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?

GPT-4o:

To determine the number of cucumbers Carla can grow per plant, we need to follow the steps given in the problem.

First, we calculate the initial number of cucumbers per plant by multiplying \( \frac{22}{3} \) by \( \frac{22}{19} \):

\[
\frac{22}{3} \times \frac{22}{19} = \frac{22 \times 22}{3 \times 19} = \frac{484}{57}
\]

Next, Carla increases her production by multiplying the initial amount by \( \frac{23}{17} \):

\[
\frac{484}{57} \times \frac{23}{17} = \frac{484 \times 23}{57 \times 17}
\]

We now perform the multiplications in the numerator and the denominator:

\[
484 \times 23 = 11132
\]
\[
57 \times 17 = 969
\]

Thus, the number of cucumbers per plant after adjusting her production method is:

\[
\frac{11132}{969}
\]

To simplify this fraction, we find the greatest common divisor (GCD) of 11132 and 969. Using the Euclidean algorithm:

\[
11132 \div 969 \approx 11.49 \quad \text{(remainder 493)}
\]
\[
969 \div 493 \approx 1.97 \quad \text{(remainder 476)}
\]
\[
493 \div 476 \approx 1.03 \quad \text{(remainder 17)}
\]
\[
476 \div 17 = 28 \quad \text{(remainder 0)}
\]

The GCD is 17. We divide both the numerator and the denominator by 17:

\[
\frac{11132 \div 17}{969 \div 17} = \frac{655}{57}
\]

Therefore, the number of cucumbers Carla is expecting to grow per plant after adjusting her production method is:

### Answer: \(\frac{655}{57}\)

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?

GPT-4o:

To determine how many kilograms of grapes Pierre has now, we need to perform the following steps:

1. Subtract the amount of grapes Pierre ate from the initial amount he had.
2. Add the amount of grapes his mother gave him to the remaining amount.

First, let's convert all fractions to have a common denominator where necessary.

Initial amount of grapes: \( \frac{19}{4} \)

Amount of grapes Pierre ate: \( \frac{7}{25} \)

To subtract \( \frac{7}{25} \) from \( \frac{19}{4} \), we need a common denominator. The least common multiple of 4 and 25 is 100.

Convert \( \frac{19}{4} \) to a fraction with a denominator of 100:
\[ \frac{19}{4} = \frac{19 \times 25}{4 \times 25} = \frac{475}{100} \]

Convert \( \frac{7}{25} \) to a fraction with a denominator of 100:
\[ \frac{7}{25} = \frac{7 \times 4}{25 \times 4} = \frac{28}{100} \]

Now, subtract the two fractions:
\[ \frac{475}{100} - \frac{28}{100} = \frac{475 - 28}{100} = \frac{447}{100} \]

Next, we add the amount of grapes his mother gave him: \( \frac{30}{9} \)

Convert \( \frac{30}{9} \) to a fraction with a denominator of 100:
\[ \frac{30}{9} = \frac{30 \times 11.1111}{9 \times 11.1111} = \frac{333.3333}{100} \]

Now, add the two fractions:
\[ \frac{447}{100} + \frac{333.3333}{100} = \frac{780.3333}{100} \]

Simplify the fraction:
\[ \frac{780.3333}{100} = 7.803333 \]

### Answer: 7.803333 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?

GPT-4o:

To determine the total fraction of the castle's annual budget that King Arthur has spent on these projects, we need to add the fractions representing each project's cost.

The fractions are:
- Wall repairs: \( \frac{26}{22} \)
- Moat renovations: \( \frac{4}{29} \)
- Defensive catapults: \( \frac{11}{3} \)

First, simplify the fraction for the wall repairs:
\[ \frac{26}{22} = \frac{13}{11} \]

Now, we need to find a common denominator to add these fractions. The denominators are 11, 29, and 3. The least common multiple (LCM) of these numbers is 957.

Convert each fraction to have the common denominator of 957:
\[ \frac{13}{11} = \frac{13 \times 87}{11 \times 87} = \frac{1131}{957} \]
\[ \frac{4}{29} = \frac{4 \times 33}{29 \times 33} = \frac{132}{957} \]
\[ \frac{11}{3} = \frac{11 \times 319}{3 \times 319} = \frac{3509}{957} \]

Now, add these fractions:
\[ \frac{1131}{957} + \frac{132}{957} + \frac{3509}{957} = \frac{1131 + 132 + 3509}{957} = \frac{4772}{957} \]

Simplify the resulting fraction:
\[ \frac{4772}{957} = \frac{4772 \div 239}{957 \div 239} = \frac{20}{4} = 5 \]

### Answer: 5

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.

GPT-4o:

To solve this problem, we need to follow these steps:

1. Calculate the daily intake of acacia leaves.
2. Square the daily intake to get the weekly feeding amount squared.
3. Multiply the weekly feeding amount squared by the daily intake to get the total weekly feeding amount.

First, let's calculate the daily intake:
\[
\text{Daily intake} = \left(\frac{25}{19}\right) \times \left(\frac{30}{26}\right)
\]

We can simplify this multiplication:
\[
\text{Daily intake} = \frac{25 \times 30}{19 \times 26} = \frac{750}{494}
\]

Next, we simplify the fraction \(\frac{750}{494}\):
\[
\frac{750}{494} = \frac{375}{247} \quad \text{(dividing both numerator and denominator by 2)}
\]

Now, we square the daily intake to get the weekly feeding amount squared:
\[
\left(\frac{375}{247}\right)^2 = \frac{375^2}{247^2} = \frac{140625}{61009}
\]

Finally, we multiply the weekly feeding amount squared by the daily intake:
\[
\left(\frac{375}{247}\right)^2 \times \frac{375}{247} = \frac{140625}{61009} \times \frac{375}{247} = \frac{140625 \times 375}{61009 \times 247}
\]

Calculating the numerator and the denominator:
\[
140625 \times 375 = 52734375
\]
\[
61009 \times 247 = 15069223
\]

Thus, the total weekly feeding amount is:
\[
\frac{52734375}{15069223}
\]

### Answer: \(\frac{52734375}{15069223}\) lbs

Expected answer: 52734375/15069223

Correct? Yes

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?

GPT-4o:

To determine the total length of materials Lara will need, we need to add the length of the yarn and the length added by the beads.

First, let's convert both fractions to have a common denominator to make the addition easier. The denominators are 3 and 30. The least common multiple of 3 and 30 is 30.

Convert \(\frac{11}{3}\) to a fraction with a denominator of 30:
\[
\frac{11}{3} = \frac{11 \times 10}{3 \times 10} = \frac{110}{30}
\]

Now, we can add \(\frac{110}{30}\) and \(\frac{8}{30}\):
\[
\frac{110}{30} + \frac{8}{30} = \frac{110 + 8}{30} = \frac{118}{30}
\]

We can simplify \(\frac{118}{30}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[
\frac{118 \div 2}{30 \div 2} = \frac{59}{15}
\]

Thus, the total length of materials Lara will need is \(\frac{59}{15}\) feet.

### Answer: \(\frac{59}{15}\) feet

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.

GPT-4o:

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

First, let's calculate the distance traveled by Plane A in one minute:
\[ \text{Distance traveled by Plane A} = \frac{24}{11} \text{ miles per minute} \times 1 \text{ minute} = \frac{24}{11} \text{ miles} \]

Next, let's calculate the distance traveled by Plane B in one minute:
\[ \text{Distance traveled by Plane B} = \frac{26}{27} \text{ miles per minute} \times 1 \text{ minute} = \frac{26}{27} \text{ miles} \]

Now, we need to find the difference between the distances traveled by Plane A and Plane B:
\[ \text{Difference} = \frac{24}{11} - \frac{26}{27} \]

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 11 and 27 is 297. We convert each fraction to have this common denominator:

\[ \frac{24}{11} = \frac{24 \times 27}{11 \times 27} = \frac{648}{297} \]
\[ \frac{26}{27} = \frac{26 \times 11}{27 \times 11} = \frac{286}{297} \]

Now, subtract the fractions:
\[ \frac{648}{297} - \frac{286}{297} = \frac{648 - 286}{297} = \frac{362}{297} \]

The fraction \(\frac{362}{297}\) can be simplified by finding the greatest common divisor (GCD) of 362 and 297. The GCD of 362 and 297 is 1, so the fraction is already in its simplest form.

### Answer: \(\frac{362}{297}\)

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.

GPT-4o:

To find the combined amount of fish that both bears eat per day, we need to multiply the fractions representing the amount of fish each bear eats.

First, let's simplify the fraction for the adult bear:
\[ \frac{14}{7} = 2 \]

Next, we multiply this by the fraction for the young bear:
\[ 2 \times \frac{25}{13} \]

To perform this multiplication, we multiply the numerators and the denominators:
\[ 2 \times \frac{25}{13} = \frac{2 \times 25}{1 \times 13} = \frac{50}{13} \]

So, the combined amount of fish that both bears eat per day is:
\[ \frac{50}{13} \]

### Answer: \(\frac{50}{13}\)

Expected answer: 50/13

Correct? Yes

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

GPT-4o:

First, let's simplify the time it takes Toby to play each song.

For the first song:
\[ \frac{12}{8} = \frac{12 \div 4}{8 \div 4} = \frac{3}{2} \text{ hours} \]

For the second song:
\[ \frac{12}{3} = 4 \text{ hours} \]

Now, we add the times together:
\[ \frac{3}{2} + 4 \]

To add these fractions, we need a common denominator. The common denominator for 2 and 1 (since 4 can be written as \(\frac{4}{1}\)) is 2.

Convert 4 to a fraction with a denominator of 2:
\[ 4 = \frac{4 \times 2}{1 \times 2} = \frac{8}{2} \]

Now add the fractions:
\[ \frac{3}{2} + \frac{8}{2} = \frac{3 + 8}{2} = \frac{11}{2} \]

So, it takes Toby \(\frac{11}{2}\) hours to play both of his songs.

### Answer: \(\frac{11}{2}\)

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?

GPT-4o:

First, let's determine the total number of chocolate bars you have.

You initially have 28 out of 29 chocolate bars. This can be written as:
\[ \frac{28}{29} \]

Next, you found 8 out of 22 more chocolate bars. This can be written as:
\[ \frac{8}{22} \]

To find the total number of chocolate bars, we need to add these two fractions. First, we simplify the second fraction:
\[ \frac{8}{22} = \frac{4}{11} \]

Now, we need a common denominator to add these fractions. The least common multiple of 29 and 11 is 319. We convert each fraction to have this common denominator:

\[ \frac{28}{29} = \frac{28 \times 11}{29 \times 11} = \frac{308}{319} \]
\[ \frac{4}{11} = \frac{4 \times 29}{11 \times 29} = \frac{116}{319} \]

Now, we add the fractions:
\[ \frac{308}{319} + \frac{116}{319} = \frac{308 + 116}{319} = \frac{424}{319} \]

So, the fraction representing the total chocolate bars you have now is:
\[ \frac{424}{319} \]

### Answer: \(\frac{424}{319}\)

Expected answer: 424/319

Correct? Yes

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

GPT-4o:

First, let's determine the amount of material needed to produce two identical needles. Each needle requires \( \frac{27}{26} \) pounds of material.

For two needles:
\[
2 \times \frac{27}{26} = \frac{54}{26} = \frac{27}{13} \text{ pounds}
\]

Next, the additional piece requires \( \frac{27}{6} \) pounds of material.

Now, we need to find the total material required for both the needles and the additional piece:
\[
\frac{27}{13} + \frac{27}{6}
\]

To add these fractions, we need a common denominator. The least common multiple of 13 and 6 is 78.

Convert each fraction to have a denominator of 78:
\[
\frac{27}{13} = \frac{27 \times 6}{13 \times 6} = \frac{162}{78}
\]
\[
\frac{27}{6} = \frac{27 \times 13}{6 \times 13} = \frac{351}{78}
\]

Now, add the fractions:
\[
\frac{162}{78} + \frac{351}{78} = \frac{162 + 351}{78} = \frac{513}{78}
\]

Simplify the fraction:
\[
\frac{513}{78} = \frac{513 \div 3}{78 \div 3} = \frac{171}{26}
\]

Thus, the total material required is:
\[
\frac{171}{26} \text{ pounds}
\]

### Answer: \(\frac{171}{26}\) pounds

Expected answer: 171/26

Correct? Yes

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?

GPT-4o:

First, let's simplify the rates at which each candle burns.

For the first candle:
\[ \frac{6}{4} \]
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{6 \div 2}{4 \div 2} = \frac{3}{2} \]

For the second candle:
\[ \frac{14}{16} \]
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{14 \div 2}{16 \div 2} = \frac{7}{8} \]

Now, we need to find the total rate at which the two candles burn together. To do this, we add the two simplified rates:
\[ \frac{3}{2} + \frac{7}{8} \]

To add these fractions, we need a common denominator. The least common multiple of 2 and 8 is 8. We convert \(\frac{3}{2}\) to a fraction with a denominator of 8:
\[ \frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8} \]

Now we can add the two fractions:
\[ \frac{12}{8} + \frac{7}{8} = \frac{12 + 7}{8} = \frac{19}{8} \]

So, the total rate at which the two candles burn together is:
\[ \frac{19}{8} \] inches per hour.

### Answer: \(\frac{19}{8}\) 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?

GPT-4o:

To determine how much money Sophia has now, we need to add the amounts she received from her friend and her brother to the amount she initially had.

1. Sophia initially has \(\frac{17}{20}\) of a dollar.
2. Her friend gives her \(\frac{1}{4}\) of a dollar.

First, we need to add these two fractions. To do this, we need a common denominator. The least common multiple of 20 and 4 is 20.

Convert \(\frac{1}{4}\) to a fraction with a denominator of 20:
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]

Now add \(\frac{17}{20}\) and \(\frac{5}{20}\):
\[
\frac{17}{20} + \frac{5}{20} = \frac{17 + 5}{20} = \frac{22}{20}
\]

Simplify \(\frac{22}{20}\):
\[
\frac{22}{20} = \frac{11}{10} = 1.1
\]

3. Her brother gives her 1 dollar.

Now add this to the previous total:
\[
1.1 + 1 = 2.1
\]

### Answer: 2.1

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))?

GPT-4o:

Let's break down the problem step by step.

1. **Initial Time Investment (p):**
   - Time spent composing the music: \( \frac{16}{4} \) hours
   - Time spent writing the lyrics: \( \frac{16}{29} \) hours

   Calculate the total initial time investment \( p \):
   \[
   p = \frac{16}{4} + \frac{16}{29}
   \]

   Simplify \( \frac{16}{4} \):
   \[
   \frac{16}{4} = 4
   \]

   So,
   \[
   p = 4 + \frac{16}{29}
   \]

2. **Total Time Including Mixing and Mastering (b):**
   - Additional time for mixing and mastering: \( \frac{28}{13} \) hours

   Calculate the new total time \( b \):
   \[
   b = p + \frac{28}{13}
   \]

   Substitute \( p \) into the equation:
   \[
   b = 4 + \frac{16}{29} + \frac{28}{13}
   \]

3. **Final Time After Drummer's Adjustment:**
   - Drummer's time reduction: \( \frac{18}{4} \) hours

   Calculate the final time:
   \[
   \text{Final Time} = b - \frac{18}{4}
   \]

   Substitute \( b \) into the equation:
   \[
   \text{Final Time} = \left( 4 + \frac{16}{29} + \frac{28}{13} \right) - \frac{18}{4}
   \]

4. **Simplify the Expression:**
   - Convert all fractions to a common denominator if necessary.

   First, find a common denominator for \( \frac{16}{29} \) and \( \frac{28}{13} \):
   \[
   \text{Common denominator} = 29 \times 13 = 377
   \]

   Convert \( \frac{16}{29} \) and \( \frac{28}{13} \) to have the common denominator:
   \[
   \frac{16}{29} = \frac{16 \times 13}{29 \times 13} = \frac{208}{377}
   \]
   \[
   \frac{28}{13} = \frac{28 \times 29}{13 \times 29} = \frac{812}{377}
   \]

   Combine the fractions:
   \[
   \frac{208}{377} + \frac{812}{377} = \frac{208 + 812}{377} = \frac{1020}{377}
   \]

   So,
   \[
   b = 4 + \frac{1020}{377}
   \]

   Now, convert \( 4 \) to a fraction with the same denominator:
   \[
   4 = \frac{4 \times 377}{377} = \frac{1508}{377}
   \]

   Combine:
   \[
   b = \frac{1508}{377} + \frac{1020}{377} = \frac{2528}{377}
   \]

   Now, subtract the drummer's time:
   \[
   \frac{18}{4} = 4.5
   \]

   Convert \( 4.5 \) to a fraction with the same denominator:
   \[
   4.5 = \frac{4.5 \times 377}{377} = \frac{1696.5}{377}
   \]

   Subtract:
   \[
   \text{Final Time} = \frac{2528}{377} - \frac{1696.5}{377} = \frac{831.5}{377}
   \]

   Simplify the fraction if possible:
   \[
   \frac{831.5}{377} = 2.205
   \]

### Answer: 2.205 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?

GPT-4o:

First, we need to find the total number of dozens of cookies Monica has before increasing her stock. We start by adding the two fractions:

\[
\frac{21}{15} + \frac{29}{17}
\]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 15 and 17 is 255. We convert each fraction to have this common denominator:

\[
\frac{21}{15} = \frac{21 \times 17}{15 \times 17} = \frac{357}{255}
\]

\[
\frac{29}{17} = \frac{29 \times 15}{17 \times 15} = \frac{435}{255}
\]

Now, we add the two fractions:

\[
\frac{357}{255} + \frac{435}{255} = \frac{357 + 435}{255} = \frac{792}{255}
\]

Next, we simplify the fraction \(\frac{792}{255}\). We find the greatest common divisor (GCD) of 792 and 255, which is 3:

\[
\frac{792 \div 3}{255 \div 3} = \frac{264}{85}
\]

So, Monica has \(\frac{264}{85}\) dozens of cookies before increasing her stock. Now, she decides to increase her total stock by a ratio of \(\frac{7}{5}\):

\[
\frac{264}{85} \times \frac{7}{5} = \frac{264 \times 7}{85 \times 5} = \frac{1848}{425}
\]

We simplify the fraction \(\frac{1848}{425}\). The GCD of 1848 and 425 is 1, so the fraction is already in its simplest form.

Thus, Monica will have \(\frac{1848}{425}\) dozens of cookies for the cookie festival.

### Answer: \(\frac{1848}{425}\) dozens

Expected answer: 1848/425

Correct? Yes

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

GPT-4o:

First, let's determine how much sugar is used to make one cake. The recipe requires \( \frac{26}{24} \) kg of sugar per cake. We can simplify this fraction:

\[
\frac{26}{24} = \frac{13}{12} \text{ kg}
\]

Next, the chef starts with 28 kg of sugar. After making one cake, the amount of sugar left is:

\[
28 - \frac{13}{12}
\]

To subtract these, we need a common denominator. The common denominator for 28 and \( \frac{13}{12} \) is 12. We convert 28 to a fraction with a denominator of 12:

\[
28 = \frac{28 \times 12}{12} = \frac{336}{12}
\]

Now, we subtract \( \frac{13}{12} \) from \( \frac{336}{12} \):

\[
\frac{336}{12} - \frac{13}{12} = \frac{336 - 13}{12} = \frac{323}{12}
\]

Next, the chef adds \( \frac{10}{6} \) kg of sugar to their supply. We simplify \( \frac{10}{6} \):

\[
\frac{10}{6} = \frac{5}{3}
\]

We need a common denominator to add \( \frac{323}{12} \) and \( \frac{5}{3} \). The common denominator for 12 and 3 is 12. We convert \( \frac{5}{3} \) to a fraction with a denominator of 12:

\[
\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}
\]

Now, we add \( \frac{323}{12} \) and \( \frac{20}{12} \):

\[
\frac{323}{12} + \frac{20}{12} = \frac{323 + 20}{12} = \frac{343}{12}
\]

Finally, we simplify \( \frac{343}{12} \):

\[
\frac{343}{12} \approx 28.5833 \text{ kg}
\]

### Answer: \( \frac{343}{12} \) kg or approximately 28.5833 kg

Expected answer: 343/12

Correct? Yes

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?

GPT-4o:

First, let's determine the total time Emily spent watching movies. The total time is given as \( \frac{16}{4} \) hours.

\[
\frac{16}{4} = 4 \text{ hours}
\]

Next, we need to find out how much time she spent watching the comedy film. This time is given as \( \frac{6}{3} \) hours.

\[
\frac{6}{3} = 2 \text{ hours}
\]

To find the time she spent watching movies other than the comedy film, we subtract the time spent on the comedy film from the total time spent watching movies.

\[
4 \text{ hours} - 2 \text{ hours} = 2 \text{ hours}
\]

### Answer: 2 hours

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.

GPT-4o:

To determine how much of the pies Princess Lily ate, we need to add the fractions of each pie she consumed.

First, let's calculate the fraction of the apple pie she ate:
\[ \text{Fraction of apple pie eaten} = \frac{10}{12} \]

Next, let's calculate the fraction of the blueberry pie she ate:
\[ \text{Fraction of blueberry pie eaten} = \frac{10}{29} \]

To find the total amount of pie she ate, we need to add these two fractions:
\[ \frac{10}{12} + \frac{10}{29} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 12 and 29 is 348. We convert each fraction to have this common denominator:

\[ \frac{10}{12} = \frac{10 \times 29}{12 \times 29} = \frac{290}{348} \]
\[ \frac{10}{29} = \frac{10 \times 12}{29 \times 12} = \frac{120}{348} \]

Now, we add the fractions:
\[ \frac{290}{348} + \frac{120}{348} = \frac{290 + 120}{348} = \frac{410}{348} \]

This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 410 and 348 is 2:

\[ \frac{410 \div 2}{348 \div 2} = \frac{205}{174} \]

Thus, the fraction representing the total amount of pie Princess Lily ate is:
\[ \frac{205}{174} \]

### Answer: \(\frac{205}{174}\)

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.

GPT-4o:

To determine how many 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 break down the expression:

1. Calculate the rate of colored pencils used per day:
   \[
   \frac{20}{11}
   \]

2. Calculate the fraction of colored pencils used for shading:
   \[
   \frac{23}{26}
   \]

3. Multiply these two fractions together:
   \[
   \left(\frac{20}{11}\right) \times \left(\frac{23}{26}\right)
   \]

To multiply the fractions, multiply the numerators together and the denominators together:
\[
\frac{20 \times 23}{11 \times 26} = \frac{460}{286}
\]

Next, we simplify the fraction \(\frac{460}{286}\). We find the greatest common divisor (GCD) of 460 and 286. The GCD of 460 and 286 is 2.

Divide both the numerator and the denominator by their GCD:
\[
\frac{460 \div 2}{286 \div 2} = \frac{230}{143}
\]

Thus, the simplified fraction is:
\[
\frac{230}{143}
\]

### Answer: \(\frac{230}{143}\)

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.

GPT-4o:

To solve this problem, we need to calculate the indicators \( i \) and \( h \) and then multiply them to find the final evidence factor \( f \).

First, let's calculate indicator \( i \):

1. The first specimen decreases its value by 26 out of every 6 units. This can be expressed as a ratio:
   \[
   \frac{26}{6}
   \]

2. The second specimen decreases its value by 25 out of every 17 units. This can be expressed as a ratio:
   \[
   \frac{25}{17}
   \]

3. The ratio of these changes (indicator \( i \)) is:
   \[
   i = \frac{\frac{26}{6}}{\frac{25}{17}} = \frac{26}{6} \times \frac{17}{25} = \frac{26 \times 17}{6 \times 25} = \frac{442}{150}
   \]

4. Simplify the fraction:
   \[
   \frac{442}{150} = \frac{221}{75}
   \]

Next, let's calculate indicator \( h \):

1. The first specimen increases its value by 18 out of every 8 units. This can be expressed as a ratio:
   \[
   \frac{18}{8}
   \]

2. The second specimen increases its value by 17 out of every 23 units. This can be expressed as a ratio:
   \[
   \frac{17}{23}
   \]

3. The difference between these two rates (indicator \( h \)) is:
   \[
   h = \frac{18}{8} - \frac{17}{23}
   \]

4. To subtract these fractions, we need a common denominator. The least common multiple of 8 and 23 is 184:
   \[
   \frac{18}{8} = \frac{18 \times 23}{8 \times 23} = \frac{414}{184}
   \]
   \[
   \frac{17}{23} = \frac{17 \times 8}{23 \times 8} = \frac{136}{184}
   \]

5. Subtract the fractions:
   \[
   h = \frac{414}{184} - \frac{136}{184} = \frac{278}{184}
   \]

6. Simplify the fraction:
   \[
   \frac{278}{184} = \frac{139}{92}
   \]

Finally, we combine these two indicators by multiplying them to get the final evidence factor \( f \):

1. Multiply \( i \) and \( h \):
   \[
   f = \frac{221}{75} \times \frac{139}{92} = \frac{221 \times 139}{75 \times 92} = \frac{30719}{6900}
   \]

2. Simplify the fraction:
   \[
   \frac{30719}{6900}
   \]

Since 30719 and 6900 have no common factors other than 1, the fraction is already in its simplest form.

### Answer: \(\frac{30719}{6900}\)

Expected answer: 30719/6900

Correct? Yes

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

GPT-4o:

First, let's find the total gestation period of both animals together.

1. The gestation period of a lioness is given as \( \frac{20}{22} \) of a year.
2. The gestation period of a giraffe is given as 15 years.

To find the total gestation period, we add these two periods together:
\[ \text{Total gestation period} = \frac{20}{22} + 15 \]

Simplify \( \frac{20}{22} \):
\[ \frac{20}{22} = \frac{10}{11} \]

So, the total gestation period is:
\[ \frac{10}{11} + 15 \]

Next, we need to find the reduced gestation period for the lioness in the second instance. The reduction is given as \( \frac{15}{20} \) of a year.

Simplify \( \frac{15}{20} \):
\[ \frac{15}{20} = \frac{3}{4} \]

Now, subtract this reduction from the total gestation period of both animals:
\[ \text{Reduced gestation period} = \left( \frac{10}{11} + 15 \right) - \frac{3}{4} \]

First, convert \( 15 \) to a fraction with a common denominator with \( \frac{10}{11} \):
\[ 15 = \frac{165}{11} \]

So, the total gestation period in terms of a common denominator is:
\[ \frac{10}{11} + \frac{165}{11} = \frac{175}{11} \]

Now, convert \( \frac{3}{4} \) to a fraction with a common denominator with \( \frac{175}{11} \):
\[ \frac{3}{4} = \frac{3 \times 11}{4 \times 11} = \frac{33}{44} \]

Convert \( \frac{175}{11} \) to a fraction with a denominator of 44:
\[ \frac{175}{11} = \frac{175 \times 4}{11 \times 4} = \frac{700}{44} \]

Subtract \( \frac{33}{44} \) from \( \frac{700}{44} \):
\[ \frac{700}{44} - \frac{33}{44} = \frac{700 - 33}{44} = \frac{667}{44} \]

Simplify \( \frac{667}{44} \):
\[ \frac{667}{44} = 15.159 \]

So, the reduced gestation period for the lioness is approximately 15.159 years.

### Answer: 15.159 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?

GPT-4o:

First, we need to find the area of the original rectangle. The area \( A \) of a rectangle is given by the formula:

\[ A = \text{length} \times \text{width} \]

Given the length is \( \frac{30}{7} \) meters and the width is \( \frac{19}{6} \) meters, we can calculate the area as follows:

\[ A = \frac{30}{7} \times \frac{19}{6} \]

To multiply these fractions, we multiply the numerators together and the denominators together:

\[ A = \frac{30 \times 19}{7 \times 6} \]

\[ A = \frac{570}{42} \]

We can simplify this fraction by finding the greatest common divisor (GCD) of 570 and 42. The GCD of 570 and 42 is 6. So, we divide both the numerator and the denominator by 6:

\[ A = \frac{570 \div 6}{42 \div 6} \]

\[ A = \frac{95}{7} \]

Now, we need to find the area of the similar rectangle, which is \( \frac{18}{17} \) times bigger than the original rectangle. We multiply the area of the original rectangle by \( \frac{18}{17} \):

\[ \text{Area of similar rectangle} = \frac{95}{7} \times \frac{18}{17} \]

Again, we multiply the numerators together and the denominators together:

\[ \text{Area of similar rectangle} = \frac{95 \times 18}{7 \times 17} \]

\[ \text{Area of similar rectangle} = \frac{1710}{119} \]

We can check if this fraction can be simplified. The GCD of 1710 and 119 is 1, so the fraction is already in its simplest form.

### Answer: \(\frac{1710}{119}\)

Expected answer: 1710/119

Correct? Yes

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?

GPT-4o:

To determine the total production of soap after the adjustments, we need to follow these steps:

1. **Initial Production**: The factory produces \(\frac{23}{8}\) tonnes of soap each day.

2. **Increase in Production**: The factory increases production by \(\frac{4}{20}\) tonnes. Simplify \(\frac{4}{20}\):
   \[
   \frac{4}{20} = \frac{1}{5}
   \]

3. **Total Production after Increase**: Add the increased amount to the initial production:
   \[
   \frac{23}{8} + \frac{1}{5}
   \]

   To add these fractions, find a common denominator. The least common multiple of 8 and 5 is 40. Convert each fraction:
   \[
   \frac{23}{8} = \frac{23 \times 5}{8 \times 5} = \frac{115}{40}
   \]
   \[
   \frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40}
   \]

   Now add the fractions:
   \[
   \frac{115}{40} + \frac{8}{40} = \frac{123}{40}
   \]

4. **Reduction in Production**: The factory reduces production by \(\frac{19}{24}\) tonnes. Convert \(\frac{123}{40}\) and \(\frac{19}{24}\) to a common denominator. The least common multiple of 40 and 24 is 120. Convert each fraction:
   \[
   \frac{123}{40} = \frac{123 \times 3}{40 \times 3} = \frac{369}{120}
   \]
   \[
   \frac{19}{24} = \frac{19 \times 5}{24 \times 5} = \frac{95}{120}
   \]

   Now subtract the fractions:
   \[
   \frac{369}{120} - \frac{95}{120} = \frac{274}{120}
   \]

5. **Simplify the Result**: Simplify \(\frac{274}{120}\) by finding the greatest common divisor (GCD) of 274 and 120, which is 2:
   \[
   \frac{274 \div 2}{120 \div 2} = \frac{137}{60}
   \]

Thus, the factory produces \(\frac{137}{60}\) tonnes of soap that day after the adjustments.

### Answer: \(\frac{137}{60}\) tonnes

Expected answer: 137/60

Correct? Yes

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

GPT-4o:

First, let's determine the initial amount of red paint mixed by the machine:
\[ \frac{24}{8} = 3 \text{ gallons} \]

Next, the machine pours away:
\[ \frac{12}{8} = 1.5 \text{ gallons} \]

So, the amount of red paint left in the machine, \( d \), is:
\[ d = 3 - 1.5 = 1.5 \text{ gallons} \]

The machine then adds \( \frac{1}{28} \) gallon of blue pigment. The total amount of paint, \( x \), is:
\[ x = d + \frac{1}{28} \]
\[ x = 1.5 + \frac{1}{28} \]

To add these, we need a common denominator. The common denominator for 1.5 (which is \( \frac{3}{2} \)) and \( \frac{1}{28} \) is 28:
\[ 1.5 = \frac{3}{2} = \frac{3 \times 14}{2 \times 14} = \frac{42}{28} \]

Now, add the fractions:
\[ x = \frac{42}{28} + \frac{1}{28} = \frac{42 + 1}{28} = \frac{43}{28} \]

### Answer: \(\frac{43}{28}\) gallons

Expected answer: 41/28

Correct? No

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

GPT-4o:

To find the product of the fractions \(\frac{27}{14}\) and \(\frac{17}{13}\), we multiply the numerators together and the denominators together:

\[
\frac{27}{14} \times \frac{17}{13} = \frac{27 \times 17}{14 \times 13}
\]

First, calculate the numerator:

\[
27 \times 17 = 459
\]

Next, calculate the denominator:

\[
14 \times 13 = 182
\]

So, the product of the fractions is:

\[
\frac{459}{182}
\]

To simplify this fraction, we need to find the greatest common divisor (GCD) of 459 and 182. We can use the Euclidean algorithm to find the GCD.

1. Divide 459 by 182 and find the remainder:
\[
459 \div 182 \approx 2.52 \quad \text{(integer part is 2)}
\]
\[
459 - 2 \times 182 = 459 - 364 = 95
\]

2. Now, divide 182 by 95 and find the remainder:
\[
182 \div 95 \approx 1.91 \quad \text{(integer part is 1)}
\]
\[
182 - 1 \times 95 = 182 - 95 = 87
\]

3. Next, divide 95 by 87 and find the remainder:
\[
95 \div 87 \approx 1.09 \quad \text{(integer part is 1)}
\]
\[
95 - 1 \times 87 = 95 - 87 = 8
\]

4. Finally, divide 87 by 8 and find the remainder:
\[
87 \div 8 \approx 10.875 \quad \text{(integer part is 10)}
\]
\[
87 - 10 \times 8 = 87 - 80 = 7
\]

5. Divide 8 by 7 and find the remainder:
\[
8 \div 7 \approx 1.14 \quad \text{(integer part is 1)}
\]
\[
8 - 1 \times 7 = 8 - 7 = 1
\]

Since the remainder is now 1, the GCD of 459 and 182 is 1. Therefore, the fraction \(\frac{459}{182}\) is already in its simplest form.

### Answer: \(\frac{459}{182}\)

Expected answer: 459/182

Correct? Yes

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

GPT-4o:

First, let's add the quantities of toothpaste used by Sonia and Anthony.

Sonia uses \( \frac{21}{12} \) oz of toothpaste daily.
Anthony uses \( \frac{6}{27} \) oz of toothpaste daily.

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

Convert \( \frac{21}{12} \) to a fraction with a denominator of 108:
\[ \frac{21}{12} = \frac{21 \times 9}{12 \times 9} = \frac{189}{108} \]

Convert \( \frac{6}{27} \) to a fraction with a denominator of 108:
\[ \frac{6}{27} = \frac{6 \times 4}{27 \times 4} = \frac{24}{108} \]

Now, add the two fractions:
\[ \frac{189}{108} + \frac{24}{108} = \frac{189 + 24}{108} = \frac{213}{108} \]

Next, simplify \( \frac{213}{108} \):
The greatest common divisor (GCD) of 213 and 108 is 3.
\[ \frac{213 \div 3}{108 \div 3} = \frac{71}{36} \]

Now, let's add the amount of toothpaste used by their mom, which is \( \frac{3}{18} \).

Convert \( \frac{3}{18} \) to a fraction with a denominator of 36:
\[ \frac{3}{18} = \frac{3 \times 2}{18 \times 2} = \frac{6}{36} \]

Now, add this to the previous total:
\[ \frac{71}{36} + \frac{6}{36} = \frac{71 + 6}{36} = \frac{77}{36} \]

Finally, simplify \( \frac{77}{36} \):
The GCD of 77 and 36 is 1, so the fraction is already in its simplest form.

### Answer: \(\frac{77}{36}\)

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.

GPT-4o:

To solve this problem, we need to follow these steps:

1. Calculate the fraction of the original ingredients left after making the special sandwiches.
2. Subtract the fraction used for the simpler sandwich from the remaining fraction.

First, let's calculate the fraction of the original ingredients left after making the special sandwiches:

Given:
- The fraction of the wheel of cheese left is \(\frac{21}{14}\).
- The fraction of the pickle jar left is \(\frac{7}{18}\).

We need to add these fractions together:
\[
\frac{21}{14} + \frac{7}{18}
\]

First, simplify \(\frac{21}{14}\):
\[
\frac{21}{14} = \frac{21 \div 7}{14 \div 7} = \frac{3}{2}
\]

Now, add \(\frac{3}{2}\) and \(\frac{7}{18}\). To do this, we need a common denominator. The least common multiple of 2 and 18 is 18.

Convert \(\frac{3}{2}\) to a fraction with a denominator of 18:
\[
\frac{3}{2} = \frac{3 \times 9}{2 \times 9} = \frac{27}{18}
\]

Now add the fractions:
\[
\frac{27}{18} + \frac{7}{18} = \frac{27 + 7}{18} = \frac{34}{18}
\]

Simplify \(\frac{34}{18}\):
\[
\frac{34}{18} = \frac{34 \div 2}{18 \div 2} = \frac{17}{9}
\]

Next, we need to subtract the fraction used for the simpler sandwich. The simpler sandwich uses half of the wheel of cheese, which is \(\frac{1}{2}\) or \(\frac{2}{4}\).

Convert \(\frac{2}{4}\) to a fraction with a denominator of 9:
\[
\frac{2}{4} = \frac{2 \times 9}{4 \times 9} = \frac{18}{36} = \frac{1}{2}
\]

Now, subtract \(\frac{1}{2}\) from \(\frac{17}{9}\). Convert \(\frac{1}{2}\) to a fraction with a denominator of 9:
\[
\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}
\]

Subtract:
\[
\frac{17}{9} - \frac{9}{18}
\]

Convert \(\frac{9}{18}\) to a fraction with a denominator of 9:
\[
\frac{9}{18} = \frac{9 \div 9}{18 \div 9} = \frac{1}{2} = \frac{9}{18}
\]

Now, subtract:
\[
\frac{17}{9} - \frac{9}{18} = \frac{34}{18} - \frac{9}{18} = \frac{34 - 9}{18} = \frac{25}{18}
\]

### Answer: \(\frac{25}{18}\)

Expected answer: 25/18

Correct? Yes

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

GPT-4o:

To find the total height of the two windows, we need to add their heights together. The heights are given as fractions: \( \frac{15}{6} \) meters and \( \frac{7}{16} \) meters.

First, let's simplify the fraction \( \frac{15}{6} \):
\[ \frac{15}{6} = \frac{15 \div 3}{6 \div 3} = \frac{5}{2} \]

Now, we need to add \( \frac{5}{2} \) and \( \frac{7}{16} \). To do this, we need a common denominator. The least common multiple of 2 and 16 is 16.

Convert \( \frac{5}{2} \) to a fraction with a denominator of 16:
\[ \frac{5}{2} = \frac{5 \times 8}{2 \times 8} = \frac{40}{16} \]

Now, add \( \frac{40}{16} \) and \( \frac{7}{16} \):
\[ \frac{40}{16} + \frac{7}{16} = \frac{40 + 7}{16} = \frac{47}{16} \]

So, the total height of the two windows is \( \frac{47}{16} \) meters.

### Answer: \( \frac{47}{16} \) meters

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?

GPT-4o:

To find the total amount of juice Jan has, we need to add the quantities of each type of juice together. 

First, let's simplify the fractions where possible:

1. Simplify \( \frac{16}{6} \):
   \[
   \frac{16}{6} = \frac{8}{3}
   \]

2. Simplify \( \frac{20}{12} \):
   \[
   \frac{20}{12} = \frac{5}{3}
   \]

Now, we add the simplified fractions together along with the cranberry juice:

\[
\frac{8}{3} + \frac{5}{3} + \frac{2}{3}
\]

Since the denominators are the same, we can add the numerators directly:

\[
\frac{8 + 5 + 2}{3} = \frac{15}{3} = 5
\]

So, Jan has a total of 5 liters of juice.

### Answer: 5 liters

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.

GPT-4o:

To determine the total points earned, we need to multiply the points per level by the number of levels played.

Given:
- Points per level = \( \frac{4}{3} \)
- Levels played = \( \frac{13}{10} \)

We multiply these fractions:

\[
\frac{4}{3} \times \frac{13}{10} = \frac{4 \times 13}{3 \times 10} = \frac{52}{30}
\]

Next, we simplify the fraction \( \frac{52}{30} \). We find the greatest common divisor (GCD) of 52 and 30, which is 2.

\[
\frac{52 \div 2}{30 \div 2} = \frac{26}{15}
\]

Thus, the simplified fraction is \( \frac{26}{15} \).

### Answer: \(\frac{26}{15}\)

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?

GPT-4o:

First, let's calculate the time the astronaut spends on each activity:

1. Time spent cycling:
\[ \frac{18}{8} \text{ hours} = 2.25 \text{ hours} \]

2. Time spent conducting scientific experiments:
\[ \frac{26}{2} \text{ hours} = 13 \text{ hours} \]

3. Time spent reviewing data:
\[ \frac{30}{8} \text{ hours} = 3.75 \text{ hours} \]

Next, we sum these times to find the total time spent on the whole daily routine:

\[ 2.25 \text{ hours} + 13 \text{ hours} + 3.75 \text{ hours} \]

Adding these together:

\[ 2.25 + 13 + 3.75 = 19 \text{ hours} \]

### Answer: 19 hours

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.

GPT-4o:

To determine how much cheese Jeremy actually received, we start with the total weight of cheese he ordered, which is \( \frac{30}{9} \) ounces. We need to subtract the amount of cheese that was missing, which is \( \frac{17}{22} \) ounces.

First, simplify \( \frac{30}{9} \):
\[ \frac{30}{9} = \frac{10}{3} \]

Next, we need to subtract \( \frac{17}{22} \) from \( \frac{10}{3} \). To do this, we need a common denominator. The least common multiple of 3 and 22 is 66.

Convert \( \frac{10}{3} \) to a fraction with a denominator of 66:
\[ \frac{10}{3} = \frac{10 \times 22}{3 \times 22} = \frac{220}{66} \]

Convert \( \frac{17}{22} \) to a fraction with a denominator of 66:
\[ \frac{17}{22} = \frac{17 \times 3}{22 \times 3} = \frac{51}{66} \]

Now, subtract the two fractions:
\[ \frac{220}{66} - \frac{51}{66} = \frac{220 - 51}{66} = \frac{169}{66} \]

Thus, Jeremy actually received \( \frac{169}{66} \) ounces of cheese.

### Answer: \(\frac{169}{66}\) 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.

GPT-4o:

To solve this problem, we need to add and subtract the fractions representing the sunglasses that blocked all UV rays and those that did not.

First, let's convert all the given fractions to a common denominator to make the calculations easier.

1. The first test result is \( \frac{13}{4} \).
2. The second test result is \( \frac{20}{18} \), which simplifies to \( \frac{10}{9} \).
3. The additional batch result is \( \frac{21}{17} \).
4. The incorrect batch result is \( \frac{16}{30} \), which simplifies to \( \frac{8}{15} \).

Now, we need to find a common denominator for these fractions. The least common multiple (LCM) of 4, 9, 17, and 15 is 3060.

Let's convert each fraction to have the denominator 3060:

1. \( \frac{13}{4} = \frac{13 \times 765}{4 \times 765} = \frac{9945}{3060} \)
2. \( \frac{10}{9} = \frac{10 \times 340}{9 \times 340} = \frac{3400}{3060} \)
3. \( \frac{21}{17} = \frac{21 \times 180}{17 \times 180} = \frac{3780}{3060} \)
4. \( \frac{8}{15} = \frac{8 \times 204}{15 \times 204} = \frac{1632}{3060} \)

Now, we add the fractions that represent sunglasses blocking all UV rays and subtract the fraction that represents sunglasses not blocking all UV rays:

\[
\frac{9945}{3060} + \frac{3400}{3060} + \frac{3780}{3060} - \frac{1632}{3060}
\]

Combine the numerators:

\[
9945 + 3400 + 3780 - 1632 = 15493
\]

So, the combined fraction is:

\[
\frac{15493}{3060}
\]

This fraction is already in its simplest form because 15493 and 3060 have no common factors other than 1.

### Answer: \(\frac{15493}{3060}\)

Expected answer: 15493/3060

Correct? Yes

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?

GPT-4o:

First, let's find the total amount of mayonnaise and sandwich spread Shawn uses for one sandwich.

1. **Mayonnaise:**
   \[
   \frac{23}{28} \text{ cups}
   \]

2. **Sandwich spread:**
   \[
   \frac{6}{9} = \frac{2}{3} \text{ cups}
   \]

To add these fractions, we need a common denominator. The least common multiple of 28 and 3 is 84.

Convert \(\frac{23}{28}\) to a fraction with a denominator of 84:
\[
\frac{23}{28} = \frac{23 \times 3}{28 \times 3} = \frac{69}{84}
\]

Convert \(\frac{2}{3}\) to a fraction with a denominator of 84:
\[
\frac{2}{3} = \frac{2 \times 28}{3 \times 28} = \frac{56}{84}
\]

Now, add the fractions:
\[
\frac{69}{84} + \frac{56}{84} = \frac{69 + 56}{84} = \frac{125}{84}
\]

So, the total amount of mayonnaise and sandwich spread is:
\[
\frac{125}{84} \text{ cups}
\]

Next, we add the cheese spread:
\[
\frac{18}{12} = \frac{3 \times 6}{2 \times 6} = \frac{3}{2} = \frac{126}{84}
\]

Now, add this to the previous total:
\[
\frac{125}{84} + \frac{126}{84} = \frac{125 + 126}{84} = \frac{251}{84}
\]

So, the total amount of ingredients for one sandwich is:
\[
\frac{251}{84} \text{ cups}
\]

Finally, if Shawn uses 4/4 cups of all ingredients combined to make an equal number of sandwiches, we need to determine how many sandwiches he can make with \(\frac{4}{4} = 1\) cup of ingredients.

To find the number of sandwiches:
\[
\frac{1}{\frac{251}{84}} = \frac{84}{251}
\]

Thus, the total amount of ingredients used to make these sandwiches is:
\[
\frac{84}{251} \times 1 = \frac{84}{251} \text{ cups}
\]

### Answer: \(\frac{84}{251}\) 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?

GPT-4o:

To determine how many key sets Cassandra has now, we need to follow these steps:

1. Start with the initial number of key sets Cassandra had, which is \( \frac{7}{6} \) of a key set.
2. Subtract the number of key sets she lost, which is \( \frac{1}{21} \) of a key set.

First, we need a common denominator to subtract these fractions. The least common multiple of 6 and 21 is 42.

Convert \( \frac{7}{6} \) to a fraction with a denominator of 42:
\[ \frac{7}{6} = \frac{7 \times 7}{6 \times 7} = \frac{49}{42} \]

Convert \( \frac{1}{21} \) to a fraction with a denominator of 42:
\[ \frac{1}{21} = \frac{1 \times 2}{21 \times 2} = \frac{2}{42} \]

Now, subtract \( \frac{2}{42} \) from \( \frac{49}{42} \):
\[ \frac{49}{42} - \frac{2}{42} = \frac{49 - 2}{42} = \frac{47}{42} \]

So, Cassandra now has \( \frac{47}{42} \) of a key set.

### Answer: \(\frac{47}{42}\)

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.

GPT-4o:

To solve this problem, we need to calculate the sum of the ratios of the two sections and then find the difference between this sum and the ratio of a rest used in the third section.

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

1. The ratio of notes to measures in the first section is \( \frac{29}{23} \).
2. The ratio of notes to measures in the second section is \( \frac{19}{17} \).

We add these two ratios together:

\[
\frac{29}{23} + \frac{19}{17}
\]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 23 and 17 is 391 (since 23 and 17 are both prime numbers, their LCM is their product).

Convert each fraction to have the common denominator of 391:

\[
\frac{29}{23} = \frac{29 \times 17}{23 \times 17} = \frac{493}{391}
\]

\[
\frac{19}{17} = \frac{19 \times 23}{17 \times 23} = \frac{437}{391}
\]

Now, add the fractions:

\[
\frac{493}{391} + \frac{437}{391} = \frac{493 + 437}{391} = \frac{930}{391}
\]

Next, we need to find the difference between this sum and the ratio of a rest, which is \( \frac{26}{26} \) (equivalent to 1):

\[
\frac{930}{391} - \frac{26}{26}
\]

Since \( \frac{26}{26} = 1 \), we can rewrite the expression as:

\[
\frac{930}{391} - 1
\]

Convert 1 to a fraction with the same denominator:

\[
1 = \frac{391}{391}
\]

Now, subtract the fractions:

\[
\frac{930}{391} - \frac{391}{391} = \frac{930 - 391}{391} = \frac{539}{391}
\]

Thus, the difference between the sum of the ratios of the two sections and the ratio of a rest used in the third section is:

### Answer: \(\frac{539}{391}\)

Expected answer: 539/391

Correct? Yes

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

GPT-4o:

To find the product of the fractions \( \frac{22}{25} \) and \( \frac{22}{8} \), we multiply the numerators together and the denominators together.

First, multiply the numerators:
\[ 22 \times 22 = 484 \]

Next, multiply the denominators:
\[ 25 \times 8 = 200 \]

So, the product of the fractions is:
\[ \frac{484}{200} \]

To simplify this fraction, we find the greatest common divisor (GCD) of 484 and 200. The GCD of 484 and 200 is 4.

Now, divide both the numerator and the denominator by their GCD:
\[ \frac{484 \div 4}{200 \div 4} = \frac{121}{50} \]

Thus, the simplified product of the fractions is:
\[ \frac{121}{50} \]

### Answer: \(\frac{121}{50}\)

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.

GPT-4o:

To determine the length of border material James will need, we need to follow these steps:

1. **Add the lengths of the pillow and the additional fluffing:**
   \[
   \text{Total length} = \frac{23}{9} + \frac{22}{25}
   \]

2. **Find a common denominator to add the fractions:**
   The least common multiple of 9 and 25 is 225. Convert each fraction to have this common denominator:
   \[
   \frac{23}{9} = \frac{23 \times 25}{9 \times 25} = \frac{575}{225}
   \]
   \[
   \frac{22}{25} = \frac{22 \times 9}{25 \times 9} = \frac{198}{225}
   \]

3. **Add the fractions:**
   \[
   \frac{575}{225} + \frac{198}{225} = \frac{575 + 198}{225} = \frac{773}{225}
   \]

4. **Multiply the total length by the factor to account for overlap and corners:**
   \[
   \text{Length of border material} = \frac{773}{225} \times \frac{16}{13}
   \]

5. **Multiply the fractions:**
   \[
   \frac{773 \times 16}{225 \times 13} = \frac{12368}{2925}
   \]

6. **Simplify the fraction if possible:**
   The greatest common divisor (GCD) of 12368 and 2925 is 1, so the fraction is already in its simplest form.

Thus, the length of border material James will need is:
\[
\frac{12368}{2925} \text{ feet}
\]

### Answer: \(\frac{12368}{2925}\) feet

Expected answer: 12368/2925

Correct? Yes

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.

GPT-4o:

First, let's determine the additional distance the car was supposed to travel. The car was supposed to travel an extra \( \frac{16}{13} \) miles, but it only traveled an additional \( \frac{1}{21} \) miles. 

To find the difference, we need to subtract \( \frac{1}{21} \) from \( \frac{16}{13} \):

\[
\frac{16}{13} - \frac{1}{21}
\]

To subtract these fractions, we need a common denominator. The least common multiple of 13 and 21 is 273. We convert each fraction:

\[
\frac{16}{13} = \frac{16 \times 21}{13 \times 21} = \frac{336}{273}
\]

\[
\frac{1}{21} = \frac{1 \times 13}{21 \times 13} = \frac{13}{273}
\]

Now, subtract the fractions:

\[
\frac{336}{273} - \frac{13}{273} = \frac{336 - 13}{273} = \frac{323}{273}
\]

Next, we need to calculate how many more miles the car was supposed to travel in total that day. The car travels \( \frac{21}{4} \) miles every hour. We multiply this speed by the additional distance:

\[
\frac{21}{4} \times \frac{323}{273}
\]

First, simplify the multiplication:

\[
\frac{21 \times 323}{4 \times 273}
\]

Calculate the numerator and the denominator:

\[
21 \times 323 = 6783
\]

\[
4 \times 273 = 1092
\]

So, the fraction becomes:

\[
\frac{6783}{1092}
\]

Simplify the fraction by finding the greatest common divisor (GCD) of 6783 and 1092. The GCD is 21:

\[
\frac{6783 \div 21}{1092 \div 21} = \frac{323}{52}
\]

Thus, the car was supposed to travel an additional \( \frac{323}{52} \) miles.

### Answer: \(\frac{323}{52}\) miles.

Expected answer: 323/52

Correct? Yes

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?

GPT-4o:

To solve this problem, we need to follow these steps:

1. Calculate the time taken by the editing team to edit a manuscript.
2. Calculate the time taken by the typesetting team to adjust the layout of a page.
3. Sum these times to get the initial total time required for the process.
4. Subtract the collective loss due to breaks.
5. Determine the extended time, which is equal to the initial total time required.
6. Multiply the initial total time required by the extended time after the reduction of the lost hours.

Let's go through each step in detail:

1. **Time taken by the editing team:**
   \[
   \text{Time taken by the editing team} = \frac{20}{5} \text{ hours} = 4 \text{ hours}
   \]

2. **Time taken by the typesetting team:**
   \[
   \text{Time taken by the typesetting team} = \frac{18}{17} \text{ hours}
   \]

3. **Initial total time required:**
   \[
   \text{Initial total time required} = 4 \text{ hours} + \frac{18}{17} \text{ hours}
   \]
   To add these times, we need a common denominator:
   \[
   4 = \frac{68}{17}
   \]
   So,
   \[
   \text{Initial total time required} = \frac{68}{17} + \frac{18}{17} = \frac{86}{17} \text{ hours}
   \]

4. **Subtract the collective loss due to breaks:**
   \[
   \text{Collective loss} = \frac{6}{15} \text{ hours} = \frac{2}{5} \text{ hours}
   \]
   Subtracting this from the initial total time:
   \[
   \text{Adjusted time} = \frac{86}{17} - \frac{2}{5}
   \]
   To subtract these, we need a common denominator:
   \[
   \frac{86}{17} = \frac{86 \times 5}{17 \times 5} = \frac{430}{85}
   \]
   \[
   \frac{2}{5} = \frac{2 \times 17}{5 \times 17} = \frac{34}{85}
   \]
   So,
   \[
   \text{Adjusted time} = \frac{430}{85} - \frac{34}{85} = \frac{396}{85} \text{ hours}
   \]

5. **Extended time (equal to the initial total time required):**
   \[
   \text{Extended time} = \frac{86}{17} \text{ hours}
   \]

6. **Multiply the initial total time required by the extended time after the reduction of the lost hours:**
   \[
   \text{Total extended time} = \left(\frac{86}{17}\right) \times \left(\frac{396}{85}\right)
   \]
   Simplify the multiplication:
   \[
   \frac{86}{17} = 5.058823529
   \]
   \[
   \frac{396}{85} = 4.658823529
   \]
   \[
   5.058823529 \times 4.658823529 = 23.56
   \]

### Answer: 23.56

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?

GPT-4o:

To determine how much Jenny will make in total by selling all her potatoes, we need to follow these steps:

1. Calculate the total number of bushels Jenny yields.
2. Calculate the total earnings from selling the bushels.

First, let's find the total number of bushels Jenny yields:

Jenny plants \( \frac{13}{11} \) rows, and each row yields \( \frac{21}{3} \) bushels.

\[
\text{Total bushels} = \frac{13}{11} \times \frac{21}{3}
\]

Simplify \( \frac{21}{3} \):

\[
\frac{21}{3} = 7
\]

Now, multiply:

\[
\frac{13}{11} \times 7 = \frac{13 \times 7}{11} = \frac{91}{11} = 8.2727 \text{ (approximately)}
\]

Next, calculate the total earnings from selling the bushels:

Each bushel earns \( \frac{21}{15} \) dollars.

\[
\text{Total earnings} = \frac{91}{11} \times \frac{21}{15}
\]

Simplify \( \frac{21}{15} \):

\[
\frac{21}{15} = \frac{7}{5}
\]

Now, multiply:

\[
\frac{91}{11} \times \frac{7}{5} = \frac{91 \times 7}{11 \times 5} = \frac{637}{55}
\]

Simplify \( \frac{637}{55} \):

\[
\frac{637}{55} \approx 11.5818 \text{ (approximately)}
\]

Thus, Jenny will make approximately 11.5818 dollars by selling all her potatoes.

### Answer: 11.5818 dollars

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?

GPT-4o:

First, let's simplify the fractions to make the calculations easier.

For the gold:
\[ \frac{14}{28} = \frac{14 \div 14}{28 \div 14} = \frac{1}{2} \]

For the silver:
\[ \frac{13}{26} = \frac{13 \div 13}{26 \div 13} = \frac{1}{2} \]

Now, we add the simplified fractions:
\[ \frac{1}{2} + \frac{1}{2} = 1 \]

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

### Answer: 1 kilogram

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?

GPT-4o:

To solve this problem, we need to determine the total amount of honey in the combined sub-sections under the given conditions.

First, let's denote the amount of honey in each honey storage sub-section and each bee rearing sub-section as \( h \).

Given:
\[ h = \frac{25}{9} \text{ gallons} \]

When the beekeeper combines the honey from one honey storage sub-section and one bee rearing sub-section, the total amount of honey \( p \) is:
\[ p = h + h = \frac{25}{9} + \frac{25}{9} = \frac{50}{9} \text{ gallons} \]

Now, consider the scenario where one honey storage sub-section has an additional \( \frac{2}{26} \) gallons of honey. The total amount of honey in this honey storage sub-section is:
\[ h + \frac{2}{26} = \frac{25}{9} + \frac{2}{26} \]

To add these fractions, we need a common denominator. The least common multiple of 9 and 26 is 234. We convert each fraction to have this common denominator:
\[ \frac{25}{9} = \frac{25 \times 26}{9 \times 26} = \frac{650}{234} \]
\[ \frac{2}{26} = \frac{2 \times 9}{26 \times 9} = \frac{18}{234} \]

Now, add these fractions:
\[ \frac{650}{234} + \frac{18}{234} = \frac{650 + 18}{234} = \frac{668}{234} \]

Simplify the fraction:
\[ \frac{668}{234} = \frac{334}{117} \]

Thus, the total amount of honey \( s \) in this scenario, combining the honey from this honey storage sub-section and a bee rearing sub-section, is:
\[ s = \frac{334}{117} + \frac{25}{9} \]

Convert \( \frac{25}{9} \) to have the same denominator:
\[ \frac{25}{9} = \frac{25 \times 13}{9 \times 13} = \frac{325}{117} \]

Add the fractions:
\[ s = \frac{334}{117} + \frac{325}{117} = \frac{334 + 325}{117} = \frac{659}{117} \]

Simplify the fraction:
\[ \frac{659}{117} = \frac{659 \div 1}{117 \div 1} = \frac{659}{117} \]

Thus, the quantity of honey \( s \) the beekeeper would have in total from this scenario is:
\[ s = \frac{659}{117} \]

### Answer: \(\frac{659}{117}\) gallons

Expected answer: 659/117

Correct? Yes

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

GPT-4o:

First, let's simplify the fraction for the bunches of leaves the dinosaur eats during the day:
\[ \frac{16}{8} = 2 \]

Next, we know the dinosaur eats \( \frac{6}{17} \) bunches of leaves every hour at night.

To find the total bunches of leaves the dinosaur eats in an hour if it is eating both day and night, we add the two amounts together:
\[ 2 + \frac{6}{17} \]

To add these, we need a common denominator. The common denominator for 2 (which can be written as \( \frac{34}{17} \)) and \( \frac{6}{17} \) is 17:
\[ 2 = \frac{34}{17} \]

Now, add the fractions:
\[ \frac{34}{17} + \frac{6}{17} = \frac{34 + 6}{17} = \frac{40}{17} \]

### Answer: \(\frac{40}{17}\)

Expected answer: 40/17

Correct? Yes

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?

GPT-4o:

To find the total pounds of fish the bear ate over the three days, we need to add the fractions:

1. First day: \( \frac{28}{6} \)
2. Second day: \( \frac{21}{18} \)
3. Third day: \( \frac{24}{22} \)

Let's simplify each fraction first:

1. Simplify \( \frac{28}{6} \):
   \[
   \frac{28}{6} = \frac{14}{3}
   \]

2. Simplify \( \frac{21}{18} \):
   \[
   \frac{21}{18} = \frac{7}{6}
   \]

3. Simplify \( \frac{24}{22} \):
   \[
   \frac{24}{22} = \frac{12}{11}
   \]

Now, we need to add these fractions together. To do this, we need a common denominator. The least common multiple (LCM) of 3, 6, and 11 is 66.

Convert each fraction to have a denominator of 66:

1. \( \frac{14}{3} \):
   \[
   \frac{14}{3} = \frac{14 \times 22}{3 \times 22} = \frac{308}{66}
   \]

2. \( \frac{7}{6} \):
   \[
   \frac{7}{6} = \frac{7 \times 11}{6 \times 11} = \frac{77}{66}
   \]

3. \( \frac{12}{11} \):
   \[
   \frac{12}{11} = \frac{12 \times 6}{11 \times 6} = \frac{72}{66}
   \]

Now, add the fractions:
\[
\frac{308}{66} + \frac{77}{66} + \frac{72}{66} = \frac{308 + 77 + 72}{66} = \frac{457}{66}
\]

Thus, the total pounds of fish the bear ate over the three days is:
\[
\frac{457}{66}
\]

### Answer: \(\frac{457}{66}\)

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?

GPT-4o:

First, let's determine the total amount of sugar Heather used in her recipes before increasing the quantity.

For the bread recipe, she used:
\[ \frac{11}{17} \text{ cups of sugar} \]

For the custard, she used:
\[ \frac{6}{2} = 3 \text{ cups of sugar} \]

Adding these amounts together:
\[ \frac{11}{17} + 3 \]

To add these fractions, we need a common denominator. The common denominator for 17 and 1 (since 3 can be written as \(\frac{3}{1}\)) is 17.

Convert 3 to a fraction with a denominator of 17:
\[ 3 = \frac{3 \times 17}{1 \times 17} = \frac{51}{17} \]

Now add the fractions:
\[ \frac{11}{17} + \frac{51}{17} = \frac{11 + 51}{17} = \frac{62}{17} \]

Next, Heather decided to increase the total quantity of sugar by a factor of \(\frac{29}{21}\). So, we multiply the total amount of sugar by this factor:
\[ \frac{62}{17} \times \frac{29}{21} \]

Multiply the numerators and the denominators:
\[ \frac{62 \times 29}{17 \times 21} = \frac{1798}{357} \]

To simplify \(\frac{1798}{357}\), we find the greatest common divisor (GCD) of 1798 and 357. The GCD is 1, so the fraction is already in its simplest form.

Thus, the total amount of sugar Heather used is:
\[ \frac{1798}{357} \approx 5.04 \text{ cups} \]

### Answer: \(\frac{1798}{357}\) 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?

GPT-4o:

To solve the expression \(\left(\frac{7}{8} + \frac{21}{18}\right)\), we need to find a common denominator for the fractions.

1. The denominators are 8 and 18. The least common multiple (LCM) of 8 and 18 is 72.

2. Convert each fraction to have the common denominator of 72:
   - For \(\frac{7}{8}\):
     \[
     \frac{7}{8} = \frac{7 \times 9}{8 \times 9} = \frac{63}{72}
     \]
   - For \(\frac{21}{18}\):
     \[
     \frac{21}{18} = \frac{21 \times 4}{18 \times 4} = \frac{84}{72}
     \]

3. Now add the fractions:
   \[
   \frac{63}{72} + \frac{84}{72} = \frac{63 + 84}{72} = \frac{147}{72}
   \]

4. Simplify the fraction \(\frac{147}{72}\):
   - Find the greatest common divisor (GCD) of 147 and 72. The GCD is 3.
   - Divide both the numerator and the denominator by their GCD:
     \[
     \frac{147 \div 3}{72 \div 3} = \frac{49}{24}
     \]

### Answer: \(\frac{49}{24}\)

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.

GPT-4o:

To solve this problem, we need to follow these steps:

1. Calculate the total amount of liquid each guest will consume.
2. Calculate the total amount of liquid the baker needs for each cake.
3. Multiply the baker's requirement by the guests' consumption.
4. Add the result to the guests' consumption to find the total amount of liquid needed.

Let's start with the guests' consumption:

1. Each guest consumes \( \frac{15}{7} \) gallons of water and \( \frac{15}{24} \) gallons of wine.
   - Total liquid per guest: 
   \[
   \frac{15}{7} + \frac{15}{24}
   \]

   To add these fractions, we need a common denominator. The least common multiple of 7 and 24 is 168.

   - Convert \( \frac{15}{7} \) to a fraction with a denominator of 168:
   \[
   \frac{15}{7} = \frac{15 \times 24}{7 \times 24} = \frac{360}{168}
   \]

   - Convert \( \frac{15}{24} \) to a fraction with a denominator of 168:
   \[
   \frac{15}{24} = \frac{15 \times 7}{24 \times 7} = \frac{105}{168}
   \]

   - Add the fractions:
   \[
   \frac{360}{168} + \frac{105}{168} = \frac{360 + 105}{168} = \frac{465}{168}
   \]

2. The baker needs \( \frac{26}{20} \) gallons of milk for each cake.
   - Simplify \( \frac{26}{20} \):
   \[
   \frac{26}{20} = \frac{13}{10}
   \]

3. Multiply the baker's requirement by the guests' consumption:
   - Multiply \( \frac{13}{10} \) by \( \frac{465}{168} \):
   \[
   \frac{13}{10} \times \frac{465}{168} = \frac{13 \times 465}{10 \times 168} = \frac{6045}{1680}
   \]

4. Add the result to the guests' consumption:
   - Convert \( \frac{465}{168} \) to a fraction with a denominator of 1680:
   \[
   \frac{465}{168} = \frac{465 \times 10}{168 \times 10} = \frac{4650}{1680}
   \]

   - Add the fractions:
   \[
   \frac{4650}{1680} + \frac{6045}{1680} = \frac{4650 + 6045}{1680} = \frac{10695}{1680}
   \]

   - Simplify \( \frac{10695}{1680} \):
   \[
   \frac{10695}{1680} = \frac{10695 \div 15}{1680 \div 15} = \frac{713}{112}
   \]

### Answer: \(\frac{713}{112}\)

Expected answer: 713/112

Correct? Yes

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?

GPT-4o:

To solve this problem, we need to follow the steps of addition and multiplication with fractions.

First, let's add the two fractions \( \frac{30}{17} \) and \( \frac{18}{15} \).

1. Find a common denominator for the fractions \( \frac{30}{17} \) and \( \frac{18}{15} \). The least common multiple (LCM) of 17 and 15 is 255.

2. Convert each fraction to have the common denominator:
   \[
   \frac{30}{17} = \frac{30 \times 15}{17 \times 15} = \frac{450}{255}
   \]
   \[
   \frac{18}{15} = \frac{18 \times 17}{15 \times 17} = \frac{306}{255}
   \]

3. Add the fractions:
   \[
   \frac{450}{255} + \frac{306}{255} = \frac{450 + 306}{255} = \frac{756}{255}
   \]

4. Simplify the fraction \( \frac{756}{255} \):
   \[
   \frac{756 \div 3}{255 \div 3} = \frac{252}{85}
   \]

Next, we need to multiply this result by \( \frac{24}{13} \).

5. Multiply the fractions:
   \[
   \frac{252}{85} \times \frac{24}{13} = \frac{252 \times 24}{85 \times 13} = \frac{6048}{1105}
   \]

Thus, Teddy's final number is \( \frac{6048}{1105} \).

### Answer: \(\frac{6048}{1105}\)

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).

GPT-4o:

To determine what fraction of the desired diameter each hole would have if Johnny uses his current drill bit, we need to compare the diameter of the drill bit to the desired diameter.

The desired diameter is given as:
\[ \frac{20}{6} \text{ cm} \]

The diameter of the drill bit is:
\[ \frac{11}{21} \text{ cm} \]

To find the fraction of the desired diameter that each hole would have, we divide the diameter of the drill bit by the desired diameter:
\[ \frac{\frac{11}{21}}{\frac{20}{6}} \]

To divide by a fraction, we multiply by its reciprocal:
\[ \frac{11}{21} \times \frac{6}{20} \]

Now, we multiply the numerators and the denominators:
\[ \frac{11 \times 6}{21 \times 20} = \frac{66}{420} \]

Thus, each hole drilled with the current drill bit would be:
\[ \frac{66}{420} \]

### Answer: \(\frac{66}{420}\)

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.

GPT-4o:

To determine how much less time the second model takes compared to the first one, we need to subtract the time taken for the second model from the time taken for the first model.

First, let's convert the fractions to a common denominator to make the subtraction easier. The denominators are 10 and 23. The least common multiple (LCM) of 10 and 23 is 230.

Convert \( \frac{17}{10} \) to a fraction with a denominator of 230:
\[ \frac{17}{10} = \frac{17 \times 23}{10 \times 23} = \frac{391}{230} \]

Convert \( \frac{12}{23} \) to a fraction with a denominator of 230:
\[ \frac{12}{23} = \frac{12 \times 10}{23 \times 10} = \frac{120}{230} \]

Now, subtract the two fractions:
\[ \frac{391}{230} - \frac{120}{230} = \frac{391 - 120}{230} = \frac{271}{230} \]

The fraction \( \frac{271}{230} \) is already in its simplest form because 271 is a prime number and does not share any common factors with 230.

Thus, the second model takes \( \frac{271}{230} \) hours less than the first model.

### Answer: \( \frac{271}{230} \)

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.

GPT-4o:

First, let's determine how much additional wood Carlos needs for the special chair. The additional wood required is given by the product of \(\frac{24}{5}\) and \(\frac{7}{6}\).

\[
\frac{24}{5} \times \frac{7}{6} = \frac{24 \times 7}{5 \times 6} = \frac{168}{30}
\]

Next, we simplify \(\frac{168}{30}\) by finding the greatest common divisor (GCD) of 168 and 30. The GCD of 168 and 30 is 6.

\[
\frac{168 \div 6}{30 \div 6} = \frac{28}{5}
\]

So, the additional wood required is \(\frac{28}{5}\) units.

Now, we need to add this to the usual amount of wood Carlos uses for a chair, which is \(\frac{20}{15}\). We simplify \(\frac{20}{15}\) first:

\[
\frac{20}{15} = \frac{4}{3}
\]

Now, we add \(\frac{4}{3}\) and \(\frac{28}{5}\). To do this, we need a common denominator. The least common multiple (LCM) of 3 and 5 is 15.

\[
\frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15}
\]

\[
\frac{28}{5} = \frac{28 \times 3}{5 \times 3} = \frac{84}{15}
\]

Now, we add the two fractions:

\[
\frac{20}{15} + \frac{84}{15} = \frac{20 + 84}{15} = \frac{104}{15}
\]

Thus, Carlos needs \(\frac{104}{15}\) units of wood to make one of these special chairs.

### Answer: \(\frac{104}{15}\)

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?

GPT-4o:

To determine the final speed of the car, we need to follow these steps:

1. **Initial Speed**: The car was initially going at \( \frac{13}{4} \) miles per minute.

2. **Speed Reduction**: The car then reduced its speed by \( \frac{14}{15} \) miles per minute. We need to subtract this from the initial speed:
   \[
   \frac{13}{4} - \frac{14}{15}
   \]

   To subtract these fractions, we need a common denominator. The least common multiple of 4 and 15 is 60. We convert both fractions to have this common denominator:
   \[
   \frac{13}{4} = \frac{13 \times 15}{4 \times 15} = \frac{195}{60}
   \]
   \[
   \frac{14}{15} = \frac{14 \times 4}{15 \times 4} = \frac{56}{60}
   \]

   Now, subtract the fractions:
   \[
   \frac{195}{60} - \frac{56}{60} = \frac{195 - 56}{60} = \frac{139}{60}
   \]

3. **Speed Increase**: The car then increased its speed by \( \frac{30}{15} \) miles per minute. Simplify \( \frac{30}{15} \):
   \[
   \frac{30}{15} = 2
   \]

   We need to add this to the current speed:
   \[
   \frac{139}{60} + 2
   \]

   Convert 2 to a fraction with a denominator of 60:
   \[
   2 = \frac{120}{60}
   \]

   Now, add the fractions:
   \[
   \frac{139}{60} + \frac{120}{60} = \frac{139 + 120}{60} = \frac{259}{60}
   \]

Thus, the final speed of the car according to Officer Davis's radar gun is \( \frac{259}{60} \) miles per minute.

### Answer: \(\frac{259}{60}\) 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?

GPT-4o:

Let's break down the problem step by step.

1. **Calculating the number of baskets produced this season:**
   - The usual production is \( \frac{19}{2} \) baskets.
   - This season, only \( \frac{19}{29} \) of the usual amount was produced.
   - To find the number of baskets produced this season, we multiply the usual production by the fraction produced this season:
     \[
     \text{Baskets produced this season} = \left( \frac{19}{2} \right) \times \left( \frac{19}{29} \right)
     \]
   - Simplifying the multiplication:
     \[
     \left( \frac{19}{2} \right) \times \left( \frac{19}{29} \right) = \frac{19 \times 19}{2 \times 29} = \frac{361}{58}
     \]
   - Simplifying the fraction:
     \[
     \frac{361}{58} = \frac{361 \div 29}{58 \div 29} = \frac{12.4483}{2} = 6.2241
     \]
   - Therefore, the vineyard produced approximately 6.2241 baskets of grapes this season.

2. **Calculating the number of baskets Jake gets to keep:**
   - Jake gets to keep \( \frac{7}{11} \) of the total amount of grapes.
   - To find the number of baskets Jake gets, we multiply the total baskets produced by \( \frac{7}{11} \):
     \[
     \text{Baskets Jake gets} = 6.2241 \times \frac{7}{11}
     \]
   - Simplifying the multiplication:
     \[
     6.2241 \times \frac{7}{11} = 6.2241 \times 0.6364 = 3.961
     \]
   - Therefore, Jake gets approximately 3.961 baskets of grapes.

3. **Calculating the number of baskets Jake uses for grape juice:**
   - Jake uses \( \frac{9}{10} \) of his grapes to make juice.
   - To find the number of baskets Jake uses for juice, we multiply the number of baskets he gets by \( \frac{9}{10} \):
     \[
     \text{Baskets used for juice} = 3.961 \times \frac{9}{10}
     \]
   - Simplifying the multiplication:
     \[
     3.961 \times \frac{9}{10} = 3.961 \times 0.9 = 3.5649
     \]
   - Therefore, Jake uses approximately 3.5649 baskets of grapes to make juice.

### Answer: 3.5649

Expected answer: 22743/6380

Correct? No

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

GPT-4o:

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

First, let's convert the fractions to a common denominator if necessary. However, in this case, we can directly add the fractions since they are already in a simple form.

The red grapes picked are:
\[ \frac{9}{2} \]

The green grapes picked are:
\[ \frac{10}{22} \]

We can simplify \(\frac{10}{22}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{10 \div 2}{22 \div 2} = \frac{5}{11} \]

Now, we need to add \(\frac{9}{2}\) and \(\frac{5}{11}\). To do this, we need a common denominator. The least common multiple of 2 and 11 is 22.

Convert \(\frac{9}{2}\) to a fraction with a denominator of 22:
\[ \frac{9}{2} = \frac{9 \times 11}{2 \times 11} = \frac{99}{22} \]

Now we can add the two fractions:
\[ \frac{99}{22} + \frac{5}{11} = \frac{99}{22} + \frac{5 \times 2}{11 \times 2} = \frac{99}{22} + \frac{10}{22} = \frac{99 + 10}{22} = \frac{109}{22} \]

So, the total number of bushels of grapes Joel picked that day is:
\[ \frac{109}{22} \]

### Answer: \(\frac{109}{22}\)

Expected answer: 109/22

Correct? Yes

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?

GPT-4o:

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

First, let's convert the diameters to a common fraction format for easier addition:

1. The diameter of the larger snowball is \( \frac{17}{8} \) feet.
2. The diameter of the smaller snowball is \( \frac{1}{20} \) feet.

Next, we need to find a common denominator to add these fractions. The least common multiple (LCM) of 8 and 20 is 40.

Convert \( \frac{17}{8} \) to a fraction with a denominator of 40:
\[ \frac{17}{8} = \frac{17 \times 5}{8 \times 5} = \frac{85}{40} \]

Convert \( \frac{1}{20} \) to a fraction with a denominator of 40:
\[ \frac{1}{20} = \frac{1 \times 2}{20 \times 2} = \frac{2}{40} \]

Now, add the two fractions:
\[ \frac{85}{40} + \frac{2}{40} = \frac{85 + 2}{40} = \frac{87}{40} \]

Thus, the total height of the snowman is \( \frac{87}{40} \) feet.

To convert this to a mixed number:
\[ \frac{87}{40} = 2 \frac{7}{40} \]

### Answer: \( 2 \frac{7}{40} \) feet

Expected answer: 87/40

Correct? Yes

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.

GPT-4o:

First, let's simplify the fractions involved.

The initial amount of sand is \( \frac{24}{7} \).

The amount of sand taken away is \( \frac{2}{16} \). Simplifying \( \frac{2}{16} \):
\[ \frac{2}{16} = \frac{1}{8} \]

Now, we need to subtract \( \frac{1}{8} \) from \( \frac{24}{7} \).

To perform this subtraction, we need a common denominator. The least common multiple of 7 and 8 is 56.

Convert \( \frac{24}{7} \) to a fraction with a denominator of 56:
\[ \frac{24}{7} = \frac{24 \times 8}{7 \times 8} = \frac{192}{56} \]

Convert \( \frac{1}{8} \) to a fraction with a denominator of 56:
\[ \frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56} \]

Now, subtract the two fractions:
\[ \frac{192}{56} - \frac{7}{56} = \frac{192 - 7}{56} = \frac{185}{56} \]

Thus, the remaining part of the sand in the sandbox is \( \frac{185}{56} \).

### Answer: \(\frac{185}{56}\)

Expected answer: 185/56

Correct? Yes

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.

GPT-4o:

To determine how much less of the zebra the lion ate compared to the wildebeest, we need to subtract the fraction of the zebra eaten from the fraction of the wildebeest eaten.

First, let's write down the fractions:
- Zebra: \( \frac{28}{26} \)
- Wildebeest: \( \frac{23}{9} \)

We need to subtract \( \frac{28}{26} \) from \( \frac{23}{9} \). To do this, we need a common denominator. The least common multiple (LCM) of 26 and 9 is 234.

Convert each fraction to have the common denominator of 234:
- For the zebra: 
  \[
  \frac{28}{26} = \frac{28 \times 9}{26 \times 9} = \frac{252}{234}
  \]
- For the wildebeest:
  \[
  \frac{23}{9} = \frac{23 \times 26}{9 \times 26} = \frac{598}{234}
  \]

Now, subtract the fractions:
\[
\frac{598}{234} - \frac{252}{234} = \frac{598 - 252}{234} = \frac{346}{234}
\]

Simplify the fraction \( \frac{346}{234} \):
- The greatest common divisor (GCD) of 346 and 234 is 2.
- Divide both the numerator and the denominator by 2:
  \[
  \frac{346 \div 2}{234 \div 2} = \frac{173}{117}
  \]

Thus, the simplified fraction is \( \frac{173}{117} \).

### Answer: \(\frac{173}{117}\)

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)).

GPT-4o:

To find out how many kilograms of chocolate the factory will produce, we need to calculate the expression \(\left(\frac{14}{4}\right) \times \left(\frac{21}{11}\right)\).

First, simplify the fractions if possible:
\[
\frac{14}{4} = \frac{7}{2}
\]

Now, multiply the simplified fractions:
\[
\left(\frac{7}{2}\right) \times \left(\frac{21}{11}\right)
\]

Multiply the numerators together and the denominators together:
\[
\frac{7 \times 21}{2 \times 11} = \frac{147}{22}
\]

Next, simplify the fraction \(\frac{147}{22}\) if possible. Since 147 and 22 have no common factors other than 1, the fraction is already in its simplest form.

Thus, the factory will produce \(\frac{147}{22}\) kilograms of chocolate.

### Answer: \(\frac{147}{22}\) kilograms

Expected answer: 147/22

Correct? Yes

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.

GPT-4o:

To find the expected number of bananas produced by the two species of banana trees on any given day, we use the given formula:

\[
\text{Expected number of bananas} = \left(\frac{12}{29}\right) + \left(\frac{30}{10}\right)
\]

First, we calculate the contribution from the first species:

\[
\frac{12}{29} \approx 0.4138
\]

Next, we calculate the contribution from the second species:

\[
\frac{30}{10} = 3
\]

Adding these two contributions together gives us the total expected number of bananas produced per day:

\[
0.4138 + 3 = 3.4138
\]

### Answer: 3.4138

Expected answer: 99/29

Correct? No

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.

GPT-4o:

First, let's simplify the fractions given:

1. The fraction \( \frac{11}{11} \) simplifies to 1 because any number divided by itself is 1.
2. The fraction \( \frac{26}{14} \) can be simplified by finding the greatest common divisor (GCD) of 26 and 14, which is 2. 

So, we divide both the numerator and the denominator by 2:
\[ \frac{26 \div 2}{14 \div 2} = \frac{13}{7} \]

Now, we need to add the simplified fractions:
\[ 1 + \frac{13}{7} \]

To add these fractions, we convert 1 to a fraction with the same denominator as \( \frac{13}{7} \):
\[ 1 = \frac{7}{7} \]

Now, we can add the fractions:
\[ \frac{7}{7} + \frac{13}{7} = \frac{7 + 13}{7} = \frac{20}{7} \]

Thus, the total ton of food the giraffe needs to eat in a day is:
\[ \frac{20}{7} \]

### Answer: \(\frac{20}{7}\) tons

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.

GPT-4o:

First, let's break down the problem step by step.

1. The bear spends 18 hours out of 24 hours each day sleeping. This can be expressed as a fraction:
   \[
   \frac{18}{24}
   \]

2. Simplify the fraction:
   \[
   \frac{18}{24} = \frac{3}{4}
   \]

3. The bear's activity is tracked for 27 days. We need to find the fraction of time the bear has spent sleeping over these 27 days. We are given that each month has 13 weeks, but this information is not necessary for our calculation.

4. Calculate the fraction of time the bear has spent sleeping over 27 days:
   \[
   \left(\frac{3}{4}\right) \times 27
   \]

5. Convert the fraction to a decimal:
   \[
   \frac{3}{4} = 0.75
   \]

6. Multiply by 27:
   \[
   0.75 \times 27 = 20.25
   \]

Therefore, the bear has spent 20.25 days sleeping over the 27 days.

### Answer: 20.25

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.

GPT-4o:

To solve the problem, we need to calculate the fraction of the trees that are either pine or birch using the given formula \( f = \left(\frac{9}{14}\right) + \left(\frac{19}{2}\right) \).

First, let's convert the fractions to have a common denominator. The least common multiple of 14 and 2 is 14.

1. Convert \(\frac{19}{2}\) to a fraction with a denominator of 14:
   \[
   \frac{19}{2} = \frac{19 \times 7}{2 \times 7} = \frac{133}{14}
   \]

2. Now, add the two fractions:
   \[
   \frac{9}{14} + \frac{133}{14} = \frac{9 + 133}{14} = \frac{142}{14}
   \]

3. Simplify the fraction:
   \[
   \frac{142}{14} = \frac{142 \div 2}{14 \div 2} = \frac{71}{7}
   \]

Thus, the fraction of the trees in the forest that are either pine or birch is \(\frac{71}{7}\).

### Answer: \(\frac{71}{7}\)

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.

GPT-4o:

First, we need to calculate the initial energy level of the Zogorian.

The initial energy level is given by:
\[
\frac{\left(\frac{14}{2}\right)}{\left(\frac{23}{17}\right)}
\]

First, simplify the numerator and the denominator separately:
\[
\frac{14}{2} = 7
\]
\[
\frac{23}{17} \text{ remains as it is.}
\]

Now, the expression becomes:
\[
\frac{7}{\frac{23}{17}}
\]

To divide by a fraction, multiply by its reciprocal:
\[
\frac{7}{\frac{23}{17}} = 7 \times \frac{17}{23} = \frac{7 \times 17}{23} = \frac{119}{23}
\]

Next, we need to add the increase in energy level, which is:
\[
\frac{16}{24}
\]

Simplify \(\frac{16}{24}\):
\[
\frac{16}{24} = \frac{2 \times 8}{3 \times 8} = \frac{2}{3}
\]

Now, add this to the initial energy level:
\[
\frac{119}{23} + \frac{2}{3}
\]

To add these fractions, find a common denominator. The least common multiple of 23 and 3 is 69:
\[
\frac{119}{23} = \frac{119 \times 3}{23 \times 3} = \frac{357}{69}
\]
\[
\frac{2}{3} = \frac{2 \times 23}{3 \times 23} = \frac{46}{69}
\]

Now, add the fractions:
\[
\frac{357}{69} + \frac{46}{69} = \frac{357 + 46}{69} = \frac{403}{69}
\]

Thus, the Zogorian's energy level after the increase is:
\[
\frac{403}{69}
\]

### Answer: \(\frac{403}{69}\)

Expected answer: 403/69

Correct? Yes

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

GPT-4o:

To find how many more friends Teddy hides in the forest than at the beach, we need to subtract the fraction of friends hidden at the beach from the fraction hidden in the forest.

First, let's find a common denominator for the fractions \(\frac{18}{11}\) and \(\frac{8}{21}\). The least common multiple of 11 and 21 is 231.

Convert \(\frac{18}{11}\) to a fraction with a denominator of 231:
\[
\frac{18}{11} = \frac{18 \times 21}{11 \times 21} = \frac{378}{231}
\]

Convert \(\frac{8}{21}\) to a fraction with a denominator of 231:
\[
\frac{8}{21} = \frac{8 \times 11}{21 \times 11} = \frac{88}{231}
\]

Now, subtract the two fractions:
\[
\frac{378}{231} - \frac{88}{231} = \frac{378 - 88}{231} = \frac{290}{231}
\]

So, the number of friends Teddy hides more in the forest than at the beach is \(\frac{290}{231}\).

Next, we need to square this number to find the total number of hiding spots, \(n\):
\[
\left(\frac{290}{231}\right)^2 = \frac{290^2}{231^2} = \frac{84100}{53361}
\]

Thus, the total number of hiding spots Teddy needs is \(\frac{84100}{53361}\).

### Answer: \(\frac{84100}{53361}\)

Expected answer: 84100/53361

Correct? Yes

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.

GPT-4o:

To determine how much energy the robot has left, we need to subtract the energy used from the initial energy.

First, let's convert the fractions to a common denominator to make the subtraction easier. The initial energy is \( \frac{25}{10} \) and the energy used is \( \frac{27}{23} \).

1. Simplify \( \frac{25}{10} \):
\[ \frac{25}{10} = 2.5 \]

2. Convert \( 2.5 \) to a fraction with the same denominator as \( \frac{27}{23} \):
\[ 2.5 = \frac{2.5 \times 23}{1 \times 23} = \frac{57.5}{23} \]

3. Now, subtract \( \frac{27}{23} \) from \( \frac{57.5}{23} \):
\[ \frac{57.5}{23} - \frac{27}{23} = \frac{57.5 - 27}{23} = \frac{30.5}{23} \]

So, the robot has \( \frac{30.5}{23} \) units of energy left.

### Answer: \(\frac{30.5}{23}\) units of energy.

Expected answer: 61/46

Correct? No

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

GPT-4o:

To solve this problem, we need to calculate the distance covered by each snail and then sum these distances.

First, let's simplify the distances covered by the first two snails in one hour.

1. The first snail covers \( \frac{17}{21} \) meters in one hour.
2. The second snail covers \( \frac{20}{24} \) meters in one hour. Simplifying \( \frac{20}{24} \):
   \[
   \frac{20}{24} = \frac{5}{6}
   \]

Now, we add the distances covered by the first two snails:
\[
\frac{17}{21} + \frac{5}{6}
\]

To add these fractions, we need a common denominator. The least common multiple of 21 and 6 is 42.

Convert each fraction to have a denominator of 42:
\[
\frac{17}{21} = \frac{17 \times 2}{21 \times 2} = \frac{34}{42}
\]
\[
\frac{5}{6} = \frac{5 \times 7}{6 \times 7} = \frac{35}{42}
\]

Now add the fractions:
\[
\frac{34}{42} + \frac{35}{42} = \frac{34 + 35}{42} = \frac{69}{42}
\]

Next, we need to consider the third snail, which covers \( \frac{18}{17} \) meters in one hour.

The total distance covered by all three snails in one hour is:
\[
\left( \frac{69}{42} \right) + \left( \frac{18}{17} \right)
\]

To find the total distance, we need to add these two fractions. First, we need a common denominator for \( \frac{69}{42} \) and \( \frac{18}{17} \). The least common multiple of 42 and 17 is 714.

Convert each fraction to have a denominator of 714:
\[
\frac{69}{42} = \frac{69 \times 17}{42 \times 17} = \frac{1173}{714}
\]
\[
\frac{18}{17} = \frac{18 \times 42}{17 \times 42} = \frac{756}{714}
\]

Now add the fractions:
\[
\frac{1173}{714} + \frac{756}{714} = \frac{1173 + 756}{714} = \frac{1929}{714}
\]

Simplify the fraction:
\[
\frac{1929}{714} = \frac{1929 \div 3}{714 \div 3} = \frac{643}{238}
\]

### Answer: \(\frac{643}{238}\)

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?

GPT-4o:

First, let's determine the difference between the original amount of fabric and the remaining fabric.

Original fabric: \(\frac{24}{14}\) yards
Remaining fabric: \(\frac{9}{29}\) yards

To find the difference, we need a common denominator. The least common multiple of 14 and 29 is 406.

Convert \(\frac{24}{14}\) to a fraction with a denominator of 406:
\[
\frac{24}{14} = \frac{24 \times 29}{14 \times 29} = \frac{696}{406}
\]

Convert \(\frac{9}{29}\) to a fraction with a denominator of 406:
\[
\frac{9}{29} = \frac{9 \times 14}{29 \times 14} = \frac{126}{406}
\]

Now, subtract the remaining fabric from the original fabric:
\[
\frac{696}{406} - \frac{126}{406} = \frac{696 - 126}{406} = \frac{570}{406}
\]

Simplify \(\frac{570}{406}\):
\[
\frac{570}{406} = \frac{285}{203}
\]

Next, Johnny used \(\frac{15}{2}\) times this difference to make more stuffed animals. Multiply \(\frac{15}{2}\) by \(\frac{285}{203}\):
\[
\frac{15}{2} \times \frac{285}{203} = \frac{15 \times 285}{2 \times 203} = \frac{4275}{406}
\]

Simplify \(\frac{4275}{406}\):
\[
\frac{4275}{406} = \frac{4275 \div 5}{406 \div 5} = \frac{855}{81.2} = \frac{855 \div 5}{81.2 \div 5} = \frac{171}{16.24}
\]

Thus, Johnny used \(\frac{171}{16.24}\) yards of the new fabric.

### Answer: \(\frac{171}{16.24}\) yards

Expected answer: 4275/406

Correct? Yes

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.

GPT-4o:

To find the total number of kids waiting for the swings, we need to add the fractions \( \frac{2}{10} \) and \( \frac{21}{4} \).

First, let's simplify \( \frac{2}{10} \):
\[ \frac{2}{10} = \frac{1}{5} \]

Next, we need a common denominator to add \( \frac{1}{5} \) and \( \frac{21}{4} \). The least common multiple of 5 and 4 is 20.

Convert \( \frac{1}{5} \) to a fraction with a denominator of 20:
\[ \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20} \]

Convert \( \frac{21}{4} \) to a fraction with a denominator of 20:
\[ \frac{21}{4} = \frac{21 \times 5}{4 \times 5} = \frac{105}{20} \]

Now, add the two fractions:
\[ \frac{4}{20} + \frac{105}{20} = \frac{4 + 105}{20} = \frac{109}{20} \]

So, the total number of kids waiting for the swings is \( \frac{109}{20} \).

### Answer: \(\frac{109}{20}\)

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.

GPT-4o:

To determine how many hours of power the spacecraft currently has, we need to calculate \(\frac{18}{30} \times \frac{22}{6}\).

First, simplify \(\frac{18}{30}\):
\[
\frac{18}{30} = \frac{3 \times 6}{5 \times 6} = \frac{3}{5}
\]

Next, multiply \(\frac{3}{5}\) by \(\frac{22}{6}\):
\[
\frac{3}{5} \times \frac{22}{6} = \frac{3 \times 22}{5 \times 6} = \frac{66}{30}
\]

Now, simplify \(\frac{66}{30}\):
\[
\frac{66}{30} = \frac{33 \times 2}{15 \times 2} = \frac{33}{15} = \frac{11 \times 3}{5 \times 3} = \frac{11}{5}
\]

Convert \(\frac{11}{5}\) to a decimal:
\[
\frac{11}{5} = 2.2
\]

Thus, the spacecraft currently has 2.2 hours of power.

### Answer: 2.2

Expected answer: 11/5

Correct? Yes

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

GPT-4o:

To find out how much of a can the cat eats in one day, we need to add the amount it eats in the morning to the amount it eats in the evening.

First, let's simplify the fractions if possible:

Morning: \( \frac{16}{12} \)
Evening: \( \frac{6}{10} \)

Simplify \( \frac{16}{12} \):
\[ \frac{16}{12} = \frac{4 \times 4}{4 \times 3} = \frac{4}{3} \]

Simplify \( \frac{6}{10} \):
\[ \frac{6}{10} = \frac{3 \times 2}{5 \times 2} = \frac{3}{5} \]

Now, we need to add \( \frac{4}{3} \) and \( \frac{3}{5} \). To do this, we need a common denominator. The least common multiple of 3 and 5 is 15.

Convert \( \frac{4}{3} \) to a fraction with a denominator of 15:
\[ \frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15} \]

Convert \( \frac{3}{5} \) to a fraction with a denominator of 15:
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

Now add the two fractions:
\[ \frac{20}{15} + \frac{9}{15} = \frac{20 + 9}{15} = \frac{29}{15} \]

So, the cat eats \( \frac{29}{15} \) of a can of cat food in one day.

### Answer: \(\frac{29}{15}\)

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?

GPT-4o:

First, let's calculate the average number of eggs per nest for the first group of nests.

The first group has 3 nests with 12 eggs in each nest:
\[ \text{Total eggs in the first group} = 3 \times 12 = 36 \]
\[ \text{Average number of eggs per nest in the first group} = \frac{36}{3} = 12 \]

Next, let's calculate the average number of eggs per nest for the second group of nests.

The second group has 4 nests with 11 eggs in each nest:
\[ \text{Total eggs in the second group} = 4 \times 11 = 44 \]
\[ \text{Average number of eggs per nest in the second group} = \frac{44}{4} = 11 \]

Now, we find the difference between the average number of eggs per nest for these two groups:
\[ \text{Difference} = 12 - 11 = 1 \]

### Answer: 1

Expected answer: 5/4

Correct? No

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?

GPT-4o:

To determine how much of the pile the monkey has left, we need to calculate the fractions of the pile that the monkey ate and gave away, and then subtract these from the whole pile.

First, let's calculate the fraction of the pile the monkey ate:
\[
\frac{22}{7} \times \frac{10}{25}
\]

We can simplify this multiplication by simplifying the fractions first:
\[
\frac{22}{7} \times \frac{10}{25} = \frac{22 \times 10}{7 \times 25} = \frac{220}{175}
\]

Next, we simplify \(\frac{220}{175}\):
\[
\frac{220}{175} = \frac{220 \div 5}{175 \div 5} = \frac{44}{35}
\]

So, the monkey ate \(\frac{44}{35}\) of the pile.

Next, let's calculate the fraction of the pile the monkey gave to his friend:
\[
\frac{3}{28}
\]

Now, we need to find the total fraction of the pile that the monkey has given away:
\[
\frac{44}{35} + \frac{3}{28}
\]

To add these fractions, we need a common denominator. The least common multiple of 35 and 28 is 140. We convert each fraction to have this common denominator:
\[
\frac{44}{35} = \frac{44 \times 4}{35 \times 4} = \frac{176}{140}
\]
\[
\frac{3}{28} = \frac{3 \times 5}{28 \times 5} = \frac{15}{140}
\]

Now, we add the fractions:
\[
\frac{176}{140} + \frac{15}{140} = \frac{176 + 15}{140} = \frac{191}{140}
\]

This is the total fraction of the pile that the monkey has eaten and given away. To find out how much of the pile the monkey has left, we subtract this from the whole pile (which is 1):
\[
1 - \frac{191}{140}
\]

We convert 1 to a fraction with the same denominator:
\[
1 = \frac{140}{140}
\]

Now, we perform the subtraction:
\[
\frac{140}{140} - \frac{191}{140} = \frac{140 - 191}{140} = \frac{-51}{140}
\]

Since a negative fraction doesn't make sense in this context, it indicates that the monkey has eaten and given away more than the whole pile, which suggests an error in the problem setup or interpretation. However, based on the calculations, the monkey has effectively consumed and given away more than the entire pile.

### Answer: \(\frac{-51}{140}\)

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?

GPT-4o:

To determine how many feet the mouse runs, we need to multiply the speed of the mouse by the time it runs.

The speed of the mouse is given as \( \frac{24}{20} \) feet per second. Simplifying this fraction, we get:
\[ \frac{24}{20} = \frac{6}{5} \text{ feet per second} \]

The time the mouse runs is given as \( \frac{23}{2} \) seconds.

Now, we multiply the speed by the time:
\[ \text{Distance} = \left( \frac{6}{5} \text{ feet per second} \right) \times \left( \frac{23}{2} \text{ seconds} \right) \]

To multiply these fractions, we multiply the numerators together and the denominators together:
\[ \text{Distance} = \frac{6 \times 23}{5 \times 2} = \frac{138}{10} \]

Simplifying the fraction \( \frac{138}{10} \):
\[ \frac{138}{10} = 13.8 \text{ feet} \]

### 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?

GPT-4o:

First, we need to determine how many ounces of beverage were consumed initially. Each glass contains \( \frac{29}{9} \) ounces, and \( \frac{26}{25} \) of these glasses were consumed.

To find the total ounces consumed initially, we multiply:
\[
\frac{29}{9} \times \frac{26}{25} = \frac{29 \times 26}{9 \times 25} = \frac{754}{225}
\]

Next, we need to add the additional \( \frac{2}{19} \) ounces consumed later:
\[
\frac{754}{225} + \frac{2}{19}
\]

To add these fractions, we need a common denominator. The least common multiple of 225 and 19 is 4275. We convert each fraction to have this common denominator:
\[
\frac{754}{225} = \frac{754 \times 19}{225 \times 19} = \frac{14326}{4275}
\]
\[
\frac{2}{19} = \frac{2 \times 225}{19 \times 225} = \frac{450}{4275}
\]

Now, we add the fractions:
\[
\frac{14326}{4275} + \frac{450}{4275} = \frac{14326 + 450}{4275} = \frac{14776}{4275}
\]

Thus, the total ounces of beverages consumed at the party is:
\[
\frac{14776}{4275}
\]

### Answer: \(\frac{14776}{4275}\) ounces

Expected answer: 14776/4275

Correct? Yes

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?

GPT-4o:

Let's break down the problem step by step.

1. **Initial Addition to Collection:**
   You add \( \frac{7}{15} \) of a new set of toothbrushes to your current collection.

2. **Gift from Friend:**
   Your friend gifts you 9 more sets of toothbrushes.

3. **Total Sets Before Display Case Limitation:**
   The total number of sets you have is:
   \[
   \frac{7}{15} + 9
   \]
   To add these, we need a common denominator. The fraction \( \frac{7}{15} \) can be converted to a fraction with a denominator of 15:
   \[
   9 = \frac{135}{15}
   \]
   So, adding these together:
   \[
   \frac{7}{15} + \frac{135}{15} = \frac{142}{15}
   \]

4. **Fitting in the Display Case:**
   You can fit \( \frac{26}{27} \) of the total sets in your display case. Therefore, the number of sets you can fit is:
   \[
   \frac{26}{27} \times \frac{142}{15}
   \]
   Multiply the numerators and the denominators:
   \[
   \frac{26 \times 142}{27 \times 15} = \frac{3692}{405}
   \]

5. **Simplifying the Fraction:**
   To simplify \( \frac{3692}{405} \), we find the greatest common divisor (GCD) of 3692 and 405. The GCD is 1, so the fraction is already in its simplest form.

6. **Converting to a Mixed Number:**
   Divide 3692 by 405:
   \[
   3692 \div 405 \approx 9.11
   \]
   Since we are dealing with sets of toothbrushes, we consider the integer part of the division:
   \[
   9 \text{ sets}
   \]

### Answer: 9

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.

GPT-4o:

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

The weight of the empty backpack is \( \frac{27}{20} \) kilograms.
The weight of the book is \( \frac{1}{6} \) kilograms.

First, we need a common denominator to add these fractions. The least common multiple of 20 and 6 is 60.

Convert \( \frac{27}{20} \) to a fraction with a denominator of 60:
\[ \frac{27}{20} = \frac{27 \times 3}{20 \times 3} = \frac{81}{60} \]

Convert \( \frac{1}{6} \) to a fraction with a denominator of 60:
\[ \frac{1}{6} = \frac{1 \times 10}{6 \times 10} = \frac{10}{60} \]

Now, add the two fractions:
\[ \frac{81}{60} + \frac{10}{60} = \frac{81 + 10}{60} = \frac{91}{60} \]

The total weight of the backpack is \( \frac{91}{60} \) kilograms.

### Answer: \(\frac{91}{60}\)

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?

GPT-4o:

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

First, simplify the fraction \(\frac{7}{7}\):
\[
\frac{7}{7} = 1
\]

Next, multiply this result by the second fraction \(\frac{25}{22}\):
\[
1 \times \frac{25}{22} = \frac{25}{22}
\]

Thus, the multiplier of the new bottle compared to the old one is \(\frac{25}{22}\).

### Answer: \(\frac{25}{22}\)

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.

GPT-4o:

To find the total amount of food Turtle Tilly has gathered, we need to add all the fractions together. The fractions are:

\[
\frac{25}{9}, \frac{8}{13}, \frac{24}{27}, \frac{21}{26}
\]

First, we need to find a common denominator for these fractions. The denominators are 9, 13, 27, and 26. The least common multiple (LCM) of these numbers is 6318.

Next, we convert each fraction to have the common denominator of 6318:

1. \(\frac{25}{9}\):
\[
\frac{25}{9} = \frac{25 \times 702}{9 \times 702} = \frac{17550}{6318}
\]

2. \(\frac{8}{13}\):
\[
\frac{8}{13} = \frac{8 \times 486}{13 \times 486} = \frac{3888}{6318}
\]

3. \(\frac{24}{27}\):
\[
\frac{24}{27} = \frac{24 \times 234}{27 \times 234} = \frac{5616}{6318}
\]

4. \(\frac{21}{26}\):
\[
\frac{21}{26} = \frac{21 \times 243}{26 \times 243} = \frac{5103}{6318}
\]

Now, we add these fractions together:

\[
\frac{17550}{6318} + \frac{3888}{6318} + \frac{5616}{6318} + \frac{5103}{6318} = \frac{17550 + 3888 + 5616 + 5103}{6318} = \frac{32157}{6318}
\]

To simplify \(\frac{32157}{6318}\), we find the greatest common divisor (GCD) of 32157 and 6318. The GCD is 3.

\[
\frac{32157 \div 3}{6318 \div 3} = \frac{10719}{2106}
\]

We simplify further by finding the GCD of 10719 and 2106, which is 3.

\[
\frac{10719 \div 3}{2106 \div 3} = \frac{3573}{702}
\]

We simplify further by finding the GCD of 3573 and 702, which is 3.

\[
\frac{3573 \div 3}{702 \div 3} = \frac{1191}{234}
\]

We simplify further by finding the GCD of 1191 and 234, which is 3.

\[
\frac{1191 \div 3}{234 \div 3} = \frac{397}{78}
\]

Thus, the simplified fraction is:

### Answer: \(\frac{397}{78}\)

Expected answer: 397/78

Correct? Yes

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.

GPT-4o:

Let's break down the problem step by step.

1. **Calculate the difference in distance to the island:**
   - Distance to the island: \( \frac{17}{2} \) nautical miles
   - Current distance from the island: \( \frac{4}{2} \) nautical miles

   The difference in distance is:
   \[
   \frac{17}{2} - \frac{4}{2} = \frac{13}{2} \text{ nautical miles}
   \]

2. **Adjust for the tide:**
   - Tide adjustment: \( \frac{14}{9} \) nautical miles

   Adding this to the previous distance:
   \[
   \frac{13}{2} + \frac{14}{9}
   \]

   To add these fractions, we need a common denominator. The least common multiple of 2 and 9 is 18.

   Convert each fraction:
   \[
   \frac{13}{2} = \frac{13 \times 9}{2 \times 9} = \frac{117}{18}
   \]
   \[
   \frac{14}{9} = \frac{14 \times 2}{9 \times 2} = \frac{28}{18}
   \]

   Now add the fractions:
   \[
   \frac{117}{18} + \frac{28}{18} = \frac{145}{18} \text{ nautical miles}
   \]

3. **Calculate fuel requirements:**
   - Fuel efficiency: \( \frac{22}{15} \) nautical miles per gallon

   Multiply the adjusted distance by the fuel efficiency rate:
   \[
   \frac{145}{18} \times \frac{15}{22}
   \]

   Simplify the multiplication:
   \[
   \frac{145 \times 15}{18 \times 22} = \frac{2175}{396}
   \]

   Simplify the fraction by finding the greatest common divisor (GCD) of 2175 and 396. The GCD is 3.

   Divide both the numerator and the denominator by 3:
   \[
   \frac{2175 \div 3}{396 \div 3} = \frac{725}{132}
   \]

   Therefore, Captain Alf’s final calculation for the fuel requirement is:
   \[
   \frac{725}{132} \text{ gallons}
   \]

### Answer: \(\frac{725}{132}\) gallons

Expected answer: 319/27

Correct? No

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?

GPT-4o:

To determine how many miles the forest ranger patrolled in the afternoon, we start by calculating the distance he patrolled in the morning, which is given as \( \frac{14}{3} \) miles.

Next, we need to find the distance he patrolled in the afternoon, which is \( \frac{2}{18} \) mile less than the morning distance. First, simplify \( \frac{2}{18} \):

\[
\frac{2}{18} = \frac{1}{9}
\]

Now, subtract \( \frac{1}{9} \) from \( \frac{14}{3} \). To do this, we need a common denominator. The least common multiple of 3 and 9 is 9. Convert \( \frac{14}{3} \) to a fraction with a denominator of 9:

\[
\frac{14}{3} = \frac{14 \times 3}{3 \times 3} = \frac{42}{9}
\]

Now, subtract \( \frac{1}{9} \) from \( \frac{42}{9} \):

\[
\frac{42}{9} - \frac{1}{9} = \frac{42 - 1}{9} = \frac{41}{9}
\]

Thus, the forest ranger patrolled \( \frac{41}{9} \) miles in the afternoon.

### Answer: \(\frac{41}{9}\) 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?

GPT-4o:

To find the total time Arthur spends practicing the piano each day on the weekend, we need to add the time he practices daily to the additional time he practices on weekends.

Arthur practices daily for \( \frac{20}{21} \) of an hour. On weekends, he practices an additional \( \frac{11}{29} \) of an hour.

First, we need to find a common denominator to add these fractions. The least common multiple (LCM) of 21 and 29 is 609.

Convert \( \frac{20}{21} \) to a fraction with a denominator of 609:
\[ \frac{20}{21} = \frac{20 \times 29}{21 \times 29} = \frac{580}{609} \]

Convert \( \frac{11}{29} \) to a fraction with a denominator of 609:
\[ \frac{11}{29} = \frac{11 \times 21}{29 \times 21} = \frac{231}{609} \]

Now, add the two fractions:
\[ \frac{580}{609} + \frac{231}{609} = \frac{580 + 231}{609} = \frac{811}{609} \]

Thus, Arthur spends \( \frac{811}{609} \) hours practicing the piano each day on the weekend.

### Answer: \( \frac{811}{609} \) hours

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.

GPT-4o:

First, let's determine how many shirts each sibling initially received. Lucas had 18 shirts and divided them equally among his 3 siblings:

\[
\frac{18}{3} = 6
\]

So, each sibling initially received 6 shirts.

Next, Lucas bought 27 more shirts and decided to keep only \(\frac{1}{19}\) of those shirts for each sibling. We need to calculate how many shirts each sibling received from the new batch:

\[
\frac{27}{19}
\]

Now, we need to find the difference in the number of shirts each sibling has now compared to before. This is given by the expression:

\[
\left( \frac{18}{3} \right) - \left( \frac{27}{19} \right)
\]

Substituting the values we calculated:

\[
6 - \frac{27}{19}
\]

To perform this subtraction, we need a common denominator. The common denominator for 6 and \(\frac{27}{19}\) is 19. We convert 6 to a fraction with a denominator of 19:

\[
6 = \frac{6 \times 19}{19} = \frac{114}{19}
\]

Now, we subtract the fractions:

\[
\frac{114}{19} - \frac{27}{19} = \frac{114 - 27}{19} = \frac{87}{19}
\]

Finally, we simplify \(\frac{87}{19}\):

\[
\frac{87}{19} = 4.578947368421053
\]

So, each sibling now has approximately 4.58 fewer shirts compared to before.

### Answer: 4.58 fewer shirts

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?

GPT-4o:

First, let's determine the total amount of light blue paint the painter initially made by mixing the white and blue paint.

The painter mixed:
- 7 gallons of white paint
- 2/5 gallon of blue paint

Total initial amount of light blue paint:
\[ 7 + \frac{2}{5} \]

To add these, we need a common denominator. The common denominator for 1 and 5 is 5. So, we convert 7 to a fraction with a denominator of 5:
\[ 7 = \frac{35}{5} \]

Now, add the fractions:
\[ \frac{35}{5} + \frac{2}{5} = \frac{37}{5} \]

So, the total initial amount of light blue paint is:
\[ \frac{37}{5} \text{ gallons} \]

Next, the painter used \( \frac{18}{4} \) gallons of the light blue paint. Simplify \( \frac{18}{4} \):
\[ \frac{18}{4} = \frac{9}{2} \]

Convert \( \frac{9}{2} \) to a fraction with a denominator of 5 to subtract from \( \frac{37}{5} \):
\[ \frac{9}{2} = \frac{9 \times 5}{2 \times 5} = \frac{45}{10} \]

Convert \( \frac{37}{5} \) to a fraction with a denominator of 10:
\[ \frac{37}{5} = \frac{37 \times 2}{5 \times 2} = \frac{74}{10} \]

Now, subtract the fractions:
\[ \frac{74}{10} - \frac{45}{10} = \frac{74 - 45}{10} = \frac{29}{10} \]

So, the painter has \( \frac{29}{10} \) gallons of light blue paint left. Converting this to a decimal:
\[ \frac{29}{10} = 2.9 \]

### 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?

GPT-4o:

To find the total number of hours Jayson spent skating over the two days, we need to add the hours he skated on each day.

First, let's convert the fractions to a common denominator to make the addition easier.

For the first day:
\[ \frac{24}{7} \]

For the second day:
\[ \frac{30}{20} \]

We can simplify \(\frac{30}{20}\):
\[ \frac{30}{20} = \frac{3}{2} \]

Now, we need to add \(\frac{24}{7}\) and \(\frac{3}{2}\). To do this, we need a common denominator. The least common multiple of 7 and 2 is 14.

Convert \(\frac{24}{7}\) to a fraction with a denominator of 14:
\[ \frac{24}{7} = \frac{24 \times 2}{7 \times 2} = \frac{48}{14} \]

Convert \(\frac{3}{2}\) to a fraction with a denominator of 14:
\[ \frac{3}{2} = \frac{3 \times 7}{2 \times 7} = \frac{21}{14} \]

Now, add the two fractions:
\[ \frac{48}{14} + \frac{21}{14} = \frac{48 + 21}{14} = \frac{69}{14} \]

So, the total number of hours Jayson spent skating over the two days is:
\[ \frac{69}{14} \]

### Answer: \(\frac{69}{14}\) hours

Expected answer: 69/14

Correct? Yes

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?

GPT-4o:

First, we need to determine the usual height a dolphin can leap out of the water. This is given by the expression \( \frac{18}{3} \).

\[
\frac{18}{3} = 6 \text{ feet}
\]

Next, we need to find out how high the dolphin jumped when it managed only \( \frac{3}{4} \) of its usual height. We calculate this by multiplying the usual height by \( \frac{3}{4} \).

\[
6 \times \frac{3}{4} = 6 \times 0.75 = 4.5 \text{ feet}
\]

### 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.

GPT-4o:

To solve this problem, we need to calculate two ratios and then multiply them together.

First, let's find the ratio of last month's sales to production. This ratio is given by the sum of two fractions:
\[ \frac{20}{15} + \frac{16}{22} \]

We can simplify each fraction individually:
\[ \frac{20}{15} = \frac{4}{3} \]
\[ \frac{16}{22} = \frac{8}{11} \]

Now, we need to add these two fractions. To do this, we need a common denominator. The least common multiple of 3 and 11 is 33:
\[ \frac{4}{3} = \frac{4 \times 11}{3 \times 11} = \frac{44}{33} \]
\[ \frac{8}{11} = \frac{8 \times 3}{11 \times 3} = \frac{24}{33} \]

Adding these fractions together:
\[ \frac{44}{33} + \frac{24}{33} = \frac{44 + 24}{33} = \frac{68}{33} \]

Next, let's find the ratio of interested customers to production for this week:
\[ \frac{22}{27} \times \frac{23}{8} \]

We multiply these fractions directly:
\[ \frac{22 \times 23}{27 \times 8} = \frac{506}{216} \]

Now, we multiply the two results together:
\[ \frac{68}{33} \times \frac{506}{216} = \frac{68 \times 506}{33 \times 216} = \frac{34408}{7128} \]

Thus, the result when she multiplies the ratio of last month's sales to production and this week's figure for the ratio of interested customers to production is:
### Answer: \(\frac{34408}{7128}\)

Expected answer: 391/81

Correct? Yes

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?

GPT-4o:

First, we need to determine the time spent on each song during the practice session. The total time spent is 30 minutes, and this time is divided equally among 15 songs.

To find the time spent on each song, we divide the total time by the number of songs:
\[
\text{Time per song} = \frac{30 \text{ minutes}}{15 \text{ songs}} = 2 \text{ minutes per song}
\]

Next, we need to convert the time per song into hours since the reduction is given in hours. There are 60 minutes in an hour, so:
\[
2 \text{ minutes} = \frac{2}{60} \text{ hours} = \frac{1}{30} \text{ hours}
\]

The band reduced the time spent on a particular song by \(\frac{1}{17}\) of an hour. We need to subtract this reduction from the original time per song:
\[
\text{Final duration} = \frac{1}{30} \text{ hours} - \frac{1}{17} \text{ hours}
\]

To perform this subtraction, we need a common denominator. The least common multiple of 30 and 17 is 510. We convert both fractions to have this common denominator:
\[
\frac{1}{30} = \frac{17}{510}
\]
\[
\frac{1}{17} = \frac{30}{510}
\]

Now we subtract the fractions:
\[
\frac{17}{510} - \frac{30}{510} = \frac{17 - 30}{510} = \frac{-13}{510} = -\frac{13}{510}
\]

Since we are dealing with time, we should consider the absolute value:
\[
\left| -\frac{13}{510} \right| = \frac{13}{510}
\]

Simplifying \(\frac{13}{510}\):
\[
\frac{13}{510} = \frac{1}{39.23} \approx 0.0255 \text{ hours}
\]

Converting this back to minutes:
\[
0.0255 \text{ hours} \times 60 \text{ minutes/hour} \approx 1.53 \text{ minutes}
\]

### Answer: 1.53 minutes

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.

GPT-4o:

First, let's convert the hours Josh rode the scooter into a fraction. Josh rode the scooter for 18 hours and an additional \( \frac{1}{12} \) of an hour. 

To combine these, we need to express 18 as a fraction with a common denominator of 12:
\[ 18 = \frac{18 \times 12}{12} = \frac{216}{12} \]

Adding the additional \( \frac{1}{12} \) hour:
\[ \frac{216}{12} + \frac{1}{12} = \frac{216 + 1}{12} = \frac{217}{12} \]

Next, we consider the time Jack rode the scooter, which is \( \frac{7}{17} \) of an hour.

To find the total time both Josh and Jack rode the scooters, we need to add \( \frac{217}{12} \) and \( \frac{7}{17} \). To do this, we need a common denominator. The least common multiple (LCM) of 12 and 17 is 204.

Convert both fractions to have the denominator of 204:
\[ \frac{217}{12} = \frac{217 \times 17}{12 \times 17} = \frac{3689}{204} \]
\[ \frac{7}{17} = \frac{7 \times 12}{17 \times 12} = \frac{84}{204} \]

Now, add the two fractions:
\[ \frac{3689}{204} + \frac{84}{204} = \frac{3689 + 84}{204} = \frac{3773}{204} \]

The fraction \( \frac{3773}{204} \) is already in its simplest form because 3773 and 204 have no common factors other than 1.

### Answer: \(\frac{3773}{204}\)

Expected answer: 3773/204

Correct? Yes

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?

GPT-4o:

To find the total fraction of the lamps in the store, we need to add the fractions of each type of lamp together. The fractions given are:

- Floor lamps: \(\frac{4}{26}\)
- Desk lamps: \(\frac{15}{11}\)
- Table lamps: \(\frac{23}{28}\)
- Decorative lamps: \(\frac{8}{19}\)

First, we simplify the fractions where possible:

\[
\frac{4}{26} = \frac{2}{13}
\]

Next, we add the fractions together. To do this, we need a common denominator. The least common multiple (LCM) of 13, 11, 28, and 19 is 7604. We convert each fraction to have this common denominator:

\[
\frac{2}{13} = \frac{2 \times 584}{13 \times 584} = \frac{1168}{7604}
\]

\[
\frac{15}{11} = \frac{15 \times 691}{11 \times 691} = \frac{10365}{7604}
\]

\[
\frac{23}{28} = \frac{23 \times 271}{28 \times 271} = \frac{6233}{7604}
\]

\[
\frac{8}{19} = \frac{8 \times 400}{19 \times 400} = \frac{3200}{7604}
\]

Now, we add these fractions together:

\[
\frac{1168}{7604} + \frac{10365}{7604} + \frac{6233}{7604} + \frac{3200}{7604} = \frac{1168 + 10365 + 6233 + 3200}{7604} = \frac{20966}{7604}
\]

We simplify the resulting fraction:

\[
\frac{20966}{7604} = \frac{20966 \div 2}{7604 \div 2} = \frac{10483}{3802}
\]

Since 10483 and 3802 have no common factors other than 1, the fraction is already in its simplest form.

### Answer: \(\frac{10483}{3802}\)

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.

GPT-4o:

First, we need to add the lengths of the two kite strings.

The lengths of the kite strings are:
\[ \frac{26}{19} \text{ meters} \]
\[ \frac{7}{11} \text{ meters} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 19 and 11 is 209.

Convert each fraction to have the common denominator of 209:
\[ \frac{26}{19} = \frac{26 \times 11}{19 \times 11} = \frac{286}{209} \]
\[ \frac{7}{11} = \frac{7 \times 19}{11 \times 19} = \frac{133}{209} \]

Now, add the fractions:
\[ \frac{286}{209} + \frac{133}{209} = \frac{286 + 133}{209} = \frac{419}{209} \]

Next, Oliver decides to use only \(\frac{5}{8}\) of this combined string. We need to multiply \(\frac{419}{209}\) by \(\frac{5}{8}\):
\[ \frac{419}{209} \times \frac{5}{8} = \frac{419 \times 5}{209 \times 8} = \frac{2095}{1672} \]

Thus, the length of the kite string that Oliver is using now is:
### Answer: \(\frac{2095}{1672}\) meters.

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

GPT-4o:

To solve the problem, we need to find the total number of snowballs Mike had after finding more. We will solve the given equations step by step.

First, let's solve for \( u \):

\[ u = \frac{9}{19} + \frac{6}{8} \]

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

Convert each fraction to have a denominator of 152:

\[ \frac{9}{19} = \frac{9 \times 8}{19 \times 8} = \frac{72}{152} \]
\[ \frac{6}{8} = \frac{6 \times 19}{8 \times 19} = \frac{114}{152} \]

Now add the fractions:

\[ u = \frac{72}{152} + \frac{114}{152} = \frac{72 + 114}{152} = \frac{186}{152} \]

Simplify the fraction:

\[ \frac{186}{152} = \frac{93}{76} \]

So, \( u = \frac{93}{76} \).

Next, we need to find \( j \):

\[ j = u + \frac{4}{1} \]

Substitute \( u \) with \( \frac{93}{76} \):

\[ j = \frac{93}{76} + \frac{4}{1} \]

Convert \( \frac{4}{1} \) to have a denominator of 76:

\[ \frac{4}{1} = \frac{4 \times 76}{1 \times 76} = \frac{304}{76} \]

Now add the fractions:

\[ j = \frac{93}{76} + \frac{304}{76} = \frac{93 + 304}{76} = \frac{397}{76} \]

So, the total number of snowballs Mike had after finding more is:

### Answer: \(\frac{397}{76}\)

Expected answer: 397/76

Correct? Yes

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

GPT-4o:

To determine the total amount of chocolate both workers can package in one minute, we need to find their individual rates and then sum them up.

First, let's find the rate for the first worker:
- The first worker packages 26 pieces of chocolate in 18 minutes.
- The rate of the first worker is \( \frac{26 \text{ pieces}}{18 \text{ minutes}} \).

To find the rate per minute, we divide 26 by 18:
\[ \frac{26}{18} = \frac{13}{9} \text{ pieces per minute} \]

Next, let's find the rate for the second worker:
- The second worker packages 15 pieces of chocolate in 15 minutes.
- The rate of the second worker is \( \frac{15 \text{ pieces}}{15 \text{ minutes}} \).

To find the rate per minute, we divide 15 by 15:
\[ \frac{15}{15} = 1 \text{ piece per minute} \]

Now, we sum the rates of both workers to find the total amount of chocolate they can package in one minute:
\[ \frac{13}{9} + 1 = \frac{13}{9} + \frac{9}{9} = \frac{22}{9} \text{ pieces per minute} \]

### Answer: \(\frac{22}{9}\) 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.

GPT-4o:

First, we need to simplify the fractions for the number of batches Joanna washed.

For the small towels:
\[ \frac{24}{20} = \frac{24 \div 4}{20 \div 4} = \frac{6}{5} \]

For the large towels:
\[ \frac{25}{15} = \frac{25 \div 5}{15 \div 5} = \frac{5}{3} \]

Next, we add the simplified fractions to find the total number of batches:
\[ \frac{6}{5} + \frac{5}{3} \]

To add these fractions, we need a common denominator. The least common multiple of 5 and 3 is 15.

Convert each fraction to have a denominator of 15:
\[ \frac{6}{5} = \frac{6 \times 3}{5 \times 3} = \frac{18}{15} \]
\[ \frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15} \]

Now, add the fractions:
\[ \frac{18}{15} + \frac{25}{15} = \frac{18 + 25}{15} = \frac{43}{15} \]

### Answer: \(\frac{43}{15}\)

Expected answer: 43/15

Correct? Yes

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?

GPT-4o:

Let's break down the problem step by step.

1. Calculate the amount of flour and sugar in the first recipe:
   - Flour: \( \frac{27}{3} = 9 \) cups
   - Sugar: \( \frac{11}{7} \) cups

2. Determine the ratio of flour to sugar:
   \[
   \text{Ratio} = \frac{\text{Flour}}{\text{Sugar}} = \frac{9}{\frac{11}{7}} = 9 \times \frac{7}{11} = \frac{63}{11}
   \]

3. Subtract \( \frac{21}{26} \) from this ratio:
   \[
   \frac{63}{11} - \frac{21}{26}
   \]

   To subtract these fractions, we need a common denominator. The least common multiple of 11 and 26 is 286.

   Convert each fraction to have the common denominator:
   \[
   \frac{63}{11} = \frac{63 \times 26}{11 \times 26} = \frac{1638}{286}
   \]
   \[
   \frac{21}{26} = \frac{21 \times 11}{26 \times 11} = \frac{231}{286}
   \]

   Now subtract the fractions:
   \[
   \frac{1638}{286} - \frac{231}{286} = \frac{1407}{286}
   \]

4. Simplify the fraction \( \frac{1407}{286} \):
   \[
   \frac{1407 \div 13}{286 \div 13} = \frac{108.23}{22} \approx 4.92
   \]

5. Add \( \frac{22}{9} \) cups of flour from the second recipe to the new ratio:
   \[
   4.92 + \frac{22}{9}
   \]

   Convert \( \frac{22}{9} \) to a decimal:
   \[
   \frac{22}{9} \approx 2.44
   \]

   Add the two values:
   \[
   4.92 + 2.44 = 7.36
   \]

### Answer: 7.36

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?

GPT-4o:

First, let's calculate the number of chickens in each farm.

For the first farm:
\[
\frac{26}{13} = 2 \text{ chickens}
\]

For the second farm:
\[
\frac{9}{16} \text{ chickens}
\]

Next, we find the difference between the number of chickens in the two farms:
\[
2 - \frac{9}{16}
\]

To subtract these fractions, we need a common denominator. The common denominator for 2 (which is \(\frac{32}{16}\)) and \(\frac{9}{16}\) is 16:
\[
2 = \frac{32}{16}
\]

So, the difference is:
\[
\frac{32}{16} - \frac{9}{16} = \frac{23}{16} \text{ chickens}
\]

After a week, the number of chickens multiplied by \(\frac{19}{21}\):
\[
\frac{23}{16} \times \frac{19}{21} = \frac{23 \times 19}{16 \times 21} = \frac{437}{336}
\]

To simplify \(\frac{437}{336}\), we check for common factors. Since 437 and 336 have no common factors other than 1, the fraction is already in its simplest form.

### Answer: \(\frac{437}{336}\)

Expected answer: 437/336

Correct? Yes

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'?

GPT-4o:

First, let's identify the distance flown for each exercise, which is given as \( w = \frac{24}{14} \) miles.

To simplify \( w \):
\[ w = \frac{24}{14} = \frac{12}{7} \]

The total distance flown for both exercises is represented as the product of \( w \) times \( w \):
\[ t = w \times w \]

Substituting \( w \) with \( \frac{12}{7} \):
\[ t = \left( \frac{12}{7} \right) \times \left( \frac{12}{7} \right) \]
\[ t = \frac{12 \times 12}{7 \times 7} \]
\[ t = \frac{144}{49} \]

### Answer: \(\frac{144}{49}\)

Expected answer: 144/49

Correct? Yes

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

GPT-4o:

To find the total fraction of the tank that the UFO refilled during the two stops, we need to add the fractions from each stop.

First refuel: \(\frac{20}{16}\)
Second refuel: \(\frac{24}{25}\)

First, simplify \(\frac{20}{16}\):
\[
\frac{20}{16} = \frac{5}{4}
\]

Now, we need to add \(\frac{5}{4}\) and \(\frac{24}{25}\). To do this, we need a common denominator. The least common multiple of 4 and 25 is 100.

Convert \(\frac{5}{4}\) to a fraction with a denominator of 100:
\[
\frac{5}{4} = \frac{5 \times 25}{4 \times 25} = \frac{125}{100}
\]

Convert \(\frac{24}{25}\) to a fraction with a denominator of 100:
\[
\frac{24}{25} = \frac{24 \times 4}{25 \times 4} = \frac{96}{100}
\]

Now, add the two fractions:
\[
\frac{125}{100} + \frac{96}{100} = \frac{125 + 96}{100} = \frac{221}{100}
\]

Thus, the total fraction of the tank that the UFO refilled during the two stops is:
\[
\frac{221}{100}
\]

### Answer: \(\frac{221}{100}\)

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?

GPT-4o:

To find the sum of the two fractions \(\frac{24}{27}\) and \(\frac{30}{26}\), we first need to find a common denominator. The denominators are 27 and 26, and their least common multiple (LCM) is 27 * 26 = 702.

Next, we convert each fraction to have this common denominator:

1. Convert \(\frac{24}{27}\):
\[
\frac{24}{27} = \frac{24 \times 26}{27 \times 26} = \frac{624}{702}
\]

2. Convert \(\frac{30}{26}\):
\[
\frac{30}{26} = \frac{30 \times 27}{26 \times 27} = \frac{810}{702}
\]

Now, we add the two fractions:
\[
\frac{624}{702} + \frac{810}{702} = \frac{624 + 810}{702} = \frac{1434}{702}
\]

To simplify \(\frac{1434}{702}\), we find the greatest common divisor (GCD) of 1434 and 702. Using the Euclidean algorithm:

1. \(1434 \div 702 = 2\) with a remainder of \(1434 - 2 \times 702 = 30\)
2. \(702 \div 30 = 23\) with a remainder of \(702 - 23 \times 30 = 12\)
3. \(30 \div 12 = 2\) with a remainder of \(30 - 2 \times 12 = 6\)
4. \(12 \div 6 = 2\) with a remainder of \(12 - 2 \times 6 = 0\)

The GCD is 6. We divide both the numerator and the denominator by 6:
\[
\frac{1434 \div 6}{702 \div 6} = \frac{239}{117}
\]

Thus, the simplified sum of the fractions is:
\[
\frac{239}{117}
\]

### Answer: \(\frac{239}{117}\)

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.

GPT-4o:

To find the total number of bananas Kiki ate, we need to add the amount she ate in the morning to the amount she ate in the afternoon.

Kiki ate \( \frac{11}{6} \) bananas in the morning and \( \frac{11}{6} \) bananas in the afternoon.

To find the total, we add these two fractions:
\[
\frac{11}{6} + \frac{11}{6}
\]

Since the denominators are the same, we can simply add the numerators:
\[
\frac{11 + 11}{6} = \frac{22}{6}
\]

Thus, Kiki ate \( \frac{22}{6} \) bananas in total.

### Answer: \(\frac{22}{6}\)

Expected answer: 11/3

Correct? Yes

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

GPT-4o:

To find out how much milk Jaden gets from one cow in one day, we need to multiply the two fractions representing the morning and evening milk yields.

First, let's simplify the fractions if possible:
- The morning yield is \( \frac{26}{14} \). We can simplify this by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
  \[
  \frac{26}{14} = \frac{26 \div 2}{14 \div 2} = \frac{13}{7}
  \]

- The evening yield is \( \frac{28}{20} \). We can simplify this by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
  \[
  \frac{28}{20} = \frac{28 \div 4}{20 \div 4} = \frac{7}{5}
  \]

Now, we multiply the simplified fractions:
\[
\frac{13}{7} \times \frac{7}{5}
\]

When multiplying fractions, we multiply the numerators together and the denominators together:
\[
\frac{13 \times 7}{7 \times 5} = \frac{91}{35}
\]

Next, we simplify \( \frac{91}{35} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 7:
\[
\frac{91}{35} = \frac{91 \div 7}{35 \div 7} = \frac{13}{5}
\]

Thus, Jaden gets \( \frac{13}{5} \) gallons of milk from one cow in one day.

### Answer: \(\frac{13}{5}\) gallons

Expected answer: 13/5

Correct? Yes