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 Flash:

Reasoning: Initially, Carla could grow 22/3 * 22/19 = <<(22/3)*(22/19) = 484/57>> cucumbers per plant. 
After adjusting her production method, she expects to grow 484/57 * 23/17 = <<(484/57)*(23/17) = 11132/969>> cucumbers per plant.

### Answer: 11132/969 

Expected answer: 11132/969

Correct? Yes

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 Flash:

Reasoning: First, we need to figure out how many kilograms of grapes Pierre has left after eating some: 19/4 - 7/25 = 455/100 - 28/100 = 427/100 kg.
Then, we need to add the grapes his mother gave him: 427/100 + 30/9 = 3843/900 + 3000/900 = 6843/900 kg.
### Answer: 6843/900 

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 Flash:

Here's how to solve this problem:

1. **Find a common denominator for all the fractions:** The smallest common denominator for 22, 29, and 3 is 1886.

2. **Convert each fraction to have the common denominator:**
   * Wall repairs: (26/22) * (86/86) = 2236/1886
   * Moat renovations: (4/29) * (65/65) = 260/1886
   * Catapults: (11/3) * (632/632) = 6952/1886

3. **Add the fractions:** 2236/1886 + 260/1886 + 6952/1886 = 9448/1886

4. **Simplify the fraction:** Both the numerator and denominator are divisible by 4: (9448/4) / (1886/4) = 2362/471.5

5. **Express as a fraction of the budget:** 2362/471.5 = **4.72/1** 

### Answer: 4.72/1 

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 Flash:

First, let's calculate the giraffe's increased daily intake:

(25/19) * (30/26) = 750/494 

Now, let's calculate the weekly feeding amount squared:

(750/494)^2 = 562500/244036

Finally, let's multiply that by the regular daily intake:

(562500/244036) * (750/494) = 421875000/120538504

Simplifying the fraction, we get:

421875000/120538504 = 3.50 (approximately)

### Answer: 3.50 

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 Flash:

Reasoning: Lara needs (11/3) + (8/30) feet of materials. 
To add these fractions, we need a common denominator.  The least common denominator of 3 and 30 is 30. 
(11/3) = (11*10)/(3*10) = (110/30)
Now we can add the fractions: (110/30) + (8/30) = (118/30)
This fraction can be simplified to (59/15). 
Lara will need (59/15) feet of materials for the necklace.
### Answer: (59/15) 

Expected answer: 59/15

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: To find the difference in distance traveled, we need to subtract the distance traveled by Plane B from the distance traveled by Plane A.

Distance traveled by Plane A in one minute: 24/11 miles.

Distance traveled by Plane B in one minute: 26/27 miles.

Difference in distance: (24/11) - (26/27) 

To subtract fractions, they need a common denominator. The least common multiple of 11 and 27 is 297.

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

Now we can subtract: (648/297) - (286/297) = 362/297

### Answer: 362/297

Expected answer: 362/297

Correct? Yes

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

Gemini-1.5 Flash:

To multiply fractions, we multiply the numerators and the denominators. 
 
 (14/7) * (25/13) = (14 * 25) / (7 * 13) = 350 / 91

Therefore, the combined amount that both bears eat per day is 350/91 pounds of fish. 
 
 ### Answer: 350/91 

Expected answer: 50/13

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: We need to add the time for each song: 12/8 + 12/3. To add fractions, they need to have the same denominator. The least common multiple of 8 and 3 is 24.  
*  12/8 * 3/3 = 36/24
*  12/3 * 8/8 = 96/24
Now we can add: 36/24 + 96/24 = 132/24
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 12:
* 132/12 = 11
* 24/12 = 2
So, the simplified fraction is 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 Flash:

Here's how to solve this problem:

1. **Start with the initial amount:** You had 28 out of 29 chocolate bars. This can be represented as the fraction 28/29.

2. **Add the new amount:** You found 8 out of 22 more chocolate bars. This can be represented as the fraction 8/22.

3. **Add the fractions:** To add fractions, they need to have the same denominator.  Find the least common multiple (LCM) of 29 and 22, which is 638.

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

4. **Add the numerators:**  616/638 + 232/638 = 848/638

5. **Simplify the fraction:** The fraction 848/638 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4:

    * 848/4 = 212
    * 638/4 = 159.5

Therefore, the fraction representing the total chocolate bars you have now is **212/159.5**. 

**Important Note:** It's unusual to have a fraction with a decimal in the denominator.  You could leave the answer as 848/638 or simplify it further by dividing both numerator and denominator by 2, resulting in 424/319.  
### Answer: 212/159.5 

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 Flash:

Here's how we can solve this problem step-by-step:

**1. Material for two needles:**

* The maker needs 27/26 pounds of material per needle.
* For two needles, he'll need (27/26) * 2 = 54/26 pounds of material.

**2. Total material needed:**

* He needs 54/26 pounds for the needles.
* He needs an additional 27/6 pounds for the extra piece.
* Total material needed is (54/26) + (27/6) = 162/78 + 351/78 = 513/78 pounds.

**Simplifying the answer:**

* 513/78 can be simplified to 171/26 pounds.

### Answer: 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?

Gemini-1.5 Flash:

Reasoning: To find the total rate, we need to add the burning rates of both candles.  First, let's simplify the fractions. 6/4 can be simplified to 3/2. 14/16 can be simplified to 7/8.
Now we have 3/2 + 7/8. To add fractions, we need a common denominator. The least common denominator of 2 and 8 is 8.
We can rewrite 3/2 as 12/8. 
So, the total burning rate is 12/8 + 7/8 = 19/8 inches per hour.
### Answer: 19/8 

Expected answer: 19/8

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: Sophia's friend gave her 1/4 * 1 = 0.25 dollars.
Before her brother gave her a dollar, Sophia had 17/20 + 0.25 = 17/20 + 1/4 = 17/20 + 5/20 = 22/20 = 1.1 dollars.
Adding her brother's dollar to that, Sophia has 1.1 + 1 = 2.1 dollars now.
### 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))?

Gemini-1.5 Flash:

Let's break down the calculation step by step:

1. **Calculate the initial time investment (p):** 
   - p = 16/4 + 16/29 
   - p = 4 + 16/29
   - p = (116 + 16)/29
   - p = 132/29 hours

2. **Calculate the total time spent before the drummer's time reduction (b):**
   - b = p + 28/13
   - b = 132/29 + 28/13
   - b = (1656 + 784)/377
   - b = 2440/377 hours

3. **Calculate the time the drummer spent less:**
   - 18/4 = 9/2 hours

4. **Calculate the final time spent on producing the song:**
   - (b - (18 / 4)) = 2440/377 - 9/2
   - (b - (18 / 4)) = (4880 - 3381)/754
   - (b - (18 / 4)) = 1499/754 hours

### Answer: 1499/754 

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 Flash:

Here's how to solve this problem step-by-step:

1. **Calculate the total cookies before the festival:**
   - Monica starts with 21/15 dozens of cookies.
   - She bakes 29/17 dozens more.
   - Total cookies before the festival: (21/15) + (29/17) = (357 + 435) / 255 = 792/255 dozens

2. **Increase the total cookies by the given ratio:**
   - Monica wants to increase her stock by a ratio of 7/5.
   - Multiply the total cookies by the ratio: (792/255) * (7/5) = 5544/1275 dozens

**Therefore, Monica will have 5544/1275 dozens of cookies for the cookie festival.** 
### Answer: 5544/1275 

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?

Gemini-1.5 Flash:

Reasoning: The chef will have 28 - 26/24 = <<28 - 26/24 = 676/24>> 676/24 kg of sugar left after baking one cake.
After adding 10/6 kg of sugar, they will have 676/24 + 10/6 = <<676/24 + 10/6 = 746/24>> 746/24 kg of sugar.
### Answer: 746/24 

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 Flash:

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

Expected answer: 2

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: Princess Lily ate 10/12 of the apple pie.
She also ate 10/29 of the blueberry pie.
In total, she ate 10/12 + 10/29 of the pies.
To add fractions, they need to have the same denominator, so we need to find the least common multiple (LCM) of 12 and 29.  The LCM of 12 and 29 is 348.
We convert 10/12 to 290/348.
We convert 10/29 to 120/348.
Therefore, she ate a total of (290+120)/348 = 410/348 of the pies.
### Answer: 410/348 

Expected answer: 205/174

Correct? Yes

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

Gemini-1.5 Flash:

We are given that Marta uses 20 out of every 11 colored pencils for art projects.  This is a ratio of 20/11.  We are also told that she uses 23 out of every 26 colored pencils for shading. This is a ratio of 23/26.  To find the number of colored pencils Marta uses for shading in an 11-day period, we need to find the fraction of the 20 colored pencils that she uses for shading.  This is done by multiplying the two ratios:

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

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

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

Therefore, Marta uses **230/143** of the colored pencils for shading over an 11-day period.

### Answer: 230/143 

Expected answer: 230/143

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to calculate the value of f:

**1. Calculate indicator i:**

* **Specimen 1:** Decreases by 26 out of every 6 units. This can be represented as a fraction: -26/6 
* **Specimen 2:** Decreases by 25 out of every 17 units. This can be represented as a fraction: -25/17
* **Ratio (indicator i):** To find the ratio of these changes, divide the first fraction by the second: (-26/6) / (-25/17) = (26/6) * (17/25) = 221/75

**2. Calculate indicator h:**

* **Specimen 1:** Increases by 18 out of every 8 units. This can be represented as a fraction: 18/8
* **Specimen 2:** Increases by 17 out of every 23 units. This can be represented as a fraction: 17/23
* **Difference (indicator h):** To find the difference, subtract the second fraction from the first: (18/8) - (17/23) = (414/184) - (136/184) = 278/184 

**3. Calculate indicator f:**

* **Multiply indicator i and h:** f = i * h = (221/75) * (278/184) = 61458/13800

**Therefore, the value of f is 61458/13800.** 

Expected answer: 30719/6900

Correct? No

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

Gemini-1.5 Flash:

Reasoning:
The lioness's gestation period is 20/22 of a year, which simplifies to 10/11 of a year.
Therefore, the total gestation period for both animals is (10/11) + 15 = 175/11 years.

For the second pregnancy, the lioness's gestation period is reduced by (15/20) * (175/11) = 131.25/11 years.

Therefore, the lioness's gestation period for her second pregnancy is (175/11) - (131.25/11) = 43.75/11 years.

### Answer: 43.75/11 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 Flash:

Reasoning: First, we need to find the area of the original rectangle: (30/7) * (19/6) = (5 * 19) / (7 * 1) = 95/7 square meters.
Then, we need to find the area of the similar rectangle: (95/7) * (18/17) = (5 * 18) / (7 * 1) = 90/7 square meters.

### Answer: 90/7 

Expected answer: 1710/119

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve this problem step by step:

1. **Calculate the increase in production:** 4/20 of a tonne is equal to 1/5 of a tonne.

2. **Add the increase to the original production:** 23/8 + 1/5 = 115/40 + 8/40 = 123/40 tonnes.

3. **Calculate the decrease in production:** 19/24 of a tonne.

4. **Subtract the decrease from the production after the increase:** 123/40 - 19/24 = 369/120 - 95/120 = 274/120 tonnes.

5. **Simplify the answer:** 274/120 can be simplified to 137/60 tonnes.

### Answer: 137/60 

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 Flash:

Here's how we can solve this step-by-step:

1. **Simplify the initial red paint:** 24/8 gallons simplifies to 3 gallons of red paint.

2. **Calculate the paint removed:** 12/8 gallons simplifies to 1.5 gallons of red paint removed.

3. **Find the remaining red paint ('d'):**  d = 3 gallons - 1.5 gallons = 1.5 gallons

4. **Convert the blue pigment:** 1/28 gallon is already in its simplest form.

5. **Calculate the total paint ('x'):** x = d - 1/28 gallon = 1.5 gallons - 1/28 gallon

6. **Find a common denominator for subtraction:**  x = (1.5 * 28)/28 - 1/28 = 42/28 - 1/28

7. **Subtract the fractions:** x = 41/28 gallons

### Answer: 41/28 

Expected answer: 41/28

Correct? Yes

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

Gemini-1.5 Flash:

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

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

Now, we can simplify this fraction by finding the greatest common factor (GCD) of 459 and 182.  The GCD is 13.  Dividing both numerator and denominator by 13:

459 / 182 = (459/13) / (182/13) = 35/14

### Answer: 35/14 

Expected answer: 459/182

Correct? No

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

Gemini-1.5 Flash:

Reasoning:
- Sonia uses 21/12 oz of toothpaste, which simplifies to 7/4 oz.
- Anthony uses 6/27 oz, which simplifies to 2/9 oz.
- Their mom uses 3/18 oz, which simplifies to 1/6 oz.

Total toothpaste used by Sonia and Anthony: 7/4 + 2/9 = (63 + 8)/36 = 71/36 oz.

Total toothpaste used by the whole family: 71/36 + 1/6 = (71 + 6)/36 = 77/36 oz.

### Answer: 77/36

Expected answer: 77/36

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Calculate the fraction of ingredients used for the special sandwich:**
   * Cheese used: (21/14) = 1.5 parts
   * Pickle used: (7/18) parts
   * Total used: (1.5 + 7/18) = (27/18 + 7/18) = 34/18

2. **Calculate the fraction of ingredients remaining after the special sandwich:**
   * Original ingredients: 1 (representing the whole)
   * Ingredients remaining: 1 - (34/18) = (18/18) - (34/18) = -16/18

3. **Simplify the fraction of ingredients remaining:**
   *  -16/18 can be simplified by dividing both numerator and denominator by their greatest common factor, 2: -16/18 = -8/9

4. **Calculate the fraction of cheese used for the simpler sandwich:**
   *  Half the wheel of cheese is (1/2) = (1/2) * (14/14) = 14/28

5. **Calculate the fraction of ingredients remaining after the simpler sandwich:**
   * Ingredients remaining after the special sandwich: -8/9
   * Cheese used for the simpler sandwich: 14/28
   * Total fraction remaining: (-8/9) - (14/28) = (-56/63) - (28/63) = -84/63

6. **Simplify the fraction of ingredients remaining after the simpler sandwich:**
   * -84/63 can be simplified by dividing both numerator and denominator by their greatest common factor, 21: -84/63 = -4/3

**Therefore, you have -4/3 of the original ingredients left after making the simpler sandwich. This indicates that you have used more than your original ingredients, which isn't possible in a real-world scenario. This indicates there might be an error in the problem setup.** 

Expected answer: 25/18

Correct? No

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

Gemini-1.5 Flash:

To find the total height of the windows, we need to add the heights of each individual window.  However, we need to make sure they have the same denominator before we can add them.

* **Find a common denominator:** The least common denominator for 6 and 16 is 48.
* **Convert the fractions:**
    * 15/6 = (15 * 8) / (6 * 8) = 120/48
    * 7/16 = (7 * 3) / (16 * 3) = 21/48
* **Add the fractions:** 120/48 + 21/48 = 141/48

**Therefore, the total height of the windows is 141/48 meters.** 
### Answer: 141/48 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 Flash:

Reasoning: To find the total amount of juice, we need to add the amounts of each type of juice. First, let's simplify the fractions. 16/6 can be simplified to 8/3 by dividing both numerator and denominator by 2. 20/12 can be simplified to 5/3 by dividing both numerator and denominator by 4.

Now we have: 8/3 liters of apple juice + 5/3 liters of orange juice + 2/3 liters of cranberry juice.

Adding the numerators, we get (8 + 5 + 2)/3 = 15/3.

Finally, 15/3 simplifies to 5 liters.

### Answer: 5 

Expected answer: 5

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning:  If each level gives you 4/3 points, and you have played 13/10 of the levels, you have earned (4/3) * (13/10) points.

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

(4/3) * (13/10) = (4 * 13) / (3 * 10) = 52/30

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

Reasoning: The astronaut spends 18/8 + 26/2 = <<18/8 + 26/2 = 32/8 + 104/8 = 136/8 = 17>>17 hours on his "work" routine before adding the new activity.
Adding the new activity, the astronaut spends 17 + 30/8 = <<17 + 30/8 = 136/8 + 30/8 = 166/8 = 20.75>> 20.75 hours on his whole daily routine now.
### Answer: 20.75 

Expected answer: 19

Correct? No

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

Gemini-1.5 Flash:

Here's how we can solve this problem:

1. **Understand the variables:**
   -  'd' represents the actual amount of cheese Jeremy received.
   - 'n' represents the amount of cheese he originally requested (30/9 ounces).

2. **Substitute the values into the equation:**
   - d = (30/9) - (17/22)

3. **Find a common denominator for the fractions:**
   - The least common denominator for 9 and 22 is 198.
   - (30/9) = (30 * 22) / (9 * 22) = 660 / 198
   - (17/22) = (17 * 9) / (22 * 9) = 153 / 198

4. **Subtract the fractions:**
   - d = (660/198) - (153/198) = 507/198

5. **Simplify the answer (optional):**
   - The fraction 507/198 can be simplified by dividing both numerator and denominator by 3. This gives us 169/66.

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

### Answer: 169/66 

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.

Gemini-1.5 Flash:

Here's how to break down Sophia's calculations:

* **Test 1:** 13/4 sunglasses blocked all UV rays.
* **Test 2:** 20/18 sunglasses blocked all UV rays.
* **Additional Batch:** 21/17 sunglasses blocked all UV rays.
* **Error:** 16/30 sunglasses did *not* block all UV rays.

To combine these fractions, we need a common denominator. The least common multiple of 4, 18, 17, and 30 is 3060.

* **Test 1:** (13/4) * (765/765) = 9945/3060
* **Test 2:** (20/18) * (170/170) = 3400/3060
* **Additional Batch:** (21/17) * (180/180) = 3780/3060
* **Error:** (16/30) * (102/102) = 1632/3060

Now we can add the fractions representing sunglasses that blocked all UV rays and subtract the fraction representing those that did not:

(9945/3060) + (3400/3060) + (3780/3060) - (1632/3060) = 15493/3060

Finally, we simplify the fraction:

15493/3060 = **5164/1020**

### Answer: 5164/1020 

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 Flash:

Reasoning:  

To find the total amount of mayonnaise and sandwich spread Shawn uses, we need to add the fractions: 23/28 + 6/9. To add fractions, they need to have the same denominator. The least common multiple of 28 and 9 is 252. 

* Convert 23/28 to have a denominator of 252: (23/28) * (9/9) = 207/252
* Convert 6/9 to have a denominator of 252: (6/9) * (28/28) = 168/252

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

Next, we need to add the cheese spread to the total.  We first simplify the fraction 18/12: 18/12 = 3/2. 

* Convert 3/2 to have a denominator of 252: (3/2) * (126/126) = 378/252

Now add the cheese spread to the previous total: 375/252 + 378/252 = 753/252

Finally, we need to determine how many cups of ingredients Shawn will use to make sandwiches with 4/4 cups of ingredients per sandwich. Since 4/4 is the same as 1 whole cup, he will use the same number of cups as the total number of sandwiches he makes.

Therefore, Shawn will use a total of 753/252 cups of ingredients to make his sandwiches. 

### Answer: 753/252 

Expected answer: 251/84

Correct? Yes

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 Flash:

Reasoning: Cassandra lost 1/21 of 7/6 of a key set, which is equal to (1/21) * (7/6) = 1/18 of a key set.
She had 7/6 - 1/18 = (21/18) - (1/18) = 20/18 = 10/9 of a key set left.
### Answer: 10/9 

Expected answer: 47/42

Correct? No

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

Gemini-1.5 Flash:

Here's how to calculate the difference:

1. **Calculate the sum of the ratios for the first two sections:**
   (29/23) + (19/17) = (493 + 417) / 391 = 910/391

2. **Calculate the ratio of the rest in the third section:**
   26/26 = 1

3. **Find the difference between the two values:**
   (910/391) - 1 = (910 - 391) / 391 = 519/391

### Answer: 519/391 

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 Flash:

To multiply fractions, we multiply the numerators (top numbers) and the denominators (bottom numbers) together. 

* Numerators: 22 * 22 = 484
* Denominators: 25 * 8 = 200

Therefore, the product of the fractions is 484/200.  

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

* 484 / 4 = 121
* 200 / 4 = 50

So, the simplified product of the fractions is 121/50. 

### Answer: 121/50 

Expected answer: 121/50

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: First, we need to add the length of the pillow and the extra length due to fluffing: 23/9 + 22/25 = (575 + 198) / 225 = 773/225 feet. 
Next, we multiply the total length by 16/13 to account for overlap and corners: (773/225) * (16/13) = 12368/2925 feet.

### Answer: 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.

Gemini-1.5 Flash:

Reasoning: The car was supposed to travel an extra 16/13 miles, but only traveled 1/21 miles. So, the car was supposed to travel (16/13)-(1/21) more miles.
(16/13)-(1/21) = (16*21)/(13*21) - (1*13)/(21*13) = 336/273 - 13/273 = (336-13)/273 = 323/273 miles.
Therefore, the car was supposed to travel an extra 323/273 miles in total.
The car travels 21/4 miles every hour. 
Multiplying the additional distance needed by the average miles the car travels in an hour gives (323/273)*(21/4) = (323*21)/(273*4) = 6783/1092 miles.
### Answer: 6783/1092 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 Flash:

Here's how to break down the problem and find the solution:

**1. Calculate the total time for editing and typesetting:**

* Editing time: 20/5 hours = 4 hours
* Typesetting time: 18/17 hours 
* Total time: 4 + 18/17 hours = 86/17 hours

**2. Calculate the time lost after the break:**

* Time lost: 6/15 hours

**3. Calculate the net time after the break:**

* Net time: 86/17 - 6/15 hours = (1290 - 68) / 255 hours = 1222/255 hours

**4. Calculate the extended time:**

* Extended time = Initial time = 86/17 hours

**5. Calculate the product of the net time and extended time:**

* Product: (1222/255) * (86/17) = 4156/85 hours

**Therefore, the total extended time in hours is 4156/85 hours.** 
### Answer: 4156/85 

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 Flash:

Reasoning: Jenny has 13/11 * 21/3 = 273/33 = 91/11 rows of potatoes. 
She will make 91/11 * 21/15 = 1911/165 dollars.

### Answer: 1911/165 

Expected answer: 637/55

Correct? Yes

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 Flash:

Reasoning: 
* We simplify the fractions for gold and silver to find the total weight of each metal.
*  14/28 is equivalent to 1/2 (dividing numerator and denominator by 14)
* 13/26 is equivalent to 1/2 (dividing numerator and denominator by 13)

The jeweler uses 1/2 + 1/2 = 1 kilogram of gold and silver combined.

### Answer: 1 

Expected answer: 1

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the problem:

* **Honey from a regular honey storage sub-section:** (25/9) gallons
* **Honey from a regular bee rearing sub-section:** (25/9) gallons
* **Total honey from regular sub-sections (p):** (25/9) + (25/9) = (50/9) gallons
* **Extra honey in the special honey storage sub-section:** (2/26) gallons
* **Total honey from the special sub-sections (s):** (25/9) + (2/26) + (25/9) = (50/9) + (2/26) gallons

**To find a common denominator for (50/9) and (2/26):**

* The least common multiple of 9 and 26 is 234.
* Convert (50/9) to have a denominator of 234: (50/9) * (26/26) = (1300/234)
* Convert (2/26) to have a denominator of 234: (2/26) * (9/9) = (18/234)

**Now we can add the fractions:**

* (1300/234) + (18/234) = (1318/234)

**Simplify the fraction (optional):**

* (1318/234) can be simplified to (659/117)

### Answer: (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.

Gemini-1.5 Flash:

Reasoning: The dinosaur eats 16/8 = <<16/8=2>>2 bunches of leaves per hour during the day.
The dinosaur eats a total of 2 + 6/17 = <<2+6/17 = 38/17>>38/17 bunches of leaves per hour.
### Answer: 38/17 

Expected answer: 40/17

Correct? No

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

Gemini-1.5 Flash:

Reasoning: To find the total amount of fish the bear ate, we need to add the amounts from each day. Before we can add fractions, they need to have a common denominator.
*  The least common denominator for 6, 18, and 22 is 198.
*  (28/6) * (33/33) = 924/198
*  (21/18) * (11/11) = 231/198
*  (24/22) * (9/9) = 216/198
* Now we can add the fractions: 924/198 + 231/198 + 216/198 = 1371/198
### Answer: 1371/198 

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 Flash:

Here's how we can solve this problem step-by-step:

1. **Calculate the total sugar for the initial recipes:**
   - The bread required 11/17 cup of sugar.
   - The custard required 6/2 = 3 cups of sugar.
   - Total sugar for the initial recipes: 11/17 + 3 = 62/17 cups

2. **Calculate the increased amount of sugar:**
   - Heather increased the sugar by a factor of 29/21.
   - Increased sugar: (62/17) * (29/21) = 1798/357 cups

3. **Calculate the total sugar used:**
   - Total sugar used: (62/17) + (1798/357) = 4022/357 cups

**Simplifying the fraction:**

The fraction 4022/357 can be simplified to approximately 11.26 cups.

### Answer: 11.26 

Expected answer: 1798/357

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they need to have the same denominator.

* **Find the Least Common Multiple (LCM) of 8 and 18:** The LCM of 8 and 18 is 72.

* **Convert the fractions to have a denominator of 72:**
    * (7/8) * (9/9) = 63/72
    * (21/18) * (4/4) = 84/72

* **Add the fractions:**
    * (63/72) + (84/72) = 147/72

* **Simplify the fraction:** Both 147 and 72 are divisible by 9.
    * (147/72) / (9/9) = 16.33333

### Answer: 16/8 

Expected answer: 49/24

Correct? No

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 Flash:

Here's how to break down the problem:

1. **Calculate total liquid per guest:**
   - Water: 15/7 gallons
   - Wine: 15/24 gallons
   - Total per guest: (15/7) + (15/24) = (360/168) + (105/168) = 465/168 gallons

2. **Calculate total milk needed for cakes:**
   - Milk per cake: 26/20 gallons
   - Since this is multiplied by the guests' consumption, we need to multiply this by the total liquid per guest: (26/20) * (465/168) = 1209/672 gallons

3. **Calculate total liquid needed for the feast:**
   - Total liquid per guest: 465/168 gallons
   - Total milk for cakes: 1209/672 gallons
   - Total liquid needed: (465/168) + (1209/672) = (1860/672) + (1209/672) = 3069/672 gallons

### Answer: 3069/672 

Expected answer: 713/112

Correct? No

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

Gemini-1.5 Flash:

First, we need to add 30/17 and 18/15. To do this, we need to find a common denominator. The least common multiple of 17 and 15 is 255. 
* 30/17 = (30 * 15) / (17 * 15) = 450/255
* 18/15 = (18 * 17) / (15 * 17) = 306/255

Now we can add them: 450/255 + 306/255 = 756/255

Next, we need to multiply this sum by 24/13:
(756/255) * (24/13) = (756 * 24) / (255 * 13)

Simplifying the multiplication: 18144 / 3315

Finally, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 9:

18144/9 = 2016 
3315/9 = 368

Therefore, Teddy's final number is **2016/368**. 
### Answer: 2016/368 

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 Flash:

To find the fraction of the desired diameter that each hole has, we need to divide the drill bit's diameter by the desired hole diameter.

This is represented by the following fraction: 
(drill bit diameter) / (desired hole diameter) = (11/21) / (20/6)

Dividing fractions is the same as multiplying by the reciprocal of the second fraction:
(11/21) / (20/6) = (11/21) * (6/20) 

Multiplying the numerators and denominators:
(11/21) * (6/20) = (11 * 6) / (21 * 20)

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

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 Flash:

To find the difference in time, we need to subtract the time for the second model from the time for the first model:

17/10 - 12/23

To subtract fractions, they need a common denominator. The least common multiple of 10 and 23 is 230.

(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 

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 Flash:

Here's how to solve the problem:

1. **Calculate the extra wood needed:** 
   (24/5) * (7/6) = (24 * 7) / (5 * 6) = 168/30 = 56/10 units of wood.

2. **Add the extra wood to the usual amount:**
   20/15 + 56/10 = (40 + 168)/30 = 208/30 units of wood.

3. **Simplify the answer:**
   208/30 = 104/15 units of wood.

### Answer: 104/15 

Expected answer: 104/15

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Start with the initial speed:** The car was initially going 13/4 miles per minute.

2. **Calculate the speed reduction:** The car slowed down by 14/15 miles per minute.

3. **Subtract the reduction from the initial speed:** (13/4) - (14/15) = (195/60) - (56/60) = 139/60 miles per minute.

4. **Calculate the speed increase:** The car increased its speed by 30/15 miles per minute, which simplifies to 2 miles per minute.

5. **Add the speed increase to the reduced speed:** (139/60) + 2 = (139/60) + (120/60) = 259/60 miles per minute.

6. **Simplify the final speed (optional):** The final speed can be simplified to 4.3167 miles per minute (approximately).

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

Expected answer: 259/60

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to break down the problem step-by-step:

**Step 1:  Grapes produced this season**

* The vineyard usually produces 19/2 baskets.
* This season, only 19/29 of the usual amount was produced.
* To find out how many baskets were produced, multiply the usual amount by the fraction representing this season's production: (19/2) * (19/29) = 361/58 baskets

**Step 2:  Grapes Jake gets to keep**

* Jake gets to keep 7/11 of the total grapes produced.
* Multiply the total amount of grapes produced by the fraction representing Jake's share: (361/58) * (7/11) = 2527/638 baskets

**Step 3:  Grapes used for juice**

* Jake uses 9/10 of his grapes to make juice.
* Multiply the amount of grapes Jake keeps by the fraction representing the grapes used for juice: (2527/638) * (9/10) = 22743/6380 baskets

**Final Answer:** Jake uses 22743/6380 baskets of grapes to make juice. 
### Answer: 22743/6380 

Expected answer: 22743/6380

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: To find the total number of bushels, we need to add the number of red grapes and green grapes.
We need to make sure the fractions have the same denominator before we add them.  The least common denominator of 2 and 22 is 22.
We can rewrite 9/2 as 99/22.
Now we can add the fractions: 99/22 + 10/22 = 109/22.
Therefore, Joel picked a total of 109/22 bushels of grapes that day.

### Answer: 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?

Gemini-1.5 Flash:

Reasoning: The radius of the larger snowball is 17/8 feet / 2 = 17/16 feet.
The radius of the smaller snowball is 1/20 feet / 2 = 1/40 feet.
The total height of the snowman is 17/16 feet + 1/40 feet = <<(17/16)+(1/40)=86/80>>86/80 feet.
### Answer: 86/80 feet

Expected answer: 87/40

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the problem:

* **Find a common denominator:** The smallest common denominator for 7 and 16 is 112.  
* **Convert fractions:**
    * 24/7 = (24 * 16) / (7 * 16) = 384/112
    * 2/16 = (2 * 7) / (16 * 7) = 14/112
* **Subtract the taken sand:** 384/112 - 14/112 = 370/112
* **Simplify (optional):** The fraction 370/112 can be simplified to 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 Flash:

Reasoning: To find the difference, we need to subtract the amount of zebra eaten from the amount of wildebeest eaten. 
First, find a common denominator for 28/26 and 23/9.  The least common denominator is 234 (26*9).
Convert 28/26 to an equivalent fraction with a denominator of 234: (28/26) * (9/9) = 252/234
Convert 23/9 to an equivalent fraction with a denominator of 234: (23/9) * (26/26) = 598/234
Now subtract the two fractions: 598/234 - 252/234 = 346/234
Simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 2: (346/2)/(234/2) = 173/117. 

### Answer: 173/117 

Expected answer: 173/117

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning:  To find the total amount of chocolate produced, we need to add the amount of cocoa and milk used. However, the amount of milk is given in liters, while the amount of cocoa is given in kilograms. We need to convert the amount of milk to kilograms. 

We are given that the factory uses 21/11 liters of milk for every kilogram of cocoa.  Therefore, we need to multiply the amount of cocoa by 21/11 to find the equivalent amount of milk in kilograms. 

The expression ((14 / 4) * (21 / 11))  will give us the total amount of chocolate produced in kilograms.

Calculating the expression:

((14 / 4) * (21 / 11)) = (3.5) * (1.91) = 6.685 

### Answer: 6.685 

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 Flash:

Reasoning: The formula ((12 / 29) + (30 / 10)) represents the expected number of bananas produced per day by each species. 

Let's break it down:

* **(12 / 29):** This represents the average number of bananas produced by the first species per day. Since it produces 12 bananas every 29 days, on average, it produces 12/29 bananas per day.
* **(30 / 10):** This represents the average number of bananas produced by the second species per day. Since it produces 30 bananas every 10 days, on average, it produces 30/10 bananas per day.

Therefore, the expected number of bananas produced by both species on a random day is:

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

### Answer: 99/29 

Expected answer: 99/29

Correct? Yes

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

Gemini-1.5 Flash:

To calculate the total ton of food the giraffe needs, we need to add the amount of acacia leaves and grasses:

11/11 ton + 26/14 ton

First, we simplify 11/11 to 1:

1 + 26/14 ton

Next, we convert the mixed number 1 26/14 to an improper fraction:

(14*1 + 26)/14 ton = 40/14 ton

Now we simplify the fraction 40/14 by dividing both numerator and denominator by their greatest common factor, which is 2:

40/14 ton = (40/2)/(14/2) ton = 20/7 ton

Therefore, the giraffe needs to eat a total of 20/7 ton of food in a day.

### Answer: 20/7 

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 Flash:

The fraction of time the bear spends sleeping in a day is 18/24.
Over 27 days, the bear spends (18/24) * 27 = 20.25 days sleeping.
The fraction of the month the bear spends sleeping is 20.25 / (13 * 7) = 20.25 / 91
### Answer: 0.223 

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 Flash:

Let's break down the calculation:

1. **Pine Trees:** The fraction representing pine trees is 9/14.
2. **Birch Trees:** The fraction representing birch trees is 19/2.
3. **Combining Fractions:** To find the total fraction of pine and birch trees, we need to add the fractions: (9/14) + (19/2). 
4. **Finding a Common Denominator:** Before adding fractions, they need the same denominator. The least common denominator of 14 and 2 is 14.  
5. **Adjusting Fractions:** We need to adjust the fraction for birch trees.  (19/2) * (7/7) = 133/14
6. **Adding the Fractions:** Now we can add the fractions: (9/14) + (133/14) = 142/14
7. **Simplifying:** The fraction 142/14 can be simplified to 71/7.

Therefore, the fraction of trees in the forest that are either pine or birch is 71/7.

### Answer: 71/7 

Expected answer: 71/7

Correct? Yes

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

Gemini-1.5 Flash:

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

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

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

### Answer: 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?

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Find the difference in friends hidden:**
   * Teddy hides 18/11 - 8/21 more friends in the forest than at the beach.
   * To subtract fractions, they need a common denominator. The least common multiple of 11 and 21 is 231.
   * (18/11) * (21/21) = 378/231
   * (8/21) * (11/11) = 88/231
   * (378/231) - (88/231) = 290/231
   * Therefore, 'f' = 290/231 

2. **Square 'f' to find 'n':**
   * 'n' = (290/231)^2
   * 'n' = 84100/53361

**Answer:** Teddy needs 84100/53361 hiding spots. 

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 Flash:

To find out how much energy the robot has left, we need to subtract the energy used from the initial energy:

* **Initial Energy:** 25/10 units
* **Energy Used:** 27/23 units

Before subtracting fractions, we need to have a common denominator.  The least common multiple of 10 and 23 is 230.

* **Converting Initial Energy:** (25/10) * (23/23) = 575/230
* **Converting Energy Used:** (27/23) * (10/10) = 270/230

Now we can subtract:

* **Energy Remaining:** (575/230) - (270/230) = 305/230

Therefore, the robot has **305/230** units of energy left.

### Answer: 305/230 

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 Flash:

Here's how we can solve this problem step-by-step:

1. **Calculate the combined distance of the first two snails:**
   - We're given the operation: ((17 / 21) + (20 / 24)) 
   - Find a common denominator for 21 and 24, which is 168.
   - (17 / 21) * (8/8) = 136/168
   - (20 / 24) * (7/7) = 140/168
   - (136/168) + (140/168) = 276/168

2. **Simplify the combined distance:**
   - Divide both numerator and denominator by their greatest common factor, 12.
   - (276/168) = (23/14) 

3. **Calculate the total distance with the third snail:**
   - We need to multiply the combined distance of the first two snails (23/14) by the third snail's speed (18/17).
   - (23/14) * (18/17) = 414/238

4. **Simplify the total distance:**
   - Divide both numerator and denominator by their greatest common factor, 2.
   - (414/238) = (207/119)

### Answer: 207/119 

Expected answer: 207/119

Correct? Yes

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 Flash:

Reasoning: First, find the difference of the original fabric and the remaining fabric: 24/14 - 9/29 = (24*29 - 9*14) / (14*29) = (696 - 126) / 406 = 570 / 406 = 285 / 203 yards.
Then multiply the difference by 15/2: (285 / 203) * (15 / 2) = (285 * 15) / (203 * 2) = 4275 / 406 yards.
### Answer: 4275/406 

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.

Gemini-1.5 Flash:

Reasoning: To add fractions, they need to have the same denominator. The least common denominator of 10 and 4 is 20. We can convert the fractions:
* 2/10 = 4/20
* 21/4 = 105/20
Now we can add them: 4/20 + 105/20 = 109/20
This means the total number of kids waiting for the swings is 109/20. 
### Answer: 109/20 

Expected answer: 109/20

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: The spacecraft has (18/30) * (22/6) = (3/5) * (11/3) = 11/5 hours of power. 

### Answer: 11/5 

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?

Gemini-1.5 Flash:

Reasoning: We need to find a common denominator for the fractions 16/12 and 6/10.  The least common denominator is 60.  So, 16/12 = (16*5)/(12*5) = 80/60, and 6/10 = (6*6)/(10*6) = 36/60.
The cat eats a total of 80/60 + 36/60 = 116/60 of a can per day.
### Answer: 116/60 

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 Flash:

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

Here's how to solve the problem step-by-step:

1. **Calculate the fraction of bananas the monkey ate:** (22/7) * (10/25) = (22 * 10) / (7 * 25) = 220/175 

2. **Simplify the fraction:** 220/175 = 44/35 

3. **Calculate the fraction of bananas the monkey had left after eating:** 1 - (44/35) = (35/35) - (44/35) = -9/35 

   Since the monkey cannot have a negative amount of bananas left, this means he ate more than the entire pile, which isn't possible. 

4. **Let's assume the problem meant the monkey ate (22/7) * (10/25) of the original pile:**
   * The monkey ate (44/35) of the pile (calculated above).

5. **Calculate the fraction of bananas left after giving some to his friend:** (44/35) - (3/28) = (176/140) - (15/140) = 161/140

6. **Since the fraction is greater than 1, this means the monkey gave away more bananas than he had left after eating, which isn't possible.  There must be an error in the problem statement.**

**It seems there's an error in the problem. It's impossible for the monkey to have a negative amount of bananas left or to give away more than he has.** 

Expected answer: 23/20

Correct? Yes

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 Flash:

To find the total distance the mouse runs, we multiply its speed by the time it runs. 

Here's how to calculate that:

* **Distance = Speed x Time**
* **Distance = (24/20 feet/second) x (23/2 seconds)**

Simplify the calculation by canceling out common factors:

* **Distance = (12/10 feet/second) x (23/1 second)**
* **Distance = (12 x 23) / (10 x 1) feet**

Now, perform the multiplication:

* **Distance = 276/10 feet**

Finally, simplify the fraction:

* **Distance = 27.6 feet**

### Answer: 27.6 

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?

Gemini-1.5 Flash:

Reasoning: To find the total ounces consumed, we need to multiply the amount in each glass by the fraction of glasses consumed. 
 
 (29/9) * (26/25) = <<(29/9)*(26/25) = 754/225>>754/225 ounces of beverage were consumed.

Next, we need to add the additional ounces consumed:

754/225 + 2/19 = <<(754/225)+(2/19) = 17282/4275>> 17282/4275 ounces of beverages were consumed in total.

### Answer: 17282/4275

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 Flash:

Let's break this problem down step by step.

1. **Initial Collection:**  You start with an unknown number of toothbrush sets, let's call this 'x'.

2. **Adding 7/15 of a set:** You add 7/15 of a new set to your collection.  This is a fraction of a set, not a whole set.

3. **Friend's Gift:** Your friend gives you 9 whole sets. 

4. **Total Sets:**  Now you have a total of x + (7/15) + 9 toothbrush sets.

5. **Display Case Limit:**  You can only fit 26/27 of your total collection in the display case.

6. **Calculating Fits:** To find out how many sets fit in the display case, we multiply the total sets by 26/27:
   
   [(x + (7/15) + 9) * (26/27)] sets

**However, we cannot determine the exact number of sets that fit in the display case without knowing the original number of sets ('x') you had.**

**Here's why:** The problem gives us a fraction of a new set (7/15) and a whole number of sets (9) that are added to an unknown original amount ('x'). 

**To solve this problem, you need to know the initial number of toothbrush sets you had ('x').** 

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 Flash:

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

First, we need to find a common denominator for the fractions 27/20 and 1/6. The least common multiple of 20 and 6 is 60.

* Convert 27/20 to an equivalent fraction with a denominator of 60: (27/20) * (3/3) = 81/60
* Convert 1/6 to an equivalent fraction with a denominator of 60: (1/6) * (10/10) = 10/60

Now we can add the fractions: 81/60 + 10/60 = 91/60

Therefore, the total weight of the backpack is **91/60 kilograms**. 
### Answer: 91/60 

Expected answer: 91/60

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: (7/7) * (25/22) simplifies to 1 * (25/22) which is equal to 25/22. This means the new bottle will be 25/22 times larger than the old bottle.

### 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 Flash:

Reasoning: First, we add the first two amounts of food: 25/9 + 8/13. To do this, we need a common denominator. The least common multiple of 9 and 13 is 117. We get:
(25/9) * (13/13) + (8/13) * (9/9) = 325/117 + 72/117 = 397/117.

Next, we add the third amount: 397/117 + 24/27. Again, we need a common denominator. The least common multiple of 117 and 27 is 351. We get:
(397/117) * (3/3) + (24/27) * (13/13) = 1191/351 + 312/351 = 1503/351.

Finally, we add the last amount: 1503/351 + 21/26. The least common multiple of 351 and 26 is 9126. We get:
(1503/351) * (26/26) + (21/26) * (351/351) = 39078/9126 + 7371/9126 = 46449/9126.

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 3:
46449/9126 = (46449/3) / (9126/3) = 15483/3042.

### Answer: 15483/3042 

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.

Gemini-1.5 Flash:

Here's how we can break down Captain Alf's calculations:

1. **Difference in location:**  
   - Distance to island: 17/2 nautical miles
   - Current location: 4/2 nautical miles
   - Difference: (17/2) - (4/2) = 13/2 nautical miles

2. **Tide Adjustment:**
   - Difference in location: 13/2 nautical miles
   - Tide adjustment: 14/9 nautical miles
   - Adjusted distance: (13/2) + (14/9) = (117/18) + (28/18) = 145/18 nautical miles

3. **Fuel Requirements:**
   - Adjusted distance: 145/18 nautical miles
   - Fuel efficiency: 22/15 nautical miles per gallon
   - Fuel requirement: (145/18) * (22/15) = 3190/270 gallons

**Simplifying the fraction:**

- The greatest common factor of 3190 and 270 is 10.
- Dividing both the numerator and denominator by 10 gives us 319/27 gallons.

### Answer: 319/27 

Expected answer: 319/27

Correct? Yes

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

Gemini-1.5 Flash:

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

Expected answer: 41/9

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: Arthur practices for 20/21 + 11/29 hours each day on the weekend.
To add these fractions, we need a common denominator. The least common denominator of 21 and 29 is 609.
20/21 = (20 * 29)/(21 * 29) = 580/609
11/29 = (11 * 21)/(29 * 21) = 231/609
Therefore, Arthur practices for 580/609 + 231/609 = 811/609 hours on the weekend.
### Answer: 811/609 

Expected answer: 811/609

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Shirts per sibling initially:** Lucas initially gave each sibling 18 shirts / 3 siblings = 6 shirts.

2. **Shirts per sibling from new purchase:** Lucas kept 27 shirts / 19 siblings = 1.42 shirts (approximately) per sibling from the new purchase.

3. **Total shirts per sibling now:** Each sibling now has 6 shirts + 1.42 shirts = 7.42 shirts (approximately).

4. **Difference in shirts:** The difference between the number of shirts each sibling has now and before is 7.42 shirts - 6 shirts = 1.42 shirts.

5. **Using the expression:** Let's calculate the difference using the expression ((18 / 3) - (27 / 19)):
   - (18 / 3) = 6
   - (27 / 19) = 1.42 (approximately)
   - (6 - 1.42) = 4.58 (approximately)

**Therefore, each sibling has approximately 1.42 more shirts now than before.**

### Answer: 1.42 

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 Flash:

Reasoning: The painter has 7+2/5 = 37/5 gallons of light blue paint before starting the project.
After using 18/4 gallons of paint, he has 37/5 - 18/4 gallons of light blue paint left.
To subtract fractions, we need a common denominator. The least common denominator for 5 and 4 is 20. 
37/5 = 148/20
18/4 = 90/20
So, the painter has 148/20 - 90/20 = 58/20 = 29/10 gallons of light blue paint left.
### Answer: 29/10 

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 Flash:

Reasoning: To find the total time Jayson spent skating, we need to add the time from the first day and the second day.

First, let's simplify the fractions:

* 24/7 hours is already in its simplest form.
* 30/20 hours can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 10: 30/20 = 3/2 hours.

Now, let's add the fractions:

* 24/7 + 3/2 

To add fractions, they need to have the same denominator.  The least common denominator of 7 and 2 is 14.

* (24/7) * (2/2) = 48/14
* (3/2) * (7/7) = 21/14

Now we can add the fractions:

* 48/14 + 21/14 = 69/14

This fraction represents the total time Jayson spent skating in hours. We can leave it as an improper fraction or convert it to a mixed number:

* 69/14 = 4 11/14 hours

### Answer: 4 11/14 hours

Expected answer: 69/14

Correct? No

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

Gemini-1.5 Flash:

Reasoning: First we need to find the usual height of the dolphin's jump. 18/3 = <<18/3=6>>6 feet.
Now we need to find 3/4 of 6 feet. 6 * (3/4) = <<6*(3/4)=4.5>> 4.5 feet.
### Answer: 4.5 

Expected answer: 9/2

Correct? Yes

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

Gemini-1.5 Flash:

First, we need to calculate the ratio of last month's sales to production. 
Last month's sales to production ratio is 20/15 + 16/22.  We can simplify this by finding a common denominator. The least common denominator for 15 and 22 is 330.  Therefore, we get (20/15 + 16/22) = (440/330 + 240/330) = (680/330).  

Next, we need to calculate the ratio of interested customers to production this week. This week's interested customers to production ratio is (22/27) * (23/8).

Finally, we need to multiply the two ratios we calculated.  This results in (680/330) * (22/27) * (23/8). 

### Answer: 680 * 22 * 23 / (330 * 27 * 8) 

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?

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Time per song:** The musician spent 30 minutes / 15 songs = 2 minutes per song.

2. **Time reduction:** 1/17 of an hour is equal to (60 minutes / 17) = approximately 3.53 minutes.

3. **Final duration:** The final duration of the song is 2 minutes - 3.53 minutes = -1.53 minutes.

**Since the result is negative, it means the time reduction is greater than the initial time spent on the song, which is not possible. Therefore, there must be an error in the problem statement.** 

It's likely that the musician couldn't have reduced the time by 1/17 of an hour, as this is more than the initial time spent on the song. 

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 Flash:

Here's how to solve the problem:

* **Josh's total riding time:** 18 hours (first day) + 1/12 hour (second day) = 18 1/12 hours

* **Converting Josh's time to a fraction:** 18 1/12 hours = (18 * 12 + 1)/12 = 217/12 hours

* **Adding Jack's riding time:** 217/12 hours + 7/17 hours 

* **Finding a common denominator:** The least common multiple of 12 and 17 is 204.  So, we'll convert the fractions: 
    * (217/12) * (17/17) = 3689/204
    * (7/17) * (12/12) = 84/204

* **Adding the fractions:** 3689/204 + 84/204 = 3773/204

### Answer: 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?

Gemini-1.5 Flash:

Reasoning: To find the total fraction of lamps, we need to add the fractions representing each type of lamp: 4/26 + 15/11 + 23/28 + 8/19. However, before adding fractions, we need to make sure they have a common denominator.

Finding the Least Common Multiple (LCM) of 26, 11, 28, and 19:
* Prime factorize each number: 
    * 26 = 2 x 13
    * 11 = 11
    * 28 = 2 x 2 x 7
    * 19 = 19
*  The LCM is the product of the highest powers of all prime factors: 2² x 7 x 11 x 13 x 19 = 48048

Converting each fraction to have a denominator of 48048:
* 4/26 = (4 x 1848) / (26 x 1848) = 7392/48048
* 15/11 = (15 x 4368) / (11 x 4368) = 65520/48048
* 23/28 = (23 x 1716) / (28 x 1716) = 39468/48048
* 8/19 = (8 x 2528) / (19 x 2528) = 20224/48048

Now, we can add the fractions:
* 7392/48048 + 65520/48048 + 39468/48048 + 20224/48048 = (7392 + 65520 + 39468 + 20224) / 48048 = 132604/48048

Simplifying the fraction (by dividing numerator and denominator by their greatest common factor, 36):
* 132604/48048 = (132604/36) / (48048/36) = 3683.44/1334.67

Therefore, these lamps constitute **3683.44/1334.67** of the store's total inventory. 
### Answer: 3683.44/1334.67 

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 Flash:

Reasoning: Oliver's combined string is 26/19 + 7/11 meters long.
He uses 5/8 * (26/19 + 7/11) meters of string.
This can be simplified to (5/8)*(26/19 + 7/11) = (5/8)*(286/209 + 133/209) = (5/8)*(419/209) = 2095/1672 meters.
### Answer: 2095/1672 

Expected answer: 2095/1672

Correct? Yes

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

Gemini-1.5 Flash:

Let's solve the equations step-by-step:

**1. Solve for 'u':**

* Find a common denominator for 9/19 and 6/8. The least common multiple of 19 and 8 is 152.
* Convert the fractions: 9/19 = (9 * 8) / (19 * 8) = 72/152
* Convert the fractions: 6/8 = (6 * 19) / (8 * 19) = 114/152
* Add the fractions: 72/152 + 114/152 = 186/152
* Simplify the fraction: 186/152 = 93/76
* Therefore, u = 93/76

**2. Solve for 'j':**

* Substitute the value of 'u' into the equation: j = 93/76 + 4/1
* Find a common denominator: 93/76 + (4 * 76) / (1 * 76) = 93/76 + 304/76
* Add the fractions: 93/76 + 304/76 = 397/76
* Therefore, j = 397/76

**Answer:** Mike had a total of 397/76 snowballs. 

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.

Gemini-1.5 Flash:

Reasoning: The first worker packages 26/18 = 1.44 pieces of chocolate in one minute.
The second worker packages 15/15 = 1 piece of chocolate in one minute. 
Therefore, together they package 1.44+1 = 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 Flash:

Reasoning: Joanna washed 24/20 + 25/15 batches of towels in total.
First, we need to find a common denominator for 20 and 15. The least common multiple of 20 and 15 is 60. 
So we have 24/20 = (24/20) * (3/3) = 72/60
and 25/15 = (25/15) * (4/4) = 100/60.
Adding these two fractions, we have 72/60 + 100/60 = (72 + 100)/60 = 172/60.
Therefore, Joanna washed a total of 172/60 batches of towels. 
### Answer: 172/60 

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?

Gemini-1.5 Flash:

Here's how we can solve this problem step-by-step:

1. **Calculate the initial flour-to-sugar ratio:** 
   (27/3) cups flour / (11/7) cups sugar = (27/3) * (7/11) = 63/11

2. **Subtract the sugar adjustment:**
   63/11 - (21/26) = (63 * 26 - 21 * 11) / (11 * 26) = 1545/286

3. **Add the flour from the second recipe:**
   1545/286 + (22/9) = (1545 * 9 + 22 * 286) / (286 * 9) = 18847 / 2574

4. **Simplify the fraction (optional):**
   This fraction can be simplified, but for the sake of this problem, we will leave it as is.

**Therefore, Debra will have 18847/2574 cups of flour in the end.**

### Answer: 18847/2574 

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 Flash:

Reasoning: 
* First, we need to find the difference between the number of chickens in the two farms: 26/13 - 9/16 = 2 - 9/16 = 23/16 chickens
* After a week, the number of chickens increased by 19/21 times the original number. 
* So, the total number of chickens is now: 23/16 * 19/21 = 437/336 chickens

### Answer: 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'?

Gemini-1.5 Flash:

Reasoning: The helicopter traveled 24/14 miles for each exercise, so 'w' = 24/14.
The total distance flown for both exercises is represented by 't' = w * w.
Therefore, 't' = (24/14) * (24/14) = 576/196. 

### Answer: 576/196

Expected answer: 144/49

Correct? Yes

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

Gemini-1.5 Flash:

To find the total fraction of the tank refilled, we need to add the fractions from each stop:

* First stop: 20/16
* Second stop: 24/25

Before we can add these fractions, we need to find a common denominator. The least common multiple of 16 and 25 is 400.

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

Now we can add the fractions:

* 500/400 + 384/400 = 884/400

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, 4:

* 884/400 = (884/4) / (400/4) = 221/100

Therefore, the UFO refilled a total of 221/100 of its fuel tank during the two stops.

### 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 Flash:

Here's how to calculate the sum of the fractions:

1. **Find a common denominator:**  The least common denominator of 27 and 26 is 702 (27 * 26).
2. **Convert the fractions:**
   * (24/27) = (24 * 26) / (27 * 26) = 624/702
   * (30/26) = (30 * 27) / (26 * 27) = 810/702
3. **Add the fractions:** (624/702) + (810/702) = (624 + 810) / 702 = 1434/702
4. **Simplify (optional):** The fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 2: 1434/702 = 717/351

### Answer: 717/351 

Expected answer: 239/117

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: Kiki ate 11/6 bananas in the morning + 11/6 bananas in the afternoon = 11/6 + 11/6 = 22/6 bananas.

### 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 Flash:

Reasoning: To find the total milk per cow per day, we need to multiply the morning milk by the evening milk.
 
 (26/14) * (28/20) = (26*28)/(14*20) =  (2*13*2*2*7)/(2*7*2*10) = (13*2)/(10) = 26/10 gallons.
 
### Answer: 26/10 gallons. 

Expected answer: 13/5

Correct? Yes