town B is 15/11 inches, and the distance between Town B and Town C is 16/7 inches.

    To add these distances, we need to have a common denominator. The least common multiple of 11 and 7 is 77. So, we can convert both distances to have a denominator of 77:

    15/11 = (15*7)/(11*7) = 105/77
    16/7 = (16*11)/(7*11) = 176/77

    Now we can add the distances:

    105/77 + 176/77 = (105 + 176)/77 = 281/77

    ### Answer: 281/77 inches

Expected answer: 281/77

Correct? Yes

🔗 Problem

Problem: A soap company produces 13/18 tons of Soap A and 4/6 tons of Soap B in a day. How many tons of soap do they produce in total each day?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 18 and 6 is 18. We can rewrite 4/6 as 8/18. Then, we can add the fractions:

    13/18 + 8/18 = 21/18

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    21 ÷ 3 = 7
    18 ÷ 3 = 6

    So, the soap company produces 7/6 tons of soap in total each day. To convert this to a mixed number, we can divide the numerator by the denominator:

    7 ÷ 6 = 1 with a remainder of 1

    So, the soap company produces 1 1/6 tons of soap in total each day.

    ### Answer: 1 1/6 tons

Expected answer: 25/18

Correct? No

🔗 Problem

Problem: Mark bought a sleeping bag that was 19/2 feet long. However, he decides to cut off 13/12 feet from it to fit his height. How long is his sleeping bag now?

Gemma 2B:

    Reasoning: To find the length of the sleeping bag Mark bought, we need to convert the mixed unit to a whole number. 19/2 = 9.5 feet.

    Mark cut off 13/12 feet from the sleeping bag. To subtract this from the original length, we need to convert 13/12 to a decimal: 13/12 = 1.083 feet.

    Now, we can subtract the length Mark cut off from the original length: 9.5 - 1.083 = 8.417 feet.

    ### Answer: 8.417 feet

Expected answer: 101/12

Correct? No

🔗 Problem

Problem: At the zoo, Mary feeds 6/20 pounds of food to the monkeys, and 18/15 pounds of food to the giraffes. How many pounds of food in total has she given to the monkeys and giraffes?

Gemma 2B:

    Reasoning: To find the total amount of food Mary has given to the monkeys and giraffes, we need to add the amount of food given to each.

    First, let's convert the fractions to decimals:
    6/20 = 0.3 pounds of food to the monkeys
    18/15 = 1.2 pounds of food to the giraffes

    Now, we can add the amounts together:
    0.3 + 1.2 = 1.5 pounds

    ### Answer: 1.5

Expected answer: 3/2

Correct? Yes

🔗 Follow-up

Problem: After feeding the monkeys and giraffes, Mary then feeds the elephants 19/11 pounds of food. How many pounds of food in total has she given to the monkeys, giraffes, and elephants at the zoo?

Gemma 2B:

    Reasoning: We already know that Mary gave 1.5 pounds of food to the monkeys and giraffes. Now, we need to add the amount of food given to the elephants.

    First, let's convert the fraction to a decimal:
    19/11 = 1.727 pounds of food to the elephants

    Now, we can add the amounts together:
    1.5 + 1.727 = 3.227 pounds

    ### Answer: 3.227

Expected answer: 71/22

Correct? No

🔗 Follow-up

Problem: Originally, Mary had given the monkeys 6/20 pounds of food and the giraffes 18/15 pounds of food. But what if she had made a mistake, and she actually gave the giraffes 18/19 pounds of food instead? How many pounds of food in total did she then give to the monkeys and giraffes?

Gemma 2B:

    Reasoning: Let's recalculate the total amount of food Mary has given to the monkeys and giraffes with the corrected amount for the giraffes.

    First, let's convert the fractions to decimals:
    6/20 = 0.3 pounds of food to the monkeys
    18/19 = 0.947 (approximately) pounds of food to the giraffes

    Now, we can add the amounts together:
    0.3 + 0.947 = 1.247 pounds

    ### Answer: 1.247

Expected answer: 237/190

Correct? No

🔗 Problem

Problem: Albert has a deck of 20/17 full sets of cards to start. He then collects another full set of 4/1 cards. How many full sets of cards does he have now?

Gemma 2B:

    Reasoning: To find the total number of full sets of cards Albert has, we need to add the number of sets he had initially to the number of sets he collected.

    First, let's convert the mixed numbers to improper fractions:
    20 17/ = 377/17 and 4 1/ = 5/1

    Now, we can add the number of sets:
    377/17 + 5/1 = 377/17 + 85/17 = 462/17

    So, Albert has 462/17 full sets of cards now.
    ### Answer: 462/17

Expected answer: 88/17

Correct? No

🔗 Problem

Problem: A jeweler has 5/14 pound of silver and adds 18/19 pounds more to the supply. How many pounds of silver does the jeweler have now to make rings?

Gemma 2B:

    Reasoning: To find the total amount of silver, we need to add the initial amount to the additional amount. To do this, we need to have the same denominator for both fractions. The least common multiple (LCM) of 14 and 19 is 266. So, we can convert both fractions to have a denominator of 266:

    5/14 = (5*19)/(14*19) = 95/266
    18/19 = (18*14)/(19*14) = 252/266

    Now we can add:

    95/266 + 252/266 = 347/266

    To simplify, we can divide both numerator and denominator by their greatest common divisor (GCD), which is 7:

    347 ÷ 7 = 49.57 (approximately)
    266 ÷ 7 = 38

    So, the jeweler has approximately 49.57/38 pounds of silver. Since we can't have a fraction of a pound, we can convert the mixed number to a decimal:

    49.57 ÷ 38 ≈ 1.30 pounds

    ### Answer: 1.30 pounds

Expected answer: 347/266

Correct? No

🔗 Problem

Problem: A turtle starts at a point and moves 11 meters northward. Then, it moves 15/15 of a meter back towards the starting point. How many meters is the turtle from its starting point after these two movement?

Gemma 2B:

    Reasoning: The turtle moves 11 meters northward, so it is 11 meters away from the starting point.

    Then, it moves 15/15 = 1 meter back towards the starting point, which means it moves 1 meter southward.

    So, the turtle is now 11 - 1 = 10 meters away from the starting point.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: Continuing from the prior situation, the turtle then decided to move further, walking an additional 15/20 of a meter towards the same direction. How many meters is the turtle from its original starting point now?

Gemma 2B:

    Reasoning: The turtle was 10 meters away from the starting point.

    Then, it moves an additional 15/20 = 0.75 meters in the same direction (southward).

    So, the turtle is now 10 - 0.75 = 9.25 meters away from the starting point.

    ### Answer: 9.25

Expected answer: 43/4

Correct? No

🔗 Follow-up

Problem: Reconsider the previous scenario, but this time the turtle returns 15/8 of a meter back towards the starting point instead of the former 15/15 meters. Now, how many meters is the turtle from its starting point after these two movements?

Gemma 2B:

    Reasoning: The turtle moves 11 meters northward, so it is 11 meters away from the starting point.

    Then, it moves 15/8 = 1.875 meters back towards the starting point, which means it moves 1.875 meters southward.

    So, the turtle is now 11 - 1.875 = 9.125 meters away from the starting point.

    ### Answer: 9.125

Expected answer: 73/8

Correct? Yes

🔗 Problem

Problem: Chloe has a chocolate bar that is 19/2 ounces. If she eats a piece that is 17/2 ounces, how many ounces of chocolate does she have left?

Gemma 2B:

    Reasoning: Chloe starts with 19/2 ounces of chocolate.
    She eats 17/2 ounces, so we need to subtract that from the total amount: 19/2 - 17/2.
    To subtract fractions with the same denominator, we subtract the numerators: 19 - 17 = 2.
    So, we have 2/2 ounces left, which simplifies to 1 ounce.
    ### Answer: 1.

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: After Chloe eats a piece of the chocolate bar, she decides to add a piece from another chocolate bar. The piece from the other bar weighs 4/14 ounces. How many ounces of chocolate does Chloe have now?

Gemma 2B:

    Reasoning: Chloe had 1 ounce of chocolate left after eating the first piece.
    She adds a piece that weighs 4/14 ounces. To add this to the 1 ounce, we need to convert 4/14 to a decimal: 4/14 = 2/7 = 0.286 (approximately).
    Now, we add 1 + 0.286 = 1.286 ounces.
    ### Answer: 1.286.

Expected answer: 9/7

Correct? No

🔗 Follow-up

Problem: Originally, Chloe had a chocolate bar that was 19/2 ounces. What if instead, at the beginning she had eaten a piece that was 9/2 ounces? How many ounces of chocolate would she have had left then?

Gemma 2B:

    Reasoning: Chloe starts with 19/2 ounces of chocolate.
    She eats 9/2 ounces, so we need to subtract that from the total amount: 19/2 - 9/2.
    To subtract fractions with the same denominator, we subtract the numerators: 19 - 9 = 10.
    So, we have 10/2 ounces left, which simplifies to 5 ounces.
    ### Answer: 5.

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: Sammy has a backpack with a capacity of 20/9 liters. If he adds another pouch to the backpack that can hold 8/4 more liters, what will be the total capacity of his backpack?

Gemma 2B:

    Reasoning: To find the total capacity of Sammy's backpack, we need to add the capacity of the original backpack and the additional pouch.

    The capacity of the original backpack is 20/9 liters.

    The capacity of the additional pouch is 8/4 liters, which can be simplified to 2 liters (since 8 ÷ 4 = 2).

    To add these capacities, we need to have the same units, so we can convert the original capacity to a decimal: 20/9 ≈ 2.22 liters.

    Now, we can add the capacities: 2.22 liters + 2 liters = 4.22 liters.

    ### Answer: 4.22 liters

Expected answer: 38/9

Correct? No

🔗 Problem

Problem: Captain Hook has 11/8 ounces of gold. He finds an additional 5/5 ounces of gold on his latest treasure hunt. What is the total weight of the gold Captain Hook now has?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 8 and 5 is 40. So, we can convert both fractions to have a denominator of 40:

    11/8 = (11*5)/(8*5) = 55/40
    5/5 = (5*8)/(5*8) = 40/40

    Now we can add:

    55/40 + 40/40 = 95/40

    So, Captain Hook now has a total of 95/40 ounces of gold.

    ### Answer: 95/40

Expected answer: 19/8

Correct? Yes

🔗 Follow-up

Problem: After counting his newly found gold, Captain Hook discovers an additional 7/11 ounces of gold hidden in a small pouch he had forgotten about. What is the total weight of all the gold Captain Hook now has?

Gemma 2B:

    Reasoning: To add this new amount to the total, we need to find a common denominator. The least common multiple of 40 and 11 is 440. So, we can convert both fractions to have a denominator of 440:

    95/40 = (95*11)/(40*11) = 1045/440
    7/11 = (7*40)/(11*40) = 280/440

    Now we can add:

    1045/440 + 280/440 = 1325/440

    So, Captain Hook now has a total of 1325/440 ounces of gold.

    ### Answer: 1325/440

Expected answer: 265/88

Correct? Yes

🔗 Follow-up

Problem: In the previous treasure hunt, Captain Hook had originally found 11/8 ounces of gold. But let's say, instead of finding 5/5 ounces of gold as he did in his latest treasure hunt, he discovered 7/5 ounces of gold. How much total weight of gold would Captain Hook have had then?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 8 and 5 is 40. So, we can convert both fractions to have a denominator of 40:

    11/8 = (11*5)/(8*5) = 55/40
    7/5 = (7*8)/(5*8) = 56/40

    Now we can add:

    55/40 + 56/40 = 111/40

    So, Captain Hook would have had a total of 111/40 ounces of gold.

    ### Answer: 111/40

Expected answer: 111/40

Correct? Yes

🔗 Problem

Problem: If Jake originally had 9/10 of a dollar and then received an additional 20/15 of a dollar, how much money does he have in his wallet now?

Gemma 2B:

    Reasoning: First, we need to find a common denominator for the two fractions. The least common multiple of 10 and 15 is 30. So, we can convert both fractions to have a denominator of 30:

    9/10 = (9*3)/(10*3) = 27/30
    20/15 = (20*2)/(15*2) = 40/30

    Now, we can add the two fractions:

    27/30 + 40/30 = 67/30

    To convert this to a mixed number, we can divide the numerator by the denominator:

    67 ÷ 30 = 2 with a remainder of 7

    So, the mixed number is 2 7/30.

    ### Answer: 2 7/30 dollars

Expected answer: 67/30

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous problem, if Jake found an additional 11/5 of a dollar on the street, how much money does he have in his wallet now?

Gemma 2B:

    Reasoning: First, we need to convert the mixed number 2 7/30 to an improper fraction:

    2 7/30 = (2*30 + 7)/30 = 67/30

    Now, we can add the additional 11/5 dollars Jake found:

    67/30 + 11/5 = ?

    To add these fractions, we need to find a common denominator. The least common multiple of 30 and 5 is 30. So, we can convert the second fraction to have a denominator of 30:

    11/5 = (11*6)/(5*6) = 66/30

    Now, we can add the two fractions:

    67/30 + 66/30 = 133/30

    To convert this to a mixed number, we can divide the numerator by the denominator:

    133 ÷ 30 = 4 with a remainder of 13

    So, the mixed number is 4 13/30.

    ### Answer: 4 13/30 dollars

Expected answer: 133/30

Correct? Yes

🔗 Follow-up

Problem: Following up on the original scenario, if Jake initially had 9/8 of a dollar instead of 9/10 of a dollar, and then received an additional 20/15 of a dollar, how much money does he have in his wallet now?

Gemma 2B:

    Reasoning: First, we need to find a common denominator for the two fractions. The least common multiple of 8 and 15 is 120. So, we can convert both fractions to have a denominator of 120:

    9/8 = (9*15)/(8*15) = 135/120
    20/15 = (20*8)/(15*8) = 160/120

    Now, we can add the two fractions:

    135/120 + 160/120 = 295/120

    To convert this to a mixed number, we can divide the numerator by the denominator:

    295 ÷ 120 = 2 with a remainder of 55

    So, the mixed number is 2 55/120.

    We can simplify the fraction 55/120 by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

    55 ÷ 5 = 11
    120 ÷ 5 = 24

    So, the simplified mixed number is 2 11/24.

    ### Answer: 2 11/24 dollars

Expected answer: 59/24

Correct? Yes

🔗 Problem

Problem: Paul has built the front half of a chair that measures 5/2 feet high. He also constructs the back portion of the chair that measures 20/14 feet. What is the combined height of the front and back portions of the chair that Paul has constructed?

Gemma 2B:

    Reasoning: To find the combined height, we need to add the heights of the front and back portions of the chair.

    The front half of the chair measures 5/2 feet high. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. So, the front half measures 5/2 = 2.5 feet high.

    The back portion of the chair measures 20/14 feet high. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2. So, the back portion measures 20/14 = 10/7 = 1.43 feet high (approximately).

    Now, we can add the heights of the front and back portions: 2.5 + 1.43 = 3.93 feet.

    ### Answer: 3.93 feet

Expected answer: 55/14

Correct? No

🔗 Problem

Problem: John has 5 shirts and he donated 12/9 of them to charity. How many shirts does he have left?

Gemma 2B:

    Reasoning: To find the number of shirts John donated, we need to multiply 5 by 12/9. This is equivalent to multiplying 5 by 12 and then dividing by 9.

    5 × 12 = 60
    60 ÷ 9 = 20/3 = 6.67 (but we can't donate a fraction of a shirt, so we'll round down to 6)

    John donated 6 shirts to charity. To find the number of shirts he has left, we subtract the number of shirts he donated from the total number of shirts he had:

    5 - 6 = -1 (but we can't have a negative number of shirts, so we'll re-evaluate the problem)

    Let's convert the fraction 12/9 to a decimal: 12/9 = 1.33. This means John donated 1.33 times as many shirts as he had, which doesn't make sense. The problem is likely incorrect, and we need more information to solve it accurately.

    However, if we assume the problem is correct, we can continue with the calculation:

    John donated 1.33 × 5 = 6.67 shirts (again, we can't donate a fraction of a shirt, so we'll round down to 6)

    John has 5 - 6 = -1 shirts left (but we can't have a negative number of shirts)

    ### Answer: The problem is likely incorrect, and we need more information to solve it accurately.

Expected answer: 11/3

Correct? No

🔗 Problem

Problem: Bob has a jacket that measures 14/3 meters in length. However, he finds the jacket is slightly too long for him so he decides to cut off 14/16 meter from the original length. What is the length of Bob's jacket after the alteration?

Gemma 2B:

    Reasoning: To find the length of the jacket after the alteration, we need to subtract the length cut off from the original length.

    Original length = 14/3 meters
    Length cut off = 14/16 meters

    To subtract these fractions, we need to find a common denominator, which is 48. So, we can convert both fractions to have a denominator of 48:

    Original length = (14/3) × (16/16) = 224/48 meters
    Length cut off = (14/16) × (3/3) = 42/48 meters

    Now, we can subtract:

    New length = 224/48 - 42/48 = 182/48 meters

    We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 2:

    New length = (182 ÷ 2) / (48 ÷ 2) = 91/24 meters

    ### Answer: 91/24 meters

Expected answer: 91/24

Correct? Yes

🔗 Follow-up

Problem: Following the alteration, Bob decides to cut off an additional 9/4 meters. After yet another alteration, what is the remaining length of Bob's jacket now?

Gemma 2B:

    Reasoning: We already found the length of Bob's jacket after the first alteration:

    Length after first alteration = 91/24 meters

    Now, we need to subtract the additional length cut off:

    Length cut off = 9/4 meters

    To subtract these fractions, we need to find a common denominator, which is 24. So, we can convert the length cut off to have a denominator of 24:

    Length cut off = (9/4) × (6/6) = 54/24 meters

    Now, we can subtract:

    New length = 91/24 - 54/24 = 37/24 meters

    ### Answer: 37/24 meters

Expected answer: 37/24

Correct? Yes

🔗 Follow-up

Problem: Initially, Bob's jacket was 16/3 meters in length instead of 14/3 meters. If he still cuts off 14/16 meter from this new original length, then what would be the length of Bob's jacket after the alteration now?

Gemma 2B:

    Reasoning: To find the length of the jacket after the alteration, we need to subtract the length cut off from the original length.

    Original length = 16/3 meters
    Length cut off = 14/16 meters

    To subtract these fractions, we need to find a common denominator, which is 48. So, we can convert both fractions to have a denominator of 48:

    Original length = (16/3) × (16/16) = 256/48 meters
    Length cut off = (14/16) × (3/3) = 42/48 meters

    Now, we can subtract:

    New length = 256/48 - 42/48 = 214/48 meters

    We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 2:

    New length = (214 ÷ 2) / (48 ÷ 2) = 107/24 meters

    ### Answer: 107/24 meters

Expected answer: 107/24

Correct? Yes

🔗 Problem

Problem: Officer Max spends 2/6 part of an hour completing paperwork. Then, he spends 14/7 parts of an hour patrolling the neighborhood. How much time, in parts of an hour, does Officer Max use for these two tasks?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 6 and 7 is 42. So, we can convert both fractions to have a denominator of 42:

    2/6 = 14/42
    14/7 = 24/42

    Now we can add:

    14/42 + 24/42 = 38/42

    ### Answer: 38/42

Expected answer: 7/3

Correct? No

🔗 Problem

Problem: John watched a movie for 10/12 of an hour and then watched a TV show for another 3/8 of an hour. What is the total time he spent watching in hours?

Gemma 2B:

    Reasoning: To find the total time John spent watching, we need to add the time he spent watching the movie and the TV show.

    First, let's convert both times to a common denominator, which is 24.

    10/12 = (10*2)/(12*2) = 20/24
    3/8 = (3*3)/(8*3) = 9/24

    Now we can add the times:
    20/24 + 9/24 = 29/24

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 1:
    29/24 = 1 5/24

    So John spent a total of 1 hour and 5/24 of an hour watching.

    ### Answer: 1 5/24

Expected answer: 29/24

Correct? Yes

🔗 Follow-up

Problem: If John watched a movie for 10/12 of an hour and then watched a TV show for another 3/8 of an hour, and then repeated this same routine, what is the total time he spent watching in hours?

Gemma 2B:

    Reasoning: Since John repeated the same routine, we need to double the total time he spent watching in the first round.

    In the first round, John spent:
    10/12 = (10*2)/(12*2) = 20/24 hours watching the movie
    3/8 = (3*3)/(8*3) = 9/24 hours watching the TV show

    Total time in the first round:
    20/24 + 9/24 = 29/24 hours

    Since John repeated the same routine, the total time he spent watching is:
    29/24 + 29/24 = 58/24 hours

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 2:
    58/24 = 29/12

    ### Answer: 29/12

Expected answer: 29/12

Correct? Yes

🔗 Follow-up

Problem: If instead of watching the movie for 10/12 of an hour, John watched it for 10/7 of an hour, and he still watched the TV show for another 3/8 of an hour, what is the total time he spent watching in hours?

Gemma 2B:

    Reasoning: To find the total time John spent watching, we need to add the time he spent watching the movie and the TV show.

    First, let's convert both times to a common denominator, which is 56.

    10/7 = (10*8)/(7*8) = 80/56
    3/8 = (3*7)/(8*7) = 21/56

    Now we can add the times:
    80/56 + 21/56 = 101/56

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 1:
    101/56 = 1 45/56

    So John spent a total of 1 hour and 45/56 of an hour watching.

    ### Answer: 1 45/56

Expected answer: 101/56

Correct? Yes

🔗 Problem

Problem: Mr. Carpenter makes crafting chairs a meticulous process. He takes 5/3 hours to build the frame and additional 10/13 hours to upholster it. How long does it take for him to build a chair from start to finish?

Gemma 2B:

    Reasoning: To find the total time it takes for Mr. Carpenter to build a chair, we need to add the time it takes to build the frame and the time it takes to upholster it.

    Time to build the frame = 5/3 hours
    Time to upholster = 10/13 hours

    To add these fractions, we need to find a common denominator, which is 39. So, we can convert both fractions to have a denominator of 39:

    Time to build the frame = (5/3) × (13/13) = 65/39 hours
    Time to upholster = (10/13) × (3/3) = 30/39 hours

    Now, we can add the two times:

    Total time = 65/39 + 30/39 = 95/39 hours

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. So, the total time remains:

    Total time = 95/39 hours

    ### Answer: 95/39 hours

Expected answer: 95/39

Correct? Yes

🔗 Follow-up

Problem: Mr. Carpenter has now taken on an additional task. After building the chair and doing the upholstery work, he spends another 8/19 hours to apply the varnish. Now, how long does the entire process of making a chair take?

Gemma 2B:

    Reasoning: We already know that the time it takes to build the chair and do the upholstery work is 95/39 hours. Now, we need to add the time it takes to apply the varnish, which is 8/19 hours.

    To add these fractions, we need to find a common denominator, which is 741. So, we can convert both fractions to have a denominator of 741:

    Time to build and upholster = (95/39) × (19/19) = 1805/741 hours
    Time to apply varnish = (8/19) × (39/39) = 312/741 hours

    Now, we can add the two times:

    Total time = 1805/741 + 312/741 = 2117/741 hours

    ### Answer: 2117/741 hours

Expected answer: 2117/741

Correct? Yes

🔗 Follow-up

Problem: In another batch of chair production, Mr. Carpenter managed to reduce his timeframe. Now, he takes only 5/10 hours to build the frame of the chair while the time for upholstery stays the same as 10/13 hours. How long does it take for him to build a chair with the new time for frame construction?

Gemma 2B:

    Reasoning: To find the total time it takes for Mr. Carpenter to build a chair, we need to add the time it takes to build the frame and the time it takes to upholster it.

    Time to build the frame = 5/10 hours
    Time to upholster = 10/13 hours

    To add these fractions, we need to find a common denominator, which is 130. So, we can convert both fractions to have a denominator of 130:

    Time to build the frame = (5/10) × (13/13) = 65/130 hours
    Time to upholster = (10/13) × (10/10) = 100/130 hours

    Now, we can add the two times:

    Total time = 65/130 + 100/130 = 165/130 hours

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5. So, we get:

    Total time = 33/26 hours

    ### Answer: 33/26 hours

Expected answer: 33/26

Correct? Yes

🔗 Problem

Problem: Anna has a bracelet that consists of small and large beads. The small beads are each 8/4 mm in diameter and the large beads are each 15/2 mm in diameter. If she adds a small and a large bead to her bracelet, what would be the total added diameter in mm?

Gemma 2B:

    Reasoning: To find the total added diameter, we need to add the diameters of the small and large beads.

    First, let's simplify the fractions:

    Small bead diameter: 8/4 = 2 mm
    Large bead diameter: 15/2 = 7.5 mm

    Now, let's add the diameters:
    Total added diameter = 2 mm + 7.5 mm = 9.5 mm

    ### Answer: 9.5 mm

Expected answer: 19/2

Correct? No

🔗 Problem

Problem: A rocket travels 11/18 light-years to an alien planet, then travels another 8/2 light-years towards a distant star. What is the total distance covered by the rocket?

Gemma 2B:

    Reasoning: The rocket travels 11/18 light-years to the alien planet. Then, it travels another 8/2 = 4 light-years towards the distant star.
    To find the total distance, we add the two distances: 11/18 + 4 = 11/18 + 72/18 = 83/18 light-years.
    ### Answer: 83/18 light-years.

Expected answer: 83/18

Correct? Yes

🔗 Follow-up

Problem: Let's reconsider our previous journey of the rocket. Assume that instead of traveling 8/2 light-years towards a distant star after reaching the alien planet, the rocket only traveled 8/13 light-years. In this case, what would be the total distance covered by the rocket?

Gemma 2B:

    Reasoning: The rocket travels 11/18 light-years to the alien planet. Then, it travels another 8/13 light-years towards the distant star.
    To find the total distance, we need to add the two distances. However, they have different denominators, so we need to find a common denominator, which is 234.
    We can convert both fractions to have a denominator of 234:
    11/18 = 143/234
    8/13 = 128/234
    Now we can add the two distances:
    143/234 + 128/234 = 271/234 light-years.
    ### Answer: 271/234 light-years.

Expected answer: 287/234

Correct? No

🔗 Problem

Problem: Johnathan needs 12/14 yards of one fabric to make a sleeping bag, and another 8/5 yards of a different fabric to create the liner. How many yards of fabric does he need in total to create his sleeping bag?

Gemma 2B:

    Reasoning: To find the total amount of fabric needed, we need to add the amount of fabric needed for the sleeping bag and the liner.

    First, let's convert the fractions to decimals to make it easier to add:
    12/14 = 0.857 (approximately)
    8/5 = 1.6

    Now, add the amounts:
    0.857 + 1.6 = 2.457

    Since we can't have a fraction of a yard, we can round up to the nearest hundredth to ensure Johnathan has enough fabric:
    2.457 ≈ 2.46 yards

    ### Answer: 2.46 yards

Expected answer: 86/35

Correct? No

🔗 Problem

Problem: In a forest, there are 5/4 acres of pine trees and 1/2 acre of oak trees. What is the total acreage of pine and oak trees in the forest?

Gemma 2B:

    Reasoning: To find the total acreage, we need to add the acreage of pine trees and oak trees. To do this, we need to have the same denominator, which is 4 in this case. So, we can convert 1/2 to 2/4. Now, we can add:

    5/4 + 2/4 = 7/4

    ### Answer: 7/4 or 1 3/4 acres.

Expected answer: 7/4

Correct? Yes

🔗 Follow-up

Problem: After further research, it is found that the forest actually had 5/3 acres of pine trees instead of 5/4 acres. Keeping the acreage of oak trees the same, what is the new total acreage of pine and oak trees in the forest?

Gemma 2B:

    Reasoning: To find the total acreage, we need to add the acreage of pine trees and oak trees. To do this, we need to have the same denominator, which is 6 in this case (the least common multiple of 3 and 2). So, we can convert 5/3 to 10/6 and 1/2 to 3/6. Now, we can add:

    10/6 + 3/6 = 13/6

    ### Answer: 13/6 or 2 1/6 acres.

Expected answer: 13/6

Correct? Yes

🔗 Problem

Problem: Jake has 12/7 of a yard of fabric. He finds another piece that measures 2/14 of a yard. If he combines both pieces, how much fabric does he have to make his shirt?

Gemma 2B:

    Reasoning: To combine the two pieces of fabric, we need to add them together. However, we need to make sure we have the same denominator. The least common multiple of 7 and 14 is 14. So, we can rewrite 12/7 as 24/14.

    Now, we can add the two pieces together:
    24/14 + 2/14 = 26/14

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
    26/14 = 13/7

    ### Answer: 13/7 yards

Expected answer: 13/7

Correct? Yes

🔗 Follow-up

Problem: After making his shirt, Jake realizes he needs to remove 4/16 of a yard of fabric for the shirt to fit perfectly. How much fabric will he have left after making this adjustment?

Gemma 2B:

    Reasoning: Jake has 13/7 yards of fabric left after making his shirt. He needs to remove 4/16 of a yard of fabric. We can rewrite 4/16 as 1/4, since 4 and 16 have a common factor of 4.

    To subtract 1/4 from 13/7, we need to find a common denominator. The least common multiple of 7 and 4 is 28. So, we can rewrite 13/7 as 52/28.

    Now, we can subtract 1/4 from 52/28:
    52/28 - 7/28 = 45/28

    ### Answer: 45/28 yards

Expected answer: 45/28

Correct? Yes

🔗 Follow-up

Problem: Let's say Jake originally had less fabric, only 12/6 yards instead of 12/7 yards. He still finds an additional piece of fabric that measures 2/14 of a yard. If he combines both these pieces now, then how much fabric does he have altogether for his shirt?

Gemma 2B:

    Reasoning: To combine the two pieces of fabric, we need to add them together. However, we need to make sure we have the same denominator. The least common multiple of 6 and 14 is 42. So, we can rewrite 12/6 as 84/42 and 2/14 as 6/42.

    Now, we can add the two pieces together:
    84/42 + 6/42 = 90/42

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6:
    90/42 = 15/7

    ### Answer: 15/7 yards

Expected answer: 15/7

Correct? Yes

🔗 Problem

Problem: At a park, a special tree produces on average 10/4 kilograms of fruit every summer. In the winter, it loses some of its fruit, amounting to 12/20 kg. What is the difference in kilograms of the fruit from summer to winter?

Gemma 2B:

    Reasoning: To find the difference, we need to subtract the amount of fruit lost in winter from the amount produced in summer.

    First, let's simplify the fractions:
    10/4 = 2.5 kg (summer)
    12/20 = 0.6 kg (winter)

    Now, subtract the amount lost in winter from the amount produced in summer:
    2.5 kg - 0.6 kg = 1.9 kg

    ### Answer: 1.9 kg

Expected answer: 19/10

Correct? No

🔗 Problem

Problem: A ballerina starts with a routine that lasts 13/5 minutes but decides to shorten it by 15/16 minutes. How long is her routine after shortening it?

Gemma 2B:

    Reasoning: To find the new length of the routine, we need to subtract the time she shortened it by from the original length.

    First, let's convert the original length from an improper fraction to a mixed number: 13/5 = 2 3/5 minutes.

    Now, subtract 15/16 minutes from 2 3/5 minutes:

    2 3/5 - 15/16 = 2 3/5 - 0.9375 (convert 15/16 to a decimal)

    = 2.6 - 0.9375

    = 1.6625 minutes

    So, the new length of the routine is approximately 1 minute and 40 seconds.

    ### Answer: 1 40/60 minutes or 1 2/3 minutes.

Expected answer: 133/80

Correct? No

🔗 Problem

Problem: Miss Daisy has 19/6 kg of fertilizers for her flowers. If she uses 17/20 kg on her roses, how much fertilizers does she have left to use on her other flowers?

Gemma 2B:

    Reasoning: To find out how much fertilizer Miss Daisy has left, we need to subtract the amount she used on her roses from the total amount she had.

    First, we need to convert both fractions to have a common denominator, which is 60. So, we can rewrite the fractions as:

    19/6 = 190/60
    17/20 = 51/60

    Now, we can subtract:

    190/60 - 51/60 = 139/60

    So, Miss Daisy has 139/60 kg of fertilizer left to use on her other flowers.

    ### Answer: 139/60 kg

Expected answer: 139/60

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous scenario, Miss Daisy finds an additional 11/11 kg of fertilizer in her shed. After she took away 17/20 kg from the original 19/6 kg to use on her roses, she added this new amount to the fertilizer she had left. How much fertilizer does she have now?

Gemma 2B:

    Reasoning: We already found out that Miss Daisy had 139/60 kg of fertilizer left after using 17/20 kg on her roses.

    Now, she finds an additional 11/11 kg of fertilizer, which is equal to 60/60 kg (since 11/11 is equal to 1 whole).

    To find the total amount of fertilizer she has now, we add the amount she had left to the new amount:

    139/60 + 60/60 = 199/60

    So, Miss Daisy has 199/60 kg of fertilizer now.

    ### Answer: 199/60 kg

Expected answer: 199/60

Correct? Yes

🔗 Follow-up

Problem: Continuing from the scenario, suppose instead of the initial 19/6 kg of fertilizers, Miss Daisy had only 14/6 kg of fertilizers. If she still uses 17/20 kg on her roses, how much fertilizers does she have left to use on her other flowers now?

Gemma 2B:

    Reasoning: Again, we need to subtract the amount Miss Daisy used on her roses from the total amount she had.

    First, we need to convert both fractions to have a common denominator, which is 60. So, we can rewrite the fractions as:

    14/6 = 140/60
    17/20 = 51/60

    Now, we can subtract:

    140/60 - 51/60 = 89/60

    So, Miss Daisy has 89/60 kg of fertilizer left to use on her other flowers.

    ### Answer: 89/60 kg

Expected answer: 89/60

Correct? Yes

🔗 Problem

Problem: Scientists have discovered that the moon is slowly moving away from Earth. If the distance increases by 4/16 meters every year, and unexpectedly there was an additional increase of 20/6 meters this year, what is the total change in distance this year?

Gemma 2B:

    Reasoning: To find the total change in distance, we need to add the regular increase in distance to the additional increase.

    First, let's convert the regular increase from an improper fraction to a mixed number: 4/16 = 1/4 meter per year.

    Next, let's convert the additional increase from an improper fraction to a mixed number: 20/6 = 3 2/3 meters.

    Now, we can add the two increases together: 1/4 + 3 2/3 = 3 11/12 meters.

    ### Answer: 3 11/12 meters.

Expected answer: 43/12

Correct? No

🔗 Problem

Problem: Bob has 11/3 dollars in one pocket of his wallet and 12/19 dollars in another pocket. How much money does he have in total in his wallet?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 3 and 19 is 57. So, we can convert both fractions to have a denominator of 57:

    11/3 = (11*19)/(3*19) = 209/57
    12/19 = (12*3)/(19*3) = 36/57

    Now we can add:

    209/57 + 36/57 = (209 + 36)/57 = 245/57

    So, Bob has 245/57 dollars in total in his wallet.

    ### Answer: 245/57

Expected answer: 245/57

Correct? Yes

🔗 Follow-up

Problem: Bob has 11/3 dollars in one pocket of his wallet and 12/19 dollars in another pocket. How much money does he have in total in his wallet? Now, if Bob duplicates the total amount of money in his wallet, how much money will he have then?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 3 and 19 is 57. So, we can convert both fractions to have a denominator of 57:

    11/3 = (11*19)/(3*19) = 209/57
    12/19 = (12*3)/(19*3) = 36/57

    Now we can add:

    209/57 + 36/57 = (209 + 36)/57 = 245/57

    So, Bob has 245/57 dollars in total in his wallet.

    If Bob duplicates the total amount of money in his wallet, he will have:

    2 × 245/57 = 490/57

    ### Answer: 490/57

Expected answer: 490/57

Correct? Yes

🔗 Follow-up

Problem: Suppose Bob starts out with 3/3 (or 1) dollar in one pocket of his wallet instead of 11/3 dollars, and still has 12/19 dollars in another pocket. Now how much money does he have in total in his wallet?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 3 and 19 is 57. So, we can convert both fractions to have a denominator of 57:

    3/3 = (3*19)/(3*19) = 57/57 = 1
    12/19 = (12*3)/(19*3) = 36/57

    Now we can add:

    57/57 + 36/57 = (57 + 36)/57 = 93/57

    So, Bob has 93/57 dollars in total in his wallet.

    ### Answer: 93/57

Expected answer: 31/19

Correct? Yes

🔗 Problem

Problem: In an ocean, a shark swims a distance of 5/5 miles in the morning and adds an additional 12/18 miles in the afternoon. How many miles in total did the shark swim that day?

Gemma 2B:

    Reasoning: We can simplify the fractions by dividing both numerator and denominator by their greatest common divisor.
    5/5 = 1 (since 5 is divisible by 5)
    12/18 = 2/3 (since 6 is the greatest common divisor of 12 and 18)

    The shark swam 1 mile in the morning and 2/3 miles in the afternoon.
    To add these distances, we need a common denominator, which is 3.
    So, we can convert 1 mile to 3/3 miles.
    Now, we can add:
    3/3 + 2/3 = 5/3

    The shark swam a total distance of 5/3 miles.
    ### Answer: 5/3

Expected answer: 5/3

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, if the shark decides to swim an additional 18/9 miles in the evening, what is the total distance the shark would have swam by the end of the day?

Gemma 2B:

    Reasoning: We can simplify the fraction 18/9 by dividing both numerator and denominator by their greatest common divisor, which is 9.
    18/9 = 2 (since 18 is divisible by 9)

    The shark swam an additional 2 miles in the evening.
    To find the total distance, we add the distance swam in the morning and afternoon (5/3 miles) to the distance swam in the evening (2 miles).
    To add these distances, we need a common denominator, which is 3.
    So, we can convert 2 miles to 6/3 miles.
    Now, we can add:
    5/3 + 6/3 = 11/3

    The shark would have swam a total distance of 11/3 miles by the end of the day.
    ### Answer: 11/3

Expected answer: 11/3

Correct? Yes

🔗 Follow-up

Problem: Continuing from the last problem, suppose the shark had only swam 5/12 miles in the morning instead of 5/5 miles, but still swam the additional 12/18 miles in the afternoon. How many miles would the shark have swam in the morning and afternoon combined?

Gemma 2B:

    Reasoning: We can simplify the fractions by dividing both numerator and denominator by their greatest common divisor.
    5/12 is already in its simplest form.
    12/18 = 2/3 (since 6 is the greatest common divisor of 12 and 18)

    The shark swam 5/12 miles in the morning and 2/3 miles in the afternoon.
    To add these distances, we need a common denominator, which is 12.
    So, we can convert 2/3 miles to 8/12 miles (by multiplying both numerator and denominator by 4).
    Now, we can add:
    5/12 + 8/12 = 13/12

    The shark swam a total distance of 13/12 miles.
    ### Answer: 13/12

Expected answer: 13/12

Correct? Yes

🔗 Problem

Problem: Jim types 20 words in 16 seconds and Mary types 9 words in 4 seconds. How many words per second do Jim and Mary type in total?

Gemma 2B:

    Let's find the words per second for each person:

    Jim types 20 words in 16 seconds, so his rate is:
    20 words / 16 seconds = 1.25 words per second

    Mary types 9 words in 4 seconds, so her rate is:
    9 words / 4 seconds = 2.25 words per second

    To find the total words per second, we add their rates:
    1.25 words/second + 2.25 words/second = 3.5 words/second

    ### Answer: 3.5

Expected answer: 7/2

Correct? Yes

🔗 Follow-up

Problem: After typing together, Jim and Mary decide to slow down their pace and reduce their combined typing speed by 2 words every 11 seconds. What becomes their new combined typing speed?

Gemma 2B:

    Initially, Jim and Mary's combined typing speed is 3.5 words per second.

    To reduce their combined typing speed by 2 words every 11 seconds, we need to find the reduction in words per second. There are 11 seconds, so the reduction in words per second is:
    2 words / 11 seconds = 2/11 words per second

    Now, we subtract this reduction from their initial combined typing speed:
    3.5 words/second - 2/11 words/second = 3.5 - 0.1818... = 3.3181...

    ### Answer: 3.3181...

Expected answer: 73/22

Correct? No

🔗 Problem

Problem: Max rode his scooter for 9/7 miles in the morning and then 1/9 miles less in the afternoon. How many miles did he ride his scooter in the afternoon?

Gemma 2B:

    Reasoning: Max rode his scooter 9/7 miles in the morning.
    To find out how many miles he rode in the afternoon, we need to subtract 1/9 from 9/7.
    First, we need to find a common denominator, which is 63.
    So, we can convert 9/7 to 81/63 and 1/9 to 7/63.
    Now, we can subtract: 81/63 - 7/63 = 74/63.
    ### Answer: 74/63.

Expected answer: 74/63

Correct? Yes

🔗 Follow-up

Problem: Suppose on another day, Max rode his scooter for 9/7 miles in the morning and then 1/4 miles less in the afternoon instead of 1/9 miles less. How many miles did he ride his scooter in the afternoon on this different day?

Gemma 2B:

    Reasoning: Max rode his scooter 9/7 miles in the morning.
    To find out how many miles he rode in the afternoon, we need to subtract 1/4 from 9/7.
    First, we need to find a common denominator, which is 28.
    So, we can convert 9/7 to 36/28 and 1/4 to 7/28.
    Now, we can subtract: 36/28 - 7/28 = 29/28.
    ### Answer: 29/28.

Expected answer: 29/28

Correct? Yes

🔗 Problem

Problem: At a circus, a clown rode a unicycle for 9/8 hours. After a short break, she juggled for another 2/10 hours. How many hours in total did she perform?

Gemma 2B:

    Reasoning: To find the total hours, we need to add the hours she rode the unicycle and the hours she juggled. To add these fractions, we need to find a common denominator, which is 40. So, we can convert both fractions to have a denominator of 40:

    9/8 = (9 x 5)/(8 x 5) = 45/40
    2/10 = (2 x 4)/(10 x 4) = 8/40

    Now we can add:

    45/40 + 8/40 = 53/40

    To convert this back to a mixed number, we can divide the numerator by the denominator:

    53 ÷ 40 = 1 with a remainder of 13

    So, the mixed number is 1 13/40.

    ### Answer: 1 13/40 hours

Expected answer: 53/40

Correct? Yes

🔗 Follow-up

Problem: Following her performances, the clown took a total break of 13/5 hours. How many hours remained after her performance time is subtracted from her total break time?

Gemma 2B:

    Reasoning: We need to subtract the performance time from the break time. First, let's convert the mixed number 1 13/40 to an improper fraction:

    1 13/40 = (1 x 40)/40 + 13/40 = 40/40 + 13/40 = 53/40

    Now, we can subtract the performance time from the break time:

    Break time: 13/5 = (13 x 8)/(5 x 8) = 104/40
    Performance time: 53/40

    Subtracting the performance time from the break time:

    104/40 - 53/40 = 51/40

    To convert this back to a mixed number, we can divide the numerator by the denominator:

    51 ÷ 40 = 1 with a remainder of 11

    So, the mixed number is 1 11/40.

    ### Answer: 1 11/40 hours

Expected answer: 51/40

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, the clown juggled for 2/10 hours. Now suppose that she actually juggled for 9/10 hours instead. In this scenario, how many hours in total did she perform, if she still rode the unicycle for 9/8 hours?

Gemma 2B:

    Reasoning: To find the total hours, we need to add the hours she rode the unicycle and the hours she juggled. To add these fractions, we need to find a common denominator, which is 40. So, we can convert both fractions to have a denominator of 40:

    9/8 = (9 x 5)/(8 x 5) = 45/40
    9/10 = (9 x 4)/(10 x 4) = 36/40

    Now we can add:

    45/40 + 36/40 = 81/40

    To convert this back to a mixed number, we can divide the numerator by the denominator:

    81 ÷ 40 = 2 with a remainder of 1

    So, the mixed number is 2 1/40.

    ### Answer: 2 1/40 hours

Expected answer: 81/40

Correct? Yes

🔗 Problem

Problem: If Timmy dumps 7/2 kg of sand into his sandbox and later adds another 1/2 kg, how much sand is now in his sandbox?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator, which is 2. So, we can convert 7/2 to 7/2 = 3 1/2. Then, we add 3 1/2 + 1/2 = 4.
    ### Answer: 4 kg.

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Following the last scenario, if Timmy later dumps another 16/3 kg of sand into the sandbox, how much sand does the sandbox contain now?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator, which is 6. So, we can convert 4 to 4 = 24/6 and 16/3 to 16/3 = 32/6. Then, we add 24/6 + 32/6 = 56/6 = 28/3 = 9 1/3.
    ### Answer: 9 1/3 kg.

Expected answer: 28/3

Correct? Yes

🔗 Follow-up

Problem: In the previous sandbox problem, if Timmy initially dumped 7/2 kg of sand into his sandbox but this time around, he decided to add only 1/20 kg of sand to it instead, how much sand is now in his sandbox?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator, which is 20. So, we can convert 7/2 to 7/2 = 70/20. Then, we add 70/20 + 1/20 = 71/20.
    ### Answer: 71/20 kg.

Expected answer: 71/20

Correct? Yes

🔗 Problem

Problem: A wizard brewed a potion that required 18/8 ounces of moon roots and 11/7 ounces of stardust. How many ounces of ingredients did the wizard use in total to prepare the potion?

Gemma 2B:

    Reasoning: To find the total amount of ingredients, we need to add the amount of moon roots and stardust used.

    First, let's convert the fractions to decimals:
    18/8 = 2.25 ounces of moon roots
    11/7 ≈ 1.57 ounces of stardust

    Now, add the amounts:
    2.25 + 1.57 = 3.82 ounces

    ### Answer: 3.82 ounces

Expected answer: 107/28

Correct? No

🔗 Problem

Problem: An alien UFO traveled 3/10 of a mile, then immediately traveled an additional 16/20 of a mile. How many miles did the UFO travel in total?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 10 and 20 is 20. So, we can rewrite 3/10 as 6/20. Then, we can add the fractions: 6/20 + 16/20 = 22/20. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us 11/10. To convert this to a mixed number, we can divide the numerator by the denominator to get 1 with a remainder of 1. So, the mixed number is 1 1/10.
    ### Answer: 1 1/10 miles.

Expected answer: 11/10

Correct? Yes

🔗 Follow-up

Problem: Originally, the alien UFO traveled 3/10 of a mile, then an additional 16/20 of a mile. But what if, instead, the UFO initially only traveled 3/10 of a mile, before traveling an extra 16/18 of a mile. How much distance did UFO cover in total this time?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 10 and 18 is 90. So, we can rewrite 3/10 as 27/90 and 16/18 as 80/90. Then, we can add the fractions: 27/90 + 80/90 = 107/90. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1 (since 107 and 90 are coprime). This gives us 107/90. To convert this to a mixed number, we can divide the numerator by the denominator to get 1 with a remainder of 17. So, the mixed number is 1 17/90.
    ### Answer: 1 17/90 miles.

Expected answer: 107/90

Correct? Yes

🔗 Problem

Problem: A chair manufacturing firm makes 4/14 of a chair every hour with one machine, and another machine makes 20/4 chairs. How many chairs are made by both machines in one hour?

Gemma 2B:

    Reasoning: Let's first find a common denominator for the two fractions. The least common multiple of 14 and 4 is 28. So, we can convert both fractions to have a denominator of 28:

    Machine 1: 4/14 = (4*2)/(14*2) = 8/28
    Machine 2: 20/4 = (20*7)/(4*7) = 140/28

    Now, we can add the fractions to find the total number of chairs made by both machines in one hour:

    8/28 + 140/28 = 148/28

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

    148 ÷ 4 = 37
    28 ÷ 4 = 7

    So, the simplified fraction is:

    37/7

    To find the total number of chairs, we can divide the numerator by the denominator:

    37 ÷ 7 = 5 2/7

    Since we can't make a fraction of a chair, we'll round down to the nearest whole number. Therefore, both machines make 5 chairs in one hour.

    ### Answer: 5

Expected answer: 37/7

Correct? No

🔗 Problem

Problem: A blue shark swam for 2/4 miles and a hammerhead shark swam for 7/10 miles. How many miles did they swim together?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 4 and 10 is 20. So, we can convert both fractions to have a denominator of 20:

    2/4 = 10/20
    7/10 = 14/20

    Now we can add:

    10/20 + 14/20 = 24/20

    We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 4:

    24/20 = 6/5

    So, the blue shark and the hammerhead shark swam a total of 6/5 miles.

    ### Answer: 6/5 miles or 1 1/5 miles.

Expected answer: 6/5

Correct? Yes

🔗 Follow-up

Problem: After the blue shark and the hammerhead shark swam their respective distances, a great white shark joined them and swam 9/14 miles. What is the total combined distance that the three sharks swam together?

Gemma 2B:

    Reasoning: We already found the total distance swam by the blue shark and the hammerhead shark: 6/5 miles.

    To add the distance swam by the great white shark, we need to convert 6/5 to an equivalent fraction with a denominator of 14 (the least common multiple of 5 and 14):

    6/5 = 16.8/14 (approximately)

    Now we can add:

    16.8/14 + 9/14 = 25.8/14

    To simplify, we can convert the mixed number to an improper fraction:

    25.8/14 = 362/14

    Dividing both numerator and denominator by their greatest common divisor, which is 2:

    362/14 = 181/7

    So, the total combined distance that the three sharks swam together is 181/7 miles.

    ### Answer: 181/7 miles or 25 6/7 miles.

Expected answer: 129/70

Correct? No

🔗 Follow-up

Problem: In the previous situation, let's imagine that the blue shark actually swam for only 2/4 miles and the hammerhead shark swam for 7/11 miles. In this case, how many miles did the blue and hammerhead sharks swim in total?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 4 and 11 is 44. So, we can convert both fractions to have a denominator of 44:

    2/4 = 22/44
    7/11 = 28/44

    Now we can add:

    22/44 + 28/44 = 50/44

    We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 2:

    50/44 = 25/22

    So, the blue shark and the hammerhead shark swam a total of 25/22 miles.

    ### Answer: 25/22 miles.

Expected answer: 25/22

Correct? Yes

🔗 Problem

Problem: Lisa has two milk bottles. One bottle has 8/18 gallons of milk while the other bottle has 18/8 gallons. How much milk does Lisa have in total?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 18 and 8 is 72. So, we can convert both fractions to have a denominator of 72:

    8/18 = (8*4)/(18*4) = 32/72
    18/8 = (18*9)/(8*9) = 162/72

    Now we can add:

    32/72 + 162/72 = 194/72

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

    194/72 = (194/2)/(72/2) = 97/36

    So, Lisa has 97/36 gallons of milk in total.
    ### Answer: 97/36 gallons

Expected answer: 97/36

Correct? Yes

🔗 Follow-up

Problem: Following the previous question, Lisa finds another bottle that has 6/16 gallon of milk. What is the total amount of milk Lisa has now, if you add the milk from this third bottle to the total from the first two bottles?

Gemma 2B:

    Reasoning: We already found that Lisa had 97/36 gallons of milk from the first two bottles. To add the milk from the third bottle, we need to convert 6/16 to have a denominator of 36:

    6/16 = (6*9)/(16*9) = 54/144 = (54/4)/(144/4) = 27/36

    Now we can add:

    97/36 + 27/36 = 124/36

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 4:

    124/36 = (124/4)/(36/4) = 31/9

    So, Lisa has 31/9 gallons of milk in total now.
    ### Answer: 31/9 gallons

Expected answer: 221/72

Correct? No

🔗 Problem

Problem: A tree grows 1/10 of its height every month. This month, it additionally has grown 12/6 feet due to a fertilizer being applied. How much has the tree grown in height this month?

Gemma 2B:

    Reasoning: The tree grows 1/10 of its height every month, but we don't know the total height of the tree. However, we are asked to find the total growth this month, which includes the additional growth due to the fertilizer.

    The additional growth due to the fertilizer is 12/6 = 2 feet.

    The total growth this month is the growth due to the natural growth (1/10 of its height) plus the growth due to the fertilizer (2 feet). Since we don't know the total height of the tree, we can't find the natural growth, but we know it's 1/10 of the total height. Let's call the total height "h". Then, the natural growth is h/10.

    The total growth this month is h/10 + 2.

    However, since we don't know the total height "h", we can't find the exact total growth. But we can say that the total growth is h/10 + 2, where h is the total height of the tree.

    ### Answer: h/10 + 2

Expected answer: 21/10

Correct? No

🔗 Problem

Problem: John sets up a large tent that occupies an area of 13/11 acres. Later in the day, he decides to set up another smaller tent which occupies an area of 8/20 acres. What is the total area occupied by both tents?

Gemma 2B:

    Reasoning: To find the total area occupied by both tents, we need to add the areas of the two tents. However, we need to have a common denominator to add the fractions. The least common multiple of 11 and 20 is 220. So, we can convert both fractions to have a denominator of 220:

    13/11 = (13*20)/(11*20) = 260/220
    8/20 = (8*11)/(20*11) = 88/220

    Now we can add the fractions:

    260/220 + 88/220 = 348/220

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

    348/220 = (348/4)/(220/4) = 87/55

    ### Answer: 87/55 acres

Expected answer: 87/55

Correct? Yes

🔗 Follow-up

Problem: John sets up a large tent that occupies an area of 13/11 acres. Later in the day, he decides to set up another smaller tent which occupies an area of 8/20 acres. The following day, John adds a third tent to the campsite. This tent occupies 1/10 of an acre. What is the total area occupied by all three tents?

Gemma 2B:

    Reasoning: We already found the total area occupied by the first two tents:

    13/11 + 8/20 = 87/55 acres

    Now, we need to add the area of the third tent to this total. To do this, we need to convert the third tent's area to have a denominator of 55, which is the least common multiple of 55 and 10:

    1/10 = (1*5.5)/(10*5.5) = 5.5/55

    Now we can add the areas:

    87/55 + 5.5/55 = 92.5/55

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 11:

    92.5/55 = (92.5/11)/(55/11) = 8.41/5

    ### Answer: 8.41/5 acres

Expected answer: 37/22

Correct? No

🔗 Follow-up

Problem: In the previous scenario, John had initially set up a large tent that occupied an area of 13/11 acres and a smaller tent which occupied an area of 8/20 acres. Instead, if John had a different small tent that occupied an area of 10/20 acres, what would be the total area occupied by these tents?

Gemma 2B:

    Reasoning: To find the total area occupied by both tents, we need to add the areas of the two tents. We can start by simplifying the fraction of the smaller tent:

    10/20 = 1/2 (since 10 is half of 20)

    Now we can add the fractions:

    13/11 + 1/2 = ?

    To add these fractions, we need to find a common denominator. The least common multiple of 11 and 2 is 22. So, we can convert both fractions to have a denominator of 22:

    13/11 = (13*2)/(11*2) = 26/22
    1/2 = (1*11)/(2*11) = 11/22

    Now we can add the fractions:

    26/22 + 11/22 = 37/22

    ### Answer: 37/22 acres

Expected answer: 37/22

Correct? Yes

🔗 Problem

Problem: Captain Jack has a treasure map that shows the treasure is at a location that is (17 / 20) km to the East and then (15 / 3) km to the North from their starting point. How far must they travel in total to reach the treasure?

Gemma 2B:

    Reasoning: To find the total distance, we need to find the distance traveled in each direction and add them together.

    First, let's find the distance traveled to the East:
    (17 / 20) km = 0.85 km (approximately)

    Next, let's find the distance traveled to the North:
    (15 / 3) km = 5 km

    Now, let's add the distances together to find the total distance:
    0.85 km + 5 km = 5.85 km

    ### Answer: 5.85 km

Expected answer: 117/20

Correct? No

🔗 Problem

Problem: At a campfire, Sarah collected 11/20 of a pound of firewood and Alex collected 9/7 pounds. How many pounds of firewood did they collect in total?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 20 and 7 is 140. So, we can convert both fractions to have a denominator of 140:

    Sarah collected 11/20 = (11*7)/(20*7) = 77/140 pounds
    Alex collected 9/7 = (9*20)/(7*20) = 180/140 pounds

    Now we can add them:

    77/140 + 180/140 = 257/140 pounds

    ### Answer: 257/140 pounds

Expected answer: 257/140

Correct? Yes

🔗 Follow-up

Problem: In addition to the wood Sarah and Alex collected, another camper named Kim contributed 11 pounds of firewood. How many pounds of firewood do they now have in total?

Gemma 2B:

    Reasoning: We already found that Sarah and Alex collected 257/140 pounds of firewood. To add Kim's contribution, we need to convert 257/140 to a mixed number:

    257/140 = 1 117/140 pounds

    Now we can add Kim's 11 pounds:

    1 117/140 + 11 = 1 117/140 + 11 0/140 = 12 117/140 pounds

    ### Answer: 12 117/140 pounds

Expected answer: 1797/140

Correct? Yes

🔗 Follow-up

Problem: Instead of initially collecting 11/20 of a pound of firewood, let's say Sarah collected only half as much, so 10/20 of a pound of firewood, while Alex still collected 9/7 pounds. How many pounds of firewood did they collect in total now?

Gemma 2B:

    Reasoning: Since 10/20 is equal to 1/2, Sarah collected 1/2 = 0.5 pounds of firewood.

    Alex collected 9/7 pounds, which is equal to 9 ÷ 7 = 1.2857 pounds (approximately).

    Now we can add the amounts of firewood they collected:

    0.5 + 1.2857 = 1.7857 pounds

    ### Answer: 1.7857 pounds

Expected answer: 25/14

Correct? No

🔗 Problem

Problem: Captain Bill sailed 19/5 miles north, before changing track and sailing an additional 12/15 miles north. How many miles north did Captain Bill sail in total?

Gemma 2B:

    Reasoning: To find the total distance sailed by Captain Bill, we need to add the two distances. However, we need to make sure they have the same denominator before adding. The least common multiple of 5 and 15 is 15. So, we can convert 19/5 to 57/15.

    Now, we can add the two distances:
    57/15 + 12/15 = 69/15

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
    69 ÷ 3 = 23
    15 ÷ 3 = 5

    So, the total distance sailed by Captain Bill is 23/5 miles.
    ### Answer: 23/5

Expected answer: 23/5

Correct? Yes

🔗 Follow-up

Problem: After traveling north for a total distance, Captain Bill decided to backtrack and went 20/17 miles south. How many miles away from the original starting point was Captain Bill located then?

Gemma 2B:

    Reasoning: We need to subtract the distance traveled south from the total distance traveled north.

    The total distance traveled north is 23/5 miles. To subtract 20/17 miles from this, we need to find a common denominator, which is 85. So, we can convert 23/5 to 391/85 and 20/17 to 100/85.

    Now, we can subtract:
    391/85 - 100/85 = 291/85

    This is the distance Captain Bill is away from the original starting point.
    ### Answer: 291/85

Expected answer: 291/85

Correct? Yes

🔗 Follow-up

Problem: After reconsidering the calculations, Captain Bill realized that he actually sailed 19/18 miles north initially instead of 19/5 miles before changing track and sailing an additional 12/15 miles north. In light of this new information, how many miles north did Captain Bill sail in total now?

Gemma 2B:

    Reasoning: To find the total distance sailed by Captain Bill, we need to add the two distances. However, we need to make sure they have the same denominator before adding. The least common multiple of 18 and 15 is 90. So, we can convert 19/18 to 95/90 and 12/15 to 72/90.

    Now, we can add the two distances:
    95/90 + 72/90 = 167/90

    This fraction is already in its simplest form, so we don't need to simplify it further.
    ### Answer: 167/90

Expected answer: 167/90

Correct? Yes

🔗 Problem

Problem: A restaurant uses 19/17 pounds of ham and 9/4 pounds of turkey for their signature sandwich. What is the total weight of the two types of meat per sandwich?

Gemma 2B:

    To find the total weight of the two types of meat per sandwich, we need to add the weights of the ham and turkey.

    First, let's convert the fractions to decimals to make it easier to add:

    19/17 = 1.117 (approximately)
    9/4 = 2.25

    Now, add the weights:

    1.117 + 2.25 = 3.367

    So, the total weight of the two types of meat per sandwich is approximately 3.367 pounds.

    ### Answer: 3.367 pounds

Expected answer: 229/68

Correct? No

🔗 Problem

Problem: Lucy has a sleeping bag that is 18/19 meter long. She got an extension for her sleeping bag which made it 8/11 meter longer. What's the total length of the sleeping bag now?

Gemma 2B:

    Reasoning: The original length of the sleeping bag is 18/19 meters. The extension adds 8/11 meters to the original length. To find the total length, we need to add the original length and the extension length.

    First, we need to find a common denominator for the two fractions. The least common multiple of 19 and 11 is 209. So, we can convert both fractions to have a denominator of 209:

    18/19 = (18*11)/(19*11) = 198/209
    8/11 = (8*19)/(11*19) = 152/209

    Now we can add the two fractions:

    198/209 + 152/209 = (198 + 152)/209 = 350/209

    So, the total length of the sleeping bag now is 350/209 meters.

    ### Answer: 350/209

Expected answer: 350/209

Correct? Yes

🔗 Follow-up

Problem: Considering the previous problem, what if Lucy's initial sleeping bag was 18/19 meter long and her extension was only 8/8 meter long. What would be the total length of her sleeping bag then?

Gemma 2B:

    Reasoning: The original length of the sleeping bag is 18/19 meters. The extension adds 8/8 meters to the original length. Since 8/8 is equal to 1, the extension is 1 meter long.

    To find the total length, we can add the original length and the extension length:

    18/19 + 1 = ?

    To add these two values, we need to convert the mixed number to an improper fraction:

    1 = 19/19 (since 19/19 = 1)

    Now we can add the two fractions:

    18/19 + 19/19 = (18 + 19)/19 = 37/19

    So, the total length of the sleeping bag now is 37/19 meters.

    ### Answer: 37/19

Expected answer: 37/19

Correct? Yes

🔗 Problem

Problem: Sarah pours 10/13 gallon of water into a container. Then she adds another 8/2 gallons of water into it. How many total gallons of water are there in the container now?

Gemma 2B:

    Reasoning: To find the total amount of water, we need to add the initial amount of water to the additional amount of water. To do this, we need to have the same denominator for both fractions. The least common multiple (LCM) of 13 and 2 is 26. So, we can convert both fractions to have a denominator of 26:

    10/13 = (10*2)/(13*2) = 20/26
    8/2 = (8*13)/(2*13) = 104/26

    Now we can add the two fractions:

    20/26 + 104/26 = (20 + 104)/26 = 124/26

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

    124/26 = (124/2)/(26/2) = 62/13

    So, there are 62/13 gallons of water in the container now.

    ### Answer: 62/13

Expected answer: 62/13

Correct? Yes

🔗 Follow-up

Problem: If originally, Sarah had poured 10/13 gallon of water, but instead of adding 8/2 gallons, she decided this time to add 16/2 gallons of water into the container, how many total gallons of water did she add now?

Gemma 2B:

    Reasoning: To find the total amount of water, we need to add the initial amount of water to the additional amount of water.

    The initial amount of water is 10/13 gallons.

    The additional amount of water is 16/2 gallons, which can be simplified to 8 gallons (since 16 divided by 2 is 8).

    Now we can add the two amounts:

    10/13 + 8 = ?

    To add a fraction and a whole number, we need to convert the whole number to a fraction with a denominator of 1:

    8 = 8/1

    Now we can add:

    10/13 + 8/1 = ?

    To add these fractions, we need to find the least common multiple (LCM) of 13 and 1, which is 13. So, we can convert the second fraction to have a denominator of 13:

    8/1 = (8*13)/(1*13) = 104/13

    Now we can add:

    10/13 + 104/13 = (10 + 104)/13 = 114/13

    So, Sarah added a total of 114/13 gallons of water.

    ### Answer: 114/13

Expected answer: 114/13

Correct? Yes

🔗 Problem

Problem: Mandy has 9/2 KGs of apples. She uses 1/4 KG of them to make apple pie. How many KGs of apples does she have left?

Gemma 2B:

    Reasoning: Mandy has 9/2 = 4.5 KGs of apples initially.
    She uses 1/4 KG of apples to make apple pie.
    To find out how many KGs of apples she has left, we subtract the amount used from the initial amount: 4.5 - 1/4 = 4.5 - 0.25 = 4.25 KGs.
    ### Answer: 4.25

Expected answer: 17/4

Correct? Yes

🔗 Follow-up

Problem: Mandy has 9/2 KGs of apples. She uses 1/4 KG of them to make apple pie. Afterwards, she finds 3/19 more KGs of apples in her refrigerator. How many KGs of apples does she have total now?

Gemma 2B:

    Reasoning: Mandy has 9/2 = 4.5 KGs of apples initially.
    She uses 1/4 KG of apples to make apple pie.
    To find out how many KGs of apples she has left, we subtract the amount used from the initial amount: 4.5 - 1/4 = 4.5 - 0.25 = 4.25 KGs.
    Then, she finds 3/19 more KGs of apples in her refrigerator.
    To find the total number of KGs of apples she has now, we add the additional apples to the remaining apples: 4.25 + 3/19 = 4.25 + 0.158 = 4.408 KGs.
    ### Answer: 4.408

Expected answer: 335/76

Correct? No

🔗 Follow-up

Problem: In the scenario where Mandy initially had 9/7 KGs of apples instead, and she still uses 1/4 KG of them for her apple pie, how many KGs of apples would she have left?

Gemma 2B:

    Reasoning: Mandy has 9/7 KGs of apples initially.
    She uses 1/4 KG of apples to make apple pie.
    To find out how many KGs of apples she has left, we subtract the amount used from the initial amount:
    First, we need to convert both fractions to have the same denominator, which is 28.
    So, 9/7 = 36/28 and 1/4 = 7/28.
    Now, we can subtract: 36/28 - 7/28 = 29/28.
    To convert this to a mixed number, we divide the numerator by the denominator: 29 ÷ 28 = 1 with a remainder of 1. So, 29/28 = 1 1/28.
    ### Answer: 1 1/28.

Expected answer: 29/28

Correct? Yes

🔗 Problem

Problem: John spends 12/7 hours fixing a watch and then spends an additional 3/9 hours polishing it. How many hours in total did he spent working on the watch?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 7 and 9 is 63. So, we can convert both fractions to have a denominator of 63:

    12/7 = (12*9)/(7*9) = 108/63
    3/9 = (3*7)/(9*7) = 21/63

    Now we can add:

    108/63 + 21/63 = 129/63

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 3:

    129/63 = (129/3)/(63/3) = 43/21

    So, John spent a total of 43/21 hours working on the watch.
    ### Answer: 43/21

Expected answer: 43/21

Correct? Yes

🔗 Follow-up

Problem: After fixing and polishing the watch, John spends an extra 12/13 hours adjusting its mechanism. How many hours in total did he spend working on the watch overall?

Gemma 2B:

    Reasoning: We already found that John spent 43/21 hours fixing and polishing the watch. Now, we need to add the additional 12/13 hours he spent adjusting the mechanism.

    To add these fractions, we need to find a common denominator. The least common multiple of 21 and 13 is 273. So, we can convert both fractions to have a denominator of 273:

    43/21 = (43*13)/(21*13) = 559/273
    12/13 = (12*21)/(13*21) = 252/273

    Now we can add:

    559/273 + 252/273 = 811/273

    So, John spent a total of 811/273 hours working on the watch overall.
    ### Answer: 811/273

Expected answer: 811/273

Correct? Yes

🔗 Follow-up

Problem: In a revised scenario, if John spends 12/7 hours fixing a watch and then spends 3/15 hours polishing it instead of the original 3/9 hours, how many hours in total did he spent working on the watch now?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 7 and 15 is 105. So, we can convert both fractions to have a denominator of 105:

    12/7 = (12*15)/(7*15) = 180/105
    3/15 = (3*7)/(15*7) = 21/105

    Now we can add:

    180/105 + 21/105 = 201/105

    So, John spent a total of 201/105 hours working on the watch.
    ### Answer: 201/105

Expected answer: 67/35

Correct? Yes

🔗 Problem

Problem: Peggy the Penguin was swimming and had traveled for 5/4 miles when she turned around to go back to her family. She swam back for 1/12 miles before deciding to rest. How many miles is Peggy from her family?

Gemma 2B:

    Reasoning: Peggy swam 5/4 miles away from her family, and then swam 1/12 miles back towards her family. To find the distance she is from her family, we need to subtract the distance she swam back from the distance she swam away.

    First, let's find a common denominator for the two fractions: 4 and 12. The least common multiple of 4 and 12 is 12. So, we can convert 5/4 to 15/12.

    Now, we can subtract: 15/12 - 1/12 = 14/12.

    We can simplify 14/12 by dividing both numerator and denominator by their greatest common divisor, which is 2: 14/12 = 7/6.

    ### Answer: 7/6 miles.

Expected answer: 7/6

Correct? Yes

🔗 Follow-up

Problem: Suppose that initially Peggy the Penguin had actually swam for 5/4 miles but she decided to turn back slightly earlier, swimming only 1/15 miles back towards her family before deciding to rest. How far would she be from her family in this scenario?

Gemma 2B:

    Reasoning: Peggy swam 5/4 miles away from her family, and then swam 1/15 miles back towards her family. To find the distance she is from her family, we need to subtract the distance she swam back from the distance she swam away.

    First, let's find a common denominator for the two fractions: 4 and 15. The least common multiple of 4 and 15 is 60. So, we can convert 5/4 to 75/60 and 1/15 to 4/60.

    Now, we can subtract: 75/60 - 4/60 = 71/60.

    We can simplify 71/60 by dividing both numerator and denominator by their greatest common divisor, which is 1 (since 71 and 60 are coprime): 71/60 = 71/60.

    ### Answer: 71/60 miles.

Expected answer: 71/60

Correct? Yes

🔗 Problem

Problem: A farmer has a fields where he grows wheat. One part of the field is 4 acres and another part is 11/12 of an acre. How many acres in total does he use to grow wheat?

Gemma 2B:

    Reasoning: To find the total area, we need to add the two parts together. The first part is 4 acres, and the second part is 11/12 of an acre. To add these, we need to convert the mixed unit to a single unit, which is acres.

    11/12 of an acre is equal to 0.9167 acres (approximately). Now, we can add the two parts together:

    4 acres + 0.9167 acres = 4.9167 acres

    ### Answer: 4.92 acres (approximately)

Expected answer: 59/12

Correct? No

🔗 Problem

Problem: If a dress designer used 11/4 yards of red fabric, and then added 5/17 yards of blue fabric, how many yards of fabric did she use in total?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 4 and 17 is 68. So, we can convert both fractions to have a denominator of 68:

    11/4 = (11*17)/(4*17) = 187/68
    5/17 = (5*4)/(17*4) = 20/68

    Now we can add:

    187/68 + 20/68 = 207/68

    ### Answer: 207/68

Expected answer: 207/68

Correct? Yes

🔗 Follow-up

Problem: If the designer also used an additional 19/10 yards of golden fabric, how many yards of fabric did she use in total now?

Gemma 2B:

    Reasoning: To add this new fraction to the total, we need to find a common denominator again. The least common multiple of 68 and 10 is 680. So, we can convert both fractions to have a denominator of 680:

    207/68 = (207*10)/(68*10) = 2070/680
    19/10 = (19*68)/(10*68) = 1292/680

    Now we can add:

    2070/680 + 1292/680 = 3362/680

    We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 20:

    3362 ÷ 20 = 168.1
    680 ÷ 20 = 34

    So, the total amount of fabric used is:

    ### Answer: 168.1/34 or 16 22/34 yards

Expected answer: 1681/340

Correct? No

🔗 Follow-up

Problem: If the dress designer initially used 11/4 yards of red fabric, but then decided to use only 5/5 yards of blue fabric, how many yards of fabric did she use in total?

Gemma 2B:

    Reasoning: We need to add the amount of red fabric and the amount of blue fabric.

    11/4 = 2.75 yards (converted to decimal)
    5/5 = 1 yard (converted to decimal)

    Now we can add:

    2.75 + 1 = 3.75

    ### Answer: 3.75 yards

Expected answer: 15/4

Correct? No

🔗 Problem

Problem: Jacob has 11/2 feet long guitar wire. If he uses 5/16 feet of it to fix a guitar, how much wire is remaining?

Gemma 2B:

    Reasoning: To find the remaining wire, we need to subtract the used wire from the total wire.

    First, let's convert the mixed number 11/2 to an improper fraction: 11/2 = 22/2 = 11.

    Now, we can subtract the used wire: 11 - 5/16.

    To subtract these fractions, we need a common denominator, which is 16. So, we can convert 11 to 11 × 16/16 = 176/16.

    Now, we can subtract: 176/16 - 5/16 = 171/16.

    So, the remaining wire is 171/16 feet.

    ### Answer: 171/16 feet.

Expected answer: 83/16

Correct? No

🔗 Problem

Problem: Samantha has a 4 fluid ounce tube of toothpaste. In one week, she uses 17/14 fluid ounces. How much toothpaste does she have left after that week?

Gemma 2B:

    Reasoning: Samantha starts with 4 fluid ounces of toothpaste.
    She uses 17/14 fluid ounces, which is equivalent to 1.21 fluid ounces (after converting the fraction to a decimal).
    To find out how much toothpaste she has left, we subtract the amount she used from the initial amount: 4 - 1.21 = 2.79 fluid ounces.
    ### Answer: 2.79 fluid ounces.

Expected answer: 39/14

Correct? No

🔗 Problem

Problem: Maria has 12 candies. She gives each of her 6 friends an equal amount of candies. Maria also has 20 stickers and she gives each of her 20 friends a sticker. How many candies and stickers does each friend get in total?

Gemma 2B:

    Reasoning: Maria has 12 candies and she gives an equal amount to 6 friends. To find out how many candies each friend gets, we can divide the total number of candies by the number of friends: 12 ÷ 6 = 2 candies per friend.

    Maria also has 20 stickers and she gives one sticker to each of her 20 friends. So, each of her 20 friends gets 1 sticker.

    Since Maria has 6 friends who get candies and 20 friends who get stickers, we need to find the common friends who get both candies and stickers. Let's assume Maria has x friends who are common to both groups. Then, we can set up the equation: x + (20 - x) = 6, where x is the number of common friends and (20 - x) is the number of friends who only get stickers. Solving for x, we get x = 6, which means all 6 friends who get candies also get stickers.

    So, each of Maria's 6 friends gets 2 candies and 1 sticker, for a total of 2 + 1 = 3 items.
    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: Maria initially had 12 candies and 20 stickers. Instead of having 6 friends, let's say she had 13 friends now. If she shares the candies among her 6 friends and the stickers among her 13 friends equally, how many candies and stickers does each friend get in total?

Gemma 2B:

    Reasoning: Maria has 12 candies and she gives an equal amount to 6 friends. To find out how many candies each friend gets, we can divide the total number of candies by the number of friends: 12 ÷ 6 = 2 candies per friend.

    Maria also has 20 stickers and she gives an equal amount to 13 friends. To find out how many stickers each friend gets, we can divide the total number of stickers by the number of friends: 20 ÷ 13 = 1 with a remainder of 7. Since we can't divide stickers, we'll ignore the remainder and each friend gets 1 sticker.

    However, not all friends get both candies and stickers. Only 6 friends get candies, and all 13 friends get stickers. So, 6 friends get 2 candies and 1 sticker, for a total of 2 + 1 = 3 items. The remaining 7 friends get only 1 sticker.
    ### Answer: 3 for 6 friends, 1 for 7 friends

Expected answer: 46/13

Correct? No

🔗 Problem

Problem: During a rainy day, the first rainfall lasted for 4/13 hours, and the next rainfall was a little longer and lasted for 11/5 hours. How many hours did it rain in total?

Gemma 2B:

    Reasoning: To add these two fractions, we need to find a common denominator. The least common multiple of 13 and 5 is 65. So, we can convert both fractions to have a denominator of 65:

    4/13 = (4*5)/(13*5) = 20/65
    11/5 = (11*13)/(5*13) = 143/65

    Now we can add:

    20/65 + 143/65 = 163/65

    To convert this back to hours, we can divide the numerator by the denominator:

    163 ÷ 65 = 2.51 hours

    ### Answer: 2.51 hours

Expected answer: 163/65

Correct? No

🔗 Problem

Problem: Jane cuts 10/12 yards of fabric from a blanket. Then, she cuts an additional 10/10 yard. How many yards of fabric has she cut from the blanket in total?

Gemma 2B:

    Reasoning: To find the total yards of fabric Jane has cut, we need to add the two fractions.

    First, we need to find a common denominator for the two fractions. The least common multiple of 12 and 10 is 60. So, we can convert both fractions to have a denominator of 60:

    10/12 = (10 x 5)/(12 x 5) = 50/60
    10/10 = (10 x 6)/(10 x 6) = 60/60

    Now we can add the fractions:

    50/60 + 60/60 = 110/60

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 10:

    110 ÷ 10 = 11
    60 ÷ 10 = 6

    So, the simplified fraction is:

    11/6

    To convert this to a mixed number, we can divide the numerator by the denominator:

    11 ÷ 6 = 1 with a remainder of 5

    So, the mixed number is:

    1 5/6

    ### Answer: 1 5/6 yards

Expected answer: 11/6

Correct? Yes

🔗 Follow-up

Problem: After cutting 10/12 yards and 10/10 yard from the blanket, Jane decides to cut an additional 4/12 yard. Now, how many yards of fabric has she cut from the blanket in total?

Gemma 2B:

    Reasoning: We already found that Jane cut a total of 1 5/6 yards from the blanket initially. Now, we need to add the additional 4/12 yard she cut.

    To add these fractions, we need to find a common denominator. The least common multiple of 6 and 12 is 12. So, we can convert the mixed number to an improper fraction with a denominator of 12:

    1 5/6 = (1 x 12) + 5)/6 = 17/6 = (17 x 2)/(6 x 2) = 34/12

    Now we can add the fractions:

    34/12 + 4/12 = 38/12

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

    38 ÷ 2 = 19
    12 ÷ 2 = 6

    So, the simplified fraction is:

    19/6

    To convert this to a mixed number, we can divide the numerator by the denominator:

    19 ÷ 6 = 3 with a remainder of 1

    So, the mixed number is:

    3 1/6

    ### Answer: 3 1/6 yards

Expected answer: 13/6

Correct? No

🔗 Follow-up

Problem: Originally, Jane cut 10/12 yard and then 10/10 yard from the blanket. However, consider if Jane had cut 11/12 yard instead of 10/12 yard at first, and then again cut 10/10 yard. How many yards of fabric would she have cut from the blanket now in this case?

Gemma 2B:

    Reasoning: Let's calculate the total yards of fabric Jane would have cut in this new scenario.

    First, Jane cuts 11/12 yard from the blanket.

    Then, she cuts an additional 10/10 yard, which is equal to 1 yard (since 10/10 = 1).

    To find the total yards of fabric Jane has cut, we add the two amounts:

    11/12 + 1 = ?

    To add these two quantities, we need to convert the mixed number to an improper fraction:

    11/12 = 11/12 (no change needed)
    1 = 12/12 (convert 1 to an improper fraction with a denominator of 12)

    Now we can add the fractions:

    11/12 + 12/12 = 23/12

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1 (since 23 and 12 do not have a common divisor other than 1):

    23 ÷ 1 = 23
    12 ÷ 1 = 12

    So, the simplified fraction is:

    23/12

    To convert this to a mixed number, we can divide the numerator by the denominator:

    23 ÷ 12 = 1 with a remainder of 11

    So, the mixed number is:

    1 11/12

    ### Answer: 1 11/12 yards

Expected answer: 23/12

Correct? Yes

🔗 Problem

Problem: A fairy sprinkles 11/12 oz of magic dust over an enchanted field. She then sprinkles an additional 9/10 oz of dust over a grove of enchanted apple trees. What is the total amount of magic dust the fairy used?

Gemma 2B:

    Reasoning: To find the total amount of magic dust used, we need to add the amount used on the enchanted field and the amount used on the grove of enchanted apple trees.

    First, let's convert both fractions to have a common denominator, which is 60.

    11/12 = (11*5)/(12*5) = 55/60
    9/10 = (9*6)/(10*6) = 54/60

    Now we can add the two amounts:

    55/60 + 54/60 = (55 + 54)/60 = 109/60

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    So, the total amount of magic dust used is 109/60 oz.

    ### Answer: 109/60 oz.

Expected answer: 109/60

Correct? Yes

🔗 Follow-up

Problem: A fairy sprinkles 11/12 oz of magic dust over an enchanted field. She then sprinkles an additional 9/10 oz of dust over a grove of enchanted apple trees. Then, she flies over to a nearby forest where she originally had 14/3 oz of magic dust. After using the dust over the field and apple trees, how much magic dust is left for the fairy now?

Gemma 2B:

    Reasoning: First, let's find the total amount of magic dust used by the fairy.

    11/12 oz + 9/10 oz = ?

    To add these fractions, we need to find a common denominator, which is 60.

    11/12 = (11*5)/(12*5) = 55/60
    9/10 = (9*6)/(10*6) = 54/60

    Now we can add the two amounts:

    55/60 + 54/60 = (55 + 54)/60 = 109/60

    To convert this fraction to a mixed number, we can divide the numerator by the denominator:

    109 ÷ 60 = 1 with a remainder of 49

    So, the total amount of magic dust used is 1 49/60 oz.

    Now, let's subtract this amount from the original amount of magic dust the fairy had:

    14/3 oz - 1 49/60 oz = ?

    To subtract these mixed numbers, we need to convert them to improper fractions:

    14/3 = (14*3)/(3*3) = 42/9
    1 49/60 = (1*60 + 49)/60 = 109/60

    Now we can subtract the two fractions:

    42/9 - 109/60 = ?

    To subtract these fractions, we need to find a common denominator, which is 180.

    42/9 = (42*20)/(9*20) = 840/180
    109/60 = (109*3)/(60*3) = 327/180

    Now we can subtract the two fractions:

    840/180 - 327/180 = (840 - 327)/180 = 513/180

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.

    513 ÷ 3 = 171
    180 ÷ 3 = 60

    So, the simplified fraction is:

    171/60

    To convert this fraction to a mixed number, we can divide the numerator by the denominator:

    171 ÷ 60 = 2 with a remainder of 51

    So, the amount of magic dust left for the fairy is 2 51/60 oz.

    ### Answer: 2 51/60 oz.

Expected answer: 57/20

Correct? Yes

🔗 Follow-up

Problem: A fairy sprinkles 11/12 oz of magic dust over an enchanted field. She then planned to sprinkle an additional 9/10 oz of dust over a grove of enchanted apple trees, but she accidentally sprinkles more, as much as 16/10 oz. What is the total amount of magic dust the fairy used now?

Gemma 2B:

    Reasoning: To find the total amount of magic dust used, we need to add the amount used on the enchanted field and the amount used on the grove of enchanted apple trees.

    First, let's convert both fractions to have a common denominator, which is 60.

    11/12 = (11*5)/(12*5) = 55/60
    16/10 = (16*6)/(10*6) = 96/60

    Now we can add the two amounts:

    55/60 + 96/60 = (55 + 96)/60 = 151/60

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    So, the total amount of magic dust used is 151/60 oz.

    ### Answer: 151/60 oz.

Expected answer: 151/60

Correct? Yes

🔗 Problem

Problem: A word game assigns 3/11 of a point for each vowel used and 8/10 of a point for each consonant. If you use 1 vowel and 1 consonant, what will your score be?

Gemma 2B:

    Let's calculate the score:

    For 1 vowel, the score is 3/11 = 0.2727 (approximately)
    For 1 consonant, the score is 8/10 = 0.8

    Total score = 0.2727 + 0.8 = 1.0727 (approximately)

    ### Answer: 1.07

Expected answer: 59/55

Correct? No

🔗 Problem

Problem: You are writing a letter that is 4/1 pages long. You remove 14/9 pages from it. How many pages is the letter now?

Gemma 2B:

    Reasoning: To find the total number of pages initially, we need to convert the mixed fraction 4/1 to an improper fraction, which is 4.

    Now, we need to subtract 14/9 from 4. To do this, we need to find a common denominator between 9 and 1, which is 9. So, we can rewrite 4 as 36/9.

    Now, we can subtract: 36/9 - 14/9 = 22/9.

    To convert this back to a mixed fraction, we divide the numerator by the denominator: 22 ÷ 9 = 2 with a remainder of 4. So, the mixed fraction is 2 4/9.

    ### Answer: 2 4/9 pages.

Expected answer: 22/9

Correct? Yes

🔗 Follow-up

Problem: You decide to add some more content to your letter. If you add 7/12 of a page, how many pages will the letter be then?

Gemma 2B:

    Reasoning: We already know the letter is 2 4/9 pages long. To add 7/12 of a page, we need to convert both fractions to have a common denominator, which is 36.

    So, 2 4/9 = 2 + 16/36 = 2 16/36, and 7/12 = 21/36.

    Now, we can add: 2 16/36 + 21/36 = 2 37/36.

    To convert this back to a mixed fraction, we divide the numerator by the denominator: 37 ÷ 36 = 1 with a remainder of 1. So, we add 1 to the whole number part: 2 + 1 = 3. The mixed fraction is 3 1/36.

    ### Answer: 3 1/36 pages.

Expected answer: 109/36

Correct? Yes

🔗 Follow-up

Problem: What if your original letter was slightly longer, being 15/1 pages in total, but you still removed the same 14/9 pages from it? How many pages would the letter be then?

Gemma 2B:

    Reasoning: We can convert the mixed fraction 15/1 to an improper fraction, which is 15.

    Now, we need to subtract 14/9 from 15. To do this, we need to find a common denominator between 9 and 1, which is 9. So, we can rewrite 15 as 135/9.

    Now, we can subtract: 135/9 - 14/9 = 121/9.

    To convert this back to a mixed fraction, we divide the numerator by the denominator: 121 ÷ 9 = 13 with a remainder of 4. So, the mixed fraction is 13 4/9.

    ### Answer: 13 4/9 pages.

Expected answer: 121/9

Correct? Yes

🔗 Problem

Problem: Anne painted 16/20 of a table, and then Bob painted an additional 5/20 of the table. How much of the table has been painted in total?

Gemma 2B:

    Reasoning: Anne painted 16/20 of the table, and Bob painted an additional 5/20 of the table. To find the total amount of the table that has been painted, we need to add the fractions.

    First, we can convert both fractions to have a common denominator, which is 20. Then, we can add:

    16/20 + 5/20 = (16 + 5)/20 = 21/20

    So, 21/20 of the table has been painted in total.

    ### Answer: 21/20

Expected answer: 21/20

Correct? Yes

🔗 Follow-up

Problem: After Anne and Bob painted parts of the table, Carl decided to add to their work by painting another 11/5 of the table. Now, how much of the table has been painted in total?

Gemma 2B:

    Reasoning: We already know that Anne and Bob painted 21/20 of the table. Carl painted an additional 11/5 of the table. To add these fractions, we need to find a common denominator.

    The least common multiple of 20 and 5 is 20. So, we can convert 11/5 to have a denominator of 20:

    11/5 = (11 × 4)/(5 × 4) = 44/20

    Now, we can add the fractions:

    21/20 + 44/20 = (21 + 44)/20 = 65/20

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5:

    65/20 = (65 ÷ 5)/(20 ÷ 5) = 13/4

    So, 13/4 of the table has been painted in total.

    ### Answer: 13/4

Expected answer: 13/4

Correct? Yes

🔗 Follow-up

Problem: Suppose before Carl added more paint, instead of Bob painting an additional 5/20 of the table, he could only manage to paint 5/14 of it. In this case, how much of the table has been painted by Anne and Bob together?

Gemma 2B:

    Reasoning: Anne painted 16/20 of the table, and Bob painted 5/14 of the table. To find the total amount of the table that has been painted, we need to add the fractions.

    First, we need to find a common denominator for the two fractions. The least common multiple of 20 and 14 is 140. So, we can convert both fractions to have a denominator of 140:

    16/20 = (16 × 7)/(20 × 7) = 112/140
    5/14 = (5 × 10)/(14 × 10) = 50/140

    Now, we can add the fractions:

    112/140 + 50/140 = (112 + 50)/140 = 162/140

    So, 162/140 of the table has been painted by Anne and Bob together.

    ### Answer: 162/140

Expected answer: 81/70

Correct? Yes

🔗 Problem

Problem: The star Alpha shines 17/3 times brighter than an average star, while the star Bravo shines 20/16 times as bright. How much brighter are both stars compared to an average star if you add up the relative brightness of these two stars?

Gemma 2B:

    Reasoning: To find the relative brightness of Alpha compared to an average star, we can simplify the fraction 17/3 by dividing both numerator and denominator by their greatest common divisor, which is 1. So, Alpha shines 17/3 = 5.67 times brighter than an average star.

    To find the relative brightness of Bravo compared to an average star, we can simplify the fraction 20/16 by dividing both numerator and denominator by their greatest common divisor, which is 4. So, Bravo shines 20/16 = 1.25 times brighter than an average star.

    To find the total relative brightness of both stars, we add their individual relative brightnesses: 5.67 + 1.25 = 6.92.

    ### Answer: 6.92

Expected answer: 83/12

Correct? No

🔗 Problem

Problem: There are 17/20 kg of red apples and 18/8 kg of green apples in a grocery store. How many kilograms of apples are in the store in total?

Gemma 2B:

    Reasoning: To add the weights of the apples, we need to have the same denominator. The least common multiple of 20 and 8 is 40. So, we can convert both fractions to have a denominator of 40:

    17/20 = (17*2)/(20*2) = 34/40
    18/8 = (18*5)/(8*5) = 90/40

    Now we can add the weights:

    34/40 + 90/40 = (34+90)/40 = 124/40

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:

    124/40 = (124/4)/(40/4) = 31/10

    So, there are 31/10 kg of apples in the store in total.

    ### Answer: 31/10 kg

Expected answer: 31/10

Correct? Yes

🔗 Follow-up

Problem: The grocery store owner also received an additional batch of yellow apples that weighs 17/15 kg. So, now how many total kilograms of apples are in the store?

Gemma 2B:

    Reasoning: We already found that there are 31/10 kg of apples in the store. To add the new batch of yellow apples, we need to have the same denominator. The least common multiple of 10 and 15 is 30. So, we can convert both fractions to have a denominator of 30:

    31/10 = (31*3)/(10*3) = 93/30
    17/15 = (17*2)/(15*2) = 34/30

    Now we can add the weights:

    93/30 + 34/30 = (93+34)/30 = 127/30

    So, there are 127/30 kg of apples in the store in total.

    ### Answer: 127/30 kg

Expected answer: 127/30

Correct? Yes

🔗 Follow-up

Problem: Instead of having 17/20 kg of red apples as stated in the original problem, suppose the store only had 3/20 kg of red apples. Along with the 18/8 kg of green apples, how many kilograms of apples would be in the store now?

Gemma 2B:

    Reasoning: To add the weights of the apples, we need to have the same denominator. The least common multiple of 20 and 8 is 40. So, we can convert both fractions to have a denominator of 40:

    3/20 = (3*2)/(20*2) = 6/40
    18/8 = (18*5)/(8*5) = 90/40

    Now we can add the weights:

    6/40 + 90/40 = (6+90)/40 = 96/40

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 8:

    96/40 = (96/8)/(40/8) = 12/5

    So, there are 12/5 kg of apples in the store in total.

    ### Answer: 12/5 kg

Expected answer: 12/5

Correct? Yes

🔗 Problem

Problem: If a bus drives 12/20 of a mile then goes an additional 12/12 of a mile, how many miles did the bus travel in total?

Gemma 2B:

    Reasoning: To find the total distance traveled, we need to add the two distances together. However, we need to make sure we have a common denominator to add the fractions.

    12/20 = 0.6 miles ( converted to decimal)
    12/12 = 1 mile ( converted to decimal)

    Now, we can add the distances:
    0.6 + 1 = 1.6 miles

    ### Answer: 1.6 miles

Expected answer: 8/5

Correct? No

🔗 Problem

Problem: In the first hour, a shark swims 3/9 miles and in the second hour height increases its speed to swim 13/5 miles. How many miles does the shark swim in total in these two hours?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 9 and 5 is 45. So, we can convert both fractions to have a denominator of 45:

    (3/9) = (15/45)
    (13/5) = (117/45)

    Now we can add:

    (15/45) + (117/45) = (132/45)

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 3:

    (132/45) = (44/15)

    So, the shark swims a total of 44/15 miles in these two hours.

    ### Answer: 44/15

Expected answer: 44/15

Correct? Yes

🔗 Follow-up

Problem: After swimming for two hours, the shark decides to swim for a third hour and it covers a distance of 14/9 miles. What is the total distance covered by the shark in these three hours?

Gemma 2B:

    Reasoning: We already found the total distance covered by the shark in the first two hours: 44/15 miles.

    To find the total distance covered in three hours, we need to add the distance covered in the third hour: 14/9 miles.

    To add these fractions, we need to find a common denominator. The least common multiple of 15 and 9 is 45. So, we can convert both fractions to have a denominator of 45:

    (44/15) = (132/45)
    (14/9) = (70/45)

    Now we can add:

    (132/45) + (70/45) = (202/45)

    So, the total distance covered by the shark in these three hours is 202/45 miles.

    ### Answer: 202/45

Expected answer: 202/45

Correct? Yes

🔗 Follow-up

Problem: In reconsideration of the first hour, what if the shark only swam for 3/7 miles instead of 3/9 miles, but still swam 13/5 miles in the the second hour. What would be the total distance covered in these two hours then?

Gemma 2B:

    Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 7 and 5 is 35. So, we can convert both fractions to have a denominator of 35:

    (3/7) = (15/35)
    (13/5) = (91/35)

    Now we can add:

    (15/35) + (91/35) = (106/35)

    So, the shark swims a total of 106/35 miles in these two hours.

    ### Answer: 106/35

Expected answer: 106/35

Correct? Yes

🔗 Problem

Problem: A drummer hits a rhythm where they hit once every 17/17 seconds for the first beat and then 2/12 seconds for the second beat. How long does it take for the drummer to hit the two beats together?

Gemma 2B:

    To find the time it takes for the drummer to hit the two beats together, we need to find the least common multiple (LCM) of 17/17 seconds and 2/12 seconds.

    First, let's convert both fractions to have the same denominator, which is 12:

    17/17 = 12/12 (since 17/17 = 1, and 1 = 12/12)
    2/12 = 2/12 (no conversion needed)

    Now, we can find the LCM of 12/12 and 2/12:

    LCM(12, 2) = 12

    So, the drummer will hit the two beats together every 12 seconds.

    ### Answer: 12 seconds

Expected answer: 7/6

Correct? No

🔗 Problem

Problem: If a fireplace burns 12/17 cord of wood in the morning and 8/19 cord in the evening, what is the total cord of wood it burns in a day?

Gemma 2B:

    Reasoning: To find the total cord of wood burned in a day, we need to add the amount burned in the morning and the evening.

    First, let's convert the fractions to have a common denominator, which is 323. We can do this by multiplying the numerator and denominator of each fraction by the necessary multiple:

    Morning: 12/17 = (12*19)/(17*19) = 228/323
    Evening: 8/19 = (8*17)/(19*17) = 136/323

    Now we can add the two fractions:

    228/323 + 136/323 = (228 + 136)/323 = 364/323

    So, the total cord of wood burned in a day is 364/323.

    ### Answer: 364/323

Expected answer: 364/323

Correct? Yes

🔗 Follow-up

Problem: In addition to the wood burned throughout the day, the fireplace burns an additional 19/20 cord of wood at night. What is the total cord of wood the fireplace burns in one full day?

Gemma 2B:

    Reasoning: We already found the total cord of wood burned during the day: 364/323. Now, we need to add the additional wood burned at night: 19/20.

    To add these fractions, we need to find a common denominator. The least common multiple of 323 and 20 is 6460. So, we can convert both fractions to have a denominator of 6460:

    Day: 364/323 = (364*20)/(323*20) = 7280/6460
    Night: 19/20 = (19*323)/(20*323) = 6137/6460

    Now we can add the two fractions:

    7280/6460 + 6137/6460 = (7280 + 6137)/6460 = 13417/6460

    So, the total cord of wood burned in one full day is 13417/6460.

    ### Answer: 13417/6460

Expected answer: 13417/6460

Correct? Yes

🔗 Problem

Problem: A butterfly's flight consisted of two segments. The first segment was 18/19 of a mile and the second was 9/17 of a mile. How long was the entire flight?

Gemma 2B:

    Reasoning: To find the total length of the flight, we need to add the lengths of the two segments. To do this, we need to find a common denominator for the two fractions. The least common multiple of 19 and 17 is 323. So, we can convert both fractions to have a denominator of 323:

    First segment: (18/19) × (17/17) = 306/323 miles
    Second segment: (9/17) × (19/19) = 171/323 miles

    Now we can add the two segments:

    Total flight = 306/323 + 171/323 = 477/323 miles

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 29:

    477 ÷ 29 = 16.45
    323 ÷ 29 = 11.14

    So, the total flight is approximately 16.45/11.14 = 1.48 miles.

    ### Answer: 1.48 miles

Expected answer: 477/323

Correct? No

🔗 Problem

Problem: While measuring a map, Jenna finds that the distance between two cities is 13/10 inches, and the distance from the second city to the third city is 14/15 inches. What is the total distance Jenna measured between the three cities on the map?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distances between the cities. However, we need to have a common denominator to add these fractions. The least common multiple of 10 and 15 is 30. So, we can convert both fractions to have a denominator of 30:

    13/10 = (13 x 3)/(10 x 3) = 39/30
    14/15 = (14 x 2)/(15 x 2) = 28/30

    Now we can add the distances:

    39/30 + 28/30 = (39 + 28)/30 = 67/30

    ### Answer: 67/30

Expected answer: 67/30

Correct? Yes

🔗 Follow-up

Problem: Instead of the distance between the first two cities on the map being 13/10 inches, suppose it is 13/7 inches. Keeping the distance from the second city to the third city the same at 14/15 inches, what would then be the total distance between the three cities on the map?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the distances between the cities. However, we need to have a common denominator to add these fractions. The least common multiple of 7 and 15 is 105. So, we can convert both fractions to have a denominator of 105:

    13/7 = (13 x 15)/(7 x 15) = 195/105
    14/15 = (14 x 7)/(15 x 7) = 98/105

    Now we can add the distances:

    195/105 + 98/105 = (195 + 98)/105 = 293/105

    ### Answer: 293/105

Expected answer: 293/105

Correct? Yes

🔗 Problem

Problem: A helium balloon rises at a rate of 13/6 feet per second. After a gust of wind, its speed increases by 3/16 feet per second. What is the new speed of the balloon in feet per second?

Gemma 2B:

    Reasoning: The original speed of the balloon is 13/6 feet per second. The speed increases by 3/16 feet per second, so we need to add this to the original speed.

    To add these fractions, we need to find a common denominator, which is 48. So, we can convert both fractions to have a denominator of 48:

    13/6 = 104/48
    3/16 = 9/48

    Now, we can add:

    104/48 + 9/48 = 113/48

    So, the new speed of the balloon is 113/48 feet per second.

    ### Answer: 113/48

Expected answer: 113/48

Correct? Yes

🔗 Follow-up

Problem: If a second identical helium balloon behaving exactly like the first one rises alongside, what would be their total combined speed in feet per second?

Gemma 2B:

    Reasoning: Since the second balloon is identical and behaves exactly like the first one, it also rises at a speed of 113/48 feet per second.

    To find the total combined speed, we simply add the speeds of the two balloons:

    113/48 + 113/48 = 226/48

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

    226 ÷ 2 = 113
    48 ÷ 2 = 24

    So, the total combined speed is:

    113/24

    ### Answer: 113/24

Expected answer: 113/24

Correct? Yes

🔗 Problem

Problem: Scarlett has 16/10 gallons of red paint. If she uses 1/20 of a gallon for a small art project, how many gallons of red paint will she have left?

Gemma 2B:

    Reasoning: Scarlett starts with 16/10 = 1.6 gallons of red paint.
    She uses 1/20 = 0.05 gallons for the small art project.
    To find out how much paint she has left, we subtract the amount used from the initial amount: 1.6 - 0.05 = 1.55 gallons.
    ### Answer: 1.55

Expected answer: 31/20

Correct? Yes

🔗 Follow-up

Problem: After finishing the small art project, Scarlett decides to mix the remaining red paint with 5/7 gallons of yellow paint to make orange paint. How many gallons of paint does she have now?

Gemma 2B:

    Reasoning: Scarlett has 1.55 gallons of red paint left.
    She adds 5/7 = 0.71 gallons of yellow paint to mix with the red paint.
    To find the total amount of paint, we add the amount of red paint and the amount of yellow paint: 1.55 + 0.71 = 2.26 gallons.
    ### Answer: 2.26

Expected answer: 317/140

Correct? No

🔗 Follow-up

Problem: Suppose Scarlett initially had 16/10 gallons of red paint. But this time, she uses 2/20 of a gallon for her small project instead. How many gallons of red paint does she have left now?

Gemma 2B:

    Reasoning: Scarlett starts with 16/10 = 1.6 gallons of red paint.
    She uses 2/20 = 0.1 gallons for the small art project.
    To find out how much paint she has left, we subtract the amount used from the initial amount: 1.6 - 0.1 = 1.5 gallons.
    ### Answer: 1.5

Expected answer: 3/2

Correct? No

🔗 Problem

Problem: Susie has a box of 12 chocolate bars. She decides to eat 2/5 of a chocolate bar herself. How many chocolate bars are left in the box?

Gemma 2B:

    Reasoning: Susie has 12 chocolate bars initially. She eats 2/5 of a chocolate bar, which means she eats 0.4 chocolate bars (since 2/5 = 0.4). So, she has 12 - 0.4 = 11.6 chocolate bars left. Since we can't have a fraction of a chocolate bar, we round down to the nearest whole number, which is 11.

    ### Answer: 11

Expected answer: 58/5

Correct? No

🔗 Problem

Problem: A plane is flying at an altitude of 2 miles, then it descends by 10/15 of a mile. What is the new altitude of the plane?

Gemma 2B:

    Reasoning: The plane is initially at an altitude of 2 miles. It descends by 10/15 of a mile, which is equivalent to 2/3 of a mile (since 10/15 = 2/3). To find the new altitude, we subtract the descent from the initial altitude: 2 - 2/3 = 2 - 0.67 = 1.33 miles.

    ### Answer: 1.33 miles

Expected answer: 4/3

Correct? No

🔗 Problem

Problem: A child goes down a slide that's 6/19 meters long, and then goes down another slide that's 17/4 meters long. How many total meters did they slide?

Gemma 2B:

    Reasoning: To find the total distance, we need to add the lengths of the two slides. However, we need to make sure we have a common denominator before adding. The least common multiple of 19 and 4 is 76. So, we can convert both fractions to have a denominator of 76:

    6/19 = (6*4)/(19*4) = 24/76
    17/4 = (17*19)/(4*19) = 323/76

    Now we can add:

    24/76 + 323/76 = 347/76

    To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 1. So, the total distance is:

    347/76 = 4.51 meters (approximately)

    ### Answer: 4.51 meters

Expected answer: 347/76

Correct? No

🔗 Problem

Problem: A colonial fireplace burns firewood at a rate of 4/15 cords per hour in the early morning. In the late night, the rate increases to 14/15 cords per hour. How much firewood does the fireplace burn in total in one hour split between the early morning and late night?

Gemma 2B:

    Let's break this down into two parts: the amount of firewood burned in the early morning and the amount burned in the late night.

    In the early morning, the fireplace burns firewood at a rate of 4/15 cords per hour. Since we're interested in the amount burned in one hour, we can simply take the rate as the amount burned: 4/15 cords.

    In the late night, the fireplace burns firewood at a rate of 14/15 cords per hour. Again, we can take the rate as the amount burned in one hour: 14/15 cords.

    To find the total amount of firewood burned, we add the amounts burned in the early morning and late night: (4/15) + (14/15) = (4 + 14)/15 = 18/15 = 1 3/15 = 1.2 cords.

    ### Answer: 1.2 cords

Expected answer: 6/5

Correct? No

🔗 Problem

Problem: An alien travelled 9/20 of a light year towards earth then decided to move forward another 11/7 light years. How many light years has the alien travelled in total?

Gemma 2B:

    Reasoning: To find the total distance traveled, we need to add the two distances. However, we need to have the same units for both distances. Since 9/20 is a fraction of a light year, we can leave it as is. The second distance, 11/7, is also a fraction of a light year, so we can add the two fractions.

    To add fractions, we need to find a common denominator. The least common multiple (LCM) of 20 and 7 is 140. So, we can convert both fractions to have a denominator of 140:

    9/20 = (9*7)/(20*7) = 63/140
    11/7 = (11*20)/(7*20) = 220/140

    Now we can add the fractions:

    63/140 + 220/140 = 283/140

    So, the alien has traveled a total distance of 283/140 light years.

    ### Answer: 283/140

Expected answer: 283/140

Correct? Yes

🔗 Follow-up

Problem: After traveling ((9 / 20) + (11 / 7)) light years towards earth, the alien continues its journey for an additional 14/2 light years. How many light years in total has the alien traveled?

Gemma 2B:

    Reasoning: First, let's evaluate the expression inside the parentheses:

    (9/20) + (11/7) = (63/140) + (220/140) = 283/140

    So, the alien has traveled 283/140 light years initially.

    Then, the alien continues its journey for an additional 14/2 light years. To add this to the initial distance, we need to convert 14/2 to an equivalent fraction with a denominator of 140:

    14/2 = (14*70)/(2*70) = 980/140

    Now, we can add the two distances:

    283/140 + 980/140 = 1263/140

    So, the alien has traveled a total distance of 1263/140 light years.

    ### Answer: 1263/140

Expected answer: 1263/140

Correct? Yes

🔗 Follow-up

Problem: The alien originally travelled ((9 / 20) + (11 / 7)) light years towards earth. But what if instead, the alien had only travelled (9 / 20) + (11 / 11) light years to start with? How many light years would the alien have travelled then?

Gemma 2B:

    Reasoning: Let's evaluate the expression (9/20) + (11/11).

    (9/20) is a fraction, and (11/11) is equal to 1, since 11 divided by 11 is 1.

    So, we can rewrite the expression as:

    (9/20) + 1

    To add a fraction and a whole number, we can convert the whole number to a fraction with a denominator of 1:

    1 = 20/20 (since 20/20 = 1)

    Now we can add the fractions:

    (9/20) + (20/20) = (9 + 20)/20 = 29/20

    So, the alien would have traveled 29/20 light years.

    ### Answer: 29/20

Expected answer: 29/20

Correct? Yes

🔗 Problem

Problem: If Bob has 10/2 of a cucumber and he adds it to 1/7 of another cucumber, how many cucumbers does he have in total?

Gemma 2B:

    Reasoning: Bob has 10/2 = 5/1 = 5 slices of a cucumber, which means he has 5/8 of a whole cucumber (since a whole cucumber has 8 slices).

    He adds 1/7 of another cucumber, which is equivalent to 1/7 × 8 = 8/7 slices.

    To find the total number of slices, we add the number of slices Bob already has to the new slices: 5 + 8/7 = 5 × 7/7 + 8/7 = 43/7 slices.

    Since a whole cucumber has 8 slices, we can convert the total number of slices to a mixed number: 43/7 = 6 1/7.

    So, Bob has a total of 6 1/7 cucumbers.
    ### Answer: 6 1/7

Expected answer: 36/7

Correct? No