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?

Gemini-1.5 Pro:

Reasoning: Initially, Carla expected to grow (22/3)*(22/19) = (22*22)/(3*19) = 484/57 cucumbers per plant. 
After adjusting her production, she expects to grow (484/57)*(23/17) = (484*23)/(57*17) = 11132/969 cucumbers per plant.
We can simplify 11132/969 to 1236/107
### Answer: 1236/107 

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?

Gemini-1.5 Pro:

Reasoning: 
First find how many kg of grapes Pierre had left after eating some: 19/4 kg - 7/25 kg = (19*25 - 7*4)/(4*25) kg = (475-28)/100 kg = 447/100 kg
Then add the amount his mother gave him to find the total amount he has: 447/100 kg + 30/9 kg = (447*9 + 30*100)/(100*9) kg = (4023+3000)/900 kg = 7023/900 kg
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 9: 7023/900 kg = (7023/9)/(900/9) kg = 780.33/100 kg = 7.8033 kg
### Answer: 7.8033 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?

Gemini-1.5 Pro:

Reasoning:  First, find a common denominator for the fractions: 22, 29, and 3. The least common multiple is their product, 1914.
Next, rewrite each fraction with the common denominator: 
* Wall repairs: (26/22) * (87/87) = 2262/1914
* Moat renovations: (4/29) * (66/66) = 264/1914
* Catapults: (11/3) * (638/638) = 7018/1914

Now, add the fractions together: (2262/1914) + (264/1914) + (7018/1914) = 9544/1914

Finally, simplify the fraction: 9544/1914 = 44/9

### Answer: 44/9 

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.

Gemini-1.5 Pro:

Reasoning: First, we need to calculate how much the giraffe eats when it's fed 25/19 lbs, which is (25/19)*(30/26) = 750/494 lbs.
Then we square this amount: (750/494)^2 = 562500/244036 lbs.
Finally, we multiply the squared amount by the regular daily intake to find the weekly amount: (562500/244036) * (25/19) = 14062500/4636684 lbs. This can be simplified by dividing both numerator and denominator by their greatest common divisor, 4, resulting in approximately 3.01 lbs.

### Answer: 3.01 lbs

Expected answer: 52734375/15069223

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To find the total length of materials needed, we need to add the length of the yarn and the length of the beads: (11/3) + (8/30).

First, we need to find a common denominator for the two fractions. The least common denominator for 3 and 30 is 30. To get a denominator of 30 for the first fraction, we multiply both the numerator and denominator by 10: (11/3) * (10/10) = (110/30)

Now we can add the two fractions: (110/30) + (8/30) = (118/30)

Finally, we can simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 2: (118/30) ÷ (2/2) = (59/15). 

Therefore, Lara needs 59/15 feet of materials to make the necklace.

### Answer: 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.

Gemini-1.5 Pro:

Reasoning: Plane A travels 24/11 miles in one minute.
Plane B travels 26/27 miles in one minute. 
To find the difference, we subtract the distance traveled by Plane B from the distance traveled by Plane A:  24/11 - 26/27 
To subtract fractions, we need a common denominator. The least common denominator for 11 and 27 is 297.
We convert both fractions to have a denominator of 297:  (24/11) * (27/27) - (26/27) * (11/11) = 648/297 - 286/297
Now we can subtract: 648/297 - 286/297 = 362/297
This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 1: 362/297 
### Answer: 362/297 miles 

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.

Gemini-1.5 Pro:

Reasoning: Multiplying the fractions together gives us (14 * 25) / (7 * 13) = 350/91
This fraction can be simplified to 50/13, which equals 3 11/13.
### Answer: 3 11/13 pounds. 

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.

Gemini-1.5 Pro:

Reasoning: 12/8 hours is equal to 3/2 hours. To add 3/2 and 12/3, we need to find a common denominator. The least common denominator is 6.  So, 3/2 is equal to 9/6 and 12/3 is equal to 24/6. Finally, 9/6 + 24/6 = 33/6, which simplifies to 11/2. 
### Answer: 11/2 

Expected answer: 11/2

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: You first had $\frac{28}{29}$ of a chocolate bar.
You found $\frac{8}{22}=\frac{4}{11}$ of a chocolate bar.
Therefore, you have a total of $\frac{28}{29} + \frac{4}{11} = \frac{28 \times 11}{29 \times 11} + \frac{4 \times 29}{11 \times 29} = \frac{308}{319} + \frac{116}{319} = \frac{424}{319}$ of a chocolate bar.
### 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?

Gemini-1.5 Pro:

Reasoning: To make two needles, the maker needs 27/26 * 2 = <<27/26*2=54/26>> 54/26 pounds of material. 

The maker needs a total of 54/26 + 27/6 = <<54/26+27/6=271/78>> 271/78 pounds of material.
### Answer: 271/78 pounds 

Expected answer: 171/26

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First, we need to find a common denominator for the two fractions. Both 4 and 16 go into 16, so we'll use that.
6/4 is equivalent to 24/16, so the total rate at which the candles burn is 24/16+14/16 = 38/16 inches per hour. 
Simplifying this fraction, we get 19/8 inches per hour. 
### Answer: 19/8 inches per hour. 

Expected answer: 19/8

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: Sophia has a total of 17/20 + 1/4 = <<17/20+1/4=22/20>> 22/20 dollars after her friend gives her 1/4 dollar.
22/20 dollars is equivalent to 22/20 * $1 = $<<22/20*1=1.10>>1.10. 
So, in total Sophia now has $1.10 + $1 = $<<1.10+1=2.10>>2.10.
### Answer: $2.10

Expected answer: 21/10

Correct? No

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

Gemini-1.5 Pro:

Let's break down the calculation step-by-step:

1. **Calculate the initial time investment (p):**
   - Composing: 16/4 hours = 4 hours
   - Lyrics: 16/29 hours 
   - p = 4 + 16/29 hours

2. **Calculate the total time before the drummer's adjustment (b):**
   - b = p + 28/13 hours
   - b = (4 + 16/29) + 28/13 hours

3. **Calculate the drummer's time reduction:**
   - Reduction: 18/4 hours = 4.5 hours

4. **Calculate the final time spent:**
   - Final time: b - 4.5 hours
   - Final time: ((4 + 16/29) + 28/13) - 4.5 hours 

To get the final answer, let's simplify the expression:

-  ((4 + 16/29) + 28/13) - 4.5 
-  = 4 + 16/29 + 28/13 - 4.5
-  = 16/29 + 28/13 - 0.5 
-  = (208 + 812 - 377) / 377
-  = 643 / 377

### Answer: 643/377 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?

Gemini-1.5 Pro:

Reasoning: 
First, find the total number of dozens of cookies Monica baked: 21/15 + 29/17 = <<21/15+29/17=658/255>>658/255 dozens. 
Then, multiply that number by 7/5 to find the number of dozens she increases her stock by: (658/255) * (7/5) = <<(658/255)*(7/5)=4606/1275>>4606/1275 dozens.
Finally, add that number to the number of dozens she already has to find her total number of dozens: 4606/1275 + 658/255 = <<4606/1275+658/255=7902/1275>>7902/1275 dozens.
### Answer: 7902/1275 dozens

Expected answer: 1848/425

Correct? No

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

Gemini-1.5 Pro:

Reasoning: The chef will have 28 - 26/24 = <<28-26/24=26.9167>>26.9167 kg of sugar left after making one cake.
The chef will then have 26.9167 + 10/6 = <<26.9167+10/6=28.5833>>28.5833 kg of sugar after adding more to their supply. 
### Answer: 28.5833 kg 

Expected answer: 343/12

Correct? No

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

Gemini-1.5 Pro:

Reasoning: Emily watched movies for 16 / 4 = <<16/4=4>>4 hours.
She watched 6 / 3 = <<6/3=2>>2 hours of movies other than the comedy film. 
### 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.

Gemini-1.5 Pro:

Reasoning: Princess Lily ate 10/12 of the apple pie.
She ate 10/29 of the blueberry pie.
Adding the fractions together, she ate 10/12 + 10/29 = 410/72 = 205/174 of the pies (combined).
### Answer: 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.

Gemini-1.5 Pro:

Reasoning: We need to multiply the proportion of colored pencils Marta uses every 11 days (20/11) by the proportion of colored pencils she uses for shading (23/26).
(20/11)*(23/26) = (20*23)/(11*26) = 460/286
Simplifying the fraction, we get 230/143. 
### Answer: 230/143 

Expected answer: 230/143

Correct? Yes

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

Gemini-1.5 Pro:

Let's break down this problem step-by-step.

**Step 1: Calculate indicator i**

* Specimen 1 decreases by 26 out of 6 units, which can be represented as a fraction: 26/6
* Specimen 2 decreases by 25 out of 17 units, represented as a fraction: 25/17 
* To find the ratio (indicator i), divide the first fraction by the second: (26/6) / (25/17) = (26/6) * (17/25) = 221/75

**Step 2: Calculate indicator h**

* Specimen 3 increases by 18 out of 8 units, represented as a fraction: 18/8
* Specimen 4 increases by 17 out of 23 units, represented as a fraction: 17/23
* To find the difference (indicator h), subtract the second fraction from the first: (18/8) - (17/23) = (207/92) - (68/92) = 139/92

**Step 3: Calculate indicator f**

* Multiply indicator i (221/75) by indicator h (139/92): (221/75) * (139/92) = 30719/6900

### Answer: f = 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?

Gemini-1.5 Pro:

Reasoning: First, we simplify the fraction representing the lioness's gestation period: 20/22 = 10/11 of a year.
Then, we calculate the total gestation period for both animals: 10/11 years + 15 years = 15 10/11 years.
Next, we determine the reduction in gestation period for the lioness: (15/20) * (15 10/11) years = 11 1/4 years.
Finally, we subtract the reduction from the initial total gestation period to find the new gestation period for the lioness: 15 10/11 years - 11 1/4 years = 4 29/44 years.
### Answer: 4 29/44 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?

Gemini-1.5 Pro:

Reasoning: 
The area of the original rectangle is (30/7)*(19/6) = <<(30/7)*(19/6)=95/7>> 95/7 square meters.
The area of the similar rectangle is (18/17)*(95/7) = <<(18/17)*(95/7)=1710/119>> 1710/119 square meters.
### Answer: 1710/119 square meters. 

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?

Gemini-1.5 Pro:

Reasoning:
First find the total increase in production: 4/20 tonne = 1/5 tonne
Then, convert 1/5 to a fraction with a denominator of 8: 1/5 * 8/8 = 8/40
Add this increase to the daily production: 23/8 + 8/40 = 115/40 + 8/40 = 123/40 tonnes
Then, convert 19/24 to a fraction with a denominator of 40: 19/24 * 5/5 = 95/120
Simplify the fraction 95/120: 95/120 = 19/24
Then, convert 19/24 to a fraction with a denominator of 40: 19/24 * 5/5 = 95/120
Simplify the fraction 95/120: 95/120 = 19/24
Then, convert 19/24 to a fraction with a denominator of 40: 19/24 * 5/5 = 95/120
Simplify the fraction 95/120 again: 95/120 = 19/24
Finally, subtract this decrease from the increased production: 123/40 - 19/24 = 369/120 - 95/120 = 274/120 tonnes.
Simplify the fraction 274/120: 274/120 = 137/60 tonnes
Thus, the factory produces 137/60 tonnes of soap that day after the adjustments.
### Answer: 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'.

Gemini-1.5 Pro:

Reasoning: 
First, simplify the fractions: 24/8 = 3 gallons and 12/8 = 1.5 gallons.
After the machine pours away some paint: d = 3 - 1.5 = 1.5 gallons
After adding the blue pigment: x = 1.5 - 1/28 = 41/28 gallons

### Answer: 41/28 gallons 

Expected answer: 41/28

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To multiply fractions, we multiply the numerators and the denominators: (27/14) * (17/13) = (27*17) / (14*13). 
Calculating the products, we get: 459 / 182.
### Answer: 459/182 

Expected answer: 459/182

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, find a common denominator for Sonia's and Anthony's toothpaste usage: 21/12 and 6/27. The least common denominator is 108.
Then, convert each fraction to have the denominator of 108:
**(21/12) * (9/9) = 189/108**
**(6/27) * (4/4) = 24/108**

Now, add the fractions representing Sonia's and Anthony's toothpaste usage:
189/108 + 24/108 = 213/108

Next, find a common denominator for the total toothpaste usage by Sonia and Anthony (213/108) and their mom's usage (3/18). The least common denominator is 108.
Convert their mom's toothpaste usage to have a denominator of 108:
**(3/18) * (6/6) = 18/108**

Finally, add this fraction to the fraction representing the total toothpaste usage of Sonia and Anthony to find the total daily usage for the family:
213/108 + 18/108 = 231/108

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 3:
**(231/3)/(108/3) = 77/36**

### Answer: 77/36 

Expected answer: 77/36

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: You used 2/4 or 1/2 of the cheese, which leaves you with (21/14) - (1/2) = (3/2) - (1/2) = 2/2 = 1 wheel of cheese left.
You have 7/18 of the pickle jar left and 1 wheel of cheese, which is a total of (7/18) + 1 = 25/18 of the original ingredients left. 
### Answer: 25/18 

Expected answer: 25/18

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add the height of the windows together, we must first find a common denominator between 15/6 and 7/16.  Both 6 and 16 share a common multiple of 48.  We can see that 15/6 = 120/48, and 7/16 = 21/48.  Adding those together, we see that 120/48 + 21/48 = 141/48, which simplifies to 47/16. 
### Answer: 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?

Gemini-1.5 Pro:

Reasoning:
First, simplify the fractions: 16/6 = 8/3, and 20/12 = 5/3.
Then add the fractions: 8/3 + 5/3 + 2/3 = 15/3
Finally, simplify the result: 15/3 = 5
### 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.

Gemini-1.5 Pro:

Reasoning: Multiply the points per level by the number of levels played to find the total points earned: (4/3)*(13/10) = 52/30
Simplify the fraction by dividing the numerator and denominator by their greatest common factor, 2: 52/30 = (52/2)/(30/2) = 26/15
### Answer: 26/15 

Expected answer: 26/15

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: The astronaut's cycling and experiments take 18/8 + 26/2 = 9/4 + 13 = 61/4 hours.
Adding data review to his routine means it takes 61/4 + 30/8 = 122/8 + 30/8 = 152/8 hours
His whole routine now takes 152/8 = <<152/8=19>>19 hours.
### Answer: 19 

Expected answer: 19

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We are given that Jeremy ordered n = 30/9 ounces of cheese.
We are also given the equation d = n - (17/22) to calculate the actual amount of cheese received, 'd'.
Substituting 'n' in the equation, we get: d = (30/9) - (17/22).
To subtract the fractions, we need a common denominator. The least common denominator for 9 and 22 is 198.
Therefore, d = (660/198) - (153/198) = 507/198.
Simplifying the fraction, Jeremy received 507/198 = 2.56 ounces of cheese.
### Answer: 2.56 ounces 

Expected answer: 169/66

Correct? No

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

Gemini-1.5 Pro:

Reasoning: Let's break down the problem step-by-step:

1. **Initial sunglasses blocking UV:** 13 + 20 + 21 = 54
2. **Total sunglasses:** 4 + 18 + 17 + 30 = 69
3. **Sunglasses NOT blocking UV:** 16
4. **Final sunglasses blocking UV:** 54 - 16 = 38
5. **Final answer as a fraction:** 38/69

### Answer: 38/69 

Expected answer: 15493/3060

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To find the total amount of mayonnaise and sandwich spread Shawn uses to make a sandwich, we add the fractions 23/28 and 6/9.
 
 To add these fractions, we first need to find a common denominator. The least common multiple of 28 and 9 is 252. 

Converting the fractions to have the denominator 252, we get (23 * 9)/(28 * 9) = 207/252 and (6 * 28)/(9 * 28) = 168/252. 

Now, we can add the fractions: 207/252 + 168/252 = 375/252. 

Simplifying the fraction 375/252, we get 125/84.

Therefore, Shawn uses 125/84 cups of mayonnaise and sandwich spread in total to make a sandwich.

To calculate the total amount of ingredients Shawn needs after adding the cheese spread, we add 18/12 to 125/84.

Simplifying 18/12, we get 3/2.

To add 3/2 and 125/84, we need to find a common denominator. The least common multiple of 2 and 84 is 84.

Converting the fraction 3/2 to have the denominator 84, we get (3 * 42) / (2 * 42) = 126/84.

Now, we can add the fractions: 126/84 + 125/84 = 251/84.

Therefore, Shawn needs a total of 251/84 cups of ingredients to make one sandwich. 

Finally, if Shawn has to make an equal number of sandwiches using 4/4 cups of all the ingredients combined, he will use 4/4 cups of ingredients in total to make those sandwiches. 

### Answer: 4/4 

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?

Gemini-1.5 Pro:

Reasoning: Cassandra's initial collection was 7/6 * 21/21 = 147/126 of a key set.
1/21 of a key set is equivalent to 1/21 * 6/6 = 6/126 of a key set.
After her loss, she has 147/126 - 6/126 = 141/126 of a key set.
This is equivalent to 1 15/126, which simplifies to 1 5/42 of a key set.
### Answer: 1 5/42 

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.

Gemini-1.5 Pro:

Reasoning: 
First, find the sum of the ratios of the first two sections: 29/23 + 19/17 = 816/391
Then, express the ratio of the rest as a fraction with the same denominator as the sum of the ratios of the first two sections: 26/26 = 391/391
Finally, subtract the ratio of the rest from the sum of the ratios of the first two sections: 816/391 - 391/391 = 425/391
### Answer: 425/391

Expected answer: 539/391

Correct? No

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

Gemini-1.5 Pro:

Reasoning: Multiplying fractions involves multiplying the numerators and the denominators:  (22/25) * (22/8) = (22 * 22) / (25 * 8) 
This simplifies to 484/200.
### Answer: 484/200 

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.

Gemini-1.5 Pro:

Reasoning: First, find the total length of the pillow after fluffing: 23/9 + 22/25 = (575 + 198)/225 = 773/225 feet.
Then, multiply the total length by 16/13 to account for the overlap and corners: (773/225) * (16/13) = 12368/2925 feet.
This fraction can be simplified to 49472/11700, and further to 12368/2925, which equals 4 648/2925.
### Answer: 4 648/2925 feet 

Expected answer: 12368/2925

Correct? No

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

Gemini-1.5 Pro:

Reasoning: We need to find the difference between the extra distance the car was supposed to travel (16/13 miles) and the actual additional distance it traveled (1/21 miles), which is (16/13 - 1/21) miles. 
Then we multiply this difference by the car's average speed of 21/4 miles per hour to find the total additional distance the car was supposed to travel: (16/13 - 1/21) * (21/4) = ((16*21 - 1*13)/(13*21))*(21/4) = (323/273)*(21/4) = (323/52) miles
### Answer: 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?

Gemini-1.5 Pro:

Reasoning: 
First find the total initial time required for editing and typesetting: 20/5 hours + 18/17 hours = (340 + 90)/85 hours = 430/85 hours = 5.06 hours. 

Now, subtract the break delay to get the reduced time: 5.06 hours - 6/15 hours = 5.06 hours - .4 hours = 4.66 hours

The manager extends this reduced time by the initial total time: 4.66 hours + 5.06 hours = 9.72 hours

Finally, multiply this extended time by the initial total time to get the total extended time: 9.72 hours * 5.06 hours = 49.22 hours

### Answer: 49.22 hours 

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?

Gemini-1.5 Pro:

Reasoning: Jenny's total yield is (13/11)*(21/3) =  << (13/11)*(21/3) = 91/11 >> 91/11 bushels.
In total, Jenny makes (91/11)*(21/15) =  << (91/11)*(21/15) = 133/5 >> 133/5 dollars by selling her potatoes.
### Answer: 133/5 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?

Gemini-1.5 Pro:

Reasoning: 14/28 kg is equal to 1/2 kg.
1/2 + 13/26 = 26/52 + 13/26 = 39/52 kg
### Answer: 39/52 kg 

Expected answer: 1

Correct? No

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?

Gemini-1.5 Pro:

Reasoning: First, find the total amount of honey represented by 'p':  p = (25/9) + (25/9) = 50/9 gallons
Next, calculate 's' by adding the extra honey to 'p': s = (50/9) + (2/26) 
To add these fractions, find a common denominator: s = (1300/1170) + (90/1170) = 1390/1170
Finally, simplify the fraction: s = 139/117 gallons 
### Answer: 139/117 gallons 

Expected answer: 659/117

Correct? No

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

Gemini-1.5 Pro:

Reasoning: The total bunches of leaves the dinosaur eats in an hour is the sum of what it eats during the day and night, which is 16/8 + 6/17 bunches.
Find the least common multiple (LCM) of 8 and 17, which is 136.
Express each fraction with the LCM as a common denominator: (16/8)*(17/17) + (6/17)*(8/8) = 272/136 + 48/136
Add the fractions: 272/136 + 48/136 = 320/136
Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCD), which is 8: (320/8)/(136/8) = 40/17
### Answer: 40/17 bunches 

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?

Gemini-1.5 Pro:

Reasoning: 
First, simplify each fraction:
* 28/6 = 14/3
* 21/18 = 7/6
* 24/22 = 12/11

To add the fractions, we need a common denominator. The least common denominator for 3, 6, and 11 is 66.

* 14/3 = 308/66
* 7/6 = 77/66
* 12/11 = 72/66

Now we can add the fractions: 308/66 + 77/66 + 72/66 = 457/66

### Answer: 457/66 

Expected answer: 457/66

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First find the total amount of sugar originally needed: 11/17 cups + 6/2 cups = 11/17 + 51/17 = 62/17 cups.
Then multiply the original amount of sugar by the increase factor to find the total amount of sugar used: 62/17 cups * 29/21 = 1798/357 cups.
Simplify the fraction: 1798/357 = 5 13/357.
### Answer: 5 13/357 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?

Gemini-1.5 Pro:

Reasoning: First find the least common multiple of 8 and 18, which is 72. Then the fractions can be written with a common denominator: (7/8)+(21/18) = (63/72)+(84/72). Now the fractions can be added and simplified: (63/72)+(84/72) = 147/72 = 49/24.
### Answer: 49/24 

Expected answer: 49/24

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:  First find the total amount of liquid each guest will consume: 15/7 gallons (water) + 15/24 gallons (wine) = 315/168 gallons
Then multiply the baker's milk requirement per cake by the amount of liquid each guest will consume: (26/20 gallons/cake) * (315/168 gallons/guest) = 8190/3360 gallons/cake/guest
Simplify the above fraction: 8190/3360 gallons/cake/guest = 273/112 gallons/cake/guest
Then add the guests' consumption to find the total amount of liquid needed per guest: 273/112 gallons/cake/guest + 315/168 gallons/guest = 1269/560 gallons/cake/guest
### Answer: x = 1269/560 gallons/cake/guest

Expected answer: 713/112

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First find the sum of Teddy's favorite number and the first number he added to it: 30/17 + 18/15 =  <<30/17+18/15=756/255>>756/255
Next, multiply this sum by the last number, 24/13: 756/255 * 24/13 = <<756/255*24/13=18144/3315>>18144/3315.
Finally, simplify this fraction: 18144/3315 = <<18144/3315=5.47>>5.47
### Answer: 5.47

Expected answer: 6048/1105

Correct? No

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

Gemini-1.5 Pro:

Reasoning: Since he is drilling the hole exactly once with his drill bit, the diameter of the hole will be equal to the diameter of the drill bit. Therefore, each hole will have a diameter of (11/21) cm. To calculate what fraction this represents of the desired diameter, we simply divide the actual diameter by the desired diameter: (11/21) / (20/6). 

### Answer: (20/6)*(11/21)

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.

Gemini-1.5 Pro:

Reasoning: To find the difference in assembly time, we need to subtract the shorter assembly time from the longer one: 17/10 - 12/23. 

Before we can subtract fractions, they need a common denominator. The least common denominator for 10 and 23 is their product, 230. Let's convert both fractions:

* (17/10) * (23/23) = 391/230
* (12/23) * (10/10) = 120/230

Now we can subtract: 391/230 - 120/230 = 271/230

### Answer: 271/230 hours 

Expected answer: 271/230

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First find how much additional wood the special chair needs: (24/5)*(7/6) = <<(24/5)*(7/6)=5.6>>5.6 units
Then add that amount to the usual amount of wood to find the total amount of wood: 5.6+20/15 = 5.6+1.33 = <<5.6+1.33=6.93>>6.93 units
Converting the decimal to a fraction, we get 6 28/33
### Answer: 6 28/33 units 

Expected answer: 104/15

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
First find the reduced speed: 13/4-14/15=161/60 miles per minute.
Then add the increase in speed to find the final speed: 161/60+30/15=281/60 miles per minute.
Simplify 281/60 to 4 41/60
### Answer: 4 41/60 miles per minute 

Expected answer: 259/60

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
Let's break down this problem step-by-step.

**Step 1: Grapes produced this season**

* The vineyard usually produces 19/2 baskets of grapes.
* This season, it produced 19/29 of the usual amount.
* To find the amount produced this season, multiply the usual amount by 19/29: (19/2) * (19/29) = 361/58 baskets

**Step 2: Jake's share**

* The total production this season was 361/58 baskets.
* Jake gets to keep 7/11 of this amount.
* Multiply the total production by Jake's share to find his portion: (361/58) * (7/11) = 2527/638 baskets

**Step 3: Grapes used for juice**

* Jake has 2527/638 baskets of grapes.
* He uses 9/10 of his grapes for juice.
* Multiply Jake's total grapes by 9/10 to find the amount used for juice: (2527/638) * (9/10) = 22743/6380 baskets

### Answer: 22743/6380 baskets 

Expected answer: 22743/6380

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We need to find the sum of the two fractions, 9/2 and 10/22. To add fractions, they must have a common denominator. The least common denominator of 2 and 22 is 22.

First, convert 9/2 to an equivalent fraction with a denominator of 22: (9/2) * (11/11) = 99/22.
Now, add the two fractions: 99/22 + 10/22 = 109/22.
### Answer: 109/22 bushels 

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?

Gemini-1.5 Pro:

Reasoning: The height of the larger snowball is equal to its diameter, which is 17/8 feet.
The height of the smaller snowball is equal to its diameter, which is 1/20 feet.
The total height of the snowman is the sum of the heights of the two snowballs, which is 17/8 + 1/20 = 87/40 feet.
### Answer: 87/40 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.

Gemini-1.5 Pro:

Reasoning: 2/16 part of the sand is equivalent to 1/8 part by simplification (dividing the numerator and denominator by 2). To subtract 1/8 from 24/7, we need a common denominator. The least common denominator is 56.
Therefore, 24/7 is equivalent to (24/7)*(8/8) = 192/56, and 1/8 is equivalent to (1/8)*(7/7) = 7/56. 
Subtracting the part of sand taken away: 192/56 - 7/56 = 185/56.
### Answer: 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.

Gemini-1.5 Pro:

Reasoning: We need to determine how much *more* wildebeest the lion ate compared to the zebra.  To do this we subtract the fraction of zebra from the fraction of wildebeest: 23/9 - 28/26.

Before we can subtract fractions, they need to have a common denominator.  The least common denominator for 9 and 26 is 234.

To get a denominator of 234, we multiply 23/9 by 26/26: (23/9)*(26/26) = 698/234

And we multiply 28/26 by 9/9: (28/26)*(9/9) = 252/234

Now we can subtract: 698/234 - 252/234 = 446/234

Finally, we simplify the fraction by dividing the numerator and denominator by their greatest common factor of 2: 446/234 = (446/2)/(234/2) = 223/117

### Answer: 223/117

Expected answer: 173/117

Correct? No

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

Gemini-1.5 Pro:

Reasoning: The factory uses 14/4 kilograms of cocoa and 21/11 liters of milk per kilogram of chocolate, but the amount of milk used does not affect the total amount of chocolate produced.
To find the amount of chocolate produced we simply simplify the expression (14/4).
(14 / 4) = 3.5
### Answer: 3.5 kilograms 

Expected answer: 147/22

Correct? No

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

Gemini-1.5 Pro:

Reasoning: We need to calculate the average number of bananas each species produces per day and add those averages together.
The first species produces 12/29 ≈ 0.41 bananas per day.
The second species produces 30/10 = 3 bananas per day.
Together, they produce approximately 0.41 + 3 = 3.41 bananas per day.
### Answer: 3.41 

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.

Gemini-1.5 Pro:

Reasoning:  First simplify 11/11 to 1. 
Then find the common denominator of 1 and 26/14 which is 14.
Convert 1 to 14/14.
Add the fractions by adding the numerators while keeping the denominators the same (14+26)/14 = 40/14
Simplify the fraction 40/14 to 20/7

### Answer: 20/7 ton 

Expected answer: 20/7

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: The fraction of a day the bear spends sleeping is 18/24. Over 27 days, this would be (18/24)*(27/13) = 1.56 (rounded to 2 decimal places).
### Answer: 1.56

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.

Gemini-1.5 Pro:

Reasoning: We need to simplify the given formula to find the fraction of pine and birch trees.
First, perform the division: f = (0.643) + (9.5)
Then, add the two decimals: f = 10.143 
This means that for every tree in the forest, there are 10.143 pine or birch trees. Since this number is larger than 1, it indicates an error in the provided information or formula. 
### Answer:  The provided information or formula is incorrect. 

Expected answer: 71/7

Correct? No

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.

Gemini-1.5 Pro:

Reasoning: 
First, find the Zogorian's initial energy level: (14 / 2) / (23 / 17) = 7 / (23 / 17) = (7 * 17) / 23 = 119 / 23 zogs.

Next, calculate the increase in energy: (16 / 24) zogs = 2 / 3 zogs

Finally, add the increase to the initial energy level to find his energy level after the increase: (119 / 23) + (2 / 3) = (357 + 46) / 69 = 403 / 69 zogs

### Answer: 403/69 zogs 

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?

Gemini-1.5 Pro:

Reasoning: First, find a common denominator for the fractions 18/11 and 8/21. The least common denominator is 231. 
To get a denominator of 231 for 18/11, we multiply both the numerator and the denominator by 21: (18 * 21) / (11 * 21) = 378/231
To get a denominator of 231 for 8/21, we multiply both the numerator and the denominator by 11: (8 * 11) / (21 * 11) = 88/231
Now, subtract the fraction of friends at the beach from the fraction of friends in the forest: 378/231 - 88/231 = 290/231. So, 'f' = 290/231
To square a fraction, we square both the numerator and the denominator: (290 * 290) / (231 * 231) = 84100/53361. So, 'n' = 84100/53361
### Answer: 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.

Gemini-1.5 Pro:

Reasoning: 
First, simplify the fractions. 25/10 simplifies to 5/2 and 27/23 cannot be simplified further. 
To subtract fractions, they must have a common denominator. The least common denominator of 2 and 23 is 46.
Convert 5/2 to a fraction with a denominator of 46: (5/2) * (23/23) = 115/46.
Subtract the energy used from the starting energy: 115/46 - 27/23 = 115/46 - 54/46 = 61/46.

### Answer: 61/46 units of energy. 

Expected answer: 61/46

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First find the total distance the first two snails cover in one hour: (17/21) + (20/24) = 139/168 meters.
Now multiply that distance by the third snail's speed to find the total distance all three snails cover: (139/168)*(18/17) = 139/153 meters.
### Answer: 139/153 meters. 

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?

Gemini-1.5 Pro:

Reasoning: 
First, we need to simplify our fractions. 24/14 simplifies to 12/7 and 9/29 cannot be simplified. Since 12/7 and 9/29 do not have a common denominator, we must find one. The least common denominator is 203, so we will rewrite 12/7 and 9/29 as 294/203 and 63/203. Now, we can find the difference: 294/203 - 63/203 = 231/203.
This means he used 231/203 yards of his original fabric.
Next, we multiply that number by 15/2 to figure out how many yards of new fabric he used: 231/203 * 15/2 = 3465/406, which simplifies to 85/14.
### Answer: 85/14 yards 

Expected answer: 4275/406

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To add the fractions, we need to find a common denominator. The least common denominator of 10 and 4 is 20. 
So, 2/10 is equivalent to (2*2)/(10*2) = 4/20, and 21/4 is equivalent to (21*5)/(4*5) = 105/20.
Therefore, the total number of kids waiting for the swing is 4/20 + 105/20 = 109/20.
### Answer: 109/20 

Expected answer: 109/20

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We first simplify the fractions: 18/30 simplifies to 3/5 and 22/6 simplifies to 11/3. 
Then, (3/5)*(11/3) = 11/5
Finally, 11/5 equals 2 and 1/5, which can be written as 2.2 hours. 
### Answer: 2.2 hours 

Expected answer: 11/5

Correct? No

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?

Gemini-1.5 Pro:

Reasoning: We need to add the fractions 16/12 and 6/10.  Before we can add fractions, they need to have a common denominator. The least common denominator for 12 and 10 is 60.

16/12 = 80/60 and 6/10 = 36/60.

So, the cat eats 80/60 + 36/60 = 116/60 cans of cat food per day. This is more than 1 can since 116 is greater than 60. Simplifying the fraction 116/60, we get 29/15. 

### Answer: 29/15 cans 

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?

Gemini-1.5 Pro:

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

### Answer: 1.25

Expected answer: 5/4

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First find the fraction of the pile the monkey eats: (22/7)*(10/25) = 220/175
We can simplify 220/175 to 44/35

Then convert 44/35 and 3/28 to fractions with a common denominator to easily subtract them:
The least common multiple of 35 and 28 is 140.
(44/35) * (4/4) = 176/140
(3/28) * (5/5) = 15/140
The monkey ate 176/140 of the bananas and gave away 15/140 of the bananas.

Subtract to find the fraction of bananas remaining: (176/140) - (15/140) = 161/140
Finally, subtract the fraction of bananas eaten and given away from 1 representing the whole pile to find the fraction of the pile remaining: 1- (161/140) = 140/140 - 161/140 = -21/140

### Answer: -21/140 

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?

Gemini-1.5 Pro:

Reasoning:  We need to multiply the mouse's speed by the time it runs to find the total distance. That means we need to calculate (24/20) * (23/2). 
(24/20)*(23/2) = 69/5
### Answer: 69/5 feet 

Expected answer: 69/5

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: If one glass contains 29/9 ounces, and 26/25 of the glasses were consumed, then (29/9)*(26/25) = <<(29/9)*(26/25)>>754/225 ounces of beverage were consumed.
Simplifying this fraction, we find that 754/225 ounces is equal to <<754/225>>3.3511111111 ounces.
If the party goers then drink an additional 2/19 ounces, the total amount of beverages consumed would be 754/225 + 2/19 = <<754/225+2/19>>14761/4275 ounces. 
Simplifying this fraction, we find that 14761/4275 ounces is equal to <<14761/4275>>3.452397688 ounces.
### Answer: 3.452397688 ounces 

Expected answer: 14776/4275

Correct? No

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

Gemini-1.5 Pro:

Reasoning: You can fit 26/27 * 9 = <<26/27*9=8.666666666666666>>8.67 sets from your friend's gift. 
That means you can fit a total of 8.67 + 7/15 = <<8.67 + 7/15=9.136666666666667>>9.14 sets in the display case.
Since you can't have a fraction of a set, we round down to the nearest whole number. 
### 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.

Gemini-1.5 Pro:

Reasoning: 
* First, we need to find a common denominator for the fractions 20 and 6, which is 60. 
* We convert 27/20 to 81/60 and 1/6 to 10/60.
* Then, we add the weight of the backpack and the book: 81/60 + 10/60 = 91/60 kilograms.
### Answer: 91/60 

Expected answer: 91/60

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To find the multiplier, we need to simplify the given fraction multiplication: (7/7) * (25/22). 
Since (7/7) equals 1, the multiplication becomes 1 * (25/22), which is simply (25/22).

### Answer: 25/22 

Expected answer: 25/22

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To find the total weight, we need to add the weight of all the food Tilly found.

First, find the combined weight of the first two finds: 25/9 kg + 8/13 kg. To add these fractions, we need a common denominator. The least common denominator for 9 and 13 is their product, 117. We get: (25/9)*(13/13) + (8/13)*(9/9) = 325/117 + 72/117 = 397/117 kg

Now, add the weight of the third find: 397/117 kg + 24/27 kg. The least common denominator for 117 and 27 is 351. We get: (397/117)*(3/3) + (24/27)*(13/13) = 1191/351 + 312/351 = 1503/351 kg

Finally, add the weight of the last find: 1503/351 kg + 21/26 kg. The least common denominator for 351 and 26 is 9126. We get: (1503/351)*(26/26) + (21/26)*(351/351) = 39078/9126 + 7371/9126 = 46449/9126 kg

This fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, 1521: (46449/1521)/(9126/1521) = 31/6 kg

### Answer: 31/6 kg

Expected answer: 397/78

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First find the difference in distance between the boat's location and the island: 17/2 - 4/2 = 13/2 nautical miles.
Then add the tide adjustment to find the adjusted distance: 13/2 + 14/9 = 145/18 nautical miles.
Finally, multiply the adjusted distance by the fuel efficiency rate to find the fuel requirement: (145/18) * (22/15) = 1595/135 = 319/27 gallons.
### Answer: 319/27 gallons 

Expected answer: 319/27

Correct? Yes

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

Gemini-1.5 Pro:

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

Expected answer: 41/9

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: Arthur's total weekend practice time is 20/21 + 11/29 = 879/609 hours. 
Let's simplify that fraction by dividing the numerator and denominator by their greatest common factor, which is 3: (879/3) / (609/3) = 293/203.
### Answer: 293/203 hours 

Expected answer: 811/609

Correct? No

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

Gemini-1.5 Pro:

Reasoning: Each sibling initially received 18 / 3 = <<18/3=6>> 6 shirts.
Lucas wanted to keep 27 / 19 = <<27/19=1.42>>1.42 shirts for each sibling from the new stock.
The difference in the number of shirts each sibling has now compared to before is 6 - 1.42 = <<6-1.42=4.58>>4.58
### Answer: Each sibling has 4.58 fewer shirts now. 

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?

Gemini-1.5 Pro:

Reasoning: The painter used 18/4 = <<18/4=4.5>>4.5 gallons of light blue paint for the project.
The painter had 7 + 2/5 = 7 + 0.4 = <<7+.4=7.4>>7.4 gallons of light blue paint initially.
The painter has 7.4 - 4.5 = <<7.4-4.5=2.9>>2.9 gallons left.
### Answer: 2.9 

Expected answer: 29/10

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We need to add the time Jayson spent skating each day. 24/7 + 30/20 = 24/7 + 3/2.
Before we can add fractions, we need to have a common denominator. The least common denominator is 14. 
24/7 is equivalent to 48/14 and 3/2 is equivalent to 21/14.
48/14 + 21/14 = 69/14.
Therefore, Jayson skated for 69/14 hours in total. 
### Answer: 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?

Gemini-1.5 Pro:

Reasoning: We need to multiply the dolphin's usual jump height by 3/4 to find the height of this jump: (18/3) * (3/4) = 54/12 = 9/2 = 4.5 
### 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.

Gemini-1.5 Pro:

First find last month's sales to production ratio: 20/15 + 16/22 = 40/30 + 240/330 = 660/330 + 240/330 = 900/330
Then find this week's figure for the ratio of interested customers to production: 22/27 * 23/8 = 506/216 
Now multiply the two figures: 900/330 * 506/216
### Answer: 455400/71280 

Expected answer: 391/81

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
First find the average time spent on each song: 30 minutes / 15 songs = 2 minutes/song
Now, convert 1/17 of an hour to minutes: (1/17 hour) * (60 minutes/hour) = 60/17 minutes
Subtract the reduction from the average song length: 2 minutes - (60/17) minutes = (34-60)/17 = -26/17 minutes. 

### Answer:  This answer doesn't make sense because it results in a negative time. It seems there might be an error in the problem statement. 

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.

Gemini-1.5 Pro:

Reasoning: First find the total time (in hours) Josh rode the scooter: 18 + 1/12 = 217/12
Then add the amount of time (in hours) Jack rode the scooter to find the total time: 217/12 + 7/17 = 3773/204
### Answer: 3773/204 hours 

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?

Gemini-1.5 Pro:

Reasoning:  To solve this problem, we need to find a common denominator for all the fractions. The least common denominator for 26, 11, 28 and 19 is 15082.
- Floor Lamps: (4/26) * (578/578) = 2312/15082
- Desk Lamps: (15/11) * (1371/1371) = 20565/15082
- Table Lamps: (23/28) * (539/539) = 12497/15082
- Decorative Lamps: (8/19) * (806/806) = 6448/15082

Adding all the fractions: 2312/15082 + 20565/15082 + 12497/15082 + 6448/15082 = 41822/15082

Simplifying the fraction: 41822/15082 = 20911/7541

### Answer: 20911/7541

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.

Gemini-1.5 Pro:

Reasoning: 
The combined length of the two kite strings is 26/19 + 7/11 = (26 * 11)/(19 * 11) + (7 * 19)/(11 * 19) = 286/209 + 133/209 = 419/209 meters.
Since Oliver used only 5/8 of the combined string, the length of the kite string he is using is (5/8) * (419/209) = 2095/1672 meters. 
### Answer: 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

Gemini-1.5 Pro:

It seems like you're trying to use variables to represent parts of the problem that aren't necessary to answer the main question. The problem is asking for the total number of snowballs Mike had, and we can find that with the information given directly:

* **Start:** Mike threw 9/19 of his snowballs, meaning he had some left over.
* **Finding More:** He finds 4 more snowballs.

The fact that John threw snowballs or how many Mike threw is irrelevant. To find the total Mike has *now*, we only need to focus on the fact that he found more. 

Since we don't know how many he started with, we can't get an exact number for how many he has in total.  

**Therefore, there's not enough information to solve for 'j' in a way that answers the main question.** 

Expected answer: 397/76

Correct? No

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

Gemini-1.5 Pro:

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

Expected answer: 22/9

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 24/20 batches of small towels are equal to 1 4/20 = <<24/20=1.2>>1.2 batches.
25/15 batches of large towels are equal to 1 10/15 = <<25/15=1.67>>1.67 batches.
Joanna washed 1.2+1.67 = <<1.2+1.67=2.87>>2.87 batches of towels in total.
### Answer: 2.87 batches. 

Expected answer: 43/15

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First find the ratio of flour to sugar in the first recipe: (27/3) / (11/7) = (27 * 7)/(11 * 3) = 63/11
Then subtract (21/26) from the ratio to find the adjusted ratio: (63/11) - (21/26) = (63*26 - 21*11) / (11 * 26) = 1407/286
Finally, add the flour from the second recipe to the adjusted ratio to find the total cups of flour:  (1407/286) + (22/9) = (1407*9 + 22*286)/(286 * 9) = 18921/2574
### Answer: 18921/2574 cups

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?

Gemini-1.5 Pro:

Reasoning:
There are 26/13 = <<26/13=2>>2 chickens in the first farm.
There are 9/16*2 = <<9/16*2=9/8>>9/8 chickens in the second farm.
The difference in the number of chickens between the two farms is 2-9/8 = <<2-9/8=7/8>>7/8.
The number of chickens after a week is 7/8*19/21 = <<7/8*19/21=19/24>>19/24.
### Answer: 19/24 

Expected answer: 437/336

Correct? No

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

Gemini-1.5 Pro:

Reasoning: We are given that the helicopter traveled w = 24/14 miles for each exercise. 
The total distance 't' is represented as the product of the distance of each exercise: t = w * w
Substituting the value of 'w', we get: t = (24/14) * (24/14) = 576/196
### Answer: t = 576/196 

Expected answer: 144/49

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To find the total fraction of the tank refilled, we need to add the fractions from the two fuel stops: 20/16 + 24/25. 
To add fractions, they must have a common denominator. The least common denominator for 16 and 25 is 400.
We can rewrite 20/16 as 500/400 and 24/25 as 384/400.
Now we can add the fractions: 500/400 + 384/400 = 884/400.
Finally, we can simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 4:  884/400 = 221/100. 

### Answer: 221/100 

Expected answer: 221/100

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have a common denominator. The least common denominator for 27 and 26 is their product, 702.

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

Therefore, (24/27) + (30/26) = (624/702) + (810/702) = 1434/702. 

This fraction can be simplified by dividing the numerator and denominator by their greatest common factor, which is 6. This gives us 239/117. 

### Answer: 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.

Gemini-1.5 Pro:

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

Expected answer: 11/3

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To find the total milk per cow, we need to add the morning and evening milk production. To add fractions, they must have a common denominator. The least common denominator for 14 and 20 is 140. 
We can get 14 to 140 by multiplying by 10, so we multiply our first fraction by 10/10: (26/14)*(10/10) = 260/140
We can get 20 to 140 by multiplying by 7, so we multiply our second fraction by 7/7: (28/20)*(7/7) = 196/140
Now we can add our two fractions: (260/140) + (196/140) = 456/140
This fraction can be simplified by dividing the top and bottom by 4: (456/4)/(140/4) = 114/35
### Answer: 114/35 gallons 

Expected answer: 13/5

Correct? No