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?

Llama 3 70B:

Reasoning: First, we need to find the initial number of cucumbers Carla could grow per plant. To do this, we multiply 22/3 by 22/19:

(22/3) × (22/19) = (22 × 22) / (3 × 19) = 484 / 57 = 8.49 (approximately)

So, Carla could initially grow approximately 8.49 cucumbers per plant.

To find the new number of cucumbers she can grow per plant after adjusting her production method, we multiply the initial amount by 23/17:

8.49 × (23/17) = 8.49 × 1.3529 (approximately) = 11.49 (approximately)

Therefore, Carla is expecting to grow approximately 11.49 cucumbers per plant after adjusting her production method.

### Answer: 11.49

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?

Llama 3 70B:

Reasoning: Pierre initially had 19/4 kg of grapes.
He ate 7/25 kg of grapes, so he had 19/4 - 7/25 kg of grapes left.
To subtract these fractions, we need to find a common denominator, which is 100. So, we can convert the fractions to:
(475 - 28) / 100 = 447 / 100 kg
Then, his mother gave him 30/9 kg more grapes. To add these fractions, we need to find a common denominator, which is 18. So, we can convert the fractions to:
(80 + 60) / 18 = 140 / 18 kg
Simplifying, we get 70/9 kg.
### Answer: 70/9 kg

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?

Llama 3 70B:

Reasoning: To find the total cost, we need to add the fractions of the budget spent on each project. To add these fractions, we need to find a common denominator. The least common multiple of 22, 29, and 3 is 638. 

We can rewrite each fraction with a denominator of 638:

Wall repairs: 26/22 = (26*29*3)/(22*29*3) = 2262/638
Moat renovations: 4/29 = (4*22*3)/(29*22*3) = 264/638
Defensive catapults: 11/3 = (11*22*29)/(3*22*29) = 7094/638

Now we can add the fractions:

2262/638 + 264/638 + 7094/638 = 9620/638

### Answer: 9620/638

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.

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
((25 / 19) * (30 / 26)) = (25/19) * (30/26) = (25*30) / (19*26) = 750 / 494 = 150/99

2. Raise the result to the power of 2:
(150/99)^2 = (150^2) / (99^2) = 22500 / 9801

3. Multiply the result by the original expression:
(22500 / 9801) * (150/99) = (22500*150) / (9801*99) = 3375000 / 970899

### Answer: 3375000/970899

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?

Llama 3 70B:

Reasoning: To find the total length of yarn needed, we need to add the length required for the necklace and the length added by the smaller beads.

First, let's find a common denominator for the two fractions. The least common multiple of 3 and 30 is 30. So, we can convert the first fraction to have a denominator of 30:

(11/3) = (11*10)/(3*10) = 110/30

Now we can add the two fractions:

(110/30) + (8/30) = (110 + 8)/30 = 118/30

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

118/30 = (118 ÷ 2)/(30 ÷ 2) = 59/15

So, Lara will need 59/15 feet of materials to make the necklace.

### Answer: 59/15

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.

Llama 3 70B:

Let's calculate the distance traveled by each plane in one minute:

Plane A: Speed = 24/11 miles/minute
Distance = Speed × Time = (24/11) × 1 = 24/11 miles

Plane B: Speed = 26/27 miles/minute
Distance = Speed × Time = (26/27) × 1 = 26/27 miles

Now, let's find the difference in distance traveled by the two planes:

Difference = Distance traveled by Plane A - Distance traveled by Plane B
= 24/11 - 26/27

To subtract these fractions, we need a common denominator, which is 297 (11 × 27). So, we can rewrite the fractions with this denominator:

24/11 = (24 × 27) / (11 × 27) = 648/297
26/27 = (26 × 11) / (27 × 11) = 286/297

Now, we can subtract:

Difference = 648/297 - 286/297 = 362/297

So, Plane A traveled 362/297 miles farther than Plane B after one minute.

### Answer: 362/297

Expected answer: 362/297

Correct? Yes

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.

Llama 3 70B:

To multiply fractions, we multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), then simplify the resulting fraction.

(14/7) × (25/13) = (14 × 25) / (7 × 13) = 350 / 91

We can simplify the fraction 350/91 by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is:

350/91

### Answer: 350/91

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.

Llama 3 70B:

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

The first song takes 12/8 hours to play. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

12 ÷ 4 = 3
8 ÷ 4 = 2

So, the first song takes 3/2 hours to play.

The second song takes 12/3 hours to play. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

12 ÷ 3 = 4
3 ÷ 3 = 1

So, the second song takes 4 hours to play.

Now, we can add the times it takes to play each song:

3/2 + 4 = ?

To add these fractions, we need to find a common denominator, which is 2. We can convert 4 to a fraction with a denominator of 2:

4 = 8/2

Now, we can add:

3/2 + 8/2 = 11/2

So, it takes Toby 11/2 hours to play both of his songs.

### 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?

Llama 3 70B:

Let's break this down step by step:

Initially, you have 28 out of 29 chocolate bars, which can be represented as a fraction: 28/29.

Then, you found 8 out of 22 more chocolate bars. To add these to the total, we need to find a common denominator between 29 and 22. The least common multiple (LCM) of 29 and 22 is 638. So, we can convert both fractions to have a denominator of 638:

28/29 = (28*22)/(29*22) = 616/638
8/22 = (8*29)/(22*29) = 232/638

Now, we can add the two fractions:

616/638 + 232/638 = 848/638

So, the total fraction of chocolate bars you have now is 848/638.

### Answer: 848/638

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?

Llama 3 70B:

Let's break this problem down step by step.

To produce one needle, the compass maker needs 27/26 pounds of material. To produce two identical needles, he will need:

2 x (27/26) = 54/26 = 27/13 pounds of material.

To produce the additional piece, the maker needs 27/6 pounds of material. To find the total amount of material needed, we add the amount needed for the two needles and the additional piece:

(27/13) + (27/6) = (27/13) + (63/26) = (54/26) + (63/26) = 117/26 pounds of material.

### Answer: 117/26 pounds.

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?

Llama 3 70B:

Reasoning: To find the total rate at which the two candles burn together, we need to add their individual burning rates.

The first candle burns at a rate of 6/4 inches per hour. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

6/4 = 3/2 inches per hour

The second candle burns at a rate of 14/16 inches per hour. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

14/16 = 7/8 inches per hour

Now, we can add the burning rates of the two candles:

3/2 + 7/8 = (3*4)/(2*4) + 7/8 = 12/8 + 7/8 = 19/8 inches per hour

### Answer: 19/8 inches per hour

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?

Llama 3 70B:

Reasoning: Sophia initially has 17/20 of a dollar, which is equivalent to 0.85 dollars (since 17/20 = 0.85).
Her friend gives her another 1/4 of a dollar, which is equivalent to 0.25 dollars. So, Sophia now has 0.85 + 0.25 = 1.10 dollars.
After some time, her brother gives her 1 dollar. So, Sophia now has 1.10 + 1.00 = 2.10 dollars.
### Answer: 2.10

Expected answer: 21/10

Correct? Yes

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))?

Llama 3 70B:

Let's break it down step by step:

Initial time investment (p) = time spent on composing music + time spent on writing lyrics
= 16/4 + 16/29
= 4 + 16/29
= 4 + 0.55 (approximately)
= 4.55 hours

Total time investment (b) = initial time investment + time spent on mixing and mastering
= 4.55 + 28/13
= 4.55 + 2.15 (approximately)
= 6.70 hours

Now, the drummer uses 18/4 hours less, which is:
= 18/4
= 4.5 hours

So, the final time spent on producing the song is:
= b - (18/4)
= 6.70 - 4.5
= 2.20 hours

### Answer: 2.20 hours

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?

Llama 3 70B:

Reasoning: Monica initially has 21/15 dozens of cookies. She bakes additional 29/17 dozens of cookies, so she now has:

(21/15) + (29/17) = (21*17 + 29*15) / (15*17) = (357 + 435) / 255 = 792 / 255 = 112/45 dozens of cookies.

To increase her total stock by a ratio of 7/5, she will have:

(112/45) * (7/5) = (112*7) / (45*5) = 784 / 225 = 56/15 dozens of cookies for the cookie festival.

### Answer: 56/15

Expected answer: 1848/425

Correct? No

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?

Llama 3 70B:

Reasoning: The chef starts with 28 kg of sugar. They use 26/24 kg of sugar to make one cake. To find the amount of sugar left, we subtract the amount used from the initial amount: 28 - 26/24 = 28 - 26/4 = 28 - 13/2 = (56 - 13)/2 = 43/2 = 21.5 kg.

Then, the chef adds 10/6 kg of sugar to their supply. To find the total amount of sugar left, we add the amount added to the amount left: 21.5 + 10/6 = 21.5 + 5/3 = (64.5 + 5)/3 = 69.5/3 = 23.17 kg ≈ 23.17 kg.

### Answer: 23.17 kg

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?

Llama 3 70B:

Reasoning: Emily watched a total of 16/4 = 4 hours of movies.
She spent 6/3 = 2 hours watching a comedy film.
To find the hours she spent watching movies other than the comedy film, we subtract the hours spent watching the comedy film from the total hours: 4 - 2 = 2 hours.
### 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.

Llama 3 70B:

Let's break it down:

Apple pie: Princess Lily ate 10 out of 12 slices, so the fraction of apple pie she ate is 10/12.

Blueberry pie: Princess Lily ate 10 out of 29 slices, so the fraction of blueberry pie she ate is 10/29.

To find the total fraction of pies she ate, we need to add these two fractions. To do this, we need a common denominator, which is 348 (12 × 29 = 348). So, we can convert both fractions to have a denominator of 348:

Apple pie: 10/12 = (10 × 29) / (12 × 29) = 290/348
Blueberry pie: 10/29 = (10 × 12) / (29 × 12) = 120/348

Now, we can add the fractions:

(290/348) + (120/348) = (290 + 120) / 348 = 410/348

So, Princess Lily ate 410/348 of the pies combined.

### Answer: 410/348

Expected answer: 205/174

Correct? Yes

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.

Llama 3 70B:

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

First, let's simplify the fractions:

(20 / 11) = 20/11 (cannot be simplified further)
(23 / 26) = 23/26 (cannot be simplified further)

Now, multiply the two fractions:

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

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

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

So, Marta uses 230/143 colored pencils for shading in her art projects over an 11-day period.

### Answer: 230/143

Expected answer: 230/143

Correct? Yes

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.

Llama 3 70B:

Let's break down the problem step by step:

**Indicator i:**
The first specimen decreases its value by 26 out of every 6 units, so the rate of decrease is 26/6.
The second specimen decreases its value by 25 out of every 17 units, so the rate of decrease is 25/17.
The ratio of these changes is:
i = (26/6) / (25/17) = (26 × 17) / (6 × 25) = 442 / 150 = 221/75

**Indicator h:**
The first specimen increases its value by 18 out of every 8 units, so the rate of increase is 18/8.
The second specimen increases its value by 17 out of every 23 units, so the rate of increase is 17/23.
The difference between these two rates is:
h = (18/8) - (17/23) = (18 × 23) / (8 × 23) - 17/23 = 414/184 - 17/23 = (414 - 136) / 184 = 278 / 184 = 139/92

**Indicator f:**
The final evidence factor f is the product of indicators h and i:
f = h × i = (139/92) × (221/75) = (139 × 221) / (92 × 75) = 30679 / 6900 = 4447/1150

### Answer: 4447/1150

Expected answer: 30719/6900

Correct? No

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?

Llama 3 70B:

Let's break this problem down into two parts:

Part 1: Find the total gestation period of both animals together.

The gestation period of a lioness is 20/22 of a year, which is equivalent to 20/22 = 0.90909 years (approximately).

The gestation period of a giraffe is 15 years.

The total gestation period of both animals together is 0.90909 + 15 = 15.90909 years.

Part 2: Find the reduced gestation period of the lioness for the second pregnancy.

The reduction in gestation period is 15/20 of a year, which is equivalent to 15/20 = 0.75 years.

The reduced gestation period of the lioness for the second pregnancy is the total gestation period of both animals together minus the reduction, which is:

15.90909 - 0.75 = 15.15909 years.

### Answer: 15.15909 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?

Llama 3 70B:

Reasoning: First, we need to find the area of the original rectangle. To do this, we multiply the length and the width:

Area = (30/7) × (19/6) = (30 × 19) / (7 × 6) = 570 / 42 = 135/7 square meters

Now, we need to find the area of the similar rectangle, which is 18/17 times bigger than the original rectangle. We can multiply the area of the original rectangle by 18/17:

New Area = (135/7) × (18/17) = (135 × 18) / (7 × 17) = 2430 / 119 square meters

### Answer: 2430/119 square meters

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?

Llama 3 70B:

Reasoning: First, let's convert the fractions to have a common denominator, which is 120. So, 23/8 = 345/120 and 4/20 = 24/120 and 19/24 = 95/120.

The factory produces 345/120 tonnes of soap initially.
Then, they increase production by 24/120 tonnes, making the total production 345/120 + 24/120 = 369/120 tonnes.
Later, they reduce production by 95/120 tonnes, making the total production 369/120 - 95/120 = 274/120 tonnes.

To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 31. So, 274/120 = 274÷31 / 120÷31 = 8 26/30 = 8 26/30 = 8 13/15 tonnes.

### Answer: 8 13/15 tonnes.

Expected answer: 137/60

Correct? No

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'.

Llama 3 70B:

Let's break this down step by step:

1. The machine starts by mixing 24/8 gallons of red paint. To simplify this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 8. So, we get:

24/8 = 3 gallons of red paint initially.

2. The machine then pours away 12/8 gallons of the mix. Again, we can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 4. So, we get:

12/8 = 3/2 gallons of red paint poured away.

Now, let's find the amount of red paint left in the machine, which is represented by 'd':

d = 3 - 3/2 = 3/2 gallons of red paint left.

3. Finally, the machine adds another 1/28 gallon of blue pigment to lighten the color. We need to subtract this amount from 'd' to find 'x', which is the total amount of paint:

x = d - 1/28 = 3/2 - 1/28

To subtract these fractions, we need to find a common denominator, which is 28. So, we can rewrite the fractions as:

x = 42/28 - 1/28 = 41/28 gallons

### Answer: 41/28

Expected answer: 41/28

Correct? Yes

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.

Llama 3 70B:

To compute the product of these fractions, we need to multiply the numerators (27 and 17) and multiply the denominators (14 and 13), then simplify the resulting fraction.

(27/14) × (17/13) = (27 × 17) / (14 × 13)
= 459 / 182

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 91.

459 ÷ 91 = 5
182 ÷ 91 = 2

So, the simplified fraction is:

5/2

### Answer: 5/2

Expected answer: 459/182

Correct? No

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.

Llama 3 70B:

Let's break it down step by step:

1. Sonia uses 21/12 oz of toothpaste daily. To simplify this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 3:

21 ÷ 3 = 7
12 ÷ 3 = 4

So, Sonia uses 7/4 oz of toothpaste daily.

2. Anthony uses 6/27 oz of toothpaste daily. To simplify this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 3:

6 ÷ 3 = 2
27 ÷ 3 = 9

So, Anthony uses 2/9 oz of toothpaste daily.

3. Now, let's add the amounts used by Sonia and Anthony:

7/4 + 2/9 = ?

To add these fractions, we need a common denominator, which is 36. So, we can convert both fractions to have a denominator of 36:

7/4 = 63/36
2/9 = 8/36

Now, we can add:

63/36 + 8/36 = 71/36

So, Sonia and Anthony use a total of 71/36 oz of toothpaste daily.

4. Their mom uses 3/18 oz of toothpaste daily. To simplify this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 3:

3 ÷ 3 = 1
18 ÷ 3 = 6

So, their mom uses 1/6 oz of toothpaste daily.

5. Finally, let's add the amount used by their mom to the total used by Sonia and Anthony:

71/36 + 1/6 = ?

To add these fractions, we need a common denominator, which is 36. So, we can convert the second fraction to have a denominator of 36:

1/6 = 6/36

Now, we can add:

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.

Llama 3 70B:

Let's break it down step by step:

Initially, you had 1 whole wheel of cheese and 1 whole pickle jar, which means you had 1 (or 14/14) of the wheel of cheese and 1 (or 18/18) of the pickle jar.

After making the special sandwiches, you were left with:

((7 / 18) + (21 / 14)) of the original ingredients
= (7/18) + (3/2) (since 21/14 = 3/2)
= (7/18) + (27/18) (to have a common denominator)
= 34/18

Now, you make the simpler sandwich, which requires half of the wheel of cheese. Since you had 34/18 of the original ingredients, you had (34/18) × (14/14) = 34/18 of the wheel of cheese. Half of that is (34/18) × (1/2) = 17/18.

To find the fraction of the original ingredients left after making the simpler sandwich, subtract the fraction used (17/18) × (2/4) = 17/36 from the fraction you had after making the first sandwich:

34/18 - 17/36
= (68/36) - (17/36) (to have a common denominator)
= 51/36

### Answer: 51/36

Expected answer: 25/18

Correct? No

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?

Llama 3 70B:

To find the total height of the windows, we need to add the heights of the two windows. However, the heights are given in different units, so we need to find a common denominator to add them.

The least common multiple (LCM) of 6 and 16 is 48. So, we can convert both fractions to have a denominator of 48:

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

Now we can add the heights:

120/48 + 21/48 = 141/48

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

141 ÷ 3 = 47
48 ÷ 3 = 16

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

### Answer: 47/16

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?

Llama 3 70B:

Reasoning: To add the apple and orange juice, we need to find a common denominator, which is 12. So, we can rewrite the fractions as:

16/6 = 32/12
20/12 = 20/12

Now, we can add them:

32/12 + 20/12 = 52/12

To add the cranberry juice, we need to convert it to a fraction with a denominator of 12:

2/3 = 8/12

Now, we can add all three:

52/12 + 8/12 = 60/12

We can simplify this fraction by dividing both the numerator and the denominator by 12:

60/12 = 5

So, Jan has 5 liters of juice in total.

### 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.

Llama 3 70B:

Reasoning: Let's multiply the number of points per level by the number of levels played:
(4/3) × (13/10) = (4 × 13) / (3 × 10) = 52 / 30

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
52 ÷ 2 = 26
30 ÷ 2 = 15

So, the simplified fraction is:
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?

Llama 3 70B:

Let's break down the time spent on each activity:

1. Cycling on the exercise bike: 18/8 hours = 2.25 hours
2. Conducting scientific experiments: 26/2 hours = 13 hours
Total "work" time: 2.25 + 13 = 15.25 hours

Now, he adds 30/8 hours of reviewing data to his routine:
30/8 hours = 3.75 hours

Total daily routine time: 15.25 + 3.75 = 19 hours

### Answer: 19

Expected answer: 19

Correct? Yes

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.

Llama 3 70B:

Let's break it down step by step!

We know that Jeremy ordered 30/9 ounces of cheese. To find the total amount of cheese he requested, we can simplify the fraction:

30/9 = 10/3 = 3 1/3 ounces

Now, we can use the given equation to find the amount of cheese he actually received:

d = n - (17/22)

where n is the amount of cheese he requested, which is 3 1/3 ounces.

First, let's convert the mixed number to an improper fraction:

3 1/3 = 10/3

Now, plug in the values:

d = 10/3 - (17/22)

To subtract fractions, we need a common denominator. The least common multiple of 3 and 22 is 66. So, we can convert both fractions to have a denominator of 66:

d = (220/66) - (51/66)

Now, subtract:

d = (220 - 51)/66
= 169/66

To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 1:

d = 169/66

So, Jeremy actually received 169/66 ounces of cheese.

### Answer: 169/66 ounces

Expected answer: 169/66

Correct? Yes

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.

Llama 3 70B:

Let's break down Sophia's calculations step by step:

1. In the first test, 13 out of every 4 sunglasses blocked all UV rays, so the fraction of sunglasses that blocked all UV rays is 13/4.
2. In the second test, 20 out of every 18 sunglasses blocked all UV rays, so the fraction of sunglasses that blocked all UV rays is 20/18 = 10/9.
3. Sophia added these numbers to her total, so she added the fractions: 13/4 + 10/9 = (13*9 + 10*4) / (4*9) = 127/36.
4. Then, she added the additional 21 out of 17 sunglasses that also blocked all UV rays, so she added the fraction 21/17 to her total: 127/36 + 21/17 = (127*17 + 21*36) / (36*17) = 2531/612.
5. 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, so she subtracted the fraction 16/30 from her total: 2531/612 - 16/30 = (2531*30 - 16*612) / (612*30) = 69149/18440.

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1223:

69149 ÷ 1223 = 56
18440 ÷ 1223 = 15

So, the final corrected number of sunglasses that blocked all UV rays, according to Sophia's tests and calculations, is:

### Answer: 56/15

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?

Llama 3 70B:

Let's break this problem down step by step:

1. To find the total amount of mayonnaise and sandwich spread Shawn uses to make a sandwich, we need to add the two fractions:

(23/28) + (6/9) = (23/28) + (16/24) = (69/84) + (48/84) = 117/84

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

117 ÷ 3 = 39
84 ÷ 3 = 28

So, the total amount of mayonnaise and sandwich spread Shawn uses to make a sandwich is 39/28 cups.

2. Now, Shawn adds 18/12 cups of cheese spread to his recipe. To find the total amount of ingredients Shawn needs to make one sandwich, we add the cheese spread to the total amount of mayonnaise and sandwich spread:

(39/28) + (18/12) = (39/28) + (42/28) = 81/28

3. Finally, if Shawn has to make an equal number of sandwiches using 4/4 cups of all the ingredients combined, we need to find the total number of cups of ingredients he will use. Let's say he makes x sandwiches. Then, the total amount of ingredients he will use is x times the total amount of ingredients per sandwich:

x × (81/28) = 4/4

To solve for x, we can cross-multiply:

x × 81 = 4 × 28
x × 81 = 112
x = 112/81

To find the total number of cups of ingredients Shawn will use, we multiply the number of sandwiches by 4/4 cups per sandwich:

(112/81) × (4/4) = 112/81 cups

### Answer: 112/81 cups

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?

Llama 3 70B:

Reasoning: Cassandra initially had 7/6 of a key set. 
She lost 1/21 of a key set, so she has 7/6 - 1/21 = (7*7 - 1*2)/(6*7) = 47/42 of a key set now.
### Answer: 47/42.

Expected answer: 47/42

Correct? Yes

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.

Llama 3 70B:

Let's break this down step by step:

First, let's calculate the sum of the ratios of the two sections:

(29/23) + (19/17) = 1.3043... + 1.1176... = 2.4220...

Next, let's calculate the ratio of a rest, which is equivalent to one whole measure:

26/26 = 1

Now, let's calculate the difference between the sum of the ratios and the ratio of a rest:

2.4220... - 1 = 1.4220...

### Answer: 1.4220...

Expected answer: 539/391

Correct? No

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.

Llama 3 70B:

To multiply two fractions, we need to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), then simplify the resulting fraction.

In this case, we have:

(22/25) × (22/8) = ?

First, let's multiply the numerators:
22 × 22 = 484

Next, let's multiply the denominators:
25 × 8 = 200

Now, we can write the product as a fraction:
484/200

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:
484 ÷ 4 = 121
200 ÷ 4 = 50

So, the simplified product is:
121/50

### Answer: 121/50

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.

Llama 3 70B:

Reasoning: First, we need to find the total length of the pillow. To do this, we add the length of the pillow to the additional length due to fluffing: 

(23/9) + (22/25) = ((23*25) + (22*9)) / (9*25) = (575 + 198) / 225 = 773 / 225 

Next, we multiply the total length by the factor to account for overlap and corners: 

(773 / 225) * (16 / 13) = (773 * 16) / (225 * 13) = 12368 / 2925 

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 41: 

12368 ÷ 41 = 302 
2925 ÷ 41 = 71 

So, the length of border material James will need is 302 / 71 feet. 

### Answer: 302/71

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.

Llama 3 70B:

Let's break this down step by step:

1. The car travels 21/4 miles every hour. To find the average miles it travels in an hour, we can leave the fraction as is, since it's already in miles per hour.

2. The car was needed to travel an extra 16/13 miles. To find out how many hours it would take to travel this distance, we can divide the extra distance by the average miles per hour:

(16/13) ÷ (21/4) = (16/13) × (4/21) = 64/273 hours

3. However, due to a detour, it only traveled an additional 1/21 miles. To find out how many hours it would take to travel this distance, we can divide the additional distance traveled by the average miles per hour:

(1/21) ÷ (21/4) = (1/21) × (4/21) = 4/441 hours

4. To find the difference in hours, subtract the actual hours traveled from the needed hours:

(64/273) - (4/441) = (256/1197) - (4/441) = (256-4)/1197 = 252/1197 hours

5. Since the car travels 21/4 miles per hour, we can multiply the difference in hours by the average miles per hour to find the difference in miles:

(252/1197) × (21/4) = (252 × 21) / (1197 × 4) = 5292 / 4796 = 33/29 miles

### Answer: 33/29 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?

Llama 3 70B:

Let's break down the problem step by step:

1. The editing team takes 20/5 hours to edit a manuscript, which is equal to 4 hours.
2. The typesetting team needs 18/17 hours to adjust the layout of a page, which is approximately 1.06 hours (we'll use this value for calculation).
3. The total initial time required is the sum of the editing and typesetting times: 4 hours + 1.06 hours = 5.06 hours.
4. There is a collective loss of 6/15 hours, which is equal to 0.4 hours. So, the reduced time is: 5.06 hours - 0.4 hours = 4.66 hours.
5. To compensate, the manager extends the working hours by the same amount of time as the initial time span, which is 5.06 hours.
6. The total extended time is the sum of the reduced time and the extended time: 4.66 hours + 5.06 hours = 9.72 hours.
7. The problem asks for the product of the time required for the entire process and the extended time after the reduction of the lost hours with the initial total time required. This means we need to multiply the reduced time, the extended time, and the initial total time: 4.66 hours × 9.72 hours × 5.06 hours.

Now, let's calculate the product:

4.66 × 9.72 × 5.06 = 244.51

### Answer: 244.51

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?

Llama 3 70B:

Reasoning: Jenny plants 13/11 rows of potatoes, and each row yields 21/3 bushels. So, the total yield is (13/11) × (21/3) = 91/11 bushels.
Each bushel earns her 21/15 dollars, so the total amount she will make is (91/11) × (21/15) = 1277/165 dollars.
### Answer: 1277/165.

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?

Llama 3 70B:

Reasoning: We can simplify the fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD). 

For the gold, the GCD of 14 and 28 is 14, so we can simplify the fraction as follows:
14/28 = 1/2

For the silver, the GCD of 13 and 26 is 13, so we can simplify the fraction as follows:
13/26 = 1/2

Now, we can add the amounts of gold and silver used:
1/2 + 1/2 = 1

So, the sum of the amount of gold and silver used by the jeweler is 1 kilogram.
### 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?

Llama 3 70B:

Let's break this down step by step:

1. Each honey storage sub-section has (25/9) gallons of honey.
2. Each bee rearing sub-section also has (25/9) gallons of honey.
3. If the beekeeper combines the honey from one honey storage sub-section and one bee rearing sub-section, the total quantity is 'p'. So, we can set up the equation:

p = (25/9) + (25/9)
p = 2(25/9)
p = 50/9

4. Now, one honey storage sub-section has an additional (2/26) gallons of honey. So, the total amount of honey in this sub-section is:

(25/9) + (2/26)

To add these fractions, we need to find a common denominator, which is 234. So, we can convert both fractions:

(25/9) = (575/234)
(2/26) = (18/234)

Now, we can add them:

(575/234) + (18/234) = (593/234)

5. If the beekeeper combines this honey storage sub-section with a bee rearing sub-section, the total amount of honey would be 's'. So, we can set up the equation:

s = (593/234) + (25/9)

Again, we need to find a common denominator, which is 234. So, we can convert the second fraction:

(25/9) = (575/234)

Now, we can add them:

s = (593/234) + (575/234)
s = (1168/234)

### Answer: 1168/234

Expected answer: 659/117

Correct? No

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.

Llama 3 70B:

Reasoning: To find the total bunches of leaves the dinosaur eats in an hour, we need to add the number of bunches it eats during the day and at night.

During the day, the dinosaur eats 16/8 bunches of leaves per hour. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 8. This gives us:

16/8 = 2/1 = 2

So, the dinosaur eats 2 bunches of leaves per hour during the day.

At night, the dinosaur eats 6/17 bunches of leaves per hour.

To find the total bunches of leaves the dinosaur eats in an hour, we add the number of bunches it eats during the day and at night:

2 + 6/17 = 2 + 0.35294117647 (approximately) = 2.35294117647 (approximately)

### Answer: 2.35 (approximately)

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?

Llama 3 70B:

Reasoning: To find the total amount of fish eaten, we need to add the amounts eaten on each day. To do this, we need to find a common denominator for the fractions.

The least common multiple (LCM) of 6, 18, and 22 is 396. So, we can convert each fraction to have a denominator of 396:

28/6 = (28*66)/(6*66) = 1848/396
21/18 = (21*22)/(18*22) = 462/396
24/22 = (24*18)/(22*18) = 432/396

Now we can add the fractions:

1848/396 + 462/396 + 432/396 = 2742/396

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

2742 ÷ 6 = 457
396 ÷ 6 = 66

So, the total amount of fish eaten is 457/66 pounds.

### Answer: 457/66

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?

Llama 3 70B:

Reasoning: First, we need to find the total amount of sugar required for the bread recipe and the custard. 
For the bread recipe, Heather needed 11/17 cups of sugar. 
For the custard, Heather needed 6/2 = 3 cups of sugar. 
So, the total amount of sugar required is 11/17 + 3 = 11/17 + 51/17 = 62/17 cups. 
Since Heather decided to increase the total quantity of sugar by a factor of 29/21, she used a total of (29/21) × (62/17) = 29 × 62 / (21 × 17) = 1798 / 357 cups of sugar. 
### Answer: 1798/357 cups.

Expected answer: 1798/357

Correct? Yes

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?

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS). First, we'll calculate the fractions inside the parentheses:

(7 / 8) = 7/8
(21 / 18) = 21/18 = 7/6 (simplified)

Now, we'll add the two fractions:

(7/8) + (7/6) = ?

To add these fractions, we need a common denominator, which is 24. So, we'll convert both fractions to have a denominator of 24:

(7/8) = (21/24)
(7/6) = (28/24)

Now, we can add:

(21/24) + (28/24) = (49/24)

So, the result of the calculation is:

### 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.

Llama 3 70B:

Let's break this problem down step by step:

1. The guests' consumption (v) is the sum of water and wine consumption:
v = 15/7 + 15/24
To add these fractions, we need a common denominator, which is 168. So, we can rewrite the fractions as:
v = 360/168 + 90/168
v = 450/168
v = 225/84

2. The royal baker's requirement is 26/20 gallons of milk per cake. Since we need to multiply this by the guests' consumption (v), we get:
i = (26/20) × (225/84)
i = 5850/1680
i = 225/64

3. Now, we need to add the guests' consumption (v) to the product of the baker's requirement and the guests' consumption (i):
x = v + i
x = 225/84 + 225/64
To add these fractions, we need a common denominator, which is 2688. So, we can rewrite the fractions as:
x = 675/2688 + 945/2688
x = 1620/2688
x = 405/672

### Answer: 405/672

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?

Llama 3 70B:

Let's break this down step by step.

First, Teddy adds 30/17 and 18/15. To add these fractions, we need to find a common denominator, which is 255. So, we can convert both fractions to have a denominator of 255:

30/17 = (30*15)/(17*15) = 450/255
18/15 = (18*17)/(15*17) = 306/255

Now, we can add them:

450/255 + 306/255 = 756/255

Next, Teddy multiplies this result by 24/13. To multiply fractions, we multiply the numerators and multiply the denominators:

(756/255) × (24/13) = (756*24)/(255*13) = 18144/3315

So, Teddy's final number is 18144/3315.

### Answer: 18144/3315

Expected answer: 6048/1105

Correct? Yes

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).

Llama 3 70B:

Reasoning: To find the fraction of the desired diameter that each hole would have, we need to divide the diameter of the drill bit by the desired diameter.

The diameter of the drill bit is (11/21) cm, and the desired diameter is (20/6) cm. So, we divide the diameter of the drill bit by the desired diameter:

((11/21) ÷ (20/6)) = ((11/21) × (6/20)) = ((11 × 6) / (21 × 20)) = (66/420)

### Answer: 66/420

Expected answer: 110/63

Correct? No

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.

Llama 3 70B:

Reasoning: To find the difference in time, we need to subtract the time taken to assemble the second model from the time taken to assemble the first model.

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

To subtract these fractions, we need to find a common denominator, which is 230. So, we can convert both fractions to have a denominator of 230:

Time taken to assemble the first model = (17/10) × (23/23) = 391/230 hours
Time taken to assemble the second model = (12/23) × (10/10) = 120/230 hours

Now, we can subtract:

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

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

271/230 = 1.173913 (approximately)

### Answer: 1.173913 or 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.

Llama 3 70B:

Let's break this down step by step:

1. Carlos usually uses 20/15 units of wood for a regular chair. To simplify this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 5:

20/15 = (20 ÷ 5) / (15 ÷ 5) = 4/3

So, Carlos usually uses 4/3 units of wood for a regular chair.

2. For the special order, he needs (24/5) times (7/6) units more wood than usual. To multiply these fractions, we multiply the numerators and denominators separately:

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

To simplify this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 6:

168/30 = (168 ÷ 6) / (30 ÷ 6) = 28/5

So, the special chair requires 28/5 units more wood than usual.

3. To find the total amount of wood needed for the special chair, we add the usual amount to the additional amount:

Total wood needed = Usual amount + Additional amount
= 4/3 + 28/5

To add these fractions, we need a common denominator, which is 15. So, we convert both fractions to have a denominator of 15:

4/3 = (4 × 5) / (3 × 5) = 20/15
28/5 = (28 × 3) / (5 × 3) = 84/15

Now we can add:

Total wood needed = 20/15 + 84/15 = (20 + 84) / 15 = 104/15

### Answer: 104/15

Expected answer: 104/15

Correct? Yes

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?

Llama 3 70B:

Let's break this down step by step:

Initially, the car's speed was 13/4 miles per minute.

The car slows down by 14/15 miles per minute, so we subtract this from the initial speed:
(13/4) - (14/15) = (195 - 56) / 60 = 139 / 60 miles per minute

Then, the car increases its speed again by 30/15 miles per minute, so we add this to the new speed:
(139/60) + (30/15) = (139 + 120) / 60 = 259 / 60 miles per minute

To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 1:
259 / 60 = 259/60 miles per minute

### Answer: 259/60 miles per minute.

Expected answer: 259/60

Correct? Yes

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?

Llama 3 70B:

Let's break this down step by step:

1. 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. To find out how many baskets were produced this season, we multiply the usual amount by the fraction of the usual amount produced:

(19/2) × (19/29) = (19 × 19) / (2 × 29) = 361 / 58 = 361/58

So, 361/58 baskets of grapes were produced this season.

2. Jake gets to keep only 7/11 of the total amount of grapes. To find out how many baskets he gets, we multiply the total amount by the fraction he gets to keep:

(361/58) × (7/11) = (361 × 7) / (58 × 11) = 2527 / 638 = 2527/638

So, Jake gets 2527/638 baskets of grapes.

3. Out of the grapes that he got, Jake wants to make some grape juice. But he only uses 9/10 of his grapes to make the juice. To find out how many baskets he uses for the juice, we multiply the number of baskets he gets by the fraction he uses for juice:

(2527/638) × (9/10) = (2527 × 9) / (638 × 10) = 22743 / 6380 = 22743/6380

So, Jake uses 22743/6380 baskets of grapes for the juice.

### Answer: 22743/6380

Expected answer: 22743/6380

Correct? Yes

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.

Llama 3 70B:

Reasoning: To find the total number of bushels of grapes Joel picked, we need to add the number of bushels of red grapes and green grapes.

First, let's simplify the fractions:
9/2 = 4.5 bushels of red grapes
10/22 = 0.45 bushels of green grapes (we can divide both numerator and denominator by 2 to get 5/11, but in this case, it's easier to convert to a decimal)

Now, let's add the number of bushels:
4.5 + 0.45 = 4.95 bushels

### Answer: 4.95

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?

Llama 3 70B:

Reasoning: To find the total height of the snowman, we need to find the radius of each snowball and then add them together.

The diameter of the larger snowball is 17/8 feet, so the radius is half of that, which is (17/8) / 2 = 17/16 feet.

The diameter of the smaller snowball is 1/20 feet, so the radius is half of that, which is (1/20) / 2 = 1/40 feet.

Now, we add the radii of the two snowballs to find the total height: 17/16 + 1/40 = (17*5)/(16*5) + 1/40 = 85/80 + 1/40 = (85+1)/80 = 86/80 = 43/40 feet.

### Answer: 43/40

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.

Llama 3 70B:

Reasoning: First, we need to find the total number of parts the sand is divided into. To do this, we find the least common multiple (LCM) of 7 and 16, which is 112. So, the sand is divided into 112 parts.

The child splits the sand into 24/7 parts, which means each part is 112/(24/7) = 112/(24/7) = 49.

The other child takes away 2/16 part of the sand, which is equivalent to 2/16 × 112 = 14 parts.

So, the remaining part of the sand is 112 - 14 = 98 parts.

To find the fraction of the remaining sand, we divide the remaining parts by the total number of parts: 98/112 = 7/8.

### Answer: 7/8

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.

Llama 3 70B:

Reasoning: To compare the amounts eaten, we need to find a common denominator for the two fractions. The least common multiple of 26 and 9 is 234. So, we can convert both fractions to have a denominator of 234:

28/26 = (28*9)/(26*9) = 252/234
23/9 = (23*26)/(9*26) = 598/234

Now we can subtract the two fractions:

598/234 - 252/234 = 346/234

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

346 ÷ 2 = 173
234 ÷ 2 = 117

So, the simplified fraction is:

173/117

### Answer: 173/117

Expected answer: 173/117

Correct? Yes

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)).

Llama 3 70B:

To evaluate the expression, we need to follow the order of operations (PEMDAS):

1. Divide 14 by 4: 14/4 = 3.5
2. Divide 21 by 11: 21/11 = 1.90909... (approximately)
3. Multiply 3.5 by 1.90909...: 3.5 × 1.90909... ≈ 6.68161...

So, the factory will produce approximately 6.68161... kilograms of chocolate.

### Answer: 6.68161...

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.

Llama 3 70B:

To find the expected number of bananas produced on a randomly chosen day, we can use the formula provided: ((12 / 29) + (30 / 10)).

First, let's calculate the number of bananas produced per day by each species:

 Species 1: 12 bananas every 29 days => 12/29 bananas per day
 Species 2: 30 bananas every 10 days => 30/10 = 3 bananas per day

Now, let's add the number of bananas produced per day by both species:

(12/29) + 3 = (12/29) + (30/10) = (12/29) + 3 = (12/29) + (3*29/29) = (12+87)/29 = 99/29

So, the expected number of bananas produced on a randomly chosen day is 99/29.

### Answer: 99/29

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.

Llama 3 70B:

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

First, let's simplify the fractions:
11/11 = 1 (since 11 divided by 11 is 1)
26/14 = 13/7 (since 26 divided by 14 is 13/7)

Now, we can add the two fractions:
1 + 13/7 = 20/7 (since 1 is equal to 7/7, and 7/7 + 13/7 = 20/7)

So, the total ton of food the giraffe needs to eat in a day is 20/7 ton.
### Answer: 20/7 ton.

Expected answer: 20/7

Correct? Yes

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.

Llama 3 70B:

Reasoning: The bear spends 18/24 of each day asleep, which is equivalent to 0.75 (since 18/24 = 3/4 = 0.75).

Over 27 days, the bear spends 0.75 × 27 days asleep.

To find the fraction of time the bear has spent sleeping over the 27 days, we need to divide the total time spent sleeping by the total time available (27 days).

There are 13 weeks in a month, and each week has 7 days, so there are 13 × 7 = 91 days in a month.

The total time available is 27 days, which is 27/91 of the total time in a month.

Now, we can calculate the fraction of time the bear has spent sleeping:

(18/24) × (27/91) = (3/4) × (27/91) = 0.75 × (27/91) ≈ 0.225

### Answer: 0.225

Expected answer: 81/52

Correct? No

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.

Llama 3 70B:

To find the fraction of trees that are either pine or birch, we can add the fractions of pine trees and birch trees.

First, let's convert the fraction of birch trees to have a denominator of 14, so we can add it to the fraction of pine trees:

(19 / 2) = (19 × 7 / 2 × 7) = (133 / 14)

Now we can add the fractions:

f = ((9 / 14) + (133 / 14))
f = (9 + 133) / 14
f = 142 / 14
f = 71 / 7
f = 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.

Llama 3 70B:

Reasoning: To evaluate the expression (14 / 2) / (23 / 17), we need to follow the order of operations (PEMDAS). First, we calculate the expressions inside the parentheses:

(14 / 2) = 7
(23 / 17) = 23/17

Now, we can rewrite the expression as:
7 / (23/17)

To divide by a fraction, we multiply by its reciprocal:
7 × (17/23) = (7 × 17) / 23 = 119 / 23

So, the Zogorian's initial energy level is 119/23 zogs.

Later, his energy level increases by (16 / 24) zogs. Again, we evaluate the expression inside the parentheses:
(16 / 24) = 2/3

Now, we add the increase to the initial energy level:
(119/23) + (2/3)

To add these fractions, we need a common denominator, which is 69. We can rewrite the fractions as:
(483/69) + (46/69) = (483 + 46)/69 = 529/69

Therefore, the Zogorian's energy level after the increase is 529/69 zogs.

### Answer: 529/69

Expected answer: 403/69

Correct? No

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?

Llama 3 70B:

Let's assume Teddy has x friends in total.

The number of friends Teddy hides in the forest is 18/11 of x, which is (18/11)x.

The number of friends Teddy hides at the beach is 8/21 of x, which is (8/21)x.

The difference between the number of friends Teddy hides in the forest and at the beach is:

f = ((18/11)x - (8/21)x)

To simplify this expression, we can find a common denominator, which is 231. Then:

f = ((378x - 88x)/231)
f = (290x/231)

Now, we need to square f to find n, the total number of hiding spots Teddy needs:

n = f^2
n = ((290x/231))^2
n = (84100x^2)/53241

Since we don't know the value of x, we can't simplify this expression further. However, we can express n in terms of x:

n = (84100x^2)/53241

### Answer: (84100x^2)/53241

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.

Llama 3 70B:

Reasoning: To subtract fractions, we need to find a common denominator. The least common multiple of 10 and 23 is 230. So, we can convert both fractions to have a denominator of 230:

25/10 = (25*23)/(10*23) = 575/230
27/23 = (27*10)/(23*10) = 270/230

Now, we can subtract:

575/230 - 270/230 = (575-270)/230 = 305/230

To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 5:

305/230 = (305/5)/(230/5) = 61/46

### Answer: 61/46

Expected answer: 61/46

Correct? Yes

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.

Llama 3 70B:

Let's break this down step by step:

1. The first snail covers 17/21 of a meter in an hour. Since it started an hour earlier, it has already covered 17/21 meters when the other two snails start moving.
2. The second snail covers 20/24 of a meter in an hour. After 1 hour, it will cover 20/24 meters.
3. The third snail covers 18/17 of a meter in an hour. After 1 hour, it will cover 18/17 meters.
4. To find the total distance covered by the first two snails, we add their distances: (17/21) + (20/24) = (408 + 350) / (504) = 758 / 504.
5. To find the total distance covered by all three snails, we multiply the result by the distance covered by the third snail: (758 / 504) × (18 / 17) = 13644 / 8512.

### Answer: 13644/8512

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?

Llama 3 70B:

Let's break this problem down step by step:

1. Johnny started with 24/14 yards of fabric.
2. He had 9/29 yards left after making some stuffed animals, so he used:
24/14 - 9/29 = (84 - 18) / (14 * 29) = 66 / 406 = 33 / 203 yards of fabric.

3. Johnny then got a new type of fabric and used 15/2 times the difference of the original and remaining fabric, which is:
(15/2) * (33/203) = (15 * 33) / (2 * 203) = 495 / 406 = 495/406 yards of the new fabric.

### Answer: 495/406

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.

Llama 3 70B:

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

2/10 = 4/20
21/4 = 105/20

Now we can add:

4/20 + 105/20 = 109/20

So, 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.

Llama 3 70B:

Reasoning: To find the total hours of power, we need to calculate the fraction of fuel tanks filled and multiply it by the hours each tank provides.

First, let's calculate the fraction of fuel tanks filled: 18/30 = 3/5 (simplified).

Next, let's calculate the hours each tank provides: 22/6 = 11/3 (simplified).

Now, multiply the fraction of fuel tanks filled by the hours each tank provides: (3/5) × (11/3) = 33/15 = 11/5.

So, the spacecraft currently has 11/5 hours of power.

### Answer: 11/5 hours or 2.2 hours.

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?

Llama 3 70B:

Reasoning: To find the total amount of cat food eaten in one day, we need to add the amount eaten in the morning and the evening.

In the morning, the cat eats 16/12 of a can, which is equivalent to 4/3 of a can (since 16/12 = 4/3).

In the evening, the cat eats 6/10 of a can.

To add these fractions, we need to find a common denominator, which is 30. So, we can convert both fractions to have a denominator of 30:

Morning: 4/3 = 40/30
Evening: 6/10 = 18/30

Now, we can add:

40/30 + 18/30 = 58/30

So, the cat eats 58/30 of a can in one day.

### Answer: 58/30

Expected answer: 29/15

Correct? Yes

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?

Llama 3 70B:

Let's break this down step by step:

Group 1: 12 eggs in 3 nests
Average number of eggs per nest = Total eggs / Number of nests = 12 / 3 = 4 eggs per nest

Group 2: 11 eggs in 4 nests
Average number of eggs per nest = Total eggs / Number of nests = 11 / 4 = 2.75 eggs per nest

Now, let's find the difference between the average number of eggs per nest for these two groups:
Difference = Average of Group 1 - Average of Group 2 = 4 - 2.75 = 1.25

### 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?

Llama 3 70B:

Let's break this down step by step:

1. The monkey eats (22/7) × (10/25) of the pile. To multiply fractions, we multiply the numerators (22 × 10 = 220) and multiply the denominators (7 × 25 = 175), then simplify:

(220/175) = (4/1) = 4

So, the monkey eats 4 times the original pile.

2. Since the monkey eats 4 times the original pile, that means he eats 4/1 of the pile. To find the fraction of the pile left, we subtract this from 1:

1 - (4/1) = 1 - 4 = -3 (but we can't have a negative amount, so we'll rewrite this as)

1 - 4/1 = 1/1 - 4/1 = (-3)/1 = -3/1

To get a positive fraction, we can divide both numerator and denominator by -1:

(-3)/1 = 3/-1 = (-3)/1 × (-1)/(-1) = 3/(-1) × (-1)/(-1) = 3/1

So, the monkey has -3/1 of the pile left, which means he has eaten the entire pile and has 3 times the original pile more to eat (but that's not possible, so let's re-evaluate).

3. Let's rethink this: the monkey eats 4 times the original pile, which means he eats the entire pile and has 3 times the original pile more to eat (but that's not possible). This means our initial calculation was incorrect.

Let's retry:

The monkey eats (22/7) × (10/25) of the pile. To multiply fractions, we multiply the numerators (22 × 10 = 220) and multiply the denominators (7 × 25 = 175), then simplify:

(220/175) = (4/1) = 4/1

So, the monkey eats 4/1 of the pile.

To find the fraction of the pile left, we subtract this from 1:

1 - (4/1) = 1 - 4 = -3 (but we can't have a negative amount, so we'll rewrite this as)

1 - 4/1 = 1/1 - 4/1 = (-3)/1 = -3/1

To get a positive fraction, we can divide both numerator and denominator by -1:

(-3)/1 = 3/-1 = (-3)/1 × (-1)/(-1) = 3/(-1) × (-1)/(-1) = 3/1

Wait, this still doesn't make sense! Let's retry again:

The monkey eats (22/7) × (10/25) of the pile. To multiply fractions, we multiply the numerators (22 × 10 = 220) and multiply the denominators (7 × 25 = 175), then simplify:

(220/175) = (4/5)

So, the monkey eats 4/5 of the pile.

To find the fraction of the pile left, we subtract this from 1:

1 - (4/5) = (5/5) - (4/5) = (1/5)

The monkey has 1/5 of the pile left.

4. Later, he gives (3/28) of the pile to his friend. To find the fraction of the pile left, we subtract this from the fraction he had left:

(1/5) - (3/28)

To subtract fractions, we need a common denominator, which is 140. So, we convert both fractions:

(1/5) = (28/140)
(3/28) = (15/140)

Now we can subtract:

(28/140) - (15/140) = (13/140)

The monkey has 13/140 of the pile left.

### Answer: 13/140

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?

Llama 3 70B:

Reasoning: To find the total distance the mouse runs, we need to multiply the speed of the mouse by the time it runs.

First, let's convert the time from an improper fraction to a mixed number: 23/2 = 11 1/2 seconds.

Now, we can multiply the speed by the time: (24/20) × (11 1/2) = (24/20) × (23/2) = (24 × 23) / (20 × 2) = 552 / 40 = 13.8 feet.

### Answer: 13.8 feet

Expected answer: 69/5

Correct? No

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?

Llama 3 70B:

Let's break this problem down step by step.

First, we need to find the total number of ounces consumed initially. Since each glass contains 29/9 ounces and 26/25 of them were consumed, we can multiply the number of glasses consumed by the number of ounces per glass:

(26/25) × (29/9) = (26 × 29) / (25 × 9) = 754 / 225 = 3.36 (approximately)

So, approximately 3.36 ounces of beverage were consumed initially.

Next, the partygoers drink an additional 2/19 ounces of beverages. To find the total number of ounces consumed, we add the initial amount to the additional amount:

3.36 + (2/19) = 3.36 + 0.105 = 3.465

Therefore, a total of approximately 3.465 ounces of beverages were consumed at the party.

### Answer: 3.465

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?

Llama 3 70B:

Let's break this down step by step:

1. You add 7/15 of a new set of toothbrushes to your current collection. This means you now have 1 + 7/15 = 22/15 sets of toothbrushes.
2. Your friend gifts you 9 more sets, so you now have 22/15 + 9 = 22/15 + 135/15 = 157/15 sets of toothbrushes.
3. You can only fit 26/27 of them in your display case. To find out how many sets you can fit, multiply the total number of sets by 26/27:

(157/15) × (26/27) = 157 × 26 / (15 × 27) = 4072 / 405 = 10.06 (approximately)

Since you can't fit a fraction of a set, we'll round down to the nearest whole number.

### Answer: 10

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.

Llama 3 70B:

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

The weight of the empty backpack is 27/20 kilograms.
The weight of the book is 1/6 kilograms.

To add these fractions, we need to find a common denominator, which is 60. So, we can convert both fractions to have a denominator of 60:

27/20 = (27*3)/(20*3) = 81/60
1/6 = (1*10)/(6*10) = 10/60

Now we can add the fractions:

81/60 + 10/60 = 91/60

So, the total weight of the backpack is 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?

Llama 3 70B:

Reasoning: To find the multiplier, we need to evaluate the expression (7 / 7) * (25 / 22).

First, simplify the fraction (7 / 7) = 1, since 7 divided by 7 is 1.

Now, multiply 1 by (25 / 22) = 1 * (25 / 22) = 25 / 22.

So, the multiplier of the new bottle compared to the old one is 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.

Llama 3 70B:

Let's break it down step by step:

1. Tilly has 25/9 kg of sea plants initially.
2. She finds 8/13 kg more, so she now has:
25/9 + 8/13 = (25*13 + 8*9) / (9*13) = (325 + 72) / 117 = 397 / 117 kg
3. She finds another 24/27 kg, so she now has:
397/117 + 24/27 = (397*27 + 24*117) / (117*27) = (10689 + 2788) / 3159 = 13477 / 3159 kg
4. Finally, she finds 21/26 kg more, so she now has:
13477/3159 + 21/26 = (13477*26 + 21*3159) / (3159*26) = (350522 + 66219) / 82234 = 416741 / 82234 kg

To simplify the fraction, we can find the greatest common divisor (GCD) of 416741 and 82234, which is 1. Therefore, the fraction is already in its simplest form:

### Answer: 416741/82234 kg

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.

Llama 3 70B:

Let's break down Captain Alf's calculations step by step:

1. Calculate the difference in his current location and the distance of the nearby island:

Distance to the island = 17/2 nautical miles
Current location = 4/2 nautical miles away from the island
Difference = 17/2 - 4/2 = (17 - 4)/2 = 13/2 nautical miles

2. Adjust for the tide:

Tide adjustment = 14/9 nautical miles
Adjusted distance = 13/2 + 14/9 = (13*9 + 14*2)/(2*9) = (117 + 28)/18 = 145/18 nautical miles

3. Calculate fuel requirements based on fuel efficiency:

Fuel efficiency = 22/15 nautical miles per gallon
Fuel requirements = Adjusted distance × Fuel efficiency = (145/18) × (22/15) = (145*22)/(18*15) = 3190/270 nautical miles per gallon

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

Fuel requirements = 319/27 nautical miles per gallon

### Answer: 319/27

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?

Llama 3 70B:

Reasoning: The forest ranger patrolled 14/3 miles in the morning. To find the distance patrolled in the afternoon, we need to subtract 2/18 from 14/3.

First, let's convert 14/3 to an equivalent fraction with a denominator of 18: 14/3 = (14*6)/(3*6) = 84/18.

Now, subtract 2/18 from 84/18: 84/18 - 2/18 = (84-2)/18 = 82/18.

To simplify, divide both numerator and denominator by their greatest common divisor, which is 2: 82/18 = (82÷2)/(18÷2) = 41/9.

### Answer: 41/9 miles.

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?

Llama 3 70B:

Reasoning: Arthur practices 20/21 hours every day. On weekends, he practices an additional 11/29 hours per day. 
To find the total hours he practices on weekends, we add the two fractions: 
(20/21) + (11/29) = ((20*29) + (11*21)) / (21*29) = (580 + 231) / 609 = 811 / 609. 
### Answer: 811/609.

Expected answer: 811/609

Correct? Yes

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.

Llama 3 70B:

Let's break it down step by step:

Initially, Lucas had 18 shirts and divided them equally among his 3 siblings, so each sibling got:
18 ÷ 3 = 6 shirts

Later, Lucas bought 27 more shirts and decided to keep 1/19 of those shirts for each sibling, so each sibling got:
27 ÷ 19 = 1.42 (approximately) shirts (we'll take it as 1 shirt since we can't divide a shirt)

Now, let's calculate the difference using the given expression:
((18 / 3) - (27 / 19)) = (6 - 1.42) = 4.58 (approximately)

Since we can't have a fraction of a shirt, we'll take the whole number part, which is 4. So, each sibling now has 4 fewer shirts compared to before.

### Answer: 4

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?

Llama 3 70B:

Reasoning: The painter mixed 7 gallons of white paint with 2/5 gallon of blue paint, so the total amount of light blue paint is 7 + 2/5 = 7 + 0.4 = 7.4 gallons.

The painter used 18/4 = 4.5 gallons of the light blue paint for the project.

To find out how many gallons the painter has left, subtract the amount used from the total amount: 7.4 - 4.5 = 2.9 gallons.

### Answer: 2.9 gallons

Expected answer: 29/10

Correct? No

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?

Llama 3 70B:

Reasoning: To find the total hours Jayson spent skate skating, we need to add the hours he spent on each day.

On the first day, Jayson spent 24/7 hours skating. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. So, 24/7 = 24/7 = 3 3/7 hours.

On the second day, Jayson spent 30/20 hours skating. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 10. So, 30/20 = 3/2 = 1 1/2 hours.

Now, we can add the hours Jayson spent on each day: 3 3/7 + 1 1/2 = 5 1/14 hours.

### Answer: 5 1/14 hours.

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?

Llama 3 70B:

Reasoning: The dolphin can leap approximately 18/3 = 6 feet out of the water.
If the dolphin only manages to jump 3/4 of his usual height, then the dolphin jumps 6 * 3/4 = 4.5 feet.
### Answer: 4.5 feet.

Expected answer: 9/2

Correct? No

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.

Llama 3 70B:

Let's break down the problem step by step:

Last month's sales to production ratio:
(20/15) + (16/22) = (4/3) + (8/11) = (44/33) + (24/33) = (68/33)

This week's ratio of interested customers to production:
(22/27) × (23/8) = (22 × 23) / (27 × 8) = (506) / (216)

Now, let's multiply the two ratios:
(68/33) × (506/216) = (68 × 506) / (33 × 216) = (34568) / (7128)

### Answer: 34568/7128

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?

Llama 3 70B:

Reasoning: The musician played a song for 30 minutes, and divided this time equally between 15 songs. To find the time spent on each song, we can divide 30 minutes by 15:

30 minutes ÷ 15 = 2 minutes per song

The band reduced the time spent on a particular song by 1/17 of an hour. Since there are 60 minutes in an hour, 1/17 of an hour is:

(1/17) × 60 = 60/17 = 3.53 minutes (approximately)

So, the band reduced the time spent on the particular song by 3.53 minutes. To find the final duration of that song, we subtract this reduction from the average time per song:

2 minutes - 3.53 minutes = -1.53 minutes

Since we can't have a negative time, we'll assume the reduction is 3 minutes and 32 seconds (approximately equal to 3.53 minutes). Therefore, the final duration of that song is:

2 minutes - 3 minutes 32 seconds = 28 seconds

### Answer: 28 seconds

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.

Llama 3 70B:

Let's break it down step by step:

Josh rode the scooter for 18 hours on the first day.
On the second day, he rode for an additional 1/12 of an hour, so the total hours he rode is:
18 + 1/12 = 18 1/12 = 217/12 hours

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

To find the total hours they both rode, we add the hours:
(217/12) + (7/17)

To add these fractions, we need a common denominator, which is 204 (the least common multiple of 12 and 17). So, we convert both fractions to have a denominator of 204:

(217/12) = (578/204)
(7/17) = (84/204)

Now we can add:
(578/204) + (84/204) = (662/204)

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 2:
(662/204) = (331/102)

### Answer: 331/102

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?

Llama 3 70B:

To find the total fraction of lamps, we need to add the fractions of each type of lamp. However, we need to have a common denominator to add these fractions. The least common multiple (LCM) of 26, 11, 28, and 19 is 15148. So, we can convert each fraction to have a denominator of 15148:

Floor lamps: 4/26 = (4*582)/15148 = 2328/15148
Desk lamps: 15/11 = (15*1376)/15148 = 20640/15148
Table lamps: 23/28 = (23*542)/15148 = 12586/15148
Decorative lamps: 8/19 = (8*796)/15148 = 6368/15148

Now, we can add these fractions:

(2328 + 20640 + 12586 + 6368)/15148 = 39922/15148

So, the fraction of lamps that are either floor lamps, desk lamps, table lamps, or decorative lamps is 39922/15148.

### Answer: 39922/15148

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.

Llama 3 70B:

Reasoning: To find the total length of the combined string, we add the lengths of the two strings:

(26/19) + (7/11) = ((26*11) + (7*19)) / (19*11) = (286 + 133) / 209 = 419 / 209

Now, Oliver is using 5/8 of this combined string, so we multiply the total length by 5/8:

(419 / 209) * (5 / 8) = (419 * 5) / (209 * 8) = 2095 / 1672

### Answer: 2095/1672

Expected answer: 2095/1672

Correct? Yes

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

Llama 3 70B:

Let's break it down step by step!

First, we need to find the value of 'u'. To do that, we'll simplify the expression:

u = 9/19 + 6/8

To add these fractions, we need a common denominator, which is 152. So, we'll convert both fractions:

u = (36/152) + (93/152)
u = 129/152

Now, we'll move on to the second equation:

j = u + 4/1

Substitute the value of 'u' we just found:

j = 129/152 + 4/1

To add these fractions, we'll convert the whole number 4 to a fraction with a denominator of 152:

j = 129/152 + 608/152
j = 737/152

So, the total number of snowballs Mike had is:

### Answer: 737/152

Expected answer: 397/76

Correct? No

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.

Llama 3 70B:

Let's analyze the situation:

Worker 1 packages 26 pieces of chocolate in 18 minutes, so the rate at which they package chocolate is:

26 pieces / 18 minutes = 26/18 pieces per minute

To find the rate per minute, we can divide by 18:

26/18 = 13/9 pieces per minute

Worker 2 packages 15 pieces of chocolate every 15 minutes, so the rate at which they package chocolate is:

15 pieces / 15 minutes = 15/15 pieces per minute

To find the rate per minute, we can divide by 15:

15/15 = 1 piece per minute

Now, let's add the rates of both workers to find the total amount of chocolate they can package in one minute:

13/9 pieces/minute + 1 piece/minute = (13/9 + 9/9) pieces/minute = 22/9 pieces/minute

### Answer: 22/9 pieces per minute

Expected answer: 22/9

Correct? Yes

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.

Llama 3 70B:

Reasoning: To find the total number of batches of towels Joanna washed, we need to add the number of batches of small towels and large towels.

First, let's convert the fractions to decimals:
24/20 = 1.2 batches of small towels
25/15 = 1.67 batches of large towels (approximately)

Now, add the number of batches:
1.2 + 1.67 = 2.87 batches

Since we can't have a fraction of a batch, we'll round up to the nearest whole number, as Joanna can't wash a part of a batch.
Total batches = 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?

Llama 3 70B:

Let's break this down step by step:

1. The first recipe requires (27 / 3) cups flour, which is 9 cups of flour.
2. The first recipe requires (11 / 7) cups sugar, which is approximately 1.57 cups of sugar.
3. The ratio of flour to sugar is 9 / 1.57, which is approximately 5.73.
4. Subtracting (21 / 26) from this ratio gives 5.73 - 0.81, which is approximately 4.92.
5. Adding (22 / 9) cups of flour from the second recipe to this ratio gives 4.92 + 2.44, which is approximately 7.36.

However, since we're looking for the total cups of flour, we need to add the original 9 cups of flour from the first recipe to the 2.44 cups of flour from the second recipe. This gives:

9 + 2.44 = 11.44

So, Debra will have approximately 11.44 cups of flour in the end.

### Answer: 11.44

Expected answer: 18955/2574

Correct? No

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?

Llama 3 70B:

Reasoning: First, we need to find the total number of chickens initially. To do this, we need to find the difference between the number of chickens in the two farms.

The number of chickens in the first farm is 26/13. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 13. This gives us 2 chickens in the first farm.

The number of chickens in the second farm is 9/16. This fraction is already in its simplest form.

To find the difference, we need to subtract the number of chickens in the second farm from the number of chickens in the first farm. However, since we want to find the total number of chickens, we will add the number of chickens in both farms instead.

The total number of chickens initially is 2 + 9/16 = 2 + 0.5625 = 2.5625.

After a week, the number of chickens multiplied by 19/21. To find the total number of chickens now, we multiply the initial total by 19/21.

The total number of chickens now is 2.5625 × 19/21 = 2.5625 × 0.90476 = 2.317.

Since we cannot have a fraction of a chicken, we round down to the nearest whole number. Therefore, there are 2 chickens now in Farmer John's farm.

### Answer: 2

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'?

Llama 3 70B:

Reasoning: Since the helicopter flew the same distance for both exercises, we can represent the total distance flown as the product of 'w' times 'w', which is w × w = w².

We are given that the distance flown for each exercise is w = 24/14 miles. To find the total distance flown, we substitute this value into the expression w²:

t = w²
= (24/14)²
= (24/14) × (24/14)
= (24 × 24) / (14 × 14)
= 576 / 196
= 36/49

### Answer: 36/49

Expected answer: 144/49

Correct? No

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.

Llama 3 70B:

Reasoning: To find the total fraction of the tank that the UFO was able to refill, we need to add the fractions from the two fuel stops.

First, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 16 and 25 is 400. So, we can convert both fractions to have a denominator of 400:

20/16 = (20 x 25) / (16 x 25) = 500/400
24/25 = (24 x 16) / (25 x 16) = 384/400

Now we can add the fractions:

(500/400) + (384/400) = (500 + 384) / 400 = 884/400

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

884 ÷ 4 = 221
400 ÷ 4 = 100

So, the simplified fraction is:

221/100

### Answer: 221/100

Expected answer: 221/100

Correct? Yes

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?

Llama 3 70B:

To find the sum of the two fractions, we need to have a common denominator. The least common multiple (LCM) of 27 and 26 is 702. So, we can convert both fractions to have a denominator of 702:

(24/27) = (24*26)/(27*26) = 624/702
(30/26) = (30*27)/(26*27) = 810/702

Now, we can add the two fractions:

(624/702) + (810/702) = (624 + 810)/702 = 1434/702

So, Professor Astro finds that the sum of the two fractions is 1434/702.

### Answer: 1434/702

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.

Llama 3 70B:

Reasoning: Kiki ate 11/6 bananas in the morning and the same amount in the afternoon, so she ate a total of 11/6 + 11/6 bananas.

To add these fractions, we need to have the same denominator, which is 6. So, we can add the numerators (11 + 11) and keep the same denominator:

(11 + 11)/6 = 22/6

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

22 ÷ 2 = 11
6 ÷ 2 = 3

So, the simplified fraction is:

11/3

### Answer: 11/3

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?

Llama 3 70B:

To find the total amount of milk Jaden gets from one cow in one day, we need to multiply the morning and evening milk production fractions.

Morning milk production: 26/14 gallons/cow
Evening milk production: 28/20 gallons/cow

To multiply these fractions, we multiply the numerators (26 and 28) and multiply the denominators (14 and 20), then write the product as a fraction:

(26 × 28) / (14 × 20) = 728 / 280

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 28:

728 ÷ 28 = 26
280 ÷ 28 = 10

So, the simplified fraction is:

26/10 = 2.6 gallons/cow/day

### Answer: 2.6 gallons/cow/day

Expected answer: 13/5

Correct? No