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GPT-4o on 6.NS.B.2

Common Core Standard 6.NS.B.2

This standard covers the following:

Fluently divide multi-digit numbers using the standard algorithm.

๐Ÿ”— Problem

Problem: There are 73841 cubic centimeters of air needed to inflate a large beach ball. If we fill the ball up at a rate of 41 cubic centimeters per second, how many seconds will it take to fully inflate the beach ball?

GPT-4o:

To determine how many seconds it will take to fully inflate the beach ball, we need to divide the total volume of air required by the rate at which the air is being added.

The total volume of air needed is 73,841 cubic centimeters, and the rate of filling is 41 cubic centimeters per second.

We perform the division:
\[ \frac{73841 \text{ cubic centimeters}}{41 \text{ cubic centimeters per second}} \]

Let's calculate this:
\[ 73841 \div 41 = 1801 \]

So, it will take 1,801 seconds to fully inflate the beach ball.

### Answer: 1801 seconds

Expected answer: 1801

Correct? Yes

๐Ÿ”— Follow-up

Problem: If we had a smaller beach ball that only required 1310 cubic centimeters of air to fully inflate, and we continue to fill it up at a rate of 41 cubic centimeters per second, how many seconds will it then take to inflate this smaller beach ball?

GPT-4o:

To determine how many seconds it will take to fully inflate the smaller beach ball, we need to divide the total volume of air required by the rate at which the air is being added.

The total volume of air needed for the smaller beach ball is 1,310 cubic centimeters, and the rate of filling is 41 cubic centimeters per second.

We perform the division:
\[ \frac{1310 \text{ cubic centimeters}}{41 \text{ cubic centimeters per second}} \]

Let's calculate this:
\[ 1310 \div 41 = 32 \]

So, it will take 32 seconds to fully inflate the smaller beach ball.

### Answer: 32 seconds

Expected answer: 1310/41

Correct? No

๐Ÿ”— Problem

Problem: A juice company produced 73528 liters of juice. If they filled the same amount of juice into 707 containers, how many liters of juice are there in each container?

GPT-4o:

To determine how many liters of juice are in each container, we need to divide the total amount of juice by the number of containers.

Given:
- Total juice produced = 73,528 liters
- Number of containers = 707

We perform the division:

\[ \frac{73,528}{707} \]

First, let's set up the division:

\[ 73,528 \div 707 \]

Performing the division step-by-step:

1. 707 goes into 735 (the first three digits of 73,528) once (1 time).
   - 707 ร— 1 = 707
   - Subtract 707 from 735: 735 - 707 = 28

2. Bring down the next digit (2), making it 282.
   - 707 goes into 282 zero times (0 times).
   - 707 ร— 0 = 0
   - Subtract 0 from 282: 282 - 0 = 282

3. Bring down the next digit (8), making it 2828.
   - 707 goes into 2828 four times (4 times).
   - 707 ร— 4 = 2828
   - Subtract 2828 from 2828: 2828 - 2828 = 0

So, the result of the division is 104.

### Answer: 104

Expected answer: 104

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the previous problem, the juice company produced 73528 liters of juice filled into 707 containers. Now consider instead that the juice company produced a new batch of fresh juice, a total of 2858 liters. If the new batch was also filled the same way into 707 containers, how many liters of juice are now in each container?

GPT-4o:

To determine how many liters of juice are in each container for the new batch, we need to divide the total amount of juice by the number of containers.

Given:
- Total juice produced in the new batch = 2,858 liters
- Number of containers = 707

We perform the division:

\[ \frac{2,858}{707} \]

First, let's set up the division:

\[ 2,858 \div 707 \]

Performing the division step-by-step:

1. 707 goes into 2858 four times (4 times).
   - 707 ร— 4 = 2828
   - Subtract 2828 from 2858: 2858 - 2828 = 30

Since there are no more digits to bring down, the division is complete.

So, the result of the division is 4 with a remainder of 30, but since we are only interested in the whole number of liters per container:

### Answer: 4

Expected answer: 2858/707

Correct? No

๐Ÿ”— Problem

Problem: A pants factory produced a total of 87780 pants and equally distributed them to 110 wholesale clothing stores. How many pants did each store receive?

GPT-4o:

To determine how many pants each store received, we need to divide the total number of pants by the number of stores.

Total number of pants produced: 87,780
Number of stores: 110

We perform the division:

\[ \frac{87780}{110} \]

First, simplify the division:

\[ \frac{87780 \div 10}{110 \div 10} = \frac{8778}{11} \]

Now, perform the division:

\[ 8778 \div 11 = 798 \]

So, each store received 798 pants.

### Answer: 798

Expected answer: 798

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the pants factory had produced a total of 4003 pants instead of 87780, and still equally distributed them to the 110 wholesale clothing stores, how many pants would each store have received now?

GPT-4o:

To determine how many pants each store would receive if the factory produced 4,003 pants and distributed them equally among 110 stores, we need to perform the division:

Total number of pants produced: 4,003
Number of stores: 110

We perform the division:

\[ \frac{4003}{110} \]

First, simplify the division:

\[ 4003 \div 110 \approx 36.39 \]

Since the number of pants must be a whole number, we can conclude that each store would receive 36 pants, and there would be some pants left over.

To find the exact number of pants each store receives and the remainder, we can use integer division and the modulus operation:

\[ 4003 \div 110 = 36 \text{ (quotient)} \]
\[ 4003 \mod 110 = 43 \text{ (remainder)} \]

So, each store would receive 36 pants, and there would be 43 pants left over.

### Answer: 36

Expected answer: 4003/110

Correct? No

๐Ÿ”— Problem

Problem: Farmer Bob has grown 71820 carrots this season and wants to sell them in bundles. If he makes each bundle consist of 684 carrots, how many bundles of carrots will he have?

GPT-4o:

To determine how many bundles of carrots Farmer Bob will have, we need to divide the total number of carrots by the number of carrots per bundle.

First, we perform the division:
\[ \frac{71820}{684} \]

Let's do the division step-by-step:

1. Divide 71820 by 684:
\[ 71820 \div 684 \approx 105 \]

To verify, we multiply 684 by 105:
\[ 684 \times 105 = 684 \times (100 + 5) = 684 \times 100 + 684 \times 5 = 68400 + 3420 = 71820 \]

Since the multiplication confirms our division, Farmer Bob will have:
### Answer: 105

Expected answer: 105

Correct? Yes

๐Ÿ”— Follow-up

Problem: Farmer Bob reconsiders and decides to increase the size of each bundle. If he now distributes his 71820 carrots into bundles of 2486 each, how many bundles will he have?

GPT-4o:

To determine how many bundles of carrots Farmer Bob will have with the new bundle size, we need to divide the total number of carrots by the number of carrots per bundle.

First, we perform the division:
\[ \frac{71820}{2486} \]

Let's do the division step-by-step:

1. Divide 71820 by 2486:
\[ 71820 \div 2486 \approx 28.9 \]

Since we cannot have a fraction of a bundle, we round down to the nearest whole number:
\[ 28 \]

To verify, we multiply 2486 by 28:
\[ 2486 \times 28 = 2486 \times (20 + 8) = 2486 \times 20 + 2486 \times 8 = 49720 + 19888 = 69608 \]

Since 69608 is less than 71820, we check if adding one more bundle (29) would exceed the total:
\[ 2486 \times 29 = 2486 \times (20 + 9) = 2486 \times 20 + 2486 \times 9 = 49720 + 22374 = 72094 \]

Since 72094 exceeds 71820, 28 is indeed the correct number of full bundles.

### Answer: 28

Expected answer: 35910/1243

Correct? No

๐Ÿ”— Problem

Problem: A popular slide has been used 85860 times over 54 consecutive days. If the usage rate is constant, how many times per day has the slide been used?

GPT-4o:

To determine the number of times the slide has been used per day, we need to divide the total number of uses by the number of days.

Given:
- Total uses: 85,860
- Number of days: 54

We perform the division:

\[ \frac{85,860}{54} \]

First, let's simplify the division step-by-step:

1. Divide 85,860 by 54:
\[ 85,860 \div 54 = 1,590 \]

So, the slide has been used 1,590 times per day.

### Answer: 1,590

Expected answer: 1590

Correct? Yes

๐Ÿ”— Follow-up

Problem: After maintaining a consistent usage rate, the same slide has been used 9018 times over 54 consecutive days. Under this rate, how many times per day has the slide been used?

GPT-4o:

To determine the number of times the slide has been used per day, we need to divide the total number of uses by the number of days.

Given:
- Total uses: 9,018
- Number of days: 54

We perform the division:

\[ \frac{9,018}{54} \]

First, let's simplify the division step-by-step:

1. Divide 9,018 by 54:
\[ 9,018 \div 54 = 167 \]

So, the slide has been used 167 times per day.

### Answer: 167

Expected answer: 167

Correct? Yes

๐Ÿ”— Problem

Problem: A ski resort receives a total of 31950 inches of snowfall evenly spread throughout 225 days of winter. How many inches of snow does the ski resort receive each day?

GPT-4o:

To determine how many inches of snow the ski resort receives each day, we need to divide the total snowfall by the number of days.

Total snowfall: 31,950 inches
Number of days: 225 days

We perform the division:

\[ \frac{31950}{225} \]

First, simplify the division:

\[ 31950 \div 225 = 142 \]

So, the ski resort receives 142 inches of snow each day.

### Answer: 142 inches

Expected answer: 142

Correct? Yes

๐Ÿ”— Follow-up

Problem: What if the snow was spread out not over 225 days, but over a period of 1814 days? How many inches of snow would the ski resort receive each day in this case?

GPT-4o:

To determine how many inches of snow the ski resort receives each day over a period of 1814 days, we need to divide the total snowfall by the number of days.

Total snowfall: 31,950 inches
Number of days: 1,814 days

We perform the division:

\[ \frac{31950}{1814} \]

First, simplify the division:

\[ 31950 \div 1814 \approx 17.62 \]

So, the ski resort receives approximately 17.62 inches of snow each day.

### Answer: 17.62 inches

Expected answer: 15975/907

Correct? No

๐Ÿ”— Problem

Problem: A jewelry manufacturer has 63802 grams of gold, and they want to make rings each of which will weigh exactly the same. If they plan to make 38 rings, how many grams of gold will be in each ring?

GPT-4o:

To determine how many grams of gold will be in each ring, we need to divide the total amount of gold by the number of rings.

Total grams of gold: 63,802 grams
Number of rings: 38

We perform the division:

\[ \frac{63802}{38} \]

First, let's do the division step-by-step:

1. 63,802 รท 38
2. 63,802 รท 38 โ‰ˆ 1,679

So, each ring will weigh approximately 1,679 grams.

### Answer: 1,679 grams

Expected answer: 1679

Correct? Yes

๐Ÿ”— Follow-up

Problem: The jewelry manufacturer now has 5240 grams of gold instead of 63802 grams. If they still want to make each ring weigh exactly the same and produce 38 rings, how many grams of gold will be in each ring now?

GPT-4o:

To determine how many grams of gold will be in each ring, we need to divide the total amount of gold by the number of rings.

Total grams of gold: 5,240 grams
Number of rings: 38

We perform the division:

\[ \frac{5240}{38} \]

Let's do the division step-by-step:

1. 5240 รท 38
2. 5240 รท 38 = 138

So, each ring will weigh 138 grams.

### Answer: 138 grams

Expected answer: 2620/19

Correct? No

๐Ÿ”— Problem

Problem: A goldsmith has a total of 60544 milligrams of gold. If each ring the goldsmith makes requires exactly 5504 milligrams of gold, how many full rings can the goldsmith make?

GPT-4o:

To determine how many full rings the goldsmith can make, we need to divide the total amount of gold by the amount of gold required for each ring.

First, let's set up the division:
\[ \frac{60544 \text{ mg}}{5504 \text{ mg/ring}} \]

Perform the division:
\[ 60544 \div 5504 \approx 11 \]

To verify, we can multiply the number of rings by the amount of gold per ring:
\[ 11 \times 5504 = 60544 \]

Since the multiplication confirms the division, the goldsmith can make exactly 11 full rings.

### Answer: 11

Expected answer: 11

Correct? Yes

๐Ÿ”— Problem

Problem: In a zoo, there are 10489 animals, and they are evenly distributed in 617 cages. What is the average number of animals in each cage?

GPT-4o:

To find the average number of animals in each cage, we need to divide the total number of animals by the total number of cages.

Total number of animals = 10,489
Total number of cages = 617

We perform the division:

\[ \frac{10489}{617} \approx 17 \]

So, the average number of animals in each cage is approximately 17.

### Answer: 17

Expected answer: 17

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now consider that instead of 617 cages, the 10,489 animals are evenly distributed in 5130 cages. How does the average number of animals per cage change now?

GPT-4o:

To find the new average number of animals per cage, we need to divide the total number of animals by the new total number of cages.

Total number of animals = 10,489
Total number of cages = 5,130

We perform the division:

\[ \frac{10489}{5130} \approx 2.045 \]

So, the average number of animals in each cage is approximately 2.045.

### Answer: 2.045

Expected answer: 10489/5130

Correct? No

๐Ÿ”— Problem

Problem: A farmer has 21652 grams of carrots, and he wants to evenly distribute them into 5413 bags. How many grams of carrots will be in each bag?

GPT-4o:

To determine how many grams of carrots will be in each bag, we need to divide the total number of grams by the number of bags.

Given:
- Total grams of carrots = 21,652 grams
- Number of bags = 5,413

We perform the division:

\[ \frac{21652}{5413} \]

Using long division or a calculator, we find:

\[ 21652 \div 5413 = 4 \]

So, each bag will contain 4 grams of carrots.

### Answer: 4 grams

Expected answer: 4

Correct? Yes

๐Ÿ”— Follow-up

Problem: The farmer had initially thought he had 21652 grams of carrots. However, upon recounting, he realizes he actually has 5652 grams of carrots. If he still wants to distribute the carrots evenly into 5413 bags, how many grams of carrots will now be in each bag?

GPT-4o:

To determine how many grams of carrots will be in each bag after recounting, we need to divide the new total number of grams by the number of bags.

Given:
- Total grams of carrots = 5,652 grams
- Number of bags = 5,413

We perform the division:

\[ \frac{5652}{5413} \]

Using long division or a calculator, we find:

\[ 5652 \div 5413 \approx 1.044 \]

Since we are distributing whole grams of carrots, each bag will contain 1 gram of carrots, and there will be some remainder.

### Answer: 1 gram

Expected answer: 5652/5413

Correct? No

๐Ÿ”— Problem

Problem: An astronaut's spaceship travels a total distance of 38745 miles on its space mission. The journey is divided into 5 equal stages. How many miles does the spaceship travel in each stage?

GPT-4o:

To determine how many miles the spaceship travels in each stage, we need to divide the total distance by the number of stages.

Total distance: 38745 miles
Number of stages: 5

We perform the division:

\[ \frac{38745}{5} \]

First, we divide 38745 by 5:

\[ 38745 \div 5 = 7749 \]

So, the spaceship travels 7749 miles in each stage.

### Answer: 7749 miles

Expected answer: 7749

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the previous space mission scenario, if instead, the spaceship had to divide its total travel distance of 38745 miles into 3113 equal stages, how many miles would it now have to travel in each stage?

GPT-4o:

To determine how many miles the spaceship travels in each stage when the total distance is divided into 3113 equal stages, we need to divide the total distance by the number of stages.

Total distance: 38745 miles
Number of stages: 3113

We perform the division:

\[ \frac{38745}{3113} \]

First, we perform the division:

\[ 38745 \div 3113 \approx 12.45 \]

So, the spaceship travels approximately 12.45 miles in each stage.

### Answer: 12.45 miles

Expected answer: 38745/3113

Correct? No

๐Ÿ”— Problem

Problem: A factory needs to distribute 84,564 liters of water evenly into 261 bottles. If each bottle gets the same amount of water, how many liters does each bottle contain?

GPT-4o:

To determine how many liters each bottle contains, we need to divide the total amount of water by the number of bottles.

Given:
- Total water: 84,564 liters
- Number of bottles: 261

We perform the division:

\[ \frac{84,564}{261} \]

First, let's do the division step-by-step:

1. 261 goes into 845 (the first three digits of 84,564) approximately 3 times (since \( 261 \times 3 = 783 \)).
2. Subtract 783 from 845 to get 62.
3. Bring down the next digit (6), making it 626.
4. 261 goes into 626 approximately 2 times (since \( 261 \times 2 = 522 \)).
5. Subtract 522 from 626 to get 104.
6. Bring down the next digit (4), making it 1044.
7. 261 goes into 1044 exactly 4 times (since \( 261 \times 4 = 1044 \)).

So, the division is exact, and each bottle contains:

\[ \frac{84,564}{261} = 324 \]

### Answer: 324 liters

Expected answer: 324

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the factory instead needed to distribute 84,564 liters of water evenly into 1,779 bottles, how many liters would each bottle contain now?

GPT-4o:

To determine how many liters each bottle contains, we need to divide the total amount of water by the number of bottles.

Given:
- Total water: 84,564 liters
- Number of bottles: 1,779

We perform the division:

\[ \frac{84,564}{1,779} \]

First, let's do the division step-by-step:

1. 1,779 goes into 8,456 (the first four digits of 84,564) approximately 4 times (since \( 1,779 \times 4 = 7,116 \)).
2. Subtract 7,116 from 8,456 to get 1,340.
3. Bring down the next digit (6), making it 13,406.
4. 1,779 goes into 13,406 approximately 7 times (since \( 1,779 \times 7 = 12,453 \)).
5. Subtract 12,453 from 13,406 to get 953.
6. Bring down the next digit (4), making it 9,534.
7. 1,779 goes into 9,534 exactly 5 times (since \( 1,779 \times 5 = 8,895 \)).
8. Subtract 8,895 from 9,534 to get 639.

So, the division is exact, and each bottle contains:

\[ \frac{84,564}{1,779} = 47.5 \]

### Answer: 47.5 liters

Expected answer: 28188/593

Correct? No

๐Ÿ”— Problem

Problem: A massive book series contains a total of 13467 pages, divided equally among 201 volumes. How many pages would you find in each volume?

GPT-4o:

To determine the number of pages in each volume, we need to divide the total number of pages by the number of volumes.

Total number of pages = 13,467
Number of volumes = 201

We perform the division:

\[ \frac{13467}{201} \]

First, let's set up the long division:

1. 201 goes into 1346 (the first four digits of 13467) approximately 6 times (since \( 201 \times 6 = 1206 \)).
2. Subtract 1206 from 1346 to get 140.
3. Bring down the next digit, 7, making it 1407.
4. 201 goes into 1407 approximately 7 times (since \( 201 \times 7 = 1407 \)).

So, the division is exact, and each volume contains:

\[ 13467 \div 201 = 67 \]

### Answer: 67

Expected answer: 67

Correct? Yes

๐Ÿ”— Problem

Problem: A fireplace uses 56888 BTU (British Thermal Units) of energy in 2188 hours when it is working continuously. How many BTU of energy does the fireplace use per hour?

GPT-4o:

To find the number of BTU of energy the fireplace uses per hour, we need to divide the total energy used by the total number of hours.

Given:
- Total energy used = 56888 BTU
- Total hours = 2188 hours

We perform the division:

\[
\frac{56888 \text{ BTU}}{2188 \text{ hours}} = 26 \text{ BTU/hour}
\]

### Answer: 26 BTU/hour

Expected answer: 26

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of 2188 hours, the fireplace was working continuously for 3809 hours with the same total energy consumption of 56888 BTU, how many BTU of energy would the fireplace use per hour then?

GPT-4o:

To find the number of BTU of energy the fireplace uses per hour when it works for 3809 hours, we need to divide the total energy used by the total number of hours.

Given:
- Total energy used = 56888 BTU
- Total hours = 3809 hours

We perform the division:

\[
\frac{56888 \text{ BTU}}{3809 \text{ hours}} \approx 14.93 \text{ BTU/hour}
\]

### Answer: 14.93 BTU/hour

Expected answer: 4376/293

Correct? No

๐Ÿ”— Problem

Problem: Across the span of 82 days in winter, a town recorded a total snowfall of 36900 inches. If the snow fell at a constant rate every day, how many inches of snow did the town receive each day?

GPT-4o:

To find the average snowfall per day, we need to divide the total snowfall by the number of days.

Total snowfall: 36,900 inches
Number of days: 82

We perform the division:

\[ \frac{36900 \text{ inches}}{82 \text{ days}} \]

First, let's simplify the division:

\[ 36900 \div 82 \]

Performing the division:

\[ 36900 \div 82 = 450 \]

So, the town received 450 inches of snow each day.

### Answer: 450 inches

Expected answer: 450

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the same town, in another winter period, the total snowfall recorded was 36900 inches as well but this time across 7138 days. If the snow fell at a constant rate every day, how many inches of snow did the town receive each day during this period?

GPT-4o:

To find the average snowfall per day, we need to divide the total snowfall by the number of days.

Total snowfall: 36,900 inches
Number of days: 7,138

We perform the division:

\[ \frac{36900 \text{ inches}}{7138 \text{ days}} \]

Performing the division:

\[ 36900 \div 7138 \approx 5.17 \]

So, the town received approximately 5.17 inches of snow each day.

### Answer: 5.17 inches

Expected answer: 18450/3569

Correct? No

๐Ÿ”— Problem

Problem: A wildlife reserve spans an area of 71292 square kilometers and is home to 2742 giraffes. If each giraffe has an equal amount of space, how many square kilometers does each giraffe get?

GPT-4o:

To determine how many square kilometers each giraffe gets, we need to divide the total area of the wildlife reserve by the number of giraffes.

The total area of the wildlife reserve is 71,292 square kilometers, and there are 2,742 giraffes.

We perform the division:
\[ \frac{71,292}{2,742} \]

First, let's simplify the division step-by-step:

1. Divide 71,292 by 2,742:
\[ 71,292 \div 2,742 \approx 26 \]

So, each giraffe gets approximately 26 square kilometers.

### Answer: 26 square kilometers

Expected answer: 26

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the wildlife reserve instead held 8787 giraffes that were spread out evenly across the 71292 square kilometers. In this case, how many square kilometers would each giraffe get?

GPT-4o:

To determine how many square kilometers each giraffe gets, we need to divide the total area of the wildlife reserve by the number of giraffes.

The total area of the wildlife reserve is 71,292 square kilometers, and there are 8,787 giraffes.

We perform the division:
\[ \frac{71,292}{8,787} \]

Let's calculate this step-by-step:

1. Divide 71,292 by 8,787:
\[ 71,292 \div 8,787 \approx 8.11 \]

So, each giraffe gets approximately 8.11 square kilometers.

### Answer: 8.11 square kilometers

Expected answer: 23764/2929

Correct? No

๐Ÿ”— Problem

Problem: A lion conservation project has successfully protected 96187 lions over a span of 13 years. If the project saved the same number of lions each year, how many lions were saved per year on average?

GPT-4o:

To find the average number of lions saved per year, we need to divide the total number of lions saved by the number of years.

Total number of lions saved: 96,187
Number of years: 13

We perform the division:

\[ \frac{96,187}{13} \]

First, let's do the division step-by-step:

1. 96,187 รท 13 โ‰ˆ 7,398.230769

Since we are looking for the average number of lions saved per year, we can round to the nearest whole number:

\[ 7,398.230769 \approx 7,398 \]

### Answer: 7,398

Expected answer: 7399

Correct? No

๐Ÿ”— Problem

Problem: A mermaid has found a total of 32812 pearls on the ocean floor and wants to divide them evenly among her 631 mermaid friends. How many pearls will each friend receive?

GPT-4o:

To determine how many pearls each mermaid friend will receive, we need to divide the total number of pearls by the number of mermaid friends.

The total number of pearls is 32,812, and the number of mermaid friends is 631.

We perform the division:

\[ 32812 \div 631 \]

First, we estimate how many times 631 can go into 32812. We can use long division for this:

1. 631 goes into 3281 (the first four digits of 32812) approximately 5 times (since \( 631 \times 5 = 3155 \)).
2. Subtract 3155 from 3281 to get 126.
3. Bring down the next digit (2) to make it 1262.
4. 631 goes into 1262 approximately 2 times (since \( 631 \times 2 = 1262 \)).

So, the division is exact, and each mermaid friend will receive:

\[ 32812 \div 631 = 52 \]

### Answer: 52

Expected answer: 52

Correct? Yes

๐Ÿ”— Follow-up

Problem: The mermaid realized that she had miscalculated and there are actually only 4198 mermaid friends, not 631. If she divides the 32812 pearls evenly among her 4198 friends now, how many pearls will each friend receive?

GPT-4o:

To determine how many pearls each mermaid friend will receive, we need to divide the total number of pearls by the new number of mermaid friends.

The total number of pearls is 32,812, and the number of mermaid friends is 4,198.

We perform the division:

\[ 32812 \div 4198 \]

Using long division:

1. 4198 goes into 32812 approximately 7 times (since \( 4198 \times 7 = 29386 \)).
2. Subtract 29386 from 32812 to get 3426.
3. Since 3426 is less than 4198, we have our quotient.

So, the division gives us:

\[ 32812 \div 4198 \approx 7 \]

Each mermaid friend will receive 7 pearls, with some pearls left over.

To find the exact number of leftover pearls:

\[ 32812 - (4198 \times 7) = 32812 - 29386 = 3426 \]

So, each mermaid friend will receive 7 pearls, and there will be 3426 pearls left over.

### Answer: 7

Expected answer: 16406/2099

Correct? No

๐Ÿ”— Problem

Problem: A farm produces a total of 36,784 apples during the 19 weeks of its growing season. If the amount of harvested apples is the same each week, how many apples does the farm produce weekly?

GPT-4o:

To determine the number of apples produced weekly, we need to divide the total number of apples by the number of weeks in the growing season.

Given:
- Total apples produced: 36,784
- Number of weeks: 19

We perform the division:

\[ \frac{36,784}{19} \]

First, let's set up the long division:

1. 19 goes into 36 one time (19 * 1 = 19).
2. Subtract 19 from 36 to get 17.
3. Bring down the next digit, 7, making it 177.
4. 19 goes into 177 nine times (19 * 9 = 171).
5. Subtract 171 from 177 to get 6.
6. Bring down the next digit, 8, making it 68.
7. 19 goes into 68 three times (19 * 3 = 57).
8. Subtract 57 from 68 to get 11.
9. Bring down the last digit, 4, making it 114.
10. 19 goes into 114 six times (19 * 6 = 114).
11. Subtract 114 from 114 to get 0.

So, the result of the division is 1,936.

### Answer: 1,936

Expected answer: 1936

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering the previous situation, what if the farm actually produced the same number of apples over a much longer period of 152 weeks rather than 19 weeks? How many apples does the farm now produce weekly?

GPT-4o:

To determine the number of apples produced weekly over a period of 152 weeks, we need to divide the total number of apples by the new number of weeks.

Given:
- Total apples produced: 36,784
- Number of weeks: 152

We perform the division:

\[ \frac{36,784}{152} \]

First, let's set up the long division:

1. 152 goes into 367 two times (152 * 2 = 304).
2. Subtract 304 from 367 to get 63.
3. Bring down the next digit, 8, making it 638.
4. 152 goes into 638 four times (152 * 4 = 608).
5. Subtract 608 from 638 to get 30.
6. Bring down the last digit, 4, making it 304.
7. 152 goes into 304 two times (152 * 2 = 304).
8. Subtract 304 from 304 to get 0.

So, the result of the division is 242.

### Answer: 242

Expected answer: 242

Correct? Yes

๐Ÿ”— Problem

Problem: A train travels 63245 miles over a period of 695 days. If the train travels the same distance each day, how many miles does it cover in a day?

GPT-4o:

To find out how many miles the train covers in a day, we need to divide the total distance traveled by the number of days.

Total distance traveled: 63,245 miles
Number of days: 695 days

We perform the division:

\[ \frac{63245}{695} \]

First, let's simplify the division step-by-step:

1. 63,245 รท 695 โ‰ˆ 91

To verify, we multiply 695 by 91:

\[ 695 \times 91 = 63,245 \]

Since the multiplication confirms our division, the train covers 91 miles each day.

### Answer: 91 miles

Expected answer: 91

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the train now travels a total of 6280 miles over the same period of 695 days. If the train still travels the same distance each day, how many miles will it cover in a day now?

GPT-4o:

To determine how many miles the train covers in a day, we need to divide the total distance traveled by the number of days.

Total distance traveled: 6,280 miles
Number of days: 695 days

We perform the division:

\[ \frac{6280}{695} \]

First, let's simplify the division step-by-step:

1. 6,280 รท 695 โ‰ˆ 9

To verify, we multiply 695 by 9:

\[ 695 \times 9 = 6,255 \]

Since 6,255 is close to 6,280, we can check the remainder:

\[ 6,280 - 6,255 = 25 \]

So, the train covers approximately 9 miles each day, with a small remainder.

### Answer: 9 miles

Expected answer: 1256/139

Correct? No

๐Ÿ”— Problem

Problem: A doll factory produced a total of 41772 dolls over a period of 708 days. If the factory kept up with the same daily production rate, how many dolls were being made in a day?

GPT-4o:

To determine the daily production rate, we need to divide the total number of dolls produced by the total number of days.

Given:
- Total number of dolls produced = 41,772
- Total number of days = 708

We perform the division:

\[ \text{Daily production rate} = \frac{41,772}{708} \]

Let's calculate this:

\[ \frac{41,772}{708} \approx 59 \]

So, the factory produced approximately 59 dolls per day.

### Answer: 59

Expected answer: 59

Correct? Yes

๐Ÿ”— Follow-up

Problem: What if the same doll factory initially planned to produce the same total number of 41772 dolls, but now over a longer period of 4664 days? If so, how many dolls would have been produced daily then?

GPT-4o:

To find the new daily production rate, we need to divide the total number of dolls by the new total number of days.

Given:
- Total number of dolls produced = 41,772
- New total number of days = 4,664

We perform the division:

\[ \text{Daily production rate} = \frac{41,772}{4,664} \]

Let's calculate this:

\[ \frac{41,772}{4,664} \approx 8.96 \]

Since we typically round to the nearest whole number when dealing with production rates, we round 8.96 to 9.

### Answer: 9

Expected answer: 10443/1166

Correct? No

๐Ÿ”— Problem

Problem: A drummer has a goal to hit his drum 61019 times. If he plans to do this over the course of 7 days, how many times will he need to hit the drum each day to meet his goal?

GPT-4o:

To determine how many times the drummer needs to hit the drum each day, we need to divide the total number of hits by the number of days.

The total number of hits is 61,019, and the number of days is 7.

We perform the division:
\[ 61019 \div 7 \]

First, we divide 61,019 by 7:
\[ 61019 \div 7 = 8717 \]

So, the drummer needs to hit the drum 8,717 times each day to meet his goal.

### Answer: 8,717

Expected answer: 8717

Correct? Yes

๐Ÿ”— Follow-up

Problem: The drummer realized that his initial goal was too lofty, and decided to reduce his goal to hitting his drum 7454 times instead. If he still plans to do this over the course of 7 days, how many times will he need to hit the drum each day to meet his new goal?

GPT-4o:

To determine how many times the drummer needs to hit the drum each day with the new goal, we need to divide the total number of hits by the number of days.

The new total number of hits is 7,454, and the number of days is 7.

We perform the division:
\[ 7454 \div 7 \]

First, we divide 7,454 by 7:
\[ 7454 \div 7 = 1064 \]

So, the drummer needs to hit the drum 1,064 times each day to meet his new goal.

### Answer: 1,064

Expected answer: 7454/7

Correct? No

๐Ÿ”— Problem

Problem: In a particular marine park, a dolphin can swim an average of 98816 meters in 128 hours. How many meters can the dolphin swim in an hour?

GPT-4o:

To determine how many meters the dolphin can swim in an hour, we need to divide the total distance by the total time.

Given:
- Total distance: 98,816 meters
- Total time: 128 hours

We perform the division:

\[ \text{Distance per hour} = \frac{98,816 \text{ meters}}{128 \text{ hours}} \]

\[ \text{Distance per hour} = 772 \text{ meters/hour} \]

### Answer: 772 meters/hour

Expected answer: 772

Correct? Yes

๐Ÿ”— Follow-up

Problem: Following the change, suppose now that the dolphin swam a total of 6186 meters within the same 128 hours. How many meters is the dolphin now swimming in an hour?

GPT-4o:

To find out how many meters the dolphin is now swimming in an hour, we need to divide the new total distance by the total time.

Given:
- New total distance: 6,186 meters
- Total time: 128 hours

We perform the division:

\[ \text{Distance per hour} = \frac{6,186 \text{ meters}}{128 \text{ hours}} \]

\[ \text{Distance per hour} = 48.359375 \text{ meters/hour} \]

Rounding to two decimal places:

\[ \text{Distance per hour} \approx 48.36 \text{ meters/hour} \]

### Answer: 48.36 meters/hour

Expected answer: 3093/64

Correct? No

๐Ÿ”— Problem

Problem: A song was streamed 71532 times in the first 1987 days after its release. How many streams did it average per day?

GPT-4o:

To find the average number of streams per day, we need to divide the total number of streams by the total number of days.

Given:
- Total streams: 71,532
- Total days: 1,987

We perform the division:

\[ \text{Average streams per day} = \frac{71,532}{1,987} \]

Let's calculate this:

\[ \frac{71,532}{1,987} \approx 36 \]

So, the song was streamed approximately 36 times per day on average.

### Answer: 36

Expected answer: 36

Correct? Yes

๐Ÿ”— Follow-up

Problem: The same song was streamed 4862 times in the first 1987 days on a less popular platform. How many streams did it average per day on this platform?

GPT-4o:

To find the average number of streams per day on the less popular platform, we need to divide the total number of streams by the total number of days.

Given:
- Total streams: 4,862
- Total days: 1,987

We perform the division:

\[ \text{Average streams per day} = \frac{4,862}{1,987} \]

Let's calculate this:

\[ \frac{4,862}{1,987} \approx 2.45 \]

So, the song was streamed approximately 2.45 times per day on average on the less popular platform.

### Answer: 2.45

Expected answer: 4862/1987

Correct? No

๐Ÿ”— Problem

Problem: A compass salesman has 33046 compasses that he wants to distribute evenly among 1066 stores. How many compasses will each store receive if they are divided equally?

GPT-4o:

To determine how many compasses each store will receive, we need to divide the total number of compasses by the number of stores.

Given:
- Total number of compasses = 33,046
- Number of stores = 1,066

We perform the division:

\[ \frac{33,046}{1,066} \]

First, let's do the division step-by-step:

1. 33,046 divided by 1,066 is approximately 31.

To verify, we multiply 31 by 1,066:

\[ 31 \times 1,066 = 33,046 \]

Since the multiplication result matches the total number of compasses, each store will receive exactly 31 compasses.

### Answer: 31

Expected answer: 31

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the compass salesman later realizes he made a mistake and that he actually has to distribute the 33046 compasses equally among 6456 stores, not 1066. How many compasses will each store receive now, if they are divided equally?

GPT-4o:

To determine how many compasses each store will receive, we need to divide the total number of compasses by the new number of stores.

Given:
- Total number of compasses = 33,046
- Number of stores = 6,456

We perform the division:

\[ \frac{33,046}{6,456} \]

First, let's do the division step-by-step:

1. 33,046 divided by 6,456 is approximately 5.11.

Since we are distributing whole compasses, we take the integer part of the division result, which is 5.

To verify, we multiply 5 by 6,456:

\[ 5 \times 6,456 = 32,280 \]

This is less than 33,046, so each store will receive 5 compasses, and there will be some compasses left over.

To find the remainder, we subtract the total distributed compasses from the original total:

\[ 33,046 - 32,280 = 766 \]

So, each store will receive 5 compasses, and there will be 766 compasses left over.

### Answer: 5

Expected answer: 16523/3228

Correct? No

๐Ÿ”— Problem

Problem: In a large farm, a total of 49822 carrots are harvested from 58 similar plots. If each plot yielded the same number of carrots, how many carrots did each plot yield?

GPT-4o:

To determine how many carrots each plot yielded, we need to divide the total number of carrots by the number of plots.

Given:
- Total number of carrots = 49,822
- Number of plots = 58

We perform the division:

\[
\frac{49,822}{58} = 859
\]

So, each plot yielded 859 carrots.

### Answer: 859

Expected answer: 859

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose in the same large farm, they only managed to produce a total of 9653 carrots from the same 58 plots the next year. If these plots yielded the same number of carrots, how many carrots did each plot yield this time?

GPT-4o:

To find out how many carrots each plot yielded, we need to divide the total number of carrots by the number of plots.

Given:
- Total number of carrots = 9,653
- Number of plots = 58

We perform the division:

\[
\frac{9,653}{58} = 166.4310345 \approx 166
\]

Since the number of carrots must be a whole number, we round to the nearest whole number.

### Answer: 166

Expected answer: 9653/58

Correct? No

๐Ÿ”— Problem

Problem: There is a cloud which covers 8744 square meters of the sky and exactly the same area is revealed when the cloud dispels. If the revealed area is divided equally over the original area, what is the ratio of the revealed area to the original area?

GPT-4o:

To determine the ratio of the revealed area to the original area, we need to understand that the revealed area is exactly the same as the area covered by the cloud, which is 8744 square meters.

When the cloud dispels, the revealed area is 8744 square meters. Since this revealed area is divided equally over the original area, the ratio of the revealed area to the original area is simply the ratio of the same area to itself.

Thus, the ratio is:
\[ \frac{\text{Revealed Area}}{\text{Original Area}} = \frac{8744 \text{ square meters}}{8744 \text{ square meters}} = 1 \]

### Answer: 1

Expected answer: 1

Correct? Yes

๐Ÿ”— Problem

Problem: A scooter travels a total distance of 97506 meters on a full charge. If the battery life of the scooter is 18 hours on a full charge, how many meters does the scooter travel per hour?

GPT-4o:

To determine how many meters the scooter travels per hour, we need to divide the total distance by the total time.

Given:
- Total distance = 97,506 meters
- Total time = 18 hours

We perform the division:
\[ \text{Distance per hour} = \frac{\text{Total distance}}{\text{Total time}} = \frac{97,506 \text{ meters}}{18 \text{ hours}} \]

Now, let's calculate:
\[ \frac{97,506}{18} = 5,417 \]

So, the scooter travels 5,417 meters per hour.

### Answer: 5,417 meters per hour.

Expected answer: 5417

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the scooter's total distance on a full charge was instead 7727 meters, keeping the battery life at 18 hours, how many meters would the scooter travel per hour now?

GPT-4o:

To determine how many meters the scooter travels per hour with the new total distance, we again divide the total distance by the total time.

Given:
- Total distance = 7,727 meters
- Total time = 18 hours

We perform the division:
\[ \text{Distance per hour} = \frac{\text{Total distance}}{\text{Total time}} = \frac{7,727 \text{ meters}}{18 \text{ hours}} \]

Now, let's calculate:
\[ \frac{7,727}{18} \approx 429.28 \]

So, the scooter travels approximately 429.28 meters per hour.

### Answer: 429.28 meters per hour.

Expected answer: 7727/18

Correct? No

๐Ÿ”— Problem

Problem: A star emits a total of 94548 units of light energy over a period of 7879 hours. If the star emits a constant amount of light energy every hour, how much light energy does it emit every hour?

GPT-4o:

To determine the amount of light energy the star emits every hour, we need to divide the total light energy by the total number of hours.

Given:
- Total light energy emitted = 94,548 units
- Total time period = 7,879 hours

We perform the division:

\[ \frac{94,548 \text{ units}}{7,879 \text{ hours}} \]

Let's calculate this:

\[ 94,548 \div 7,879 \approx 12 \]

So, the star emits approximately 12 units of light energy every hour.

### Answer: 12 units per hour

Expected answer: 12

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead, the star emitted a total of 94548 units of light energy over a shorter period of 3349 hours, still at a constant rate, how much light energy would it emit every hour now?

GPT-4o:

To determine the amount of light energy the star emits every hour over the shorter period, we need to divide the total light energy by the new total number of hours.

Given:
- Total light energy emitted = 94,548 units
- Total time period = 3,349 hours

We perform the division:

\[ \frac{94,548 \text{ units}}{3,349 \text{ hours}} \]

Let's calculate this:

\[ 94,548 \div 3,349 \approx 28.22 \]

So, the star emits approximately 28.22 units of light energy every hour.

### Answer: 28.22 units per hour

Expected answer: 94548/3349

Correct? No

๐Ÿ”— Problem

Problem: A forest contains a total of 80752 trees and it is split evenly into 412 sections. How many trees are there in each section?

GPT-4o:

To determine how many trees are in each section, we need to divide the total number of trees by the number of sections.

Given:
- Total number of trees = 80,752
- Number of sections = 412

We perform the division:

\[ \frac{80,752}{412} \]

Let's calculate this step-by-step:

1. Divide 80,752 by 412:
\[ 80,752 \div 412 \approx 196 \]

So, there are approximately 196 trees in each section.

### Answer: 196

Expected answer: 196

Correct? Yes

๐Ÿ”— Follow-up

Problem: Given the same forest as before with 80752 trees, what if it was divided into 1778 sections instead of 412? How many trees would there be in each section now?

GPT-4o:

To determine how many trees are in each section when the forest is divided into 1,778 sections, we need to divide the total number of trees by the new number of sections.

Given:
- Total number of trees = 80,752
- Number of sections = 1,778

We perform the division:

\[ \frac{80,752}{1,778} \]

Let's calculate this step-by-step:

1. Divide 80,752 by 1,778:
\[ 80,752 \div 1,778 \approx 45.42 \]

Since the number of trees must be a whole number, we round to the nearest whole number:

\[ 80,752 \div 1,778 \approx 45 \]

So, there are approximately 45 trees in each section.

### Answer: 45

Expected answer: 5768/127

Correct? No

๐Ÿ”— Problem

Problem: A farm harvested 44280 cucumbers over 216 days. If they harvested an equal amount of cucumbers each day, how many cucumbers were harvested each day?

GPT-4o:

To determine how many cucumbers were harvested each day, we need to divide the total number of cucumbers by the number of days.

Given:
- Total cucumbers harvested = 44,280
- Total days = 216

We perform the division:

\[ \frac{44280}{216} \]

First, simplify the division:

\[ 44280 \div 216 = 205 \]

So, the farm harvested 205 cucumbers each day.

### Answer: 205

Expected answer: 205

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of 44280 cucumbers, the farm only harvested 4076 cucumbers over the same 216 days, how many cucumbers were harvested each day given this new quantity?

GPT-4o:

To determine how many cucumbers were harvested each day with the new quantity, we need to divide the total number of cucumbers by the number of days.

Given:
- Total cucumbers harvested = 4,076
- Total days = 216

We perform the division:

\[ \frac{4076}{216} \]

First, simplify the division:

\[ 4076 \div 216 \approx 18.87 \]

So, the farm harvested approximately 18.87 cucumbers each day.

### Answer: 18.87

Expected answer: 1019/54

Correct? No

๐Ÿ”— Problem

Problem: A cookie factory produced a total of 77545 cookies that were evenly divided into 1193 packages. How many cookies are there in each package?

GPT-4o:

To determine how many cookies are in each package, we need to divide the total number of cookies by the number of packages.

Given:
- Total number of cookies = 77,545
- Number of packages = 1,193

We perform the division:

\[ \frac{77,545}{1,193} \]

Let's calculate this step-by-step:

1. 77,545 divided by 1,193 gives approximately 65. 

To verify:
\[ 1,193 \times 65 = 77,545 \]

Thus, each package contains 65 cookies.

### Answer: 65

Expected answer: 65

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering the same scenario where the cookie factory is producing cookies, imagine now they increased their packaging capabilities and packaged the same 77545 cookies into 1834 packages instead of 1193. How many cookies are there in each package now?

GPT-4o:

To determine how many cookies are in each package with the new number of packages, we need to divide the total number of cookies by the new number of packages.

Given:
- Total number of cookies = 77,545
- Number of packages = 1,834

We perform the division:

\[ \frac{77,545}{1,834} \]

Let's calculate this step-by-step:

1. 77,545 divided by 1,834 gives approximately 42.28.

Since the number of cookies per package must be a whole number, we round down to the nearest whole number, which is 42.

To verify:
\[ 1,834 \times 42 = 77,028 \]

This is slightly less than 77,545, indicating that there will be some leftover cookies. However, the question asks for the number of cookies in each package, so we use the whole number result.

### Answer: 42

Expected answer: 77545/1834

Correct? No

๐Ÿ”— Problem

Problem: A star emits 51750 units of light energy every 125 seconds. How much light energy does the star emit every second?

GPT-4o:

To determine how much light energy the star emits every second, we need to divide the total light energy emitted by the total time in seconds.

Given:
- Total light energy emitted = 51,750 units
- Total time = 125 seconds

We perform the division:
\[ \text{Light energy per second} = \frac{51,750 \text{ units}}{125 \text{ seconds}} \]

Now, let's calculate this:
\[ \frac{51,750}{125} = 414 \]

So, the star emits 414 units of light energy every second.

### Answer: 414 units per second

Expected answer: 414

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead, over a different period, the star emitted 51750 units of light energy every 8670 seconds, how much light energy would it be emitting per second?

GPT-4o:

To determine how much light energy the star emits every second, we need to divide the total light energy emitted by the total time in seconds.

Given:
- Total light energy emitted = 51,750 units
- Total time = 8,670 seconds

We perform the division:
\[ \text{Light energy per second} = \frac{51,750 \text{ units}}{8,670 \text{ seconds}} \]

Now, let's calculate this:
\[ \frac{51,750}{8,670} \approx 5.97 \]

So, the star emits approximately 5.97 units of light energy every second.

### Answer: 5.97 units per second

Expected answer: 1725/289

Correct? No

๐Ÿ”— Problem

Problem: A candy factory produced 25144 candies evenly over 56 days. How many candies did the factory make each day?

GPT-4o:

To find out how many candies the factory produced each day, we need to divide the total number of candies by the number of days.

Given:
- Total candies produced = 25,144
- Number of days = 56

We perform the division:

\[ \frac{25144}{56} \]

First, let's do the division step-by-step:

1. 25144 รท 56
2. 251 รท 56 โ‰ˆ 4 (since 56 * 4 = 224)
3. Subtract 224 from 251 to get the remainder: 251 - 224 = 27
4. Bring down the next digit (1) to get 271
5. 271 รท 56 โ‰ˆ 4 (since 56 * 4 = 224)
6. Subtract 224 from 271 to get the remainder: 271 - 224 = 47
7. Bring down the next digit (4) to get 474
8. 474 รท 56 โ‰ˆ 8 (since 56 * 8 = 448)
9. Subtract 448 from 474 to get the remainder: 474 - 448 = 26
10. Bring down the next digit (4) to get 264
11. 264 รท 56 โ‰ˆ 4 (since 56 * 4 = 224)
12. Subtract 224 from 264 to get the remainder: 264 - 224 = 40

So, the quotient is 448 and the remainder is 40. Since we are looking for the number of candies produced each day, we only need the quotient.

### Answer: 448

Expected answer: 449

Correct? No

๐Ÿ”— Problem

Problem: A party needs 34240 slices of bread for sandwiches. If each loaf of bread contains 10 slices, how many loaves of bread are needed for the party?

GPT-4o:

To determine how many loaves of bread are needed, we need to divide the total number of slices by the number of slices per loaf.

Given:
- Total slices needed = 34,240
- Slices per loaf = 10

We perform the division:
\[ \frac{34,240 \text{ slices}}{10 \text{ slices/loaf}} = 3,424 \text{ loaves} \]

### Answer: 3,424

Expected answer: 3424

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead the party needed 7638 slices of bread for sandwiches, still considering that each loaf of bread contains 10 slices, how many loaves of bread would then be needed for the party?

GPT-4o:

To determine how many loaves of bread are needed, we need to divide the total number of slices by the number of slices per loaf.

Given:
- Total slices needed = 7,638
- Slices per loaf = 10

We perform the division:
\[ \frac{7,638 \text{ slices}}{10 \text{ slices/loaf}} = 763.8 \text{ loaves} \]

Since we cannot have a fraction of a loaf, we need to round up to the next whole number because even a partial loaf means we need an additional loaf to meet the requirement.

Therefore, we round 763.8 up to 764.

### Answer: 764

Expected answer: 3819/5

Correct? No

๐Ÿ”— Problem

Problem: A forest ranger has noticed that over 119 days, 20111 trees have sprouted throughout the forest. If each day has the same number of new trees sprouting, how many new trees sprout each day?

GPT-4o:

To determine the number of new trees that sprout each day, we need to divide the total number of trees by the number of days.

Given:
- Total number of trees: 20,111
- Number of days: 119

We perform the division:

\[ \frac{20,111}{119} \]

First, let's do the division step-by-step:

1. 20111 รท 119 โ‰ˆ 169 (since 119 * 169 = 20111)

Thus, the number of new trees that sprout each day is 169.

### Answer: 169

Expected answer: 169

Correct? Yes

๐Ÿ”— Follow-up

Problem: The same forest ranger now considers a different area of the forest. This time, over a period of 119 days, he noticed that 6216 new trees had sprouted. If the same number of new trees sprouted each day, how many new trees sprouted each day in this different area of the forest?

GPT-4o:

To determine the number of new trees that sprout each day in the different area of the forest, we need to divide the total number of trees by the number of days.

Given:
- Total number of trees: 6,216
- Number of days: 119

We perform the division:

\[ \frac{6,216}{119} \]

First, let's do the division step-by-step:

1. 6216 รท 119 โ‰ˆ 52 (since 119 * 52 = 6188, and 6216 - 6188 = 28, which is less than 119, confirming the quotient is correct)

Thus, the number of new trees that sprout each day is 52.

### Answer: 52

Expected answer: 888/17

Correct? No

๐Ÿ”— Problem

Problem: A dog food factory distributed 91,104 cans of dog food uniformly over 52 weeks. How many cans of dog food did they distribute per week?

GPT-4o:

To determine how many cans of dog food the factory distributed per week, we need to divide the total number of cans by the number of weeks.

Given:
- Total cans of dog food = 91,104
- Number of weeks = 52

We perform the division:

\[ \frac{91,104}{52} \]

First, let's set up the division:

\[ 91,104 \div 52 \]

1. 52 goes into 91 once (1 time), because \( 52 \times 1 = 52 \).
   - Subtract 52 from 91: \( 91 - 52 = 39 \).
   - Bring down the next digit (1), making it 391.

2. 52 goes into 391 seven times (7 times), because \( 52 \times 7 = 364 \).
   - Subtract 364 from 391: \( 391 - 364 = 27 \).
   - Bring down the next digit (0), making it 270.

3. 52 goes into 270 five times (5 times), because \( 52 \times 5 = 260 \).
   - Subtract 260 from 270: \( 270 - 260 = 10 \).
   - Bring down the next digit (4), making it 104.

4. 52 goes into 104 two times (2 times), because \( 52 \times 2 = 104 \).
   - Subtract 104 from 104: \( 104 - 104 = 0 \).

So, the result of the division is 1,752.

### Answer: 1,752

Expected answer: 1752

Correct? Yes

๐Ÿ”— Follow-up

Problem: Following the previous question, now consider that the same dog food factory distributed a different brand of dog food, this time totaling 5,981 cans, uniformly over the same 52 weeks. How many cans of this different brand of dog food did they distribute per week?

GPT-4o:

To determine how many cans of the different brand of dog food the factory distributed per week, we need to divide the total number of cans by the number of weeks.

Given:
- Total cans of the different brand of dog food = 5,981
- Number of weeks = 52

We perform the division:

\[ \frac{5,981}{52} \]

First, let's set up the division:

\[ 5,981 \div 52 \]

1. 52 goes into 59 once (1 time), because \( 52 \times 1 = 52 \).
   - Subtract 52 from 59: \( 59 - 52 = 7 \).
   - Bring down the next digit (8), making it 78.

2. 52 goes into 78 once (1 time), because \( 52 \times 1 = 52 \).
   - Subtract 52 from 78: \( 78 - 52 = 26 \).
   - Bring down the next digit (1), making it 261.

3. 52 goes into 261 five times (5 times), because \( 52 \times 5 = 260 \).
   - Subtract 260 from 261: \( 261 - 260 = 1 \).

So, the result of the division is 115 with a remainder of 1.

Therefore, the factory distributed 115 cans per week, with 1 can left over.

### Answer: 115

Expected answer: 5981/52

Correct? No

๐Ÿ”— Problem

Problem: A blanket manufacturing company has 19944 yards of fabric. They use the same amount of fabric to produce each blanket, and from this total amount of fabric, they can make 18 blankets. How many yards of fabric is used for each blanket?

GPT-4o:

To determine how many yards of fabric are used for each blanket, we need to divide the total amount of fabric by the number of blankets produced.

Given:
- Total fabric = 19944 yards
- Number of blankets = 18

We perform the division:
\[ \text{Fabric per blanket} = \frac{19944 \text{ yards}}{18 \text{ blankets}} \]

Let's calculate this:
\[ \frac{19944}{18} = 1108 \]

So, each blanket uses 1108 yards of fabric.

### Answer: 1108 yards

Expected answer: 1108

Correct? Yes

๐Ÿ”— Problem

Problem: A farmer has harvested a total of 45764 potatoes from his 2692 plants. On average, how many potatoes does each plant produce?

GPT-4o:

To find the average number of potatoes each plant produces, we need to divide the total number of potatoes by the total number of plants.

Given:
- Total number of potatoes = 45,764
- Total number of plants = 2,692

We perform the division:

\[ \text{Average number of potatoes per plant} = \frac{45,764}{2,692} \]

Let's calculate this:

\[ 45,764 \div 2,692 \approx 17 \]

So, on average, each plant produces approximately 17 potatoes.

### Answer: 17

Expected answer: 17

Correct? Yes

๐Ÿ”— Follow-up

Problem: Following up on the previous scenario, the farmer discovered that he actually harvested a total of 7664 potatoes, not 45764. With the same number of plants (2692), what would be the new average of potatoes each plant produces?

GPT-4o:

To find the new average number of potatoes each plant produces, we need to divide the corrected total number of potatoes by the total number of plants.

Given:
- Corrected total number of potatoes = 7,664
- Total number of plants = 2,692

We perform the division:

\[ \text{Average number of potatoes per plant} = \frac{7,664}{2,692} \]

Let's calculate this:

\[ 7,664 \div 2,692 \approx 2.85 \]

So, on average, each plant produces approximately 2.85 potatoes.

### Answer: 2.85

Expected answer: 1916/673

Correct? No

๐Ÿ”— Problem

Problem: A marshmallow factory produced 85560 marshmallows in 713 hours. If the factory produces the same amount every hour, how many marshmallows are made each hour?

GPT-4o:

To determine how many marshmallows the factory produces each hour, we need to divide the total number of marshmallows produced by the total number of hours.

Given:
- Total marshmallows produced = 85,560
- Total hours = 713

We perform the division:

\[ \frac{85,560}{713} \]

Let's calculate this:

\[ 85,560 \div 713 \approx 120 \]

So, the factory produces approximately 120 marshmallows each hour.

### Answer: 120

Expected answer: 120

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the same marshmallow factory, another batch of marshmallows was made over a longer production period. This time, 85560 marshmallows were produced in 7544 hours. If the factory produces the same amount each hour during this period, how many marshmallalls were made each hour now?

GPT-4o:

To determine how many marshmallows the factory produces each hour during this longer production period, we need to divide the total number of marshmallows produced by the total number of hours.

Given:
- Total marshmallows produced = 85,560
- Total hours = 7,544

We perform the division:

\[ \frac{85,560}{7,544} \]

Let's calculate this:

\[ 85,560 \div 7,544 \approx 11.34 \]

So, the factory produces approximately 11.34 marshmallows each hour during this period.

### Answer: 11.34

Expected answer: 465/41

Correct? No

๐Ÿ”— Problem

Problem: On a farm, there is a total area of 49,928 square meters to plant crops. If this area is divided into uniform plots of 6,241 square meters each, how many plots are there on the farm?

GPT-4o:

To determine how many plots of 6,241 square meters each can be made from a total area of 49,928 square meters, we need to divide the total area by the area of each plot.

\[
\text{Number of plots} = \frac{\text{Total area}}{\text{Area of each plot}} = \frac{49,928 \text{ square meters}}{6,241 \text{ square meters}}
\]

Performing the division:

\[
49,928 \div 6,241 = 8
\]

So, there are 8 plots on the farm.

### Answer: 8

Expected answer: 8

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of subdividing the total area of 49,928 square meters into plots of 6,241 square meters each, the farmer decides to subdivide it into smaller plots, each measuring 23 square meters. How many plots are there on the farm now?

GPT-4o:

To determine how many plots of 23 square meters each can be made from a total area of 49,928 square meters, we need to divide the total area by the area of each plot.

\[
\text{Number of plots} = \frac{\text{Total area}}{\text{Area of each plot}} = \frac{49,928 \text{ square meters}}{23 \text{ square meters}}
\]

Performing the division:

\[
49,928 \div 23 = 2,170
\]

So, there are 2,170 plots on the farm.

### Answer: 2,170

Expected answer: 49928/23

Correct? No

๐Ÿ”— Problem

Problem: A baker used 62118 grams of flour to make cookies over the course of 2142 days. How many grams of flour were used to make cookies each day?

GPT-4o:

To determine how many grams of flour were used each day, we need to divide the total amount of flour by the number of days.

Given:
- Total flour used: 62,118 grams
- Number of days: 2,142 days

We perform the division:

\[
\frac{62118}{2142} = 29
\]

So, the baker used 29 grams of flour each day.

### Answer: 29 grams

Expected answer: 29

Correct? Yes

๐Ÿ”— Follow-up

Problem: The baker realized that he actually used a total of 62118 grams of flour over the course of 2755 days, not 2142 days as previously thought. How does the daily use of flour for cookies change with this correction?

GPT-4o:

To determine the new daily use of flour, we need to divide the total amount of flour by the corrected number of days.

Given:
- Total flour used: 62,118 grams
- Corrected number of days: 2,755 days

We perform the division:

\[
\frac{62118}{2755} \approx 22.54
\]

So, the baker used approximately 22.54 grams of flour each day with the corrected number of days.

### Answer: 22.54 grams

Expected answer: 2142/95

Correct? No

๐Ÿ”— Problem

Problem: A shoemaker has 91100 centimeters of shoelaces and he distributes them equally in 3644 pairs of shoes. How many centimeters of shoelace does each pair get?

GPT-4o:

To determine how many centimeters of shoelace each pair of shoes gets, we need to divide the total length of shoelaces by the number of pairs of shoes.

Given:
- Total length of shoelaces = 91100 centimeters
- Number of pairs of shoes = 3644

We perform the division:

\[ \frac{91100}{3644} \]

First, let's simplify the division step-by-step:

1. Divide 91100 by 3644:
\[ 91100 \div 3644 \approx 25 \]

To verify, we multiply 3644 by 25:
\[ 3644 \times 25 = 91100 \]

Since the multiplication confirms our division, each pair of shoes gets 25 centimeters of shoelace.

### Answer: 25

Expected answer: 25

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the shoemaker only had 9498 pairs of shoes but the same amount of shoelace (91100 centimeters), how many centimeters of shoelace would each pair get then?

GPT-4o:

To determine how many centimeters of shoelace each pair of shoes gets with the new number of pairs, we need to divide the total length of shoelaces by the new number of pairs of shoes.

Given:
- Total length of shoelaces = 91100 centimeters
- Number of pairs of shoes = 9498

We perform the division:

\[ \frac{91100}{9498} \]

First, let's simplify the division step-by-step:

1. Divide 91100 by 9498:
\[ 91100 \div 9498 \approx 9.59 \]

To verify, we can multiply 9498 by 9.59:
\[ 9498 \times 9.59 \approx 91100 \]

Since the multiplication confirms our division, each pair of shoes gets approximately 9.59 centimeters of shoelace.

### Answer: 9.59

Expected answer: 45550/4749

Correct? No

๐Ÿ”— Problem

Problem: A farmer harvests 505 bushels of apples and equally distributes them into 5 bins. How many bushels of apples does each bin contain?

GPT-4o:

To determine how many bushels of apples each bin contains, we need to divide the total number of bushels by the number of bins.

Given:
- Total bushels of apples = 505
- Number of bins = 5

We perform the division:
\[ \frac{505}{5} = 101 \]

So, each bin contains 101 bushels of apples.

### Answer: 101

Expected answer: 101

Correct? Yes

๐Ÿ”— Follow-up

Problem: The farmer has now harvested a bigger lot of 7798 bushels of apples and once again distributes them equally into 5 bins. Now, how many bushels of apples does each bin contain?

GPT-4o:

To determine how many bushels of apples each bin contains, we need to divide the total number of bushels by the number of bins.

Given:
- Total bushels of apples = 7798
- Number of bins = 5

We perform the division:
\[ \frac{7798}{5} = 1559.6 \]

So, each bin contains 1559.6 bushels of apples.

### Answer: 1559.6

Expected answer: 7798/5

Correct? Yes

๐Ÿ”— Problem

Problem: At a party, there were a total of 65325 confetti pieces and they were equally spread across 5025 square feet of area. How many confetti pieces were there per square foot?

GPT-4o:

To find the number of confetti pieces per square foot, we need to divide the total number of confetti pieces by the total area in square feet.

Total number of confetti pieces: 65,325
Total area in square feet: 5,025

We perform the division:

\[
\frac{65,325}{5,025} = 13
\]

So, there were 13 confetti pieces per square foot.

### Answer: 13

Expected answer: 13

Correct? Yes

๐Ÿ”— Follow-up

Problem: What if instead, the total confetti pieces at the party were spread across 9944 square feet of area instead of 5025? How many confetti pieces would be there per square foot in that case?

GPT-4o:

To find the number of confetti pieces per square foot when the total area is 9,944 square feet, we need to divide the total number of confetti pieces by the new total area.

Total number of confetti pieces: 65,325
Total area in square feet: 9,944

We perform the division:

\[
\frac{65,325}{9,944} \approx 6.57
\]

So, there would be approximately 6.57 confetti pieces per square foot.

### Answer: 6.57

Expected answer: 65325/9944

Correct? No

๐Ÿ”— Problem

Problem: A crayon factory produced 26691 crayons which are evenly distributed into 123 boxes. How many crayons are there in each box?

GPT-4o:

To determine how many crayons are in each box, we need to divide the total number of crayons by the number of boxes.

The total number of crayons is 26,691, and the number of boxes is 123.

We perform the division:

\[ \frac{26691}{123} \]

First, let's do the division step-by-step:

1. 26691 รท 123 โ‰ˆ 217 (since 123 * 217 = 26691)

So, each box contains:

\[ 26691 รท 123 = 217 \]

### Answer: 217

Expected answer: 217

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the crayon factory now produced 4521 crayons instead of 26691, and these were still evenly distributed into 123 boxes. How many crayons would there be in each box under this new scenario?

GPT-4o:

To determine how many crayons are in each box with the new total of 4,521 crayons distributed into 123 boxes, we need to perform the division:

\[ \frac{4521}{123} \]

Let's do the division step-by-step:

1. 4521 รท 123 โ‰ˆ 36.78

Since we are dealing with whole crayons, we round to the nearest whole number:

\[ 4521 รท 123 = 36 \]

So, each box contains:

### Answer: 36

Expected answer: 1507/41

Correct? No

๐Ÿ”— Problem

Problem: A firefighter unit extinguished a total of 45843 fires over the course of 413 weeks. If the firefighter unit extinguished the same number of fires each week, how many fires did they extinguish per week?

GPT-4o:

To determine the number of fires extinguished per week, we need to divide the total number of fires by the total number of weeks.

Given:
- Total number of fires = 45,843
- Total number of weeks = 413

We perform the division:

\[ \frac{45,843}{413} \]

Let's calculate this step-by-step:

1. Divide 45,843 by 413.
2. Perform the division:

\[ 45,843 \div 413 \approx 111 \]

So, the firefighter unit extinguished approximately 111 fires per week.

### Answer: 111

Expected answer: 111

Correct? Yes

๐Ÿ”— Follow-up

Problem: Following the previous scenario of the firefighter unit, suppose the total number of fires they actually extinguished over the period was 45843, but the time frame was 4913 weeks instead of 413 weeks. If they extinguished the same number of fires each week, how many fires did they extinguish per week now?

GPT-4o:

To determine the number of fires extinguished per week, we need to divide the total number of fires by the total number of weeks.

Given:
- Total number of fires = 45,843
- Total number of weeks = 4,913

We perform the division:

\[ \frac{45,843}{4,913} \]

Let's calculate this step-by-step:

1. Divide 45,843 by 4,913.
2. Perform the division:

\[ 45,843 \div 4,913 \approx 9.33 \]

So, the firefighter unit extinguished approximately 9.33 fires per week.

### Answer: 9.33

Expected answer: 45843/4913

Correct? No

๐Ÿ”— Problem

Problem: A park is 57546 square meters large and is divided into 9591 identical sections. What is the area of each section in square meters?

GPT-4o:

To find the area of each section, we need to divide the total area of the park by the number of sections.

Given:
- Total area of the park = 57546 square meters
- Number of sections = 9591

We perform the division:

\[ \text{Area of each section} = \frac{57546}{9591} \]

Let's calculate this:

\[ \frac{57546}{9591} = 6 \]

So, the area of each section is 6 square meters.

### Answer: 6 square meters

Expected answer: 6

Correct? Yes

๐Ÿ”— Follow-up

Problem: After re-evaluating the park layout, the park authority has decided to divide the 57546 square meter park into 131 identical sections instead of 9591. What is the area of each section in square meters now?

GPT-4o:

To find the area of each section after the park is divided into 131 identical sections, we need to divide the total area of the park by the new number of sections.

Given:
- Total area of the park = 57546 square meters
- Number of sections = 131

We perform the division:

\[ \text{Area of each section} = \frac{57546}{131} \]

Let's calculate this:

\[ \frac{57546}{131} = 439 \]

So, the area of each section is 439 square meters.

### Answer: 439 square meters

Expected answer: 57546/131

Correct? No

๐Ÿ”— Problem

Problem: A toothpaste company produced 93822 tubes of toothpaste using 4938 boxes of raw materials. If each box of raw materials can produce the same amount of toothpaste tubes, how many toothpaste tubes are generated from one box of raw materials?

GPT-4o:

To determine how many toothpaste tubes are generated from one box of raw materials, we need to divide the total number of toothpaste tubes by the total number of boxes of raw materials.

Given:
- Total number of toothpaste tubes produced = 93,822
- Total number of boxes of raw materials = 4,938

We perform the division:
\[ \frac{93,822}{4,938} \]

Let's calculate this step-by-step:

1. Divide 93,822 by 4,938:
\[ 93,822 \div 4,938 \approx 19 \]

So, each box of raw materials produces approximately 19 toothpaste tubes.

### Answer: 19

Expected answer: 19

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the toothpaste company changes its manufacturing process and is now able to produce only 9206 tubes of toothpaste with the same 4938 boxes of raw materials. If each box of raw materials still produces the same number of toothpaste tubes, how many toothpaste tubes are now generated from one box of raw materials?

GPT-4o:

To determine how many toothpaste tubes are now generated from one box of raw materials, we need to divide the total number of toothpaste tubes by the total number of boxes of raw materials.

Given:
- Total number of toothpaste tubes produced = 9,206
- Total number of boxes of raw materials = 4,938

We perform the division:
\[ \frac{9,206}{4,938} \]

Let's calculate this step-by-step:

1. Divide 9,206 by 4,938:
\[ 9,206 \div 4,938 \approx 1.864 \]

So, each box of raw materials now produces approximately 1.864 toothpaste tubes.

### Answer: 1.864

Expected answer: 4603/2469

Correct? No

๐Ÿ”— Problem

Problem: A park's Jungle gym is used by a total of 40740 children over the span of 84 days. If the Jungle gym is used by the same number of kids each day, how many children use the Jungle gym each day?

GPT-4o:

To find out how many children use the Jungle gym each day, we need to divide the total number of children by the number of days.

Given:
- Total number of children = 40,740
- Number of days = 84

We perform the division:

\[ \frac{40,740}{84} \]

First, let's simplify the division step-by-step:

1. Divide 40,740 by 84:
\[ 40,740 \div 84 = 485 \]

So, 485 children use the Jungle gym each day.

### Answer: 485

Expected answer: 485

Correct? Yes

๐Ÿ”— Follow-up

Problem: Imagine now that over a period of 84 days, 8576 children use the park's Jungle gym instead of 40740 children. If the Jungle gym is used equally by kids each day, how many children are now using the Jungle gym per day?

GPT-4o:

To determine how many children use the Jungle gym each day, we need to divide the total number of children by the number of days.

Given:
- Total number of children = 8,576
- Number of days = 84

We perform the division:

\[ \frac{8,576}{84} \]

First, let's simplify the division step-by-step:

1. Divide 8,576 by 84:
\[ 8,576 \div 84 = 102 \]

So, 102 children use the Jungle gym each day.

### Answer: 102

Expected answer: 2144/21

Correct? No

๐Ÿ”— Problem

Problem: A snowman competition uses 39482 cc (cubic centimeters) of snow to make 38 identical snowmen. How many cubic centimeters of snow are used for each snowman?

GPT-4o:

To determine how many cubic centimeters of snow are used for each snowman, we need to divide the total amount of snow by the number of snowmen.

Given:
- Total snow: 39,482 cc
- Number of snowmen: 38

We perform the division:
\[ \frac{39482 \text{ cc}}{38} \]

First, let's do the division step-by-step:

1. Divide 39482 by 38:
\[ 39482 \div 38 \approx 1038 \]

So, each snowman uses approximately 1038 cubic centimeters of snow.

### Answer: 1038 cc

Expected answer: 1039

Correct? No

๐Ÿ”— Problem

Problem: A large window spanning 67673 square inches is being divided into 1147 equally sized smaller squares. Find the area in square inches of each of these smaller squares.

GPT-4o:

To find the area of each smaller square, we need to divide the total area of the large window by the number of smaller squares.

The total area of the large window is 67,673 square inches, and it is being divided into 1,147 smaller squares.

We perform the division:
\[ \frac{67673}{1147} \]

Let's calculate this step-by-step:

1. Divide 67,673 by 1,147:
\[ 67673 \div 1147 = 59 \]

So, each smaller square has an area of 59 square inches.

### Answer: 59 square inches

Expected answer: 59

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the large window instead spanned a smaller area of 7562 square inches, and it is still being divided into 1147 equally sized smaller squares, now what would be the area in square inches of each of these smaller squares?

GPT-4o:

To find the area of each smaller square, we need to divide the total area of the large window by the number of smaller squares.

The total area of the large window is 7,562 square inches, and it is being divided into 1,147 smaller squares.

We perform the division:
\[ \frac{7562}{1147} \]

Let's calculate this step-by-step:

1. Divide 7,562 by 1,147:
\[ 7562 \div 1147 \approx 6.59 \]

So, each smaller square has an area of approximately 6.59 square inches.

### Answer: 6.59 square inches

Expected answer: 7562/1147

Correct? No

๐Ÿ”— Problem

Problem: A farmer has a large field of orange trees. In total, the trees produce 49,920 oranges. If the oranges are evenly distributed among the 195 trees, how many oranges does each tree produce?

GPT-4o:

To determine how many oranges each tree produces, we need to divide the total number of oranges by the number of trees.

Given:
- Total number of oranges = 49,920
- Number of trees = 195

We perform the division:

\[ \frac{49,920}{195} \]

First, let's simplify the division step-by-step:

1. Divide 49,920 by 195:
\[ 49,920 \div 195 \approx 256 \]

To verify, we can multiply 256 by 195 to check if it equals 49,920:
\[ 256 \times 195 = 256 \times (200 - 5) = 256 \times 200 - 256 \times 5 \]
\[ 256 \times 200 = 51,200 \]
\[ 256 \times 5 = 1,280 \]
\[ 51,200 - 1,280 = 49,920 \]

The calculation confirms that each tree produces 256 oranges.

### Answer: 256

Expected answer: 256

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now, the farmer decided to distribute the same total number of 49,920 oranges but now only among 9,289 of his best-performing trees. How many oranges does each of these selected trees produce?

GPT-4o:

To determine how many oranges each of the 9,289 best-performing trees produces, we need to divide the total number of oranges by the number of trees.

Given:
- Total number of oranges = 49,920
- Number of trees = 9,289

We perform the division:

\[ \frac{49,920}{9,289} \]

Let's calculate this division:

\[ 49,920 \div 9,289 \approx 5.375 \]

So, each of the 9,289 best-performing trees produces approximately 5.375 oranges.

### Answer: 5.375

Expected answer: 49920/9289

Correct? No

๐Ÿ”— Problem

Problem: A consumption study found that 34160 children had a sandwich for lunch out of the total 4270 schools in the country. If every school has an equal number of children, how many children in each school had a sandwich for lunch?

GPT-4o:

To determine how many children in each school had a sandwich for lunch, we need to divide the total number of children who had a sandwich by the total number of schools.

Given:
- Total number of children who had a sandwich: 34,160
- Total number of schools: 4,270

We perform the division:

\[ \frac{34,160}{4,270} \]

First, simplify the division:

\[ \frac{34,160 \div 10}{4,270 \div 10} = \frac{3,416}{427} \]

Now, perform the division:

\[ 3,416 \div 427 = 8 \]

So, each school had 8 children who had a sandwich for lunch.

### Answer: 8

Expected answer: 8

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the same consumption study, it was later revealed that the actual number of children who had a sandwich for lunch is 34160, but among a total of 7823 schools in the country. With this revised information, how many children in each school had a sandwich for lunch now?

GPT-4o:

To determine how many children in each school had a sandwich for lunch with the revised information, we need to divide the total number of children who had a sandwich by the total number of schools.

Given:
- Total number of children who had a sandwich: 34,160
- Total number of schools: 7,823

We perform the division:

\[ \frac{34,160}{7,823} \]

Perform the division:

\[ 34,160 \div 7,823 \approx 4.37 \]

So, each school had approximately 4.37 children who had a sandwich for lunch.

### Answer: 4.37

Expected answer: 34160/7823

Correct? No

๐Ÿ”— Problem

Problem: A toothpaste tube contains 3366 grams of paste and each brushing uses an average of 306 grams. How many times can you brush your teeth with this tube of toothpaste?

GPT-4o:

To determine how many times you can brush your teeth with the tube of toothpaste, we need to divide the total amount of toothpaste by the amount used per brushing.

Given:
- Total toothpaste: 3366 grams
- Toothpaste used per brushing: 306 grams

We perform the division:
\[ \frac{3366 \text{ grams}}{306 \text{ grams/brush}} \]

First, let's simplify the division:
\[ 3366 \div 306 \]

Performing the division:
\[ 3366 \div 306 = 11 \]

So, you can brush your teeth 11 times with the tube of toothpaste.

### Answer: 11

Expected answer: 11

Correct? Yes

๐Ÿ”— Follow-up

Problem: Consider the previous toothpaste problem, but this time, the toothpaste tube contains 9060 grams of paste. How many times can you now brush your teeth with this tube of toothpaste if each brushing still uses an average of 306 grams?

GPT-4o:

To determine how many times you can brush your teeth with the new tube of toothpaste, we need to divide the total amount of toothpaste by the amount used per brushing.

Given:
- Total toothpaste: 9060 grams
- Toothpaste used per brushing: 306 grams

We perform the division:
\[ \frac{9060 \text{ grams}}{306 \text{ grams/brush}} \]

First, let's simplify the division:
\[ 9060 \div 306 \]

Performing the division:
\[ 9060 \div 306 = 30 \]

So, you can brush your teeth 30 times with the tube of toothpaste.

### Answer: 30

Expected answer: 1510/51

Correct? No

๐Ÿ”— Problem

Problem: A textile factory produces 49742 towels, evenly distributed among 1309 boxes. How many towels are in each box?

GPT-4o:

To determine how many towels are in each box, we need to divide the total number of towels by the number of boxes.

\[ \text{Total number of towels} = 49742 \]
\[ \text{Number of boxes} = 1309 \]

We perform the division:

\[ \frac{49742}{1309} \approx 38 \]

So, each box contains approximately 38 towels.

### Answer: 38

Expected answer: 38

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now consider that the textile factory actually produced 8337 towels, still evenly distributed among 1309 boxes. How many towels are now in each box?

GPT-4o:

To find out how many towels are in each box, we need to divide the total number of towels by the number of boxes.

\[ \text{Total number of towels} = 8337 \]
\[ \text{Number of boxes} = 1309 \]

We perform the division:

\[ \frac{8337}{1309} \approx 6.37 \]

Since the number of towels per box must be a whole number, we round down to the nearest whole number:

\[ \lfloor 6.37 \rfloor = 6 \]

So, each box contains 6 towels.

### Answer: 6

Expected answer: 1191/187

Correct? No

๐Ÿ”— Problem

Problem: An alien civilization sends 43134 messages over a period of 3318 Earth days. If they send exactly the same number of messages each day, how many messages do they send per day?

GPT-4o:

To determine how many messages the alien civilization sends per day, we need to divide the total number of messages by the number of days.

Given:
- Total messages = 43,134
- Total days = 3,318

We perform the division:

\[ \frac{43134}{3318} \]

First, let's simplify the division step-by-step:

1. Divide 43134 by 3318:
\[ 43134 \div 3318 \approx 13 \]

To verify, we multiply 3318 by 13:
\[ 3318 \times 13 = 43134 \]

Since the multiplication confirms the division, the alien civilization sends 13 messages per day.

### Answer: 13

Expected answer: 13

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of 3318 Earth days, consider that the alien civilization uses a different form of time measurement, where each of their "days" represents 8212 of our Earth days. In this scenario, if they were still sending 43134 messages throughout this period, how many messages would they be sending per their "day"?

GPT-4o:

To determine how many messages the alien civilization sends per their "day," we need to divide the total number of messages by the number of their "days."

Given:
- Total messages = 43,134
- Each of their "days" = 8,212 Earth days

First, we need to find out how many of their "days" correspond to the total period of 43,134 messages. Since we are given the total number of messages and the length of their "day" in Earth days, we can directly calculate the number of messages per their "day."

\[ \text{Messages per their "day"} = \frac{43134}{1} \]

Since the total period is already given in terms of their "days," we simply divide the total number of messages by 1 (as we are considering the entire period as one of their "days").

\[ \frac{43134}{1} = 43134 \]

Thus, the alien civilization sends 43,134 messages per their "day."

### Answer: 43134

Expected answer: 21567/4106

Correct? No

๐Ÿ”— Problem

Problem: A school district has 80,011 students who are equally distributed across 31 school buses. How many students are there per bus?

GPT-4o:

To find the number of students per bus, we need to divide the total number of students by the number of buses.

Total number of students: 80,011
Number of buses: 31

We perform the division:

\[ \frac{80,011}{31} \]

First, we estimate the quotient by performing the division step-by-step:

1. 80,011 รท 31 โ‰ˆ 2580.032258064516

Since we are dealing with whole students, we round down to the nearest whole number:

\[ 80,011 \div 31 \approx 2580 \]

Thus, each bus will have approximately 2580 students.

### Answer: 2580

Expected answer: 2581

Correct? No

๐Ÿ”— Problem

Problem: A camera store sold 54020 cameras over a period of 730 days. If they sell the same number of cameras each day, how many cameras are sold daily?

GPT-4o:

To determine the number of cameras sold daily, we need to divide the total number of cameras sold by the number of days.

Given:
- Total cameras sold = 54,020
- Total number of days = 730

We perform the division:

\[ \text{Cameras sold daily} = \frac{54020}{730} \]

Let's calculate this:

\[ \frac{54020}{730} = 74 \]

So, the camera store sells 74 cameras each day.

### Answer: 74

Expected answer: 74

Correct? Yes

๐Ÿ”— Follow-up

Problem: After a successful marketing campaign, the camera store's sales increased, and they were able to sell 54020 cameras in just 5546 days. If they still sold the same number of cameras each day, how many cameras are now sold daily?

GPT-4o:

To determine the number of cameras sold daily after the marketing campaign, we need to divide the total number of cameras sold by the new number of days.

Given:
- Total cameras sold = 54,020
- Total number of days = 5,546

We perform the division:

\[ \text{Cameras sold daily} = \frac{54020}{5546} \]

Let's calculate this:

\[ \frac{54020}{5546} \approx 9.74 \]

So, the camera store now sells approximately 9.74 cameras each day.

### Answer: 9.74

Expected answer: 27010/2773

Correct? No

๐Ÿ”— Problem

Problem: An ice cream factory makes 25774 liters of ice cream that were packed into 526 containers evenly. How many liters of ice cream does each container accommodate?

GPT-4o:

To determine how many liters of ice cream each container accommodates, we need to divide the total amount of ice cream by the number of containers.

Given:
- Total liters of ice cream = 25,774 liters
- Number of containers = 526

We perform the division:

\[ \frac{25774}{526} \]

First, let's set up the division:

\[ 25774 \div 526 \]

Performing the division step-by-step:

1. 25774 รท 526 โ‰ˆ 49 (since 526 * 49 = 25774)

So, each container accommodates:

\[ 49 \text{ liters} \]

### Answer: 49 liters

Expected answer: 49

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of packing the 25774 liters of ice cream into 526 containers, the factory decides to use only 418 containers. If they divide the ice cream evenly among these containers, how many liters of ice cream does each container now accommodate?

GPT-4o:

To determine how many liters of ice cream each container accommodates when using 418 containers, we need to divide the total amount of ice cream by the new number of containers.

Given:
- Total liters of ice cream = 25,774 liters
- Number of containers = 418

We perform the division:

\[ \frac{25774}{418} \]

First, let's set up the division:

\[ 25774 \div 418 \]

Performing the division step-by-step:

1. 25774 รท 418 โ‰ˆ 61.64 (since 418 * 61 = 25498 and 25774 - 25498 = 276, and 276/418 โ‰ˆ 0.66)

So, each container accommodates approximately:

\[ 61.64 \text{ liters} \]

### Answer: 61.64 liters

Expected answer: 12887/209

Correct? No

๐Ÿ”— Problem

Problem: A city's public transportation system logs a total of 85300 miles driven among its fleet of 3412 buses in a week. Assuming each bus travels the same distance, how many miles does each bus drive in a week?

GPT-4o:

To determine how many miles each bus drives in a week, we need to divide the total number of miles driven by the total number of buses.

Given:
- Total miles driven: 85,300 miles
- Total number of buses: 3,412 buses

We perform the division:

\[
\frac{85,300 \text{ miles}}{3,412 \text{ buses}} = 25 \text{ miles per bus}
\]

### Answer: 25 miles per bus.

Expected answer: 25

Correct? Yes

๐Ÿ”— Follow-up

Problem: With the same fleet of 3412 buses, the city's public transportation system only logs a total of 3940 miles driven next week. If each bus shared the work evenly again, how many miles did each bus drive in this week?

GPT-4o:

To determine how many miles each bus drives in a week, we need to divide the total number of miles driven by the total number of buses.

Given:
- Total miles driven: 3,940 miles
- Total number of buses: 3,412 buses

We perform the division:

\[
\frac{3,940 \text{ miles}}{3,412 \text{ buses}} \approx 1.155 \text{ miles per bus}
\]

### Answer: 1.155 miles per bus.

Expected answer: 985/853

Correct? No

๐Ÿ”— Problem

Problem: A wind turbine generates a total of 92250 kilowatts of energy over 75 hours. How much energy does it produce per hour?

GPT-4o:

To determine how much energy the wind turbine produces per hour, we need to divide the total energy generated by the total number of hours.

Given:
- Total energy generated = 92,250 kilowatts
- Total time = 75 hours

We use the formula:
\[ \text{Energy per hour} = \frac{\text{Total energy}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Energy per hour} = \frac{92,250 \text{ kW}}{75 \text{ hours}} \]

Perform the division:
\[ \text{Energy per hour} = 1,230 \text{ kW/hour} \]

### Answer: 1,230 kW/hour

Expected answer: 1230

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the same wind turbine instead generates a total of 5837 kilowatts of energy over the same 75 hours, how much energy does it now produce per hour?

GPT-4o:

To determine how much energy the wind turbine produces per hour with the new total energy generated, we again divide the total energy by the total number of hours.

Given:
- Total energy generated = 5,837 kilowatts
- Total time = 75 hours

We use the formula:
\[ \text{Energy per hour} = \frac{\text{Total energy}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Energy per hour} = \frac{5,837 \text{ kW}}{75 \text{ hours}} \]

Perform the division:
\[ \text{Energy per hour} = 77.8267 \text{ kW/hour} \]

Rounding to two decimal places:
\[ \text{Energy per hour} \approx 77.83 \text{ kW/hour} \]

### Answer: 77.83 kW/hour

Expected answer: 5837/75

Correct? No

๐Ÿ”— Problem

Problem: A baby gained a total of 3734 grams over a span of 1867 days. How many grams did the baby gain daily on average?

GPT-4o:

To find the average daily weight gain, we need to divide the total weight gain by the number of days.

Total weight gain: 3734 grams
Number of days: 1867 days

Average daily weight gain = Total weight gain / Number of days
\[ \text{Average daily weight gain} = \frac{3734 \text{ grams}}{1867 \text{ days}} \]

Perform the division:
\[ \frac{3734}{1867} = 2 \]

So, the baby gained an average of 2 grams per day.

### Answer: 2 grams per day

Expected answer: 2

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the baby's weight gain was recalculated over a span of 1651 days. If the total weight gain was still 3734 grams, what would be the average daily weight gain now?

GPT-4o:

To find the new average daily weight gain, we need to divide the total weight gain by the new number of days.

Total weight gain: 3734 grams
Number of days: 1651 days

Average daily weight gain = Total weight gain / Number of days
\[ \text{Average daily weight gain} = \frac{3734 \text{ grams}}{1651 \text{ days}} \]

Perform the division:
\[ \frac{3734}{1651} \approx 2.26 \]

So, the baby gained an average of approximately 2.26 grams per day.

### Answer: 2.26 grams per day

Expected answer: 3734/1651

Correct? No

๐Ÿ”— Problem

Problem: A firefighter uses a hose that releases 33,532 liters of water. If the hose releases the same amount of water each minute for 8,383 minutes, how many liters of water are released per minute?

GPT-4o:

To find out how many liters of water are released per minute, we need to divide the total amount of water by the total number of minutes.

Given:
- Total water released = 33,532 liters
- Total time = 8,383 minutes

We perform the division:

\[ \frac{33,532 \text{ liters}}{8,383 \text{ minutes}} \]

Let's calculate this:

\[ 33,532 \div 8,383 \approx 4 \]

So, the hose releases approximately 4 liters of water per minute.

### Answer: 4 liters per minute

Expected answer: 4

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the firefighter instead uses a different hose that releases the same total amount of water, 33,532 liters, but this time it's over 7,845 minutes, how many liters of water are released per minute with this hose?

GPT-4o:

To determine how many liters of water are released per minute with the new hose, we need to divide the total amount of water by the total number of minutes.

Given:
- Total water released = 33,532 liters
- Total time = 7,845 minutes

We perform the division:

\[ \frac{33,532 \text{ liters}}{7,845 \text{ minutes}} \]

Let's calculate this:

\[ 33,532 \div 7,845 \approx 4.275 \]

So, the hose releases approximately 4.275 liters of water per minute.

### Answer: 4.275 liters per minute

Expected answer: 33532/7845

Correct? No

๐Ÿ”— Problem

Problem: A farmer collects eggs from her chickens. She collects a total of 96,120 eggs evenly from 20 chickens. How many eggs does each chicken contribute?

GPT-4o:

To determine how many eggs each chicken contributes, we need to divide the total number of eggs by the number of chickens.

Total number of eggs: 96,120
Number of chickens: 20

We perform the division:

\[ \frac{96,120}{20} \]

First, simplify the division by dividing both the numerator and the denominator by 10:

\[ \frac{96,120 \div 10}{20 \div 10} = \frac{9,612}{2} \]

Now, divide 9,612 by 2:

\[ 9,612 \div 2 = 4,806 \]

So, each chicken contributes 4,806 eggs.

### Answer: 4,806

Expected answer: 4806

Correct? Yes

๐Ÿ”— Follow-up

Problem: The farmer realizes that she miscalculated and she actually collected a total of 96,120 eggs but it was from 9,046 chickens, not 20. How many eggs did each chicken actually contribute?

GPT-4o:

To determine how many eggs each chicken actually contributed, we need to divide the total number of eggs by the number of chickens.

Total number of eggs: 96,120
Number of chickens: 9,046

We perform the division:

\[ \frac{96,120}{9,046} \]

Using long division or a calculator, we find:

\[ 96,120 \div 9,046 \approx 10.62 \]

So, each chicken actually contributed approximately 10.62 eggs.

### Answer: 10.62

Expected answer: 48060/4523

Correct? No

๐Ÿ”— Problem

Problem: A town receives 11458 millimeters of rain over 17 days. How much rain does the town receive each day if it rains the same amount every day?

GPT-4o:

To find out how much rain the town receives each day, we need to divide the total amount of rain by the number of days.

Total rain received: 11458 millimeters
Number of days: 17

We perform the division:

\[ \frac{11458}{17} \]

First, let's do the division step-by-step:

1. 17 goes into 114 five times (since \( 17 \times 5 = 85 \)).
   \[ 114 - 85 = 29 \]

2. Bring down the next digit (5), making it 295.
   17 goes into 295 seventeen times (since \( 17 \times 17 = 289 \)).
   \[ 295 - 289 = 6 \]

3. Bring down the next digit (8), making it 68.
   17 goes into 68 four times (since \( 17 \times 4 = 68 \)).
   \[ 68 - 68 = 0 \]

So, the division \( \frac{11458}{17} = 674 \).

Therefore, the town receives 674 millimeters of rain each day.

### Answer: 674 millimeters

Expected answer: 674

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of 11458 millimeters of rain falling over 17 days, suppose now that 11458 millimeters of rain fell over 8513 days. How much rain does the town now receive each day if it rains the same amount every day?

GPT-4o:

To determine how much rain the town receives each day, we need to divide the total amount of rain by the number of days.

Total rain received: 11458 millimeters
Number of days: 8513

We perform the division:

\[ \frac{11458}{8513} \]

Let's do the division step-by-step:

1. Since 11458 is greater than 8513, 8513 goes into 11458 one time.
   \[ 11458 - 8513 = 2945 \]

So, the division \( \frac{11458}{8513} \) is approximately 1.345.

Therefore, the town receives approximately 1.345 millimeters of rain each day.

### Answer: 1.345 millimeters

Expected answer: 11458/8513

Correct? No

๐Ÿ”— Problem

Problem: A pen factory produced 2526 pens in 842 hours. If they produced pens at an equal pace all the time, how many pens were produced every hour?

GPT-4o:

To determine how many pens were produced every hour, we need to divide the total number of pens by the total number of hours.

Given:
- Total number of pens = 2526
- Total number of hours = 842

We perform the division:

\[ \text{Pens per hour} = \frac{2526}{842} \]

Now, let's calculate this:

\[ \frac{2526}{842} \approx 3 \]

So, the factory produced approximately 3 pens every hour.

### Answer: 3

Expected answer: 3

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the pen factory had instead produced 2526 pens in 547 hours under the same even-paced conditions, how many pens would have been produced each hour?

GPT-4o:

To determine how many pens were produced every hour, we need to divide the total number of pens by the total number of hours.

Given:
- Total number of pens = 2526
- Total number of hours = 547

We perform the division:

\[ \text{Pens per hour} = \frac{2526}{547} \]

Now, let's calculate this:

\[ \frac{2526}{547} \approx 4.62 \]

So, the factory produced approximately 4.62 pens every hour.

### Answer: 4.62

Expected answer: 2526/547

Correct? No

๐Ÿ”— Problem

Problem: A school decided to equally distribute 285 erasers among 19 classrooms. How many erasers does each classroom get?

GPT-4o:

To determine how many erasers each classroom gets, we need to divide the total number of erasers by the number of classrooms.

The total number of erasers is 285, and the number of classrooms is 19.

We perform the division:
\[ 285 \div 19 \]

First, we estimate how many times 19 goes into 285. We can start by checking:
\[ 19 \times 10 = 190 \]
\[ 19 \times 15 = 285 \]

Since \( 19 \times 15 = 285 \), each classroom will get exactly 15 erasers.

### Answer: 15

Expected answer: 15

Correct? Yes

๐Ÿ”— Follow-up

Problem: Initially a school decided to equally distribute 285 erasers among 19 classrooms. But later, the school received a donation and the total number of erasers increased to 4681. If these erasers are equally distributed among the same 19 classrooms, how many erasers does each classroom get now?

GPT-4o:

To determine how many erasers each classroom gets after the donation, we need to divide the new total number of erasers by the number of classrooms.

The new total number of erasers is 4681, and the number of classrooms remains 19.

We perform the division:
\[ 4681 \div 19 \]

First, we estimate how many times 19 goes into 4681. We can use long division for this:

1. 19 goes into 46 (the first two digits of 4681) 2 times (since \( 19 \times 2 = 38 \)).
2. Subtract 38 from 46 to get 8, and bring down the next digit (8), making it 88.
3. 19 goes into 88 4 times (since \( 19 \times 4 = 76 \)).
4. Subtract 76 from 88 to get 12, and bring down the next digit (1), making it 121.
5. 19 goes into 121 6 times (since \( 19 \times 6 = 114 \)).
6. Subtract 114 from 121 to get 7.

So, the quotient is 246 and the remainder is 7. This means each classroom gets 246 erasers, with 7 erasers left over.

### Answer: 246

Expected answer: 4681/19

Correct? No

๐Ÿ”— Problem

Problem: A penguin slides down a glacier at a constant speed and covers a distance of 41020 feet in 5 hours. What is the penguin's speed in feet per hour?

GPT-4o:

To find the penguin's speed in feet per hour, we need to divide the total distance by the total time.

Given:
- Total distance = 41,020 feet
- Total time = 5 hours

We use the formula for speed:
\[ \text{Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the given values:
\[ \text{Speed} = \frac{41,020 \text{ feet}}{5 \text{ hours}} \]

Perform the division:
\[ \text{Speed} = 8,204 \text{ feet per hour} \]

### Answer: 8,204 feet per hour

Expected answer: 8204

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the last problem, the penguin covered a distance of 41020 feet in 5 hours. Now, consider a situation where the penguin only covered a distance of 4325 feet in the same 5 hours. What would be the penguin's speed in feet per hour in this new scenario?

GPT-4o:

To find the penguin's speed in feet per hour in the new scenario, we again divide the total distance by the total time.

Given:
- Total distance = 4,325 feet
- Total time = 5 hours

We use the formula for speed:
\[ \text{Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the given values:
\[ \text{Speed} = \frac{4,325 \text{ feet}}{5 \text{ hours}} \]

Perform the division:
\[ \text{Speed} = 865 \text{ feet per hour} \]

### Answer: 865 feet per hour

Expected answer: 865

Correct? Yes

๐Ÿ”— Problem

Problem: A water company has a reservoir that can hold 63360 gallons of water. If the reservoir is divided into 576 equal sections, how many gallons of water does each section hold?

GPT-4o:

To determine how many gallons of water each section holds, we need to divide the total capacity of the reservoir by the number of sections.

The total capacity of the reservoir is 63,360 gallons, and it is divided into 576 equal sections.

We perform the division:
\[
\frac{63360 \text{ gallons}}{576 \text{ sections}} = 110 \text{ gallons per section}
\]

### Answer: 110 gallons per section.

Expected answer: 110

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead the reservoir could hold 63360 gallons of water but now it's divided into 9999 equal sections. How many gallons of water does each section then hold?

GPT-4o:

To find out how many gallons of water each section holds when the reservoir is divided into 9999 equal sections, we need to divide the total capacity of the reservoir by the number of sections.

The total capacity of the reservoir is 63,360 gallons, and it is divided into 9999 equal sections.

We perform the division:
\[
\frac{63360 \text{ gallons}}{9999 \text{ sections}} \approx 6.336 \text{ gallons per section}
\]

### Answer: 6.336 gallons per section.

Expected answer: 640/101

Correct? No

๐Ÿ”— Problem

Problem: A fashion company made a total of 21868 skirts distributed equally among 77 stores. How many skirts did each store get?

GPT-4o:

To determine how many skirts each store received, we need to divide the total number of skirts by the number of stores.

\[
\text{Total number of skirts} = 21868
\]
\[
\text{Number of stores} = 77
\]

We perform the division:

\[
21868 \div 77
\]

First, let's estimate the quotient by simplifying the division:

\[
21868 \div 77 \approx 21868 \div 80 = 273.35
\]

Now, let's perform the exact division:

1. Divide 21868 by 77:
   - 21868 รท 77 = 284

Thus, each store received:

\[
\boxed{284}
\]

### Answer: 284

Expected answer: 284

Correct? Yes

๐Ÿ”— Problem

Problem: A TV channel broadcasts a total of 56109 minutes of advertisements over a 59-day period. On average, how many minutes of advertisements are shown each day?

GPT-4o:

To find the average number of minutes of advertisements shown each day, we need to divide the total number of minutes by the number of days.

Total minutes of advertisements: 56109 minutes
Number of days: 59 days

We perform the division:

\[ \frac{56109}{59} \]

First, let's do the division step-by-step:

1. 56109 รท 59 โ‰ˆ 951

To verify, we multiply 951 by 59:

\[ 951 \times 59 = 951 \times (60 - 1) = 951 \times 60 - 951 \times 1 \]
\[ 951 \times 60 = 57060 \]
\[ 951 \times 1 = 951 \]
\[ 57060 - 951 = 56109 \]

The calculation is correct.

### Answer: 951

Expected answer: 951

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the TV channel decided to reduce the total minutes of advertisements. Now, over a 59-day period, they only broadcast a total of 5352 minutes of advertisements. What is the new average of advertisement minutes shown each day?

GPT-4o:

To find the new average number of minutes of advertisements shown each day, we need to divide the new total number of minutes by the number of days.

Total minutes of advertisements: 5352 minutes
Number of days: 59 days

We perform the division:

\[ \frac{5352}{59} \]

First, let's do the division step-by-step:

1. 5352 รท 59 โ‰ˆ 90.7

To verify, we multiply 90.7 by 59:

\[ 90.7 \times 59 = 90.7 \times (60 - 1) = 90.7 \times 60 - 90.7 \times 1 \]
\[ 90.7 \times 60 = 5442 \]
\[ 90.7 \times 1 = 90.7 \]
\[ 5442 - 90.7 = 5351.3 \]

Since we are dealing with minutes, we should round to the nearest whole number:

\[ 5352 รท 59 โ‰ˆ 91 \]

### Answer: 91

Expected answer: 5352/59

Correct? No

๐Ÿ”— Problem

Problem: A teacher marks a total of 59748 marks distributed evenly over 1149 exam papers. How many marks are in each exam paper?

GPT-4o:

To determine how many marks are in each exam paper, we need to divide the total number of marks by the number of exam papers.

Given:
- Total marks = 59,748
- Number of exam papers = 1,149

We perform the division:

\[ \frac{59,748}{1,149} \]

Let's do the division step-by-step:

1. 59,748 รท 1,149 โ‰ˆ 52

To verify, we multiply 52 by 1,149:

\[ 52 \times 1,149 = 59,748 \]

Since the multiplication confirms our division, each exam paper has:

### Answer: 52 marks

Expected answer: 52

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the teacher, instead of marking 59748 marks, marked a total of 7117 marks distributed evenly over the same 1149 exam papers, how many marks would be in each exam paper now?

GPT-4o:

To determine how many marks are in each exam paper, we need to divide the total number of marks by the number of exam papers.

Given:
- Total marks = 7,117
- Number of exam papers = 1,149

We perform the division:

\[ \frac{7,117}{1,149} \]

Let's do the division step-by-step:

1. 7,117 รท 1,149 โ‰ˆ 6.19

Since we are dealing with marks, we typically round to the nearest whole number. Therefore, each exam paper has approximately:

### Answer: 6 marks

Expected answer: 7117/1149

Correct? No

๐Ÿ”— Problem

Problem: A reservoir holds 44840 liters of water. If this water is equally distributed across 76 houses in a village, how many liters of water will each house get?

GPT-4o:

To determine how many liters of water each house will get, we need to divide the total amount of water by the number of houses.

The total amount of water is 44,840 liters, and there are 76 houses.

We perform the division:
\[ \frac{44840}{76} \]

First, let's simplify the division step-by-step:

1. Divide 44840 by 76:
\[ 44840 \div 76 = 590 \]

So, each house will get 590 liters of water.

### Answer: 590 liters

Expected answer: 590

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the reservoir now has 6614 houses to supply. If the reservoir still holds 44840 liters of water, how many liters can be distributed to each house?

GPT-4o:

To determine how many liters of water each house will get, we need to divide the total amount of water by the number of houses.

The total amount of water is 44,840 liters, and there are 6,614 houses.

We perform the division:
\[ \frac{44840}{6614} \]

Let's calculate this step-by-step:

1. Divide 44840 by 6614:
\[ 44840 \div 6614 \approx 6.78 \]

So, each house will get approximately 6.78 liters of water.

### Answer: 6.78 liters

Expected answer: 22420/3307

Correct? No

๐Ÿ”— Problem

Problem: A butterfly during its lifetime lay 5385 eggs, and she spread these eggs evenly across 359 flowers. How many eggs did she lay on each flower?

GPT-4o:

To determine how many eggs the butterfly laid on each flower, we need to divide the total number of eggs by the number of flowers.

Given:
- Total number of eggs = 5385
- Number of flowers = 359

We perform the division:

\[ \frac{5385}{359} \]

First, let's do the division step-by-step:

1. 5385 divided by 359 is approximately 15.

To verify:
\[ 359 \times 15 = 5385 \]

Thus, the butterfly laid 15 eggs on each flower.

### Answer: 15

Expected answer: 15

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the butterfly had instead spread a total of 9710 eggs across the same 359 flowers. How many eggs did she lay on each flower in this case?

GPT-4o:

To determine how many eggs the butterfly laid on each flower in this case, we need to divide the total number of eggs by the number of flowers.

Given:
- Total number of eggs = 9710
- Number of flowers = 359

We perform the division:

\[ \frac{9710}{359} \]

First, let's do the division step-by-step:

1. 9710 divided by 359 is approximately 27.

To verify:
\[ 359 \times 27 = 9693 \]
\[ 9710 - 9693 = 17 \]

Since 17 is the remainder, we can confirm that 9710 divided by 359 is 27 with a remainder of 17. However, since we are looking for the number of eggs per flower, we consider only the quotient.

Thus, the butterfly laid 27 eggs on each flower.

### Answer: 27

Expected answer: 9710/359

Correct? No

๐Ÿ”— Problem

Problem: A camera has a total of 95038 pixels divided evenly into 61 rows. How many pixels are there in each row?

GPT-4o:

To find the number of pixels in each row, we need to divide the total number of pixels by the number of rows.

Given:
- Total pixels = 95,038
- Number of rows = 61

We perform the division:

\[ \frac{95038}{61} \]

First, we perform the division step-by-step:

1. 95,038 รท 61 โ‰ˆ 1,558 (since 61 * 1,558 = 94,998)
2. Subtract the product from the total pixels to check for any remainder:
   \[ 95,038 - 94,998 = 40 \]

Since the remainder is less than 61, the division is complete.

Thus, the number of pixels in each row is 1,558.

### Answer: 1,558

Expected answer: 1558

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead of 95038 pixels, the camera has only 2122 pixels and still divides them evenly into 61 rows. How many pixels would there be in each row now?

GPT-4o:

To find the number of pixels in each row, we need to divide the total number of pixels by the number of rows.

Given:
- Total pixels = 2,122
- Number of rows = 61

We perform the division:

\[ \frac{2122}{61} \]

First, we perform the division step-by-step:

1. 2,122 รท 61 โ‰ˆ 34 (since 61 * 34 = 2,074)
2. Subtract the product from the total pixels to check for any remainder:
   \[ 2,122 - 2,074 = 48 \]

Since the remainder is less than 61, the division is complete.

Thus, the number of pixels in each row is 34.

### Answer: 34

Expected answer: 2122/61

Correct? No

๐Ÿ”— Problem

Problem: An ice cream factory produces a total of 45580 cones of ice cream over a period of 53 days. If the ice cream cones are produced uniformly across these days, how many ice cream cones are made each day?

GPT-4o:

To determine the number of ice cream cones produced each day, we need to divide the total number of cones by the number of days.

Total number of ice cream cones: 45,580
Number of days: 53

We perform the division:

\[ \frac{45580}{53} \]

First, let's do the division step-by-step:

1. 45580 รท 53
2. 53 goes into 455 (the first three digits of 45580) approximately 8 times (since 53 * 8 = 424).
3. Subtract 424 from 455 to get 31.
4. Bring down the next digit (8), making it 318.
5. 53 goes into 318 approximately 6 times (since 53 * 6 = 318).
6. Subtract 318 from 318 to get 0.
7. Bring down the last digit (0), making it 0.
8. 53 goes into 0 exactly 0 times.

So, the division is exact, and the result is:

\[ 45580 รท 53 = 860 \]

Therefore, the factory produces 860 ice cream cones each day.

### Answer: 860

Expected answer: 860

Correct? Yes

๐Ÿ”— Follow-up

Problem: The same ice cream factory has adjusted their volume and now makes a total of 4660 cones over the same 53 day period. If production is still uniform, how many ice cream cones are they making each day now?

GPT-4o:

To determine the number of ice cream cones produced each day with the new total, we need to divide the new total number of cones by the number of days.

Total number of ice cream cones: 4,660
Number of days: 53

We perform the division:

\[ \frac{4660}{53} \]

First, let's do the division step-by-step:

1. 4660 รท 53
2. 53 goes into 466 (the first three digits of 4660) approximately 8 times (since 53 * 8 = 424).
3. Subtract 424 from 466 to get 42.
4. Bring down the next digit (0), making it 420.
5. 53 goes into 420 approximately 7 times (since 53 * 7 = 371).
6. Subtract 371 from 420 to get 49.
7. Since there are no more digits to bring down, we can conclude the division.

So, the division is:

\[ 4660 รท 53 = 88 \]

Therefore, the factory now produces 88 ice cream cones each day.

### Answer: 88

Expected answer: 4660/53

Correct? No

๐Ÿ”— Problem

Problem: A textile factory produces 36135 square inches of towel fabric that is divided evenly among 219 towels. How many square inches of fabric is each towel?

GPT-4o:

To determine how many square inches of fabric each towel receives, we need to divide the total amount of fabric by the number of towels.

Given:
- Total fabric = 36,135 square inches
- Number of towels = 219

We perform the division:

\[ \frac{36135}{219} \]

First, let's set up the long division:

1. 219 goes into 361 once (since 219 * 1 = 219).
2. Subtract 219 from 361 to get 142.
3. Bring down the next digit (1), making it 1421.
4. 219 goes into 1421 six times (since 219 * 6 = 1314).
5. Subtract 1314 from 1421 to get 107.
6. Bring down the next digit (3), making it 1073.
7. 219 goes into 1073 four times (since 219 * 4 = 876).
8. Subtract 876 from 1073 to get 197.
9. Bring down the last digit (5), making it 1975.
10. 219 goes into 1975 nine times (since 219 * 9 = 1971).
11. Subtract 1971 from 1975 to get 4.

So, the quotient is 165 and the remainder is 4. Since we are looking for the number of square inches per towel, we consider only the quotient.

### Answer: 165

Expected answer: 165

Correct? Yes

๐Ÿ”— Problem

Problem: A fireplace burns 36300 kilojoules of energy in 4 hours. How much energy does it burn in one hour?

GPT-4o:

To determine how much energy the fireplace burns in one hour, we need to divide the total energy burned by the number of hours.

Given:
- Total energy burned in 4 hours = 36,300 kilojoules
- Number of hours = 4

We calculate the energy burned per hour as follows:
\[
\text{Energy burned per hour} = \frac{\text{Total energy burned}}{\text{Number of hours}} = \frac{36,300 \text{ kJ}}{4}
\]

Performing the division:
\[
\frac{36,300}{4} = 9,075 \text{ kJ}
\]

### Answer: 9,075 kJ

Expected answer: 9075

Correct? Yes

๐Ÿ”— Follow-up

Problem: In another scenario, a different fireplace burns 8712 kilojoules of energy in 4 hours. Assuming it also burns energy at a constant rate, how much energy does this fireplace burn in one hour?

GPT-4o:

To determine how much energy the different fireplace burns in one hour, we need to divide the total energy burned by the number of hours.

Given:
- Total energy burned in 4 hours = 8,712 kilojoules
- Number of hours = 4

We calculate the energy burned per hour as follows:
\[
\text{Energy burned per hour} = \frac{\text{Total energy burned}}{\text{Number of hours}} = \frac{8,712 \text{ kJ}}{4}
\]

Performing the division:
\[
\frac{8,712}{4} = 2,178 \text{ kJ}
\]

### Answer: 2,178 kJ

Expected answer: 2178

Correct? Yes

๐Ÿ”— Problem

Problem: A snowman-making competition has 9 teams, each of them was provided an equal amount of snow weighing up to 51156 kilograms in total. How much snow, in kilograms, did each team get to make their snowman?

GPT-4o:

To determine how much snow each team received, we need to divide the total amount of snow by the number of teams.

Total amount of snow: 51,156 kilograms
Number of teams: 9

We perform the division:

\[ \frac{51156}{9} \]

First, we divide 51,156 by 9:

\[ 51156 \div 9 = 5684 \]

So, each team received 5,684 kilograms of snow.

### Answer: 5684 kilograms

Expected answer: 5684

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead of 51156 kilograms of snow, only 6407 kilograms of snow was available for the same 9 teams in the snowman-making competition. How much snow, in kilograms, would each team get to make their snowman now?

GPT-4o:

To determine how much snow each team would receive with the new total amount of snow, we need to divide the total amount of snow by the number of teams.

Total amount of snow: 6,407 kilograms
Number of teams: 9

We perform the division:

\[ \frac{6407}{9} \]

First, we divide 6,407 by 9:

\[ 6407 \div 9 = 711 \text{ remainder } 8 \]

So, each team would receive 711 kilograms of snow, with 8 kilograms remaining.

### Answer: 711 kilograms

Expected answer: 6407/9

Correct? No

๐Ÿ”— Problem

Problem: An apple orchard yielded a total of 56250 apples. Over the course of 30 days, they managed to harvest the same number of apples every day. How many apples were harvested each day?

GPT-4o:

To determine how many apples were harvested each day, we need to divide the total number of apples by the number of days.

Total apples: 56,250
Number of days: 30

We perform the division:
\[ \frac{56250}{30} \]

First, simplify the division:
\[ \frac{56250 \div 10}{30 \div 10} = \frac{5625}{3} \]

Now, perform the division:
\[ 5625 \div 3 = 1875 \]

So, the number of apples harvested each day is 1,875.

### Answer: 1875

Expected answer: 1875

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of the original 30 days, the workers actually took 3028 days to harvest a total of 56250 apples, harvesting the same number of apples every day. In light of this new information, how many apples were actually harvested each day?

GPT-4o:

To determine how many apples were harvested each day with the new information, we need to divide the total number of apples by the new number of days.

Total apples: 56,250
Number of days: 3,028

We perform the division:
\[ \frac{56250}{3028} \]

Let's calculate this division step-by-step:

\[ 56250 \div 3028 \approx 18.57 \]

So, the number of apples harvested each day is approximately 18.57.

### Answer: 18.57

Expected answer: 28125/1514

Correct? No

๐Ÿ”— Problem

Problem: A baby spoke her first word after 82992 seconds of being awake in her life. If one day is considered 1729 seconds, after how many days did she speak her first word?

GPT-4o:

To determine how many days it took for the baby to speak her first word, we need to divide the total number of seconds she was awake by the number of seconds in one day.

Given:
- Total seconds awake = 82992 seconds
- Seconds in one day = 1729 seconds

We perform the division:

\[
\frac{82992 \text{ seconds}}{1729 \text{ seconds/day}} = 48 \text{ days}
\]

Thus, the baby spoke her first word after 48 days.

### Answer: 48

Expected answer: 48

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering the baby from the previous problem, suppose now that she spoke her first word after being awake for a shorter time of 8741 seconds. Keeping our day duration constant at 1729 seconds, after how many days in this scenario did she speak her first word?

GPT-4o:

To determine how many days it took for the baby to speak her first word in this new scenario, we need to divide the total number of seconds she was awake by the number of seconds in one day.

Given:
- Total seconds awake = 8741 seconds
- Seconds in one day = 1729 seconds

We perform the division:

\[
\frac{8741 \text{ seconds}}{1729 \text{ seconds/day}} \approx 5.056 \text{ days}
\]

Since we are typically interested in whole days, we can round this to the nearest whole number. In this case, it rounds to 5 days.

### Answer: 5

Expected answer: 8741/1729

Correct? No

๐Ÿ”— Problem

Problem: A map has a scale of 91368 centimeters representing 216 kilometers. How many centimeters on the map represent 1 kilometer in real life?

GPT-4o:

To determine how many centimeters on the map represent 1 kilometer in real life, we need to set up a proportion based on the given scale.

The given scale is:
\[ 91368 \text{ centimeters} \text{ on the map} = 216 \text{ kilometers} \text{ in real life} \]

We need to find how many centimeters on the map (let's call this \( x \)) represent 1 kilometer in real life. We can set up the proportion as follows:
\[ \frac{91368 \text{ cm}}{216 \text{ km}} = \frac{x \text{ cm}}{1 \text{ km}} \]

To solve for \( x \), we can cross-multiply and solve the equation:
\[ 91368 \text{ cm} \times 1 \text{ km} = 216 \text{ km} \times x \text{ cm} \]
\[ 91368 = 216x \]

Now, divide both sides by 216 to isolate \( x \):
\[ x = \frac{91368}{216} \]

Perform the division:
\[ x = 423 \]

So, 423 centimeters on the map represent 1 kilometer in real life.

### Answer: 423 centimeters

Expected answer: 423

Correct? Yes

๐Ÿ”— Follow-up

Problem: Following the previous scenario, the map maker decides to make a new map where 6884 centimeters represent the same 216 kilometers. Now, how many centimeters on this new map would represent 1 kilometer in real life?

GPT-4o:

To determine how many centimeters on the new map represent 1 kilometer in real life, we need to set up a proportion based on the new scale.

The new scale is:
\[ 6884 \text{ centimeters} \text{ on the map} = 216 \text{ kilometers} \text{ in real life} \]

We need to find how many centimeters on the new map (let's call this \( y \)) represent 1 kilometer in real life. We can set up the proportion as follows:
\[ \frac{6884 \text{ cm}}{216 \text{ km}} = \frac{y \text{ cm}}{1 \text{ km}} \]

To solve for \( y \), we can cross-multiply and solve the equation:
\[ 6884 \text{ cm} \times 1 \text{ km} = 216 \text{ km} \times y \text{ cm} \]
\[ 6884 = 216y \]

Now, divide both sides by 216 to isolate \( y \):
\[ y = \frac{6884}{216} \]

Perform the division:
\[ y \approx 31.88 \]

So, approximately 31.88 centimeters on the new map represent 1 kilometer in real life.

### Answer: 31.88 centimeters

Expected answer: 1721/54

Correct? No

๐Ÿ”— Problem

Problem: A fashion designer plans to use 33536 beads to embellish a dress uniformly across 131 different sections. How many beads will be used for each section?

GPT-4o:

To determine how many beads will be used for each section, we need to divide the total number of beads by the number of sections.

Given:
- Total number of beads = 33,536
- Number of sections = 131

We perform the division:

\[ \frac{33,536}{131} \]

Let's calculate this step-by-step:

1. Divide 33,536 by 131:
   \[ 33,536 \div 131 \approx 256 \]

So, each section will have approximately 256 beads.

### Answer: 256

Expected answer: 256

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now, imagine that the fashion designer decides to use the same total number of 33536 beads, but wants to distribute them uniformly over a larger number of sections. If they decides to spread these beads over 3206 different sections on the dress, how many beads will there be in each section?

GPT-4o:

To determine how many beads will be used for each section when the total number of beads is 33,536 and the number of sections is 3,206, we need to divide the total number of beads by the number of sections.

Given:
- Total number of beads = 33,536
- Number of sections = 3,206

We perform the division:

\[ \frac{33,536}{3,206} \]

Let's calculate this step-by-step:

1. Divide 33,536 by 3,206:
   \[ 33,536 \div 3,206 \approx 10.46 \]

Since the number of beads must be a whole number, we round to the nearest whole number:

\[ 10.46 \approx 10 \]

So, each section will have approximately 10 beads.

### Answer: 10

Expected answer: 16768/1603

Correct? No

๐Ÿ”— Problem

Problem: A firefighter sprays 69966 gallons of water on a fire in 299 minutes. If the firefighter sprays the same amount of water every minute, how many gallons does he spray each minute?

GPT-4o:

To determine how many gallons of water the firefighter sprays each minute, we need to divide the total amount of water by the total number of minutes.

Given:
- Total water sprayed: 69,966 gallons
- Total time: 299 minutes

We perform the division:

\[ \frac{69966 \text{ gallons}}{299 \text{ minutes}} \]

Let's calculate this:

\[ 69966 \div 299 = 234 \]

So, the firefighter sprays 234 gallons of water each minute.

### Answer: 234 gallons per minute.

Expected answer: 234

Correct? Yes

๐Ÿ”— Follow-up

Problem: After the fire is controlled, a firefighter continues to spray 8749 gallons of water to cool down the area over the next 299 minutes. If the firefighter sprays the same amount of water every minute as before, how many gallons does he spray each minute now?

GPT-4o:

To determine how many gallons of water the firefighter sprays each minute during the cooling down period, we need to divide the total amount of water by the total number of minutes.

Given:
- Total water sprayed: 8,749 gallons
- Total time: 299 minutes

We perform the division:

\[ \frac{8749 \text{ gallons}}{299 \text{ minutes}} \]

Let's calculate this:

\[ 8749 \div 299 \approx 29.25 \]

So, the firefighter sprays approximately 29.25 gallons of water each minute during the cooling down period.

### Answer: 29.25 gallons per minute.

Expected answer: 673/23

Correct? No

๐Ÿ”— Problem

Problem: The latest model of window that a company has designed will require 6354 square inches of glass material. The manufacturer's current stock can cover 2118 same-sized windows. How many square inches of glass are required for a single window?

GPT-4o:

To determine the number of square inches of glass required for a single window, we need to divide the total amount of glass material by the number of windows that can be covered.

Given:
- Total glass material: 6354 square inches
- Number of windows: 2118

We perform the division:
\[ \text{Square inches per window} = \frac{6354 \text{ square inches}}{2118 \text{ windows}} \]

\[ \text{Square inches per window} = 3 \text{ square inches} \]

### Answer: 3 square inches

Expected answer: 3

Correct? Yes

๐Ÿ”— Follow-up

Problem: After revising their design slightly, the company now finds that they will only need 6354 square inches of glass material to produce 6122 of the new model of windows. How many square inches of glass are now required for each of the new model windows?

GPT-4o:

To determine the number of square inches of glass required for each of the new model windows, we need to divide the total amount of glass material by the number of windows.

Given:
- Total glass material: 6354 square inches
- Number of windows: 6122

We perform the division:
\[ \text{Square inches per window} = \frac{6354 \text{ square inches}}{6122 \text{ windows}} \]

\[ \text{Square inches per window} \approx 1.038 \text{ square inches} \]

### Answer: 1.038 square inches

Expected answer: 3177/3061

Correct? No

๐Ÿ”— Problem

Problem: A frog jumps a total of 12288 centimeters in 512 jumps. If the frog jumps the same distance each time, how many centimeters does the frog jump per jump?

GPT-4o:

To find out how many centimeters the frog jumps per jump, we need to divide the total distance jumped by the total number of jumps.

Total distance jumped: 12288 centimeters
Total number of jumps: 512

We perform the division:

\[ \frac{12288}{512} \]

First, simplify the division by finding the greatest common divisor (GCD) of 12288 and 512. However, we can directly divide:

\[ 12288 \div 512 = 24 \]

So, the frog jumps 24 centimeters per jump.

### Answer: 24

Expected answer: 24

Correct? Yes

๐Ÿ”— Follow-up

Problem: After practicing for a while, the frog now jumps a total of 9064 centimeters in the same 512 jumps. If the frog jumps the same distance each time, how many centimeters does the frog now jump per jump?

GPT-4o:

To determine how many centimeters the frog now jumps per jump, we need to divide the total distance jumped by the total number of jumps.

Total distance jumped: 9064 centimeters
Total number of jumps: 512

We perform the division:

\[ \frac{9064}{512} \]

First, simplify the division by performing the calculation:

\[ 9064 \div 512 = 17.703125 \]

So, the frog now jumps approximately 17.703125 centimeters per jump.

### Answer: 17.703125

Expected answer: 1133/64

Correct? Yes

๐Ÿ”— Problem

Problem: A gardener planted a total of 1392 flowers evenly into 116 pots. How many flowers are there in each pot?

GPT-4o:

To determine how many flowers are in each pot, we need to divide the total number of flowers by the number of pots.

\[
\text{Number of flowers per pot} = \frac{\text{Total number of flowers}}{\text{Number of pots}} = \frac{1392}{116}
\]

Performing the division:

\[
1392 \div 116 = 12
\]

So, there are 12 flowers in each pot.

### Answer: 12

Expected answer: 12

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of planting a total of 1392 flowers, the gardener planted a total of 7275 flowers evenly into the 116 pots, then how many flowers would there be in each pot now?

GPT-4o:

To find out how many flowers are in each pot, we need to divide the total number of flowers by the number of pots.

\[
\text{Number of flowers per pot} = \frac{\text{Total number of flowers}}{\text{Number of pots}} = \frac{7275}{116}
\]

Performing the division:

\[
7275 \div 116 = 62.72
\]

Since the number of flowers must be a whole number, we round to the nearest whole number if necessary. However, in this case, the division results in a whole number.

So, there are approximately 62.72 flowers in each pot, but since we need a whole number, we can say:

### Answer: 62 flowers per pot

Expected answer: 7275/116

Correct? No

๐Ÿ”— Problem

Problem: An ice cream shop sold a total of 31,176 scoops of ice cream over 9 weeks. How many scoops of ice cream did they sell each week?

GPT-4o:

To find out how many scoops of ice cream the shop sold each week, we need to divide the total number of scoops by the number of weeks.

Total scoops of ice cream: 31,176
Number of weeks: 9

We perform the division:

\[ 31,176 \div 9 = 3,464 \]

So, the shop sold 3,464 scoops of ice cream each week.

### Answer: 3,464

Expected answer: 3464

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead of 9 weeks, it took the ice cream shop 4035 days to sell a total of 31,176 scoops of ice cream. How many scoops of ice cream did they sell each day?

GPT-4o:

To determine how many scoops of ice cream the shop sold each day, we need to divide the total number of scoops by the number of days.

Total scoops of ice cream: 31,176
Number of days: 4,035

We perform the division:

\[ 31,176 \div 4,035 \approx 7.72 \]

So, the shop sold approximately 7.72 scoops of ice cream each day.

### Answer: 7.72

Expected answer: 10392/1345

Correct? No

๐Ÿ”— Problem

Problem: A very active mouse runs 14824 meters in 4 hours. If he runs at a constant rate, how many meters per hour does he run?

GPT-4o:

To determine the number of meters the mouse runs per hour, we need to divide the total distance by the total time.

The total distance the mouse runs is 14,824 meters, and the total time is 4 hours.

We perform the division:
\[ \frac{14824 \text{ meters}}{4 \text{ hours}} = 3706 \text{ meters per hour} \]

### Answer: 3706 meters per hour

Expected answer: 3706

Correct? Yes

๐Ÿ”— Problem

Problem: In a large monkey sanctuary, there are 88,508 bananas to be split evenly among 406 monkeys. If every monkey will receive an equal number of bananas, how many bananas would each monkey get?

GPT-4o:

To determine how many bananas each monkey will receive, we need to divide the total number of bananas by the number of monkeys.

First, we perform the division:
\[ 88,508 \div 406 \]

Let's do the long division step-by-step:

1. **Divide 885 by 406**:
   - 406 goes into 885 two times (since \( 406 \times 2 = 812 \)).
   - Subtract 812 from 885 to get the remainder: \( 885 - 812 = 73 \).

2. **Bring down the next digit (0)**:
   - Now we have 730.
   - 406 goes into 730 one time (since \( 406 \times 1 = 406 \)).
   - Subtract 406 from 730 to get the remainder: \( 730 - 406 = 324 \).

3. **Bring down the next digit (8)**:
   - Now we have 3248.
   - 406 goes into 3248 eight times (since \( 406 \times 8 = 3248 \)).
   - Subtract 3248 from 3248 to get the remainder: \( 3248 - 3248 = 0 \).

So, the quotient is 218, and there is no remainder.

### Answer: 218

Expected answer: 218

Correct? Yes

๐Ÿ”— Follow-up

Problem: What if the sanctuary in the previous problem had only 9,073 bananas instead of 88,508? How many bananas would each monkey get then, if they still had to be split evenly among the 406 monkeys?

GPT-4o:

To determine how many bananas each monkey will receive when there are 9,073 bananas to be split among 406 monkeys, we need to perform the division:

\[ 9,073 \div 406 \]

Let's do the long division step-by-step:

1. **Divide 907 by 406**:
   - 406 goes into 907 two times (since \( 406 \times 2 = 812 \)).
   - Subtract 812 from 907 to get the remainder: \( 907 - 812 = 95 \).

2. **Bring down the next digit (3)**:
   - Now we have 953.
   - 406 goes into 953 two times (since \( 406 \times 2 = 812 \)).
   - Subtract 812 from 953 to get the remainder: \( 953 - 812 = 141 \).

So, the quotient is 22, and the remainder is 141.

Each monkey will get 22 bananas, and there will be 141 bananas left over.

### Answer: 22

Expected answer: 9073/406

Correct? No

๐Ÿ”— Problem

Problem: A furniture maker has a large order placed by a hotel owner for tables. The order is for 15110 table legs, making the assumption that each table will have 2 legs. How many tables is the hotel owner ordering?

GPT-4o:

To determine the number of tables ordered, we need to divide the total number of table legs by the number of legs per table.

Given:
- Total number of table legs = 15,110
- Number of legs per table = 2

We perform the division:
\[ \text{Number of tables} = \frac{15,110}{2} \]

Calculating the division:
\[ \text{Number of tables} = 7,555 \]

### Answer: 7,555

Expected answer: 7555

Correct? Yes

๐Ÿ”— Follow-up

Problem: The furniture maker later realizes that there was a mistake in the initial order, and the hotel owner actually only wanted 3774 table legs, with each table having 2 legs. With this corrected order, how many tables is the hotel owner actually ordering?

GPT-4o:

To determine the number of tables ordered with the corrected number of table legs, we need to divide the total number of table legs by the number of legs per table.

Given:
- Total number of table legs = 3,774
- Number of legs per table = 2

We perform the division:
\[ \text{Number of tables} = \frac{3,774}{2} \]

Calculating the division:
\[ \text{Number of tables} = 1,887 \]

### Answer: 1,887

Expected answer: 1887

Correct? Yes

๐Ÿ”— Problem

Problem: A hat maker has 3560 feathers which will be used to decorate hats. If each hat will have 890 feathers, how many hats can be made?

GPT-4o:

To determine how many hats can be made, we need to divide the total number of feathers by the number of feathers required for each hat.

Given:
- Total feathers = 3560
- Feathers per hat = 890

We perform the division:
\[ \frac{3560}{890} \]

First, let's simplify the division:
\[ 3560 \div 890 = 4 \]

So, the hat maker can make 4 hats with the feathers available.

### Answer: 4

Expected answer: 4

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the previous scenario, suppose the hat maker did not have 3560 feathers, but only had 1416 feathers instead. If each hat will still have 890 feathers, how many hats can be produced now?

GPT-4o:

To determine how many hats can be made with 1416 feathers, we need to divide the total number of feathers by the number of feathers required for each hat.

Given:
- Total feathers = 1416
- Feathers per hat = 890

We perform the division:
\[ \frac{1416}{890} \]

First, let's simplify the division:
\[ 1416 \div 890 \approx 1.59 \]

Since we cannot make a fraction of a hat, we take the integer part of the result, which is 1.

So, the hat maker can make 1 hat with the feathers available.

### Answer: 1

Expected answer: 708/445

Correct? No

๐Ÿ”— Problem

Problem: A card game involves a total of 17394 points distributed equally over 3 players. How many points does each player have?

GPT-4o:

To determine how many points each player has, we need to divide the total number of points by the number of players.

The total number of points is 17394, and there are 3 players.

We perform the division:
\[ 17394 \div 3 \]

Let's do the division step-by-step:

1. Divide 17 by 3, which gives 5 with a remainder of 2.
2. Bring down the next digit, 3, making it 23.
3. Divide 23 by 3, which gives 7 with a remainder of 2.
4. Bring down the next digit, 9, making it 29.
5. Divide 29 by 3, which gives 9 with a remainder of 2.
6. Bring down the next digit, 4, making it 24.
7. Divide 24 by 3, which gives 8 with no remainder.

So, the division process is:
\[ 17394 \div 3 = 5798 \]

Each player has 5798 points.

### Answer: 5798

Expected answer: 5798

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now, consider a similar game where the total of 17394 points is now distributed evenly among 7489 players instead. In this case, how many points would each player have?

GPT-4o:

To determine how many points each player would have if 17394 points are distributed evenly among 7489 players, we need to perform the division:

\[ 17394 \div 7489 \]

Let's perform the division step-by-step:

1. Since 17394 is less than 7489, we know that each player will get less than 1 point.
2. To find the exact number of points each player gets, we can perform the division to get a decimal value.

Using a calculator for precision:
\[ 17394 \div 7489 \approx 2.322 \]

However, since we are distributing points and typically points are whole numbers, we can say that each player would get approximately 2 points, and there would be some remainder.

To find the exact remainder:
\[ 17394 - (7489 \times 2) = 17394 - 14978 = 2416 \]

So, each player gets 2 points, and there are 2416 points left over.

### Answer: Each player would get approximately 2 points, with 2416 points remaining.

Expected answer: 17394/7489

Correct? No

๐Ÿ”— Problem

Problem: The central park covers a big land area of 3276 acres divided into 126 identical sections. How many acres does each section have?

GPT-4o:

To determine how many acres each section covers, we need to divide the total land area by the number of sections.

Given:
- Total land area = 3276 acres
- Number of sections = 126

We perform the division:

\[ \frac{3276 \text{ acres}}{126 \text{ sections}} \]

First, we simplify the division:

\[ 3276 \div 126 = 26 \]

So, each section covers 26 acres.

### Answer: 26 acres

Expected answer: 26

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of the original size, the park was smaller, covering only 139 acres, but the sections remained the same, each with an equal area, how many acres would each section cover?

GPT-4o:

To determine how many acres each section covers in the smaller park, we need to divide the new total land area by the number of sections.

Given:
- New total land area = 139 acres
- Number of sections = 126

We perform the division:

\[ \frac{139 \text{ acres}}{126 \text{ sections}} \]

Performing the division:

\[ 139 \div 126 \approx 1.103 \]

So, each section would cover approximately 1.103 acres.

### Answer: 1.103 acres

Expected answer: 139/126

Correct? No

๐Ÿ”— Problem

Problem: A pants manufacturer has 54736 yards of fabric. If they are planning to make each pair of pants using the same amount of fabric and each will consume an equal portion of the total fabric, how many yards of fabric are needed for each pair if they intend to produce 11 pairs?

GPT-4o:

To determine how many yards of fabric are needed for each pair of pants, we need to divide the total amount of fabric by the number of pairs they intend to produce.

Given:
- Total fabric = 54,736 yards
- Number of pairs = 11

We perform the division:

\[ \frac{54736}{11} \]

First, let's do the division step-by-step:

1. 54,736 รท 11
2. 11 goes into 54 four times (since 11 * 4 = 44), leaving a remainder of 10.
3. Bring down the next digit (7), making it 107.
4. 11 goes into 107 nine times (since 11 * 9 = 99), leaving a remainder of 8.
5. Bring down the next digit (3), making it 83.
6. 11 goes into 83 seven times (since 11 * 7 = 77), leaving a remainder of 6.
7. Bring down the last digit (6), making it 66.
8. 11 goes into 66 six times (since 11 * 6 = 66), leaving no remainder.

So, the division yields:

\[ 54736 \div 11 = 4976 \]

Therefore, each pair of pants will require 4,976 yards of fabric.

### Answer: 4976 yards

Expected answer: 4976

Correct? Yes

๐Ÿ”— Follow-up

Problem: The pants manufacturer now only has 4769 yards of fabric left. If they still plan on making 11 pairs of pants with this fabric, and each pair will still consume an equal portion of the total fabric, how many yards of fabric are needed for each pair now?

GPT-4o:

To determine how many yards of fabric are needed for each pair of pants with the remaining fabric, we need to divide the total amount of fabric by the number of pairs they intend to produce.

Given:
- Total fabric = 4,769 yards
- Number of pairs = 11

We perform the division:

\[ \frac{4769}{11} \]

First, let's do the division step-by-step:

1. 4,769 รท 11
2. 11 goes into 47 four times (since 11 * 4 = 44), leaving a remainder of 3.
3. Bring down the next digit (6), making it 36.
4. 11 goes into 36 three times (since 11 * 3 = 33), leaving a remainder of 3.
5. Bring down the last digit (9), making it 39.
6. 11 goes into 39 three times (since 11 * 3 = 33), leaving a remainder of 6.

So, the division yields:

\[ 4769 \div 11 = 433 \text{ remainder } 6 \]

Since we are looking for the exact amount of fabric per pair, we can express the remainder as a fraction:

\[ 433 \frac{6}{11} \]

Thus, each pair of pants will require \( 433 \frac{6}{11} \) yards of fabric.

### Answer: 433 \(\frac{6}{11}\) yards

Expected answer: 4769/11

Correct? Yes

๐Ÿ”— Problem

Problem: The minute hand of a clock rotates 49716 degrees throughout 18 hours. If the rotation is uniform, how many degrees does it rotate each hour?

GPT-4o:

To determine how many degrees the minute hand of a clock rotates each hour, we need to divide the total degrees rotated by the number of hours.

Given:
- Total degrees rotated in 18 hours = 49716 degrees
- Number of hours = 18

We perform the division:
\[ \frac{49716 \text{ degrees}}{18 \text{ hours}} \]

Let's calculate this step-by-step:

1. Divide 49716 by 18:
\[ 49716 \div 18 = 2762 \]

So, the minute hand rotates 2762 degrees each hour.

### Answer: 2762 degrees

Expected answer: 2762

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering that the minute hand of the clock actually rotates 49716 degrees throughout 9706 hours instead of 18, how many degrees does it rotate each hour?

GPT-4o:

To determine how many degrees the minute hand of a clock rotates each hour, we need to divide the total degrees rotated by the number of hours.

Given:
- Total degrees rotated in 9706 hours = 49716 degrees
- Number of hours = 9706

We perform the division:
\[ \frac{49716 \text{ degrees}}{9706 \text{ hours}} \]

Let's calculate this step-by-step:

1. Divide 49716 by 9706:
\[ 49716 \div 9706 \approx 5.12 \]

So, the minute hand rotates approximately 5.12 degrees each hour.

### Answer: 5.12 degrees

Expected answer: 24858/4853

Correct? No

๐Ÿ”— Problem

Problem: A toy company has made 1865 stuffed animals spread over 373 different designs. If each design has the same number of stuffed animals, how many stuffed animals are there for each design?

GPT-4o:

To determine how many stuffed animals there are for each design, we need to divide the total number of stuffed animals by the number of designs.

Given:
- Total number of stuffed animals = 1865
- Number of designs = 373

We perform the division:

\[ \frac{1865}{373} \]

Let's calculate this step-by-step:

1. 1865 divided by 373 is approximately 5.

To verify:
\[ 373 \times 5 = 1865 \]

Since the multiplication confirms our division, each design has 5 stuffed animals.

### Answer: 5

Expected answer: 5

Correct? Yes

๐Ÿ”— Follow-up

Problem: In an alternate scenario, the toy company made 2542 stuffed animals, still spread over 373 different designs. If each design had the same number of stuffed animals in this scenario, how many stuffed animals would there be for each design?

GPT-4o:

To determine how many stuffed animals there are for each design in this scenario, we need to divide the total number of stuffed animals by the number of designs.

Given:
- Total number of stuffed animals = 2542
- Number of designs = 373

We perform the division:

\[ \frac{2542}{373} \]

Let's calculate this step-by-step:

1. 2542 divided by 373 is approximately 6.81.

Since we are looking for an exact number of stuffed animals per design, we need to perform the division more precisely:

\[ 2542 \div 373 \approx 6.81 \]

Since each design must have a whole number of stuffed animals, we conclude that the exact division is not possible without a remainder. However, if we are to consider the integer part of the division:

\[ 2542 \div 373 = 6 \text{ (with a remainder)} \]

Thus, each design would have 6 stuffed animals, with some leftover.

### Answer: 6

Expected answer: 2542/373

Correct? No

๐Ÿ”— Problem

Problem: A bear travels a total of 31470 feet in 30 days. If the bear travels the same distance each day, how many feet does it travel each day?

GPT-4o:

To determine how many feet the bear travels each day, we need to divide the total distance traveled by the number of days.

The total distance traveled by the bear is 31,470 feet, and the number of days is 30.

We perform the division:
\[ \frac{31,470 \text{ feet}}{30 \text{ days}} = 1,049 \text{ feet/day} \]

### Answer: 1,049 feet/day

Expected answer: 1049

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering our previous calculation, if a bear travels a total of 31470 feet but this time over 1406 days instead of 30 days and still travels the same distance each day, how many feet does it travel each day now?

GPT-4o:

To determine how many feet the bear travels each day, we need to divide the total distance traveled by the number of days.

The total distance traveled by the bear is 31,470 feet, and the number of days is 1,406.

We perform the division:
\[ \frac{31,470 \text{ feet}}{1,406 \text{ days}} \approx 22.38 \text{ feet/day} \]

### Answer: 22.38 feet/day

Expected answer: 15735/703

Correct? No

๐Ÿ”— Problem

Problem: A pen manufacturer produced 9636 pen units and distributed them equally among its 44 retailers. How many pen units did each retailer receive?

GPT-4o:

To determine how many pen units each retailer received, we need to divide the total number of pen units by the number of retailers.

Given:
- Total pen units = 9636
- Number of retailers = 44

We perform the division:

\[ \frac{9636}{44} \]

First, let's simplify the division step-by-step:

1. Divide 9636 by 44:
\[ 9636 \div 44 = 219 \]

So, each retailer received 219 pen units.

### Answer: 219

Expected answer: 219

Correct? Yes