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

Qwen2-Math 72B:

 Reasoning: First, we need to calculate the initial number of cucumbers Carla could grow per plant by multiplying 22/3 by 22/19.
(22/3) * (22/19) = <<(22/3)*(22/19)=16.205368421052632>>16.205368421052632
Next, we need to multiply this initial amount by 23/17 to find out how many cucumbers she is expecting to grow per plant after adjusting her production method.
16.205368421052632 * (23/17) = <<16.205368421052632*(23/17)=21.02676842105263>>21.02676842105263
### Answer: 21.02676842105263

Expected answer: 11132/969

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Pierre has 19/4 - 7/25 = <<19/4-7/25=4.75-0.28=4.47>>4.47 kg of grapes left after eating some.
Pierre has 4.47 + 30/9 = <<4.47+30/9=4.47+3.33=7.8>>7.8 kg of grapes now.
### Answer: 7.8

Expected answer: 2341/300

Correct? No

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

Qwen2-Math 72B:

 Reasoning: First, we need to find a common denominator for the fractions. The least common multiple of 22, 29, and 3 is 1914. We convert each fraction to have this common denominator:
- Wall repairs: \( \frac{26}{22} = \frac{26 \times 87}{22 \times 87} = \frac{2262}{1914} \)
- Moat renovations: \( \frac{4}{29} = \frac{4 \times 66}{29 \times 66} = \frac{264}{1914} \)
- Catapults: \( \frac{11}{3} = \frac{11 \times 638}{3 \times 638} = \frac{6918}{1914} \)

Adding these fractions together gives us the total cost as a fraction of the budget:
\[ \frac{2262}{1914} + \frac{264}{1914} + \frac{6918}{1914} = \frac{9444}{1914} \]

Simplifying this fraction, we get:
\[ \frac{9444}{1914} = \frac{4722}{957} = \frac{1574}{319} \]

### Answer: \( \frac{1574}{319} \)

Expected answer: 4772/957

Correct? No

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

Qwen2-Math 72B:

 Reasoning: First, calculate the daily feeding amount: (25 / 19) * (30 / 26) = <<(25/19)*(30/26)=1.6176470588235294>>1.6176470588235294 lbs.
Next, calculate the weekly feeding amount squared: (1.6176470588235294)^2 = <<(1.6176470588235294)^2=2.616976>>2.616976 lbs^2.
Finally, multiply the weekly feeding amount squared by the daily feeding amount: 2.616976 * 1.6176470588235294 = <<2.616976*1.6176470588235294=4.227987>>4.227987 lbs.
### Answer: 4.227987

Expected answer: 52734375/15069223

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Lara needs (11/3) + (8/30) = <<(11/3)+(8/30)=118/30>>118/30 feet of materials to make the necklace.
### Answer: 118/30

Expected answer: 59/15

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: Plane A travels 24/11 miles in one minute.
Plane B travels 26/27 miles in one minute.
The difference in distance traveled is 24/11 - 26/27 = <<(24*27-26*11)/(11*27)=430/297>>430/297 miles.
### Answer: 430/297

Expected answer: 362/297

Correct? No

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

Qwen2-Math 72B:

 Reasoning: To find the combined amount of fish that both bears eat per day, we need to multiply the amount that the adult bear eats by the amount that the young bear eats.
14/7 * 25/13 = <<14/7*25/13=50/13>>50/13 pounds of fish per day.
### Answer: 50/13

Expected answer: 50/13

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To find the total time, we add the fractions: 12/8 + 12/3.
First, find a common denominator, which is 24. Convert the fractions: 12/8 becomes 36/24 and 12/3 becomes 96/24.
Adding these fractions gives us 36/24 + 96/24 = 132/24.
Simplifying the fraction 132/24, we divide both the numerator and the denominator by their greatest common divisor, which is 12, resulting in 11/2.
### Answer: 11/2

Expected answer: 11/2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The total number of chocolate bars you have now is 28/29 + 8/22.
To add these fractions, we need a common denominator. The least common multiple of 29 and 22 is 638.
So, 28/29 = <<28*22/29*22=616/638>>616/638 and 8/22 = <<8*29/22*29=232/638>>232/638.
Adding these fractions, we get 616/638 + 232/638 = <<616+232=848>>848/638.
Simplifying this fraction, we get 424/319.
### Answer: 424/319

Expected answer: 424/319

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To produce two needles, the maker will need 2 * (27/26) = <<2*27/26=27/13>>27/13 pounds of material.
To produce the additional piece, the maker will need 27/6 pounds of material.
Therefore, the total material required is 27/13 + 27/6 = <<27/13+27/6=81/26>>81/26 pounds of material.
### Answer: 81/26

Expected answer: 171/26

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The first candle burns at a rate of 6/4 inches per hour, which simplifies to 3/2 inches per hour.
The second candle burns at a rate of 14/16 inches per hour, which simplifies to 7/8 inches per hour.
To find the total rate at which the two candles burn together, we add the rates: 3/2 + 7/8 = 12/8 + 7/8 = 19/8 inches per hour.
### Answer: 19/8

Expected answer: 19/8

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: Sophia has 17/20 + 1/4 = <<17/20+1/4=27/20>>27/20 dollars after her friend gives her money.
Sophia has 27/20 + 1 = <<27/20+1=47/20>>47/20 dollars after her brother gives her money.
### Answer: 47/20

Expected answer: 21/10

Correct? No

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

Qwen2-Math 72B:

 Reasoning: First, we need to find the initial time investment (p) by adding the time spent on composing the music and writing the lyrics: p = 16/4 + 16/29 = <<16/4+16/29=16/4+16/29=4+0.5517241379310345=4.5517241379310345>>4.5517241379310345 hours.

Next, we need to find the new total time (b) by adding the time spent on mixing and mastering to the initial time investment: b = p + 28/13 = <<4.5517241379310345+28/13=4.5517241379310345+28/13=4.5517241379310345+2.1538461538461537=6.705570291777188>>6.705570291777188 hours.

Finally, we need to find the final time spent on producing the song by subtracting the time the drummer used less from the new total time: (b - (18 / 4)) = <<6.705570291777188-18/4=6.705570291777188-18/4=6.705570291777188-4.5=2.205570291777188>>2.205570291777188 hours.
### Answer: 2.205570291777188

Expected answer: 1663/754

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Monica has 21/15 + 29/17 = <<(21/15)+(29/17)=1.4+1.7058823529411765=3.1058823529411765>>3.1058823529411765 dozens of cookies in total.
Monica decides to increase her stock by a ratio of 7/5, so she will have 3.1058823529411765 * 7/5 = <<(3.1058823529411765)*(7/5)=4.348235294117647>>4.348235294117647 dozens of cookies for the cookie festival.
### Answer: 4.348235294117647

Expected answer: 1848/425

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The chef uses 26/24 = <<26/24=1.0833333333333333>>1.0833333333333333 kg of sugar for one cake.
After making one cake, the chef has 28-1.0833333333333333 = <<28-1.0833333333333333=26.916666666666668>>26.916666666666668 kg of sugar left.
After adding 10/6 = <<10/6=1.6666666666666667>>1.6666666666666667 kg of sugar, the chef has 26.916666666666668+1.6666666666666667 = <<26.916666666666668+1.6666666666666667=28.583333333333336>>28.583333333333336 kg of sugar.
### Answer: 28.583333333333336

Expected answer: 343/12

Correct? No

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

Qwen2-Math 72B:

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

Expected answer: 2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The fraction of apple pie eaten is 10/12 = <<10/12=5/6>>5/6.
The fraction of blueberry pie eaten is 10/29 = <<10/29=10/29>>10/29.
The total fraction of pie eaten is 5/6 + 10/29 = <<5/6+10/29=145/174>>145/174.
### Answer: 145/174

Expected answer: 205/174

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Marta uses 20 colored pencils every 11 days, so she uses 20/11 colored pencils per day.
Marta uses 23 out of every 26 colored pencils for shading techniques, so she uses 23/26 of her colored pencils for shading.
To find out how many colored pencils Marta uses for shading in her art projects over an 11-day period, we need to multiply the number of colored pencils she uses per day by the number of days and then multiply that by the fraction of colored pencils she uses for shading.
So, Marta uses (20/11) * 11 * (23/26) = <<(20/11)*11*(23/26)=230/26>>230/26 colored pencils for shading in her art projects over an 11-day period.
### Answer: 230/26

Expected answer: 230/143

Correct? No

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

Qwen2-Math 72B:

 Reasoning: To find the value of indicator i, we need to calculate the ratio of the changes in the first two evidence specimens. The first specimen decreases its value by 26 out of every 6 units, and the second specimen decreases its value by 25 out of every 17 units. Therefore, the ratio of these changes is (26/6) / (25/17) = (26 * 17) / (6 * 25) = 442 / 150 = 221 / 75.

To find the value of indicator h, we need to calculate the difference between the changes in the second pair of evidence specimens. The first specimen increases its value by 18 out of every 8 units, and the second specimen increases its value by 17 out of every 23 units. Therefore, the difference between these changes is (18/8) - (17/23) = (18 * 23) / (8 * 23) - (17 * 8) / (23 * 8) = 414 / 184 - 136 / 184 = 278 / 184 = 139 / 92.

To find the value of indicator f, we need to multiply the values of indicators h and i. Therefore, the value of f is (221 / 75) * (139 / 92) = 30719 / 6900.

### Answer: 30719 / 6900

Expected answer: 30719/6900

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, we need to find the total gestation period of both animals together.
The gestation period of a lioness is 20/22 of a year, and the gestation period of a giraffe is 15 years.
To find the total gestation period, we add the gestation periods of the lioness and the giraffe:
Total gestation period = 20/22 + 15 = <<20/22+15=15.909090909090908>>15.909090909090908 years.

Next, we need to find the gestation period of the lioness this second time. 
The gestation period of the lioness this second time is reduced by 15/20 of a year compared to the earlier total gestation period of both animals.
To find the gestation period of the lioness this second time, we subtract 15/20 of a year from the earlier total gestation period:
Gestation period of the lioness this second time = 15.909090909090908 - 15/20 = <<15.909090909090908-15/20=15.409090909090908>>15.409090909090908 years.

### Answer: 15.409090909090908 years.

Expected answer: 667/44

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The area of the original rectangle is (30/7) * (19/6) = <<(30/7)*(19/6)=145/7>>145/7 square meters.
The area of the similar rectangle is (18/17) * (145/7) = <<(18/17)*(145/7)=2610/119>>2610/119 square meters.
### Answer: 2610/119

Expected answer: 1710/119

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The factory initially produces 23/8 tonnes of soap each day.
They increase production by 4/20 of a tonne, which is equivalent to 1/5 of a tonne.
So, the new production is 23/8 + 1/5 = <<23/8 + 1/5 = 115/40 + 8/40 = 123/40>>123/40 tonnes.
However, due to a power cut, they reduce production by 19/24 of a tonne.
So, the final production is 123/40 - 19/24 = <<123/40 - 19/24 = 369/120 - 95/120 = 274/120>>274/120 tonnes.
### Answer: 274/120

Expected answer: 137/60

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The machine starts with 24/8 gallons of red paint.
It then pours away 12/8 gallons, leaving 24/8 - 12/8 = <<24/8-12/8=12/8>>12/8 gallons of red paint.
Finally, the machine adds 1/28 gallon of blue pigment, so the total amount of paint is 12/8 - 1/28 = <<12/8-1/28=33/28>>33/28 gallons.
### Answer: 33/28

Expected answer: 41/28

Correct? No

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

Qwen2-Math 72B:

 Reasoning: To find the product of the fractions (27 / 14) and (17 / 13), we multiply the numerators and denominators separately.
(27 / 14) * (17 / 13) = (27 * 17) / (14 * 13) = 459 / 182
The product of the fractions is 459 / 182.
### Answer: 459 / 182

Expected answer: 459/182

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To find the total daily toothpaste usage by Sonia and Anthony, we need to add their individual daily usage amounts. Sonia uses 21/12 oz of toothpaste daily, and Anthony uses 6/27 oz daily. To add these fractions, we need to find a common denominator. The least common multiple of 12 and 27 is 108. So, we convert both fractions to have a denominator of 108:

21/12 = (21 * 9) / (12 * 9) = 189/108
6/27 = (6 * 4) / (27 * 4) = 24/108

Now, we can add the two fractions:

189/108 + 24/108 = 213/108

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

213/108 = (213 ÷ 3) / (108 ÷ 3) = 71/36

So, the total daily toothpaste usage by Sonia and Anthony is 71/36 oz.

Next, we need to add the amount of toothpaste used by their mom, which is 3/18 oz daily. To add this fraction to the total used by Sonia and Anthony, we need to find a common denominator. The least common multiple of 36 and 18 is 36. So, we convert the fraction 3/18 to have a denominator of 36:

3/18 = (3 * 2) / (18 * 2) = 6/36

Now, we can add the two fractions:

71/36 + 6/36 = 77/36

So, the final total daily toothpaste usage for the whole family is 77/36 oz.
### Answer: 77/36

Expected answer: 77/36

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, we need to find the fraction of the original ingredients left after making the first sandwich. We have ((7 / 18) + (21 / 14)) of the original ingredients left.

To simplify this expression, we need to find a common denominator for the two fractions. The least common multiple of 18 and 14 is 126. So, we can rewrite the expression as ((7 * 7) / (18 * 7)) + ((21 * 9) / (14 * 9)) = (49 / 126) + (189 / 126) = (49 + 189) / 126 = 238 / 126.

Next, we need to subtract (2 / 4) from this fraction. To do this, we need to find a common denominator for the two fractions. The least common multiple of 126 and 4 is 252. So, we can rewrite the expression as (238 / 126) - (2 * 63) / (4 * 63) = (238 / 126) - (126 / 252) = (238 * 2) / (126 * 2) - 126 / 252 = 476 / 252 - 126 / 252 = (476 - 126) / 252 = 350 / 252.

Finally, we can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 14. So, the fraction of the original ingredients left after making the simpler sandwich is (350 / 14) / (252 / 14) = 25 / 18.

### Answer: 25 / 18

Expected answer: 25/18

Correct? Yes

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

Qwen2-Math 72B:

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

Expected answer: 47/16

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, we need to find the total amount of juice Jan has. We can do this by adding the amount of apple juice, orange juice, and cranberry juice together.
The amount of apple juice is 16/6 liters.
The amount of orange juice is 20/12 liters.
The amount of cranberry juice is 2/3 liters.
To add these fractions, we need to find a common denominator. The least common multiple of 6, 12, and 3 is 12.
So, we convert each fraction to have a denominator of 12:
16/6 = <<16*2/6*2=32/12>>32/12 liters of apple juice
20/12 = <<20/12=20/12>>20/12 liters of orange juice
2/3 = <<2*4/3*4=8/12>>8/12 liters of cranberry juice
Now, we can add the fractions:
32/12 + 20/12 + 8/12 = <<32+20+8=60>>60/12 liters of juice
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 12:
60/12 = <<60/12=5>>5 liters of juice
### Answer: 5

Expected answer: 5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To find the total points earned, multiply the points per level by the number of levels played: (4/3) * (13/10) = <<(4/3)*(13/10)=52/30>>52/30.
Simplify the fraction: 52/30 = <<52/30=26/15>>26/15.
### Answer: 26/15

Expected answer: 26/15

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The astronaut spends 18/8 + 26/2 = <<18/8+26/2=31>>31 hours a day on cycling and conducting scientific experiments.
The astronaut spends 31 + 30/8 = <<31+30/8=34>>34 hours a day on his whole daily routine.
### Answer: 34

Expected answer: 19

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The total weight of cheese Jeremy requested is 30/9 ounces.
The weight of cheese Jeremy actually received is d = n - (17 / 22) = 30/9 - 17/22 = <<30/9-17/22=1.2222222222222223>>1.22 ounces.
### Answer: 1.22

Expected answer: 169/66

Correct? No

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

Qwen2-Math 72B:

 Reasoning: First, we need to add the fractions representing the sunglasses that blocked all UV rays in the first two tests:
13/4 + 20/18 = <<13/4+20/18=117/36+40/36=157/36>>157/36

Next, we add the fraction representing the sunglasses from the third batch:
157/36 + 21/17 = <<157/36+21/17=2669/612+756/612=3425/612>>3425/612

Finally, we subtract the fraction representing the sunglasses that did not block all UV rays:
3425/612 - 16/30 = <<3425/612-16/30=102750/18360-9792/18360=92958/18360>>92958/18360

Simplifying the fraction, we get:
92958/18360 = <<92958/18360=5164/1020=1291/255>>1291/255

### Answer: 1291/255

Expected answer: 15493/3060

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Shawn uses 23/28 cups of mayonnaise and 6/9 cups of sandwich spread. To find the total amount of these two ingredients, we add them together: 23/28 + 6/9 = <<(23/28)+(6/9)=1.25>>1.25 cups.

Shawn then adds 18/12 cups of cheese spread to his recipe. To find the total amount of ingredients he now needs to make one sandwich, we add the cheese spread to the previous total: 1.25 + 18/12 = <<1.25+(18/12)=2.5>>2.5 cups.

Shawn has to make an equal number of sandwiches using 4/4 cups of all the ingredients combined. To find out how many cups of ingredients he will use in total to make those sandwiches, we multiply the total amount of ingredients by the number of sandwiches: 2.5 * 4/4 = <<2.5*(4/4)=2.5>>2.5 cups.

### Answer: 2.5

Expected answer: 251/84

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Cassandra lost 1/21 of a key set, which is equivalent to 1/21 * 7/6 = <<1/21*7/6=1/18>>1/18 of a key set.
Cassandra now has 7/6 - 1/18 = <<7/6-1/18=20/18>>20/18 of a key set.
### Answer: 20/18

Expected answer: 47/42

Correct? No

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

Qwen2-Math 72B:

 Reasoning: First, we need to calculate the sum of the ratios of the two sections. The ratio of the first section is 29/23 and the ratio of the second section is 19/17. Adding these two ratios together, we get (29/23) + (19/17) = <<(29/23)+(19/17)=1.2608695652173913+1.1176470588235294=2.3785166240409207>>2.3785166240409207.

Next, we need to calculate the ratio of a rest, which is equivalent to one whole measure (26/26). This ratio is simply 1.

Finally, we need to calculate the difference between the sum of the ratios of the two sections and the ratio of a rest. Subtracting the ratio of a rest from the sum of the ratios of the two sections, we get 2.3785166240409207 - 1 = <<2.3785166240409207-1=1.3785166240409207>>1.3785166240409207.

### Answer: 1.3785166240409207

Expected answer: 539/391

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To multiply two fractions, you multiply the numerators together and the denominators together.
So, (22/25) * (22/8) = (22*22) / (25*8) = 484 / 200 = 2.42
### Answer: 2.42

Expected answer: 121/50

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The total length of the pillow is 23/9 + 22/25 = <<(23/9)+(22/25)=1.0222222222222222>>1.0222222222222222 feet.
The length of border material needed is 1.0222222222222222 * 16/13 = <<(1.0222222222222222)*(16/13)=1.256>>1.256 feet.
### Answer: 1.256

Expected answer: 12368/2925

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The car was supposed to travel an additional 16/13 miles, but it only traveled 1/21 miles. Therefore, the car was supposed to travel an additional 16/13 - 1/21 miles.
To find the total additional miles the car was supposed to travel, we need to multiply the additional distance needed by the average miles the car travels in an hour.
The car travels 21/4 miles every hour, so the total additional miles the car was supposed to travel is (16/13 - 1/21) * (21/4) miles.
### Answer: (16/13 - 1/21) * (21/4) miles

Expected answer: 323/52

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The editing team takes 20/5 = <<20/5=4>>4 hours to edit a manuscript of a book.
The typesetting team needs 18/17 = <<18/17=1.0588235294117647>>1.0588235294117647 hours to adjust the layout of a page.
The total time required for the entire process is 4+1.0588235294117647 = <<4+1.0588235294117647=5.0588235294117647>>5.0588235294117647 hours.
The total time required for the entire process after the reduction of the lost hours is 5.0588235294117647-6/15 = <<5.0588235294117647-6/15=4.8588235294117647>>4.8588235294117647 hours.
The total extended time in hours is 5.0588235294117647*4.8588235294117647 = <<5.0588235294117647*4.8588235294117647=24.5588235294117647>>24.5588235294117647 hours.
### Answer: 24.5588235294117647

Expected answer: 34056/1445

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Jenny plants 13/11 rows of potatoes in her garden. Each row yields approximately 21/3 bushels. If Jenny sells her yield at the farmer's market where each bushel earns her 21/15 dollars, how many dollars will she make in total by selling all her potatoes?
First, we need to find out how many bushels Jenny will get from her potatoes. Since each row yields approximately 21/3 bushels, and she has 13/11 rows, she will get (13/11) * (21/3) = <<(13/11)*(21/3)=91/11>>91/11 bushels.
Next, we need to find out how much money she will make by selling all her potatoes. Since each bushel earns her 21/15 dollars, she will make (91/11) * (21/15) = <<(91/11)*(21/15)=189/11>>189/11 dollars.
### Answer: 189/11

Expected answer: 637/55

Correct? No

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

Qwen2-Math 72B:

 Reasoning: 14/28 = <<14/28=0.5>>0.5 kilograms of gold is used.
13/26 = <<13/26=0.5>>0.5 kilograms of silver is used.
The sum of the amount of gold and silver used by the jeweler is 0.5+0.5 = <<0.5+0.5=1>>1 kilograms.
### Answer: 1

Expected answer: 1

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The total amount of honey from a honey storage sub-section and a bee rearing sub-section is p = (25 / 9) + (25 / 9) = <<25/9+25/9=50/9>>50/9 gallons.

The total amount of honey from a honey storage sub-section with an additional (2 / 26) gallons and a bee rearing sub-section is s = (25 / 9) + (2 / 26) + (25 / 9) = <<25/9+2/26+25/9=50/9+2/26=50/9+1/13=650/117+9/117=659/117>>659/117 gallons.

### Answer: 659/117

Expected answer: 659/117

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The dinosaur eats 16/8+6/17 = <<16/8+6/17=1.2352941176470588>>1.2352941176470588 bunches of leaves in an hour.
### Answer: 1.2352941176470588

Expected answer: 40/17

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The bear ate 28/6 + 21/18 + 24/22 = <<28/6 + 21/18 + 24/22 = 14/3 + 7/6 + 12/11 = 154/33 + 38.5/33 + 36/33 = 228.5/33>>228.5/33 pounds of fish in total.
### Answer: 228.5/33

Expected answer: 457/66

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The total amount of sugar required for the first course and the custard is 11/17 + 6/2 = <<11/17+6/2=107/34>>107/34 cups of sugar.
Heather decided to increase the total quantity of sugar by a factor of 29/21, so she used 107/34 * 29/21 = <<107/34*29/21=107/24>>107/24 cups of sugar in total.
### Answer: 107/24

Expected answer: 1798/357

Correct? No

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

Qwen2-Math 72B:

 Reasoning: First, simplify the fractions: (7 / 8) and (21 / 18) can be simplified to (7 / 8) and (7 / 6) respectively.
Next, find a common denominator, which is 24 in this case.
Convert the fractions: (7 / 8) becomes (21 / 24) and (7 / 6) becomes (28 / 24).
Add the fractions: (21 / 24) + (28 / 24) = (49 / 24).
### Answer: 49/24

Expected answer: 49/24

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, we need to calculate the total liquid consumed by the guests (i). Each guest consumes 15/7 gallons of water and 15/24 gallons of wine. So, the total liquid consumed by each guest is 15/7 + 15/24 = <<(15/7)+(15/24)=1.5+0.625=2.125>>2.125 gallons.

Next, we need to calculate the baker's requirement (v). The baker needs 26/20 gallons of milk for each cake. So, the baker's requirement is 26/20 = <<26/20=1.3>>1.3 gallons.

Now, we need to multiply the baker's requirement (v) by the guests' consumption (i) to find the total amount of liquid (v) that will be consumed. So, the total amount of liquid (v) is 2.125 * 1.3 = <<2.125*1.3=2.7625>>2.7625 gallons.

Finally, we need to add the total amount of liquid (v) to the guests' consumption (v) to find the total amount of liquid (x) needed for the feast. So, the total amount of liquid (x) is 2.7625 + 2.125 = <<2.7625+2.125=4.8875>>4.8875 gallons.

### Answer: 4.8875

Expected answer: 713/112

Correct? No

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

Qwen2-Math 72B:

 Reasoning: Teddy's favorite number is 30/17.
Teddy added 18/15 to his favorite number, so his new number is 30/17 + 18/15 = <<(30*15+18*17)/(17*15)=1026/255>>1026/255.
Teddy then multiplied his new number by 24/13, so his final number is 1026/255 * 24/13 = <<(1026*24)/(255*13)=24624/3315>>24624/3315.
### Answer: 24624/3315

Expected answer: 6048/1105

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The fraction of the desired diameter that each hole would have is (20/6) * (11 / 21) = <<(20/6) * (11 / 21) = 220/126>>220/126.
### Answer: 220/126

Expected answer: 110/63

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To find out how much less time the second model takes, we need to subtract the time it takes to assemble the second model from the time it takes to assemble the first model.

Time to assemble the first model: 17/10 hours
Time to assemble the second model: 12/23 hours

Difference in time: 17/10 - 12/23

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 10 and 23 is 230.

Converting both fractions to have the common denominator of 230:
17/10 = (17 * 23) / (10 * 23) = 391/230
12/23 = (12 * 10) / (23 * 10) = 120/230

Now we can subtract the fractions:
391/230 - 120/230 = (391 - 120) / 230 = 271/230

The second model takes 271/230 hours less than the first model.

### Answer: 271/230 hours

Expected answer: 271/230

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, we need to calculate how many units of wood the special chair uses more than the regular chair. We do this by multiplying the two fractions given:

(24/5) * (7/6) = (24 * 7) / (5 * 6) = 168 / 30

Now, we simplify the fraction:

168 / 30 = 5.6

So, the special chair uses 5.6 units more wood than the regular chair. 

Next, we add this to the amount of wood used for a regular chair:

20/15 + 5.6 = 1.3333 + 5.6 = 6.9333

However, we need to express this in simplest form. Since 6.9333 is not a fraction, we convert it to a fraction:

6.9333 = 69333/10000

This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1:

69333/10000 = 69333/10000

Therefore, Carlos would need 69333/10000 units of wood to make one of these special chairs.
### Answer: 69333/10000

Expected answer: 104/15

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The car was initially going 13/4 miles per minute.
The car slowed down by 14/15 miles per minute, so the new speed was 13/4 - 14/15 = <<13/4-14/15=19/60>>19/60 miles per minute.
The car then increased its speed by 30/15 miles per minute, so the final speed was 19/60 + 30/15 = <<19/60+30/15=119/60>>119/60 miles per minute.
### Answer: 119/60

Expected answer: 259/60

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The vineyard produced 19/2 * 19/29 = <<(19/2)*(19/29)=19/2>>19/2 baskets of grapes this season.
Jake gets to keep 19/2 * 7/11 = <<(19/2)*(7/11)=133/22>>133/22 baskets of grapes.
Jake uses 133/22 * 9/10 = <<(133/22)*(9/10)=1197/220>>1197/220 baskets of grapes for the juice.
### Answer: 1197/220

Expected answer: 22743/6380

Correct? No

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

Qwen2-Math 72B:

 Reasoning: To find the total number of bushels of grapes Joel picked, we need to add the number of bushels of red grapes and the number of bushels of green grapes.
The number of bushels of red grapes is 9/2 = <<9/2=4.5>>4.5.
The number of bushels of green grapes is 10/22 = <<10/22=0.4545454545454545>>0.4545454545454545.
The total number of bushels of grapes Joel picked is 4.5 + 0.4545454545454545 = <<4.5+0.4545454545454545=4.954545454545455>>4.954545454545455.
### Answer: 4.954545454545455

Expected answer: 109/22

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The height of the larger snowball is equal to its diameter, which is 17/8 feet.
The height of the smaller snowball is equal to its diameter, which is 1/20 feet.
The total height of the snowman is the sum of the heights of the two snowballs, which is 17/8 + 1/20 = <<17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20=17/8+1/20

Expected answer: 87/40

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The child splits up 24/7 parts of the sand in a fair way, so each part is 24/7/24 = <<24/7/24=1/7>>1/7.
Another child takes away 2/16 part of the sand, which is 2/16/24 = <<2/16/24=1/192>>1/192.
The remaining part of sand in the sandbox is 1/7 - 1/192 = <<1/7-1/192=185/1344>>185/1344.
### Answer: 185/1344

Expected answer: 185/56

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The lion ate 28/26 - 23/9 = <<28/26 - 23/9 = 126/234 - 598/234 = -472/234 = -236/117>>-236/117 of the zebra less than the wildebeest.
### Answer: -236/117

Expected answer: 173/117

Correct? No

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

Qwen2-Math 72B:

 Reasoning: ((14 / 4) * (21 / 11)) = <<((14 / 4) * (21 / 11))=7.818181818181818>>7.818181818181818
### Answer: 7.818181818181818

Expected answer: 147/22

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The first species produces 12 bananas every 29 days, which means it produces 12/29 = <<12/29=0.41379310344827586>>0.41379310344827586 bananas per day.
The second species produces 30 bananas every 10 days, which means it produces 30/10 = <<30/10=3>>3 bananas per day.
The expected number of bananas that the two species together will have produced on a randomly chosen day is ((12 / 29) + (30 / 10)) = <<((12 / 29) + (30 / 10))=3.4137931034482758>>3.4137931034482758 bananas.
### Answer: 3.4137931034482758

Expected answer: 99/29

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The total ton of food the giraffe needs to eat in a day is 11/11+26/14 = <<11/11+26/14=2.5>>2.5 ton.
### Answer: 2.5

Expected answer: 20/7

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The bear sleeps for 18/24 = <<18/24=0.75>>0.75 of each day.
Over 27 days, the bear sleeps for 0.75 * 27 = <<0.75*27=20.25>>20.25 days.
Since each month has 13 weeks, the bear sleeps for 20.25 / 13 = <<20.25/13=1.5576923076923077>>1.5576923076923077 weeks.
### Answer: 1.5576923076923077

Expected answer: 81/52

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To find the fraction of trees that are either pine or birch, we need to add the fractions representing the proportion of pine trees and birch trees in the forest.
The fraction of pine trees is 9/14, and the fraction of birch trees is 19/2.
To add these fractions, we need to find a common denominator. The least common multiple of 14 and 2 is 14.
So, we convert 19/2 to a fraction with a denominator of 14: 19/2 = (19 * 7) / (2 * 7) = 133/14.
Now, we can add the fractions: f = (9/14) + (133/14) = (9 + 133) / 14 = 142/14.
Simplifying the fraction, we get f = 71/7.
Therefore, the fraction of trees in the forest that are either pine or birch is 71/7.
### Answer: 71/7

Expected answer: 71/7

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, calculate the initial energy level: (14 / 2) / (23 / 17) = <<(14 / 2) / (23 / 17) = 14 * 17 / (2 * 23) = 119 / 23>>119 / 23 zogs.
Next, add the energy increase: 119 / 23 + 16 / 24 = <<(119 * 24 + 16 * 23) / (23 * 24) = (2856 + 368) / 552 = 3224 / 552>>3224 / 552 zogs.
### Answer: 3224 / 552

Expected answer: 403/69

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, we need to find the difference between the number of friends Teddy hides in the forest and the number of friends he hides at the beach. This is given by the expression: f = 18/11 - 8/21.
To find the value of 'f', we need to find a common denominator for the fractions 18/11 and 8/21. The least common multiple of 11 and 21 is 231. So, we can rewrite the fractions as: 18/11 = 378/231 and 8/21 = 88/231.
Now, we can subtract the fractions: f = 378/231 - 88/231 = 290/231.
Next, we need to square 'f' to find 'n', the total number of hiding spots Teddy needs. This is given by the expression: n = f^2.
Substituting the value of 'f' we found earlier, we get: n = (290/231)^2.
To find the value of 'n', we need to square the fraction 290/231. This gives us: n = (290/231)^2 = 84100/53361.
Finally, we need to simplify the fraction 84100/53361 to find the total number of hiding spots Teddy needs. This gives us: n = 84100/53361 = 1.576.
### Answer: 1.576

Expected answer: 84100/53361

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The robot starts with 25/10 units of energy.
It uses 27/23 units of energy.
The remaining energy is 25/10 - 27/23 = <<(25/10)-(27/23)=0.043478260869565216>>0.043478260869565216 units.
### Answer: 0.043478260869565216

Expected answer: 61/46

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The first snail covers 17/21 meters in an hour, and the second snail covers 20/24 meters in an hour. The total distance covered by the first two snails in an hour is ((17 / 21) + (20 / 24)) = <<((17 / 21) + (20 / 24))=1.4761904761904762>>1.4761904761904762 meters. The third snail covers 18/17 meters in an hour. The total distance covered by all three snails in an hour is ((17 / 21) + (20 / 24)) * (18 / 17) = <<((17 / 21) + (20 / 24)) * (18 / 17)=1.5>>1.5 meters.
### Answer: 1.5

Expected answer: 207/119

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The difference between the original and remaining fabric is 24/14 - 9/29 = <<24/14-9/29=12/7-9/29=36/21-9/29=108/63-9/29=108/63-27/63=81/63=9/7>>9/7 yards.
Johnny used 15/2 * 9/7 = <<15/2*9/7=135/14>>135/14 yards of the new fabric.
### Answer: 135/14

Expected answer: 4275/406

Correct? No

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

Qwen2-Math 72B:

 Reasoning: To add 2/10 and 21/4, we need to find a common denominator. The least common multiple of 10 and 4 is 20. So, we convert 2/10 to 4/20 and 21/4 to 105/20. Now, we can add the two fractions: 4/20 + 105/20 = 109/20. Therefore, the total number of kids waiting for the swing is 109/20.
### Answer: 109/20

Expected answer: 109/20

Correct? Yes

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

Qwen2-Math 72B:

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

Expected answer: 11/5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The cat eats 16/12 + 6/10 = <<16/12+6/10=2.2>>2.2 cans of cat food in one day.
### Answer: 2.2

Expected answer: 29/15

Correct? No

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

Qwen2-Math 72B:

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

Expected answer: 5/4

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The monkey eats (22 / 7) * (10 / 25) = <<(22/7)*(10/25)=88/175>>88/175 of the pile.
The monkey gives away (3 / 28) of the pile, which is (3 / 28) * (175 / 88) = <<(3/28)*(175/88)=15/88>>15/88 of the pile.
The monkey has 1 - (88/175 + 15/88) = <<1-(88/175+15/88)=1-103/175=72/175>>72/175 of the pile left.
### Answer: 72/175

Expected answer: 23/20

Correct? No

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

Qwen2-Math 72B:

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

Expected answer: 69/5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The number of ounces of beverage consumed is 29/9 * 26/25 = <<(29/9)*(26/25)=2.5177777777777777>>2.5177777777777777 ounces.
The total number of ounces of beverages consumed at the party is 2.5177777777777777 + 2/19 = <<2.5177777777777777+2/19=2.594736842105263>>2.594736842105263 ounces.
### Answer: 2.594736842105263

Expected answer: 14776/4275

Correct? No

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

Qwen2-Math 72B:

 Reasoning: You start with 7/15 of a set of toothbrushes.
Your friend gives you 9 more sets, so you have 7/15 + 9 = <<7/15+9=9.466666666666666>>9.466666666666666 sets.
You can only fit 26/27 of your collection in the display case, so you can fit 9.466666666666666 * 26/27 = <<9.466666666666666*26/27=9.11111111111111>>9.11111111111111 sets in your display case.
### Answer: 9.11111111111111

Expected answer: 3692/405

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The total weight of the backpack is 27/20 + 1/6 = <<27/20+1/6=81/60+10/60=91/60>>91/60 kilograms.
### Answer: 91/60

Expected answer: 91/60

Correct? Yes

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

Qwen2-Math 72B:

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

Expected answer: 25/22

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: Tilly has 25/9 + 8/13 = <<25/9+8/13=325/117+72/117=397/117>>397/117 kg of food from the first two sources.
Tilly has 397/117 + 24/27 = <<397/117+24/27=397/117+96/117=493/117>>493/117 kg of food from the first three sources.
Tilly has 493/117 + 21/26 = <<493/117+21/26=493/117+84/117=577/117>>577/117 kg of food in total.
### Answer: 577/117

Expected answer: 397/78

Correct? No

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

Qwen2-Math 72B:

 Let's break down the problem step by step:

1. Calculate the difference in location and distance to the island:
   \[
   \frac{17}{2} - \frac{4}{2} = \frac{17 - 4}{2} = \frac{13}{2}
   \]

2. Adjust for the tide:
   \[
   \frac{13}{2} + \frac{14}{9}
   \]
   To add these fractions, we need a common denominator. The least common multiple of 2 and 9 is 18. So, we convert each fraction:
   \[
   \frac{13}{2} = \frac{13 \times 9}{2 \times 9} = \frac{117}{18}
   \]
   \[
   \frac{14}{9} = \frac{14 \times 2}{9 \times 2} = \frac{28}{18}
   \]
   Now, add the fractions:
   \[
   \frac{117}{18} + \frac{28}{18} = \frac{117 + 28}{18} = \frac{145}{18}
   \]

3. Calculate the fuel requirements:
   \[
   \frac{145}{18} \times \frac{22}{15}
   \]
   To multiply these fractions, multiply the numerators and the denominators:
   \[
   \frac{145 \times 22}{18 \times 15} = \frac{3190}{270}
   \]
   Simplify the fraction:
   \[
   \frac{3190}{270} = \frac{3190 \div 10}{270 \div 10} = \frac{319}{27}
   \]

So, Captain Alf’s final calculation comes to:
\[
\frac{319}{27} \text{ nautical miles per gallon}
\]

### Answer: $\frac{319}{27}$ nautical miles per gallon

Expected answer: 319/27

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The forest ranger patrolled 14/3 - 2/18 = <<14/3 - 2/18 = 84/18 - 2/18 = 82/18>>82/18 miles in the afternoon.
### Answer: 82/18

Expected answer: 41/9

Correct? Yes

Problem: Arthur practices piano for 20/21 of an hour every day. On weekends, he practices an additional 11/29 of an hour per day. How many hours in total does Arthur spend practicing the piano each day on the weekend?

Qwen2-Math 72B:

 Reasoning: Arthur practices 20/21 + 11/29 = <<20/21+11/29=1.0476190476190477>>1.0476190476190477 hours each day on the weekend.
### Answer: 1.0476190476190477

Expected answer: 811/609

Correct? No

Problem: Lucas has a shirt store. Initially, he had 18 shirts which he divided equally among his 3 siblings. Later, he bought 27 more shirts but wanted to sell them at a higher price, so he decided to keep only 1/19 of those shirts for each sibling. How many more or fewer shirts does each sibling now have as compared to before? Calculate the difference using the expression ((18 / 3) - (27 / 19)) and find out the result.

Qwen2-Math 72B:

 Reasoning: Initially, each sibling had 18 / 3 = <<18/3=6>>6 shirts.
Later, each sibling had 27 / 19 = <<27/19=1.4210526315789473684210526315789>>1.42 shirts.
The difference is (18 / 3) - (27 / 19) = <<6-1.4210526315789473684210526315789=4.5789473684210526315789473684211>>4.58 shirts.
### Answer: 4.58

Expected answer: 87/19

Correct? No

Problem: A painter mixed 7 gallons of white paint with 2/5 gallon of blue paint to make a light blue paint. After using 18/4 gallons of the light blue paint for a project, how many gallons does the painter have left?

Qwen2-Math 72B:

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

Expected answer: 29/10

Correct? Yes

Problem: Jayson went to the roller rink and spent 24/7 hours skating on the first day. On the second day, he decided to skate for an additional 30/20 hours. How many hours in total did Jayson spend skate skating over the two days?

Qwen2-Math 72B:

 Reasoning: Jayson spent 24/7 + 30/20 = <<24/7+30/20=12/7+3/2=24/14+21/14=45/14>>45/14 hours skating over the two days.
### Answer: 45/14

Expected answer: 69/14

Correct? No

Problem: Dolphins can leap approximately 18/3 feet out of the water. If a dolphin only manages to jump 3/4 of his usual height one day, how high did the dolphin jump?

Qwen2-Math 72B:

 Reasoning: The dolphin jumps 18/3 * 3/4 = <<18/3*3/4=4.5>>4.5 feet.
### Answer: 4.5

Expected answer: 9/2

Correct? Yes

Problem: Callie owns a pen business. Last month, she sold 20 pens for every 15 she produced. At the same time, she sold an additional 16 pens for every 22 she put out for sale. Meanwhile, she found that for every 22 pens she advertised, 27 were interested customers. For each 23 pens she produced this week, she was able to sell 8. What is the result when she multiplies the ratio of last month's sales to production (20/15 + 16/22) and this week's figure for the ratio of interested customers to production (22/27 * 23/8)? Leave your answer as an unsimplified fraction.

Qwen2-Math 72B:

 Reasoning: Last month's sales to production ratio is 20/15 + 16/22 = <<20/15+16/22=1.3333333333333333+0.7272727272727273=2.0606060606060605>>2.0606060606060605.
This week's interested customers to production ratio is 22/27 * 23/8 = <<22/27*23/8=0.8148148148148148*2.875=2.34375>>2.34375.
The result when she multiplies the two ratios is 2.0606060606060605 * 2.34375 = <<2.0606060606060605*2.34375=4.833333333333333>>4.833333333333333.
### Answer: 4.833333333333333

Expected answer: 391/81

Correct? No

Problem: Consider a band practice session in which a musician played a song for exactly 30 minutes. After dividing this time equally between 15 songs, how much time did they spend on each song? From this average time per song, the band reduced the time spent on a particular song by 1/17 of an hour. Can you calculate the final duration of that song?

Qwen2-Math 72B:

 Reasoning: The musician played each song for 30/15 = <<30/15=2>>2 minutes.
The band reduced the time spent on a particular song by 1/17 of an hour, which is 60/17 = <<60/17=3.5294117647058824>>3.5294117647058824 minutes.
The final duration of that song is 2-3.5294117647058824 = <<2-3.5294117647058824=-1.5294117647058824>>-1.5294117647058824 minutes.
### Answer: -1.5294117647058824

Expected answer: 33/17

Correct? No

Problem: Josh rented a scooter for a day. He rode the scooter for a total of 18 hours during the first day. The next day, he rode the scooter for an additional 1/12 of an hour. Later that afternoon, his friend Jack also rented a scooter and rode it for 7/17 of an hour. How many hours did they both ride scooters in total (expressed as a fraction)? Combine the hours they both rode and simplify the fraction to get the answer.

Qwen2-Math 72B:

 Reasoning: Josh rode the scooter for 18 hours on the first day and an additional 1/12 of an hour on the second day. So, the total hours Josh rode the scooter is 18 + 1/12 = <<18+1/12=217/12>>217/12 hours.

Jack rode the scooter for 7/17 of an hour. 

To find the total hours they both rode scooters, we need to add the hours Josh rode and the hours Jack rode. 

So, the total hours they both rode scooters is 217/12 + 7/17 = <<217/12+7/17=3709/204>>3709/204 hours.

### Answer: 3709/204

Expected answer: 3773/204

Correct? No

Problem: A lamp store owner is doing inventory of all the lamps in his store. He found that he has 4/26 of lamps that are floor lamps, 15/11 that are desk lamps, he also discovered he has 23/28 of table lamps and finally 8/19 of lamps that are decorative. What fraction of his total inventory do these lamps constitute?

Qwen2-Math 72B:

 Reasoning: The fraction of floor lamps is 4/26 = <<4/26=2/13>>2/13.
The fraction of desk lamps is 15/11 = <<15/11=1.3636363636363635>>1.3636363636363635.
The fraction of table lamps is 23/28 = <<23/28=0.8214285714285714>>0.8214285714285714.
The fraction of decorative lamps is 8/19 = <<8/19=0.42105263157894735>>0.42105263157894735.
The total fraction of lamps is 2/13 + 1.3636363636363635 + 0.8214285714285714 + 0.42105263157894735 = <<2/13+1.3636363636363635+0.8214285714285714+0.42105263157894735=3.3636363636363638>>3.3636363636363638.
### Answer: 3.3636363636363638

Expected answer: 209967/76076

Correct? No

Problem: Oliver has a kite string that is 26/19 meters long and another kite string that is 7/11 meters long. He decides to add these two strings to create an even longer kite string. Later on, he decides to use only 5/8 of this combined string. How long is the kite string that he is using now? Do not simplify your fractions within your calculation.

Qwen2-Math 72B:

 Reasoning: The combined length of the two kite strings is 26/19 + 7/11 = <<(26/19 + 7/11)*19*11/19/11>>325/19 meters.
The length of the kite string that Oliver is using now is 5/8 * 325/19 = <<(5/8 * 325/19)*8*19/8/19>>1625/152 meters.
### Answer: 1625/152

Expected answer: 2095/1672

Correct? No

Problem: In a snow fight, Mike threw 9/19 of his snowballs and his friend, John threw 6/8 of his snowballs. After a while, Mike found 4 more snowballs to throw. The question is, if 'u' represents the number of snowballs thrown by both Mike and John and 'j' is the total number of snowballs Mike had after finding more, how many snowballs did Mike have in total? Solve the following equations to find the variable 'j': u = 9/19 + 6/8 j = u + 4/1

Qwen2-Math 72B:

 Reasoning: First, we need to find the total number of snowballs thrown by both Mike and John, which is represented by 'u'. To do this, we add the fractions 9/19 and 6/8.

u = 9/19 + 6/8

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

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

u = 72/152 + 114/152

Now, we can add the numerators since the denominators are the same.

u = (72 + 114) / 152

u = 186 / 152

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

u = 93 / 76

Now, we need to find the total number of snowballs Mike had after finding more, which is represented by 'j'. To do this, we add 4 to 'u'.

j = u + 4/1

j = 93/76 + 4/1

To add these fractions, we need a common denominator. The least common multiple of 76 and 1 is 76. So, we convert 4/1 to have a denominator of 76.

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

j = 93/76 + 304/76

Now, we can add the numerators since the denominators are the same.

j = (93 + 304) / 76

j = 397 / 76

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

j = 397 / 76

Therefore, Mike had a total of 397/76 snowballs after finding more.

### Answer: 397/76

Expected answer: 397/76

Correct? Yes

Problem: In a chocolate factory, one worker packages 26 pieces of chocolate in 18 minutes, while another worker can package 15 pieces of chocolate every 15 minutes. Find out the total amount of chocolate they can package in one minute.

Qwen2-Math 72B:

 Reasoning: The first worker packages 26/18 = <<26/18=1.4444444444444444>>1.44 pieces of chocolate per minute.
The second worker packages 15/15 = <<15/15=1>>1 piece of chocolate per minute.
Together, they can package 1.44+1 = <<1.44+1=2.44>>2.44 pieces of chocolate per minute.
### Answer: 2.44

Expected answer: 22/9

Correct? No

Problem: Yesterday, Joanna washed 24/20 batches of small towels and 25/15 batches of large towels. Find the total number of batches of towels she washed.

Qwen2-Math 72B:

 Reasoning: To find the total number of batches of towels Joanna washed, we need to add the number of small towel batches to the number of large towel batches.
First, we simplify the fractions:
24/20 = <<24/20=1.2>>1.2 batches of small towels
25/15 = <<25/15=1.6666666666666667>>1.6666666666666667 batches of large towels
Next, we add the two numbers together:
1.2 + 1.6666666666666667 = <<1.2+1.6666666666666667=2.8666666666666665>>2.8666666666666665
Since we cannot have a fraction of a batch, we round up to the nearest whole number:
2.8666666666666665 rounds up to 3
### Answer: 3

Expected answer: 43/15

Correct? No

Problem: Debra is baking cookies and she realizes she has two different recipes for the same type of cookie. She's wondering if she combines the ingredients from both, if she will end up with even more cookies or not. The first recipe requires (27 / 3) cups flour and (11 / 7) cups sugar. She determines the ratio of flour to sugar by dividing the amount of flour by the amount of sugar. She then subtracts (21 / 26) from this ratio because that's how many cups of sugar her friend says makes the cookies too sweet. After that, she adds (22 / 9) cups of flour from the second recipe to the new ratio to see how many total cups of flour she will need. How many cups of flour will she have in the end?

Qwen2-Math 72B:

 Reasoning: The ratio of flour to sugar is (27 / 3) / (11 / 7) = <<(27 / 3) / (11 / 7) = 27 * 7 / 3 * 11 = 189 / 33 = 5.727272727272727>>5.727272727272727.
Subtracting (21 / 26) from this ratio gives 5.727272727272727 - (21 / 26) = <<5.727272727272727 - (21 / 26) = 5.727272727272727 - 0.8076923076923077 = 4.919580419580419>>4.919580419580419.
Adding (22 / 9) to this gives 4.919580419580419 + (22 / 9) = <<4.919580419580419 + (22 / 9) = 4.919580419580419 + 2.4444444444444446 = 7.364024864024864>>7.364024864024864.
### Answer: 7.364024864024864

Expected answer: 18955/2574

Correct? Yes

Problem: There are 26/13 chickens in one farm and 9/16 chickens in another farm. Farmer John calculated the difference between the number of chickens in the two farms. After a week, the number of chickens multiplied by 19/21 due to new chickens born. How many chickens are there now in Farmer John's farm?

Qwen2-Math 72B:

 Reasoning: The difference between the number of chickens in the two farms is 26/13 - 9/16 = <<(26/13 - 9/16)*19/21=1/2>>1/2.
After a week, the number of chickens multiplied by 19/21, so there are now 1/2 * 19/21 = <<(1/2 * 19/21)*19/21=19/42>>19/42 chickens in Farmer John's farm.
### Answer: 19/42

Expected answer: 437/336

Correct? No

Problem: A helicopter traveled a distance of 24/14 miles for a training exercise. During a second exercise, the helicopter flew the same distance. If we let 'w' be the distance flown for each exercise and 't' be the total distance flown for both exercises represented as the product of 'w' times 'w', what is the value of 't'?

Qwen2-Math 72B:

 Reasoning: The distance flown for each exercise is given as 24/14 miles, so 'w' = 24/14.
The total distance flown for both exercises is the product of 'w' times 'w', so 't' = w * w.
Substituting the value of 'w' into the equation for 't', we get t = (24/14) * (24/14).
Simplifying the expression, we get t = 576/196.
### Answer: 576/196

Expected answer: 144/49

Correct? Yes

Problem: A UFO has made two fuel stops. During the first refuel, the UFO was able to fill 20/16 of its fuel tank. At the second fuel stop, the UFO filled another 24/25 of its tank. Calculate the total fraction of the tank that the UFO was able to refill during these two stops.

Qwen2-Math 72B:

 Reasoning: The total fraction of the tank refilled is 20/16 + 24/25 = <<(20/16 + 24/25)*800/800=1000/800>>1000/800.
### Answer: 1000/800

Expected answer: 221/100

Correct? No

Problem: Professor Astro is working on his telescope. He believes the power of his telescope is directly proportional to the sum of two fractions. The first fraction is the light gathering power of the lens, which is 24 out of 27. The second fraction is the zooming potential, which is 30 out of 26. So, Professor Astro calculates the sum of these two fractions ((24 / 27) + (30 / 26)). What does he find?

Qwen2-Math 72B:

 Reasoning: To find the sum of the two fractions, we need to find a common denominator. The least common multiple of 27 and 26 is 702. So, we convert the fractions to have the same denominator: (24/27) = (24*26)/(27*26) = 624/702 and (30/26) = (30*27)/(26*27) = 810/702.
Now, we can add the two fractions: 624/702 + 810/702 = 1434/702.
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2: 1434/702 = 717/351.
### Answer: 717/351

Expected answer: 239/117

Correct? Yes

Problem: Kiki is a lively little monkey. She loves eating bananas. She ate 11/6 bananas in the morning and the same amount in the afternoon. How many bananas did she eat in total? Express your answer as an improper fraction.

Qwen2-Math 72B:

 Reasoning: Kiki ate 11/6 bananas in the morning and 11/6 bananas in the afternoon.
So, she ate 11/6 + 11/6 = <<11/6+11/6=22/6>>22/6 bananas in total.
### Answer: 22/6

Expected answer: 11/3

Correct? Yes

Problem: Jaden is a dairy farmer who milks his cows twice a day. In the morning, his cows give him 26/14 gallons of milk per cow, and in the evening, they give 28/20 gallons of milk per cow. If he multiplies these two fractions together, how much milk is he getting from one cow in one day?

Qwen2-Math 72B:

 Reasoning: Jaden gets 26/14 * 28/20 = <<(26/14)*(28/20)=2.6>>2.6 gallons of milk from one cow in one day.
### Answer: 2.6

Expected answer: 13/5

Correct? Yes