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Gemma 2B on 5.NBT.B.6

Common Core Standard 5.NBT.B.6

This standard covers the following:

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

๐Ÿ”— Problem

Problem: A school bus drives 2496 miles over 52 weeks taking students to various competitions. How many miles does the bus drive on average each week?

Gemma 2B:

To find the average number of miles the school bus drives each week, we need to divide the total number of miles by the number of weeks.

Total miles driven: 2496 miles
Number of weeks: 52 weeks

We perform the division:

\[ \text{Average miles per week} = \frac{2496 \text{ miles}}{52 \text{ weeks}} \]

Let's do the division:

\[ 2496 \div 52 = 48 \]

So, the school bus drives an average of 48 miles each week.

### Answer: 48 miles per week.

Expected answer: 48

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the school bus had instead driven 6100 miles over the same 52 weeks, how many miles would the bus have driven on average each week?

Gemma 2B:

To find the average number of miles the school bus drives each week, we need to divide the total number of miles by the number of weeks.

Total miles driven: 6100 miles
Number of weeks: 52 weeks

We perform the division:

\[ \text{Average miles per week} = \frac{6100 \text{ miles}}{52 \text{ weeks}} \]

Let's do the division:

\[ 6100 \div 52 \approx 117.31 \]

So, the school bus drives an average of approximately 117.31 miles each week.

### Answer: 117.31 miles per week.

Expected answer: 1525/13

Correct? No

๐Ÿ”— Problem

Problem: An astronaut has a 90-day mission in space during which he consumes a total of 3870 liters of oxygen. If his oxygen consumption is the same every day, how much oxygen does he use daily?

Gemma 2B:

To determine the daily oxygen consumption of the astronaut, we need to divide the total amount of oxygen consumed by the number of days in the mission.

Given:
- Total oxygen consumption: 3870 liters
- Duration of the mission: 90 days

We perform the division:
\[ \text{Daily oxygen consumption} = \frac{3870 \text{ liters}}{90 \text{ days}} \]

\[ \text{Daily oxygen consumption} = 43 \text{ liters/day} \]

### Answer: 43 liters/day

Expected answer: 43

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the astronaut's mission got extended to 124 days instead of 90, and he still used a total of 3870 liters of oxygen, how much oxygen did he use daily?

Gemma 2B:

To determine the new daily oxygen consumption of the astronaut after the mission extension, we need to divide the total amount of oxygen consumed by the new number of days in the mission.

Given:
- Total oxygen consumption: 3870 liters
- Extended duration of the mission: 124 days

We perform the division:
\[ \text{Daily oxygen consumption} = \frac{3870 \text{ liters}}{124 \text{ days}} \]

\[ \text{Daily oxygen consumption} = 31.2097 \text{ liters/day} \]

Rounding to two decimal places:
\[ \text{Daily oxygen consumption} \approx 31.21 \text{ liters/day} \]

### Answer: 31.21 liters/day

Expected answer: 1935/62

Correct? No

๐Ÿ”— Problem

Problem: A dinosaur lays 50 eggs evenly in 10 nests. How many eggs are there in each nest?

Gemma 2B:

To determine how many eggs are in each nest, we need to divide the total number of eggs by the number of nests.

Given:
- Total number of eggs = 50
- Number of nests = 10

We perform the division:
\[ \frac{50 \text{ eggs}}{10 \text{ nests}} = 5 \text{ eggs per nest} \]

### Answer: 5 eggs per nest.

Expected answer: 5

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of 50 eggs, a dinosaur lays 2603 eggs and distributes them evenly into 10 nests. How many eggs are there in each nest now?

Gemma 2B:

To find out how many eggs are in each nest, we need to divide the total number of eggs by the number of nests.

Given:
- Total number of eggs = 2603
- Number of nests = 10

We perform the division:
\[ \frac{2603 \text{ eggs}}{10 \text{ nests}} = 260.3 \text{ eggs per nest} \]

### Answer: 260.3 eggs per nest.

Expected answer: 2603/10

Correct? No

๐Ÿ”— Problem

Problem: A family decided to donate 455 towels to a local shelter. They plan to donate an equal amount of towels each day for 5 days. How many towels will they donate each day?

Gemma 2B:

To determine how many towels the family will donate each day, we need to divide the total number of towels by the number of days.

Given:
- Total number of towels = 455
- Number of days = 5

We perform the division:
\[ \frac{455}{5} = 91 \]

So, the family will donate 91 towels each day.

### Answer: 91

Expected answer: 91

Correct? Yes

๐Ÿ”— Follow-up

Problem: The family, after reviewing their stock, realized that they actually have 4581 towels to donate instead of 455. If they still plan to donate equal amounts for 5 days, how many towels will they donate each day now?

Gemma 2B:

To determine how many towels the family will donate each day with the updated total, we need to divide the new total number of towels by the number of days.

Given:
- Total number of towels = 4581
- Number of days = 5

We perform the division:
\[ \frac{4581}{5} = 916.2 \]

So, the family will donate 916.2 towels each day.

### Answer: 916.2

Expected answer: 4581/5

Correct? Yes

๐Ÿ”— Problem

Problem: A school has 1089 students and plans to take them on a field trip using buses. If each bus can carry exactly 11 students, how many buses does the school need to hire for the field trip?

Gemma 2B:

To determine how many buses the school needs to hire, we need to divide the total number of students by the capacity of each bus.

First, we perform the division:
\[ \frac{1089}{11} \]

Let's do the division step-by-step:
1. 1089 divided by 11 gives us 99 with no remainder.

So, the school needs 99 buses to carry all the students.

### Answer: 99

Expected answer: 99

Correct? Yes

๐Ÿ”— Follow-up

Problem: Following the field trip, the school finds out that they will now be taking 4570 students for the next excursion. If each bus can still only carry 11 students, how many buses will the school need to hire for this next field trip?

Gemma 2B:

To determine how many buses the school needs to hire for 4570 students, we need to divide the total number of students by the capacity of each bus.

First, we perform the division:
\[ \frac{4570}{11} \]

Let's do the division step-by-step:
1. 4570 divided by 11 gives us approximately 415.4545.

Since we cannot have a fraction of a bus, we need to round up to the next whole number to ensure all students have a seat.

Therefore, the school needs 416 buses to carry all the students.

### Answer: 416

Expected answer: 4570/11

Correct? No

๐Ÿ”— Problem

Problem: A bed sheet manufacturer produces 2520 bed sheets in 28 days. If they produce the same number of sheets every day, how many bed sheets are manufactured each day?

Gemma 2B:

To determine how many bed sheets are manufactured each day, we need to divide the total number of bed sheets by the number of days.

Given:
- Total bed sheets produced = 2520
- Number of days = 28

We perform the division:
\[ \frac{2520}{28} \]

First, simplify the division:
\[ 2520 \div 28 = 90 \]

So, the manufacturer produces 90 bed sheets each day.

### Answer: 90

Expected answer: 90

Correct? Yes

๐Ÿ”— Follow-up

Problem: Let's now consider a different bed sheet manufacturer who manages to produce a total of 7208 bed sheets in the same 28-day period. If they also produced the same number of sheets every day, how many bed sheets are manufactured each day in this case?

Gemma 2B:

To find out how many bed sheets are manufactured each day, we need to divide the total number of bed sheets by the number of days.

Given:
- Total bed sheets produced = 7208
- Number of days = 28

We perform the division:
\[ \frac{7208}{28} \]

First, simplify the division:
\[ 7208 \div 28 = 257 \]

So, the manufacturer produces 257 bed sheets each day.

### Answer: 257

Expected answer: 1802/7

Correct? No

๐Ÿ”— Problem

Problem: A dog food manufacturer produces 2900 pounds of dog food in a day. If this amount is evenly distributed into 50 bags, how many pounds of food does each bag contain?

Gemma 2B:

To determine how many pounds of dog food each bag contains, we need to divide the total amount of dog food produced in a day by the number of bags.

Given:
- Total dog food produced in a day = 2900 pounds
- Number of bags = 50

We perform the division:
\[ \frac{2900 \text{ pounds}}{50 \text{ bags}} = 58 \text{ pounds per bag} \]

### Answer: 58 pounds per bag.

Expected answer: 58

Correct? Yes

๐Ÿ”— Follow-up

Problem: The manufacturer changes the production procedure and now it can only produce 2301 pounds of dog food in a day, while maintaining the same number of bags which is 50. How many pounds of food does each bag contain now?

Gemma 2B:

To find out how many pounds of dog food each bag contains with the new production amount, we need to divide the total amount of dog food produced in a day by the number of bags.

Given:
- Total dog food produced in a day = 2301 pounds
- Number of bags = 50

We perform the division:
\[ \frac{2301 \text{ pounds}}{50 \text{ bags}} = 46.02 \text{ pounds per bag} \]

### Answer: 46.02 pounds per bag.

Expected answer: 2301/50

Correct? No

๐Ÿ”— Problem

Problem: A cat catches 2187 mice over a period of 27 months. How many mice does the cat catch each month?

Gemma 2B:

To determine how many mice the cat catches each month, we need to divide the total number of mice by the number of months.

The total number of mice caught is 2187, and the period is 27 months.

We perform the division:
\[ \frac{2187}{27} \]

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

1. Divide 2187 by 27:
\[ 2187 \div 27 = 81 \]

So, the cat catches 81 mice each month.

### Answer: 81

Expected answer: 81

Correct? Yes

๐Ÿ”— Follow-up

Problem: The cat's hunting skills have improved! Now this cat catches 2784 mice over the same period of 27 months. How many mice does the cat now catch each month?

Gemma 2B:

To determine how many mice the cat now catches each month, we need to divide the new total number of mice by the same period of 27 months.

The new total number of mice caught is 2784, and the period is still 27 months.

We perform the division:
\[ \frac{2784}{27} \]

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

1. Divide 2784 by 27:
\[ 2784 \div 27 = 103 \]

So, the cat now catches 103 mice each month.

### Answer: 103

Expected answer: 928/9

Correct? No

๐Ÿ”— Problem

Problem: A vineyard has harvested 1426 grapes and wants to pack them evenly among 62 boxes. How many grapes will be in each box?

Gemma 2B:

To determine how many grapes will be in each box, we need to divide the total number of grapes by the number of boxes.

\[
\text{Number of grapes per box} = \frac{1426}{62}
\]

Performing the division:

\[
1426 \div 62 \approx 23
\]

So, each box will contain approximately 23 grapes.

### Answer: 23

Expected answer: 23

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of 1426 grapes, the vineyard harvested 4830 grapes and still wanted to distribute them evenly among the 62 boxes, how many grapes would now be in each box?

Gemma 2B:

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

\[
\text{Number of grapes per box} = \frac{4830}{62}
\]

Performing the division:

\[
4830 \div 62 = 77.9
\]

Since we are distributing whole grapes, we round down to the nearest whole number:

\[
\text{Number of grapes per box} = 77
\]

### Answer: 77

Expected answer: 2415/31

Correct? No

๐Ÿ”— Problem

Problem: A group of scientists studying marine life have found 1152 starfish distributed evenly over 72 square feet of seafloor. How many starfish are there in each square foot of seafloor?

Gemma 2B:

To determine how many starfish are in each square foot of seafloor, we need to divide the total number of starfish by the total area in square feet.

Given:
- Total number of starfish = 1152
- Total area in square feet = 72

We perform the division:
\[ \frac{1152}{72} \]

First, let's simplify the division step-by-step:
\[ 1152 \div 72 = 16 \]

So, there are 16 starfish per square foot of seafloor.

### Answer: 16

Expected answer: 16

Correct? Yes

๐Ÿ”— Follow-up

Problem: The scientists then study a different area of seafloor and find 833 starfish distributed evenly over the same 72 square feet. How many starfish are there in each square foot of this different seafloor area?

Gemma 2B:

To determine how many starfish are in each square foot of the new seafloor area, we need to divide the total number of starfish by the total area in square feet.

Given:
- Total number of starfish = 833
- Total area in square feet = 72

We perform the division:
\[ \frac{833}{72} \]

Let's calculate this step-by-step:
\[ 833 \div 72 \approx 11.57 \]

So, there are approximately 11.57 starfish per square foot of this different seafloor area.

### Answer: 11.57

Expected answer: 833/72

Correct? No

๐Ÿ”— Problem

Problem: In a sandbox, a child splits 36 toy trucks evenly between his 18 stuffed animals. How many toy trucks does each stuffed animal get?

Gemma 2B:

To determine how many toy trucks each stuffed animal gets, we need to divide the total number of toy trucks by the number of stuffed animals.

Given:
- Total number of toy trucks = 36
- Total number of stuffed animals = 18

We perform the division:
\[ \frac{36 \text{ toy trucks}}{18 \text{ stuffed animals}} = 2 \text{ toy trucks per stuffed animal} \]

### Answer: 2

Expected answer: 2

Correct? Yes

๐Ÿ”— Follow-up

Problem: The child then finds another huge stash of toy trucks totalling 2925. He continues to distribute them evenly among his 18 stuffed animals. How many additional toy trucks does each stuffed animal get now?

Gemma 2B:

To determine how many additional toy trucks each stuffed animal gets, we need to divide the total number of new toy trucks by the number of stuffed animals.

Given:
- Total number of new toy trucks = 2925
- Total number of stuffed animals = 18

We perform the division:
\[ \frac{2925 \text{ toy trucks}}{18 \text{ stuffed animals}} \]

Let's calculate this step-by-step:

1. Divide 2925 by 18:
\[ 2925 \div 18 = 162.5 \]

So, each stuffed animal gets 162.5 additional toy trucks.

### Answer: 162.5

Expected answer: 325/2

Correct? Yes

๐Ÿ”— Problem

Problem: A police officer patrols a city that has been divided into 240 blocks. The city is divided evenly among 30 officers. How many blocks is each officer responsible for?

Gemma 2B:

To determine how many blocks each officer is responsible for, we need to divide the total number of blocks by the number of officers.

Given:
- Total number of blocks = 240
- Number of officers = 30

We perform the division:
\[ \frac{240 \text{ blocks}}{30 \text{ officers}} = 8 \text{ blocks per officer} \]

### Answer: 8

Expected answer: 8

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now consider a larger city that is spread across 3698 blocks. It is also monitored by 30 police officers. How many blocks would each officer be responsible for in this larger city?

Gemma 2B:

To determine how many blocks each officer is responsible for in the larger city, we need to divide the total number of blocks by the number of officers.

Given:
- Total number of blocks = 3698
- Number of officers = 30

We perform the division:
\[ \frac{3698 \text{ blocks}}{30 \text{ officers}} \approx 123.27 \text{ blocks per officer} \]

Since the number of blocks per officer must be a whole number, we can say that each officer is responsible for approximately 123 blocks, with some officers possibly covering an additional block to account for the remainder.

### Answer: 123 blocks per officer (approximately)

Expected answer: 1849/15

Correct? No

๐Ÿ”— Problem

Problem: In an enchanted forest, there are 7917 unicorns spread evenly among 87 meadows. How many unicorns are there in each meadow?

Gemma 2B:

To find out how many unicorns are in each meadow, we need to divide the total number of unicorns by the number of meadows.

\[ \text{Number of unicorns per meadow} = \frac{7917}{87} \]

Let's perform the division:

1. Divide 7917 by 87.
2. 87 goes into 7917 approximately 91 times (since \( 87 \times 91 = 7917 \)).

So, each meadow has:

\[ \frac{7917}{87} = 91 \]

### Answer: 91

Expected answer: 91

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the enchanted forest had originally contained 2842 unicorns evenly distributed among the 87 meadows instead of 7917, how many unicorns would there be in each meadow?

Gemma 2B:

To determine how many unicorns are in each meadow, we need to divide the total number of unicorns by the number of meadows.

\[ \text{Number of unicorns per meadow} = \frac{2842}{87} \]

Let's perform the division:

1. Divide 2842 by 87.
2. 87 goes into 2842 approximately 32.67 times.

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

\[ \frac{2842}{87} \approx 32.67 \]

Rounding to the nearest whole number, we get 33 unicorns per meadow.

### Answer: 33

Expected answer: 98/3

Correct? No

๐Ÿ”— Problem

Problem: A river flows 902 kilometers through a country, passing through 82 cities along its course. If the river's length is evenly distributed among these cities, how many kilometers of the river's length are there within each city?

Gemma 2B:

To determine how many kilometers of the river's length are within each city, we need to divide the total length of the river by the number of cities it passes through.

The total length of the river is 902 kilometers, and it passes through 82 cities.

We perform the division:
\[ \frac{902 \text{ kilometers}}{82 \text{ cities}} \]

Let's calculate this:
\[ 902 \div 82 = 11 \]

So, the river's length within each city is approximately 11 kilometers.

### Answer: 11 kilometers

Expected answer: 11

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead, the river was longer and flowed 3767 kilometers through the same country, passing through the same 82 cities along its course. If the river's length is evenly distributed among these cities under this new scenario, how many kilometers of the river's length would there be within each city?

Gemma 2B:

To determine how many kilometers of the river's length are within each city, we need to divide the total length of the river by the number of cities it passes through.

The total length of the river is 3767 kilometers, and it passes through 82 cities.

We perform the division:
\[ \frac{3767 \text{ kilometers}}{82 \text{ cities}} \]

Let's calculate this:
\[ 3767 \div 82 \approx 45.94 \]

So, the river's length within each city is approximately 45.94 kilometers.

### Answer: 45.94 kilometers

Expected answer: 3767/82

Correct? No

๐Ÿ”— Problem

Problem: A sunglasses manufacturer produces a total of 552 sunglasses across 69 different production runs. If every run produces an equal number of sunglasses, how many sunglasses are made in each run?

Gemma 2B:

To determine how many sunglasses are made in each production run, we need to divide the total number of sunglasses by the number of production runs.

Given:
- Total number of sunglasses = 552
- Number of production runs = 69

We perform the division:

\[ \frac{552}{69} \]

First, let's simplify the fraction by finding the greatest common divisor (GCD) of 552 and 69. We can use the Euclidean algorithm to find the GCD.

1. Divide 552 by 69 and find the remainder:
   \[ 552 \div 69 = 8 \text{ remainder } 0 \]

Since the remainder is 0, the GCD is 69.

Now, we can simplify the division:

\[ \frac{552}{69} = 8 \]

So, each production run produces 8 sunglasses.

### Answer: 8

Expected answer: 8

Correct? Yes

๐Ÿ”— Follow-up

Problem: The sunglasses manufacturer actually made a total of 7712 sunglasses across the same 69 production runs. If every run now produced an equal number of sunglasses, how many sunglasses would be made in each run?

Gemma 2B:

To determine how many sunglasses are made in each production run, we need to divide the total number of sunglasses by the number of production runs.

Given:
- Total number of sunglasses = 7712
- Number of production runs = 69

We perform the division:

\[ \frac{7712}{69} \]

Let's carry out the division step-by-step:

1. Divide 7712 by 69:
   \[ 7712 \div 69 \approx 111.6 \]

Since we are looking for an exact number of sunglasses per run, we need to perform the division more precisely:

\[ 7712 \div 69 = 111.6 \]

This means each production run produces 111 sunglasses, with a remainder indicating that the division is not exact. However, since we are asked for the number of sunglasses made in each run, we consider the integer part of the division.

### Answer: 111

Expected answer: 7712/69

Correct? No

๐Ÿ”— Problem

Problem: A baby grows at an average rate of 2125 grams in his first 25 days. What is the average daily weight gain of the baby?

Gemma 2B:

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

The total weight gain is 2125 grams, and the number of days is 25.

So, the average daily weight gain is calculated as follows:
\[
\text{Average daily weight gain} = \frac{\text{Total weight gain}}{\text{Number of days}} = \frac{2125 \text{ grams}}{25 \text{ days}}
\]

Now, perform the division:
\[
\frac{2125}{25} = 85 \text{ grams/day}
\]

### Answer: 85 grams/day

Expected answer: 85

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead, the baby grows at an average rate of 392 grams in his first 25 days, what is now the average daily weight gain of the baby?

Gemma 2B:

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

The total weight gain is 392 grams, and the number of days is 25.

So, the average daily weight gain is calculated as follows:
\[
\text{Average daily weight gain} = \frac{\text{Total weight gain}}{\text{Number of days}} = \frac{392 \text{ grams}}{25 \text{ days}}
\]

Now, perform the division:
\[
\frac{392}{25} = 15.68 \text{ grams/day}
\]

### Answer: 15.68 grams/day

Expected answer: 392/25

Correct? No

๐Ÿ”— Problem

Problem: A lamp factory has produced a total of 1073 lamps over 37 consecutive days. If the factory makes the same quantity each day, how many lamps does it manufacture daily?

Gemma 2B:

To determine how many lamps the factory manufactures daily, we need to divide the total number of lamps produced by the number of days.

Given:
- Total lamps produced = 1073
- Number of days = 37

We perform the division:

\[ \frac{1073}{37} \]

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

1. 1073 divided by 37.
2. 37 goes into 107 approximately 2 times (since \( 37 \times 2 = 74 \)).
3. Subtract 74 from 107 to get 33.
4. Bring down the next digit (3) to make it 333.
5. 37 goes into 333 approximately 9 times (since \( 37 \times 9 = 333 \)).

So, the factory manufactures:

\[ \frac{1073}{37} = 29 \]

### Answer: 29

Expected answer: 29

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the lamp factory had instead produced a total of 7668 lamps over the same 37 consecutive days, how many lamps would it have manufactured daily?

Gemma 2B:

To determine how many lamps the factory manufactures daily, we need to divide the total number of lamps produced by the number of days.

Given:
- Total lamps produced = 7668
- Number of days = 37

We perform the division:

\[ \frac{7668}{37} \]

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

1. 37 goes into 76 approximately 2 times (since \( 37 \times 2 = 74 \)).
2. Subtract 74 from 76 to get 2.
3. Bring down the next digit (6) to make it 26.
4. 37 goes into 26 zero times, so we bring down the next digit (6) to make it 266.
5. 37 goes into 266 approximately 7 times (since \( 37 \times 7 = 259 \)).
6. Subtract 259 from 266 to get 7.
7. Bring down the next digit (8) to make it 78.
8. 37 goes into 78 approximately 2 times (since \( 37 \times 2 = 74 \)).
9. Subtract 74 from 78 to get 4.

So, the factory manufactures:

\[ \frac{7668}{37} = 207 \]

### Answer: 207

Expected answer: 7668/37

Correct? No

๐Ÿ”— Problem

Problem: A tiger walked a total of 2556 meters in 36 minutes. How many meters did the tiger walk in one minute?

Gemma 2B:

To find out how many meters the tiger walked in one minute, we need to divide the total distance by the total time.

Given:
- Total distance = 2556 meters
- Total time = 36 minutes

We use the formula:
\[ \text{Distance per minute} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Distance per minute} = \frac{2556 \text{ meters}}{36 \text{ minutes}} \]

Now, perform the division:
\[ \text{Distance per minute} = 71 \text{ meters per minute} \]

### Answer: 71 meters per minute.

Expected answer: 71

Correct? Yes

๐Ÿ”— Follow-up

Problem: After some recalibration, it was discovered that the tiger actually walked a total of 2301 meters, and not 2556 meters, in 36 minutes. Given this new information, how many meters did the tiger walk in one minute?

Gemma 2B:

To find out how many meters the tiger walked in one minute with the new information, we need to divide the new total distance by the total time.

Given:
- New total distance = 2301 meters
- Total time = 36 minutes

We use the formula:
\[ \text{Distance per minute} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Distance per minute} = \frac{2301 \text{ meters}}{36 \text{ minutes}} \]

Now, perform the division:
\[ \text{Distance per minute} = \frac{2301}{36} \approx 63.9167 \]

Rounding to the nearest whole number:
\[ \text{Distance per minute} \approx 64 \text{ meters per minute} \]

### Answer: 64 meters per minute.

Expected answer: 767/12

Correct? No

๐Ÿ”— Problem

Problem: There are 30 keys on a piano that you are considering to buy. If each key contributes equally to the total cost of the piano, and the piano costs 30 dollars, how much does each key cost?

Gemma 2B:

To determine the cost of each key, we need to divide the total cost of the piano by the number of keys.

The total cost of the piano is $30, and there are 30 keys on the piano.

We perform the division:
\[
\frac{30 \text{ dollars}}{30 \text{ keys}} = 1 \text{ dollar per key}
\]

### Answer: 1 dollar per key.

Expected answer: 1

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now suppose you are considering a much more expensive piano that has the same number of keys but costs $6906 in total. If each key contributes equally to the total cost, how much does each key on this piano cost?

Gemma 2B:

To determine the cost of each key on the more expensive piano, we need to divide the total cost of the piano by the number of keys.

The total cost of the piano is $6906, and there are 30 keys on the piano.

We perform the division:
\[
\frac{6906 \text{ dollars}}{30 \text{ keys}} = 230.2 \text{ dollars per key}
\]

### Answer: 230.2 dollars per key.

Expected answer: 1151/5

Correct? No

๐Ÿ”— Problem

Problem: On the beach, there are 1804 seashells scattered across a 41-meter stretch of sand. If the seashells are distributed evenly across this stretch, how many seashells are there per meter?

Gemma 2B:

To determine the number of seashells per meter, we need to divide the total number of seashells by the length of the stretch of sand.

Given:
- Total number of seashells = 1804
- Length of the stretch of sand = 41 meters

We perform the division:

\[
\frac{1804}{41} = 44
\]

So, there are 44 seashells per meter.

### Answer: 44

Expected answer: 44

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now consider this: instead of 1804 seashells, there are 9083 seashells evenly scattered across the same 41-meter stretch of beach sand. How many seashells would there be per meter now?

Gemma 2B:

To find the number of seashells per meter, we need to divide the total number of seashells by the length of the stretch of sand.

Given:
- Total number of seashells = 9083
- Length of the stretch of sand = 41 meters

We perform the division:

\[
\frac{9083}{41} = 221.5365854 \approx 221.54
\]

So, there are approximately 221.54 seashells per meter.

### Answer: 221.54

Expected answer: 9083/41

Correct? No

๐Ÿ”— Problem

Problem: A kite is flown for a total of 1311 minutes over the course of 23 days during the summer. If the kite is flown for the same amount of time each day, how many minutes is the kite in the air per day?

Gemma 2B:

To determine how many minutes the kite is flown each day, we need to divide the total number of minutes by the number of days.

Total minutes flown: 1311 minutes
Number of days: 23 days

We perform the division:

\[ \frac{1311 \text{ minutes}}{23 \text{ days}} \]

First, we set up the division:

\[ 1311 \div 23 \]

We can perform the division step-by-step:

1. 23 goes into 131 a total of 5 times (since \( 23 \times 5 = 115 \)).
2. Subtract 115 from 131 to get the remainder: \( 131 - 115 = 16 \).
3. Bring down the next digit (1), making it 161.
4. 23 goes into 161 a total of 7 times (since \( 23 \times 7 = 161 \)).

So, the division is exact, and the quotient is 57.

Therefore, the kite is flown for 57 minutes each day.

### Answer: 57

Expected answer: 57

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of 1311 minutes of total flight time, suppose the kite was flown for a total of 9051 minutes over the same duration of 23 days. How many minutes per day was the kite in the air now?

Gemma 2B:

To determine how many minutes the kite is flown each day, we need to divide the total number of minutes by the number of days.

Total minutes flown: 9051 minutes
Number of days: 23 days

We perform the division:

\[ \frac{9051 \text{ minutes}}{23 \text{ days}} \]

First, we set up the division:

\[ 9051 \div 23 \]

We can perform the division step-by-step:

1. 23 goes into 90 a total of 3 times (since \( 23 \times 3 = 69 \)).
2. Subtract 69 from 90 to get the remainder: \( 90 - 69 = 21 \).
3. Bring down the next digit (5), making it 215.
4. 23 goes into 215 a total of 9 times (since \( 23 \times 9 = 207 \)).
5. Subtract 207 from 215 to get the remainder: \( 215 - 207 = 8 \).
6. Bring down the next digit (1), making it 81.
7. 23 goes into 81 a total of 3 times (since \( 23 \times 3 = 69 \)).
8. Subtract 69 from 81 to get the remainder: \( 81 - 69 = 12 \).

So, the quotient is 393 with a remainder of 12. Since we are looking for the number of minutes per day, we consider only the quotient.

Therefore, the kite is flown for 393 minutes each day.

### Answer: 393

Expected answer: 9051/23

Correct? No

๐Ÿ”— Problem

Problem: A farmer harvested 2065 kilograms of tomatoes evenly from her 59 tomato plants. How many kilograms of tomatoes were produced by each plant on average?

Gemma 2B:

To find the average number of kilograms of tomatoes produced by each plant, we need to divide the total kilograms of tomatoes by the number of tomato plants.

Total kilograms of tomatoes: 2065 kg
Number of tomato plants: 59

We perform the division:

\[ \frac{2065 \text{ kg}}{59 \text{ plants}} \]

Let's calculate this:

\[ 2065 \div 59 = 35 \]

So, on average, each tomato plant produced 35 kilograms of tomatoes.

### Answer: 35 kg

Expected answer: 35

Correct? Yes

๐Ÿ”— Follow-up

Problem: The farmer then realized she made a mistake in her count. She actually harvested 1021 kilograms of tomatoes from her 59 tomato plants instead of 2065 kilograms. Based on this new information, how many kilograms of tomatoes were produced by each plant on average now?

Gemma 2B:

To find the average number of kilograms of tomatoes produced by each plant with the corrected total, we need to divide the new total kilograms of tomatoes by the number of tomato plants.

Total kilograms of tomatoes: 1021 kg
Number of tomato plants: 59

We perform the division:

\[ \frac{1021 \text{ kg}}{59 \text{ plants}} \]

Let's calculate this:

\[ 1021 \div 59 \approx 17.3 \]

So, on average, each tomato plant produced approximately 17.3 kilograms of tomatoes.

### Answer: 17.3 kg

Expected answer: 1021/59

Correct? No

๐Ÿ”— Problem

Problem: A small indoor mouse can travel a total distance of 4928 meters by running all over the house in 77 hours. On average, how many meters does the mouse run in one hour?

Gemma 2B:

To find the average distance the mouse runs in one hour, we need to divide the total distance by the total time.

The total distance the mouse travels is 4928 meters, and the total time is 77 hours.

We use the formula for average speed:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Average speed} = \frac{4928 \text{ meters}}{77 \text{ hours}} \]

Now, we perform the division:
\[ \text{Average speed} = \frac{4928}{77} \]

To simplify this, we can perform the division:
\[ 4928 \div 77 = 64 \]

So, the mouse runs an average of 64 meters per hour.

### Answer: 64 meters per hour.

Expected answer: 64

Correct? Yes

๐Ÿ”— Follow-up

Problem: Consider instead that the indoor mouse had the ability to travel a total distance of 4928 meters in a shorter time span of 3690 minutes. On average, how many meters does the mouse run in one minute now?

Gemma 2B:

To find the average distance the mouse runs in one minute, we need to divide the total distance by the total time in minutes.

The total distance the mouse travels is 4928 meters, and the total time is 3690 minutes.

We use the formula for average speed:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Average speed} = \frac{4928 \text{ meters}}{3690 \text{ minutes}} \]

Now, we perform the division:
\[ \text{Average speed} = \frac{4928}{3690} \]

To simplify this, we can perform the division:
\[ 4928 \div 3690 \approx 1.334 \]

So, the mouse runs an average of approximately 1.334 meters per minute.

### Answer: 1.334 meters per minute.

Expected answer: 2464/1845

Correct? No

๐Ÿ”— Problem

Problem: A kite flies at a height of 1800 feet using a 50-foot string. How high is the kite flying per each foot of the used string?

Gemma 2B:

To determine how high the kite is flying per each foot of the used string, we need to divide the total height by the length of the string.

Given:
- Height of the kite: 1800 feet
- Length of the string: 50 feet

We perform the division:
\[ \frac{1800 \text{ feet}}{50 \text{ feet}} = 36 \text{ feet per foot of string} \]

### Answer: 36 feet per foot of string

Expected answer: 36

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the kite now flies at a height of 5659 feet using the same 50-foot string. Now, how high is the kite flying per each foot of the used string?

Gemma 2B:

To determine how high the kite is flying per each foot of the used string, we need to divide the total height by the length of the string.

Given:
- Height of the kite: 5659 feet
- Length of the string: 50 feet

We perform the division:
\[ \frac{5659 \text{ feet}}{50 \text{ feet}} = 113.18 \text{ feet per foot of string} \]

### Answer: 113.18 feet per foot of string

Expected answer: 5659/50

Correct? No

๐Ÿ”— Problem

Problem: During a camping trip, you gather 2208 ounces of firewood, which needs to be evenly divided over 96 hours of maintaining the campfire. How many ounces of firewood are used per hour?

Gemma 2B:

To determine how many ounces of firewood are used per hour, we need to divide the total amount of firewood by the total number of hours.

Given:
- Total firewood: 2208 ounces
- Total hours: 96 hours

We perform the division:

\[ \frac{2208 \text{ ounces}}{96 \text{ hours}} \]

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

1. Divide 2208 by 96 directly:

\[ 2208 \div 96 = 23 \]

So, 23 ounces of firewood are used per hour.

### Answer: 23 ounces per hour.

Expected answer: 23

Correct? Yes

๐Ÿ”— Problem

Problem: A princess has received 600 gifts for her birthday. She decides to evenly distribute these gifts among 50 of her closest friends. How many gifts does each friend receive?

Gemma 2B:

To determine how many gifts each friend receives, we need to divide the total number of gifts by the number of friends.

Given:
- Total number of gifts = 600
- Number of friends = 50

We perform the division:

\[ \frac{600}{50} = 12 \]

So, each friend receives 12 gifts.

### Answer: 12

Expected answer: 12

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the following year, the princess receives 4030 gifts for her birthday. She again decides to evenly distribute this larger amount of presents among her 50 close friends. How many gifts does each friend get in this year?

Gemma 2B:

To find out how many gifts each friend receives, we need to divide the total number of gifts by the number of friends.

Given:
- Total number of gifts = 4030
- Number of friends = 50

We perform the division:

\[ \frac{4030}{50} = 80.6 \]

So, each friend receives 80.6 gifts.

### Answer: 80.6

Expected answer: 403/5

Correct? Yes

๐Ÿ”— Problem

Problem: Over the course of a 52-week year, you burned a total of 4264 logs in your fireplace. How many logs did you burn on average each week?

Gemma 2B:

To find the average number of logs burned each week, we need to divide the total number of logs burned by the number of weeks in a year.

Given:
- Total logs burned in a year = 4264 logs
- Number of weeks in a year = 52 weeks

We calculate the average as follows:
\[
\text{Average logs per week} = \frac{\text{Total logs}}{\text{Number of weeks}} = \frac{4264}{52}
\]

Performing the division:
\[
4264 \div 52 = 82
\]

So, on average, you burned 82 logs each week.

### Answer: 82

Expected answer: 82

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now, consider that throughout this year, you actually burned a total of 4264 logs, but over a shorter period of 3764 hours. How many logs did you burn on average each hour?

Gemma 2B:

To find the average number of logs burned each hour, we need to divide the total number of logs burned by the total number of hours.

Given:
- Total logs burned = 4264 logs
- Total hours = 3764 hours

We calculate the average as follows:
\[
\text{Average logs per hour} = \frac{\text{Total logs}}{\text{Total hours}} = \frac{4264}{3764}
\]

Performing the division:
\[
4264 \div 3764 \approx 1.133
\]

So, on average, you burned approximately 1.133 logs each hour.

### Answer: 1.133

Expected answer: 1066/941

Correct? No

๐Ÿ”— Problem

Problem: An unidentified flying object (UFO) traveled a distance of 1278 miles in 71 minutes. Assuming the UFO traveled at a constant speed, what was the UFO's speed in miles per minute?

Gemma 2B:

To determine the UFO's speed in miles per minute, we need to divide the total distance traveled by the total time taken.

Given:
- Distance traveled = 1278 miles
- Time taken = 71 minutes

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

Substituting the given values:
\[ \text{Speed} = \frac{1278 \text{ miles}}{71 \text{ minutes}} \]

Now, we perform the division:
\[ \text{Speed} = \frac{1278}{71} \approx 18 \text{ miles per minute} \]

### Answer: 18 miles per minute

Expected answer: 18

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead, the UFO traveled the same distance of 1278 miles, but this time over a longer period of 218 minutes, what then would be the UFO's speed in miles per minute?

Gemma 2B:

To determine the UFO's speed in miles per minute for the new time period, we again use the formula for speed:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Given:
- Distance traveled = 1278 miles
- Time taken = 218 minutes

Substituting the given values:
\[ \text{Speed} = \frac{1278 \text{ miles}}{218 \text{ minutes}} \]

Now, we perform the division:
\[ \text{Speed} = \frac{1278}{218} \approx 5.86 \text{ miles per minute} \]

### Answer: 5.86 miles per minute

Expected answer: 639/109

Correct? No

๐Ÿ”— Problem

Problem: A snail travels a total distance of 1610 cm in 35 days. If the snail travels the same distance each day, how many centimeters does the snail travel daily?

Gemma 2B:

To find out how many centimeters the snail travels daily, we need to divide the total distance by the number of days.

Total distance traveled by the snail = 1610 cm
Number of days = 35

Daily distance traveled = Total distance / Number of days
\[ \text{Daily distance traveled} = \frac{1610 \text{ cm}}{35 \text{ days}} \]

Now, we perform the division:
\[ \frac{1610}{35} = 46 \text{ cm/day} \]

### Answer: 46 cm/day

Expected answer: 46

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead, the snail traveled a total distance of 9521 cm over the same 35 days, how many centimeters would the snail travel daily?

Gemma 2B:

To determine how many centimeters the snail travels daily, we need to divide the total distance by the number of days.

Total distance traveled by the snail = 9521 cm
Number of days = 35

Daily distance traveled = Total distance / Number of days
\[ \text{Daily distance traveled} = \frac{9521 \text{ cm}}{35 \text{ days}} \]

Now, we perform the division:
\[ \frac{9521}{35} = 272 \text{ cm/day} \]

### Answer: 272 cm/day

Expected answer: 9521/35

Correct? No

๐Ÿ”— Problem

Problem: A beach resort is hosting a sandcastle-building competition. They brought 960 pounds of sand for the event, and they need to divide it evenly among 80 competitor stations. How much sand will there be at each station?

Gemma 2B:

To determine how much sand each competitor station will receive, we need to divide the total amount of sand by the number of stations.

Given:
- Total sand = 960 pounds
- Number of stations = 80

We perform the division:
\[ \frac{960 \text{ pounds}}{80 \text{ stations}} = 12 \text{ pounds per station} \]

### Answer: 12 pounds per station.

Expected answer: 12

Correct? Yes

๐Ÿ”— Follow-up

Problem: What if the beach resort decided to bring in more sand for the sandcastle-building competition and now they have 1120 pounds distributed among the same 80 competitor stations? Now, how much sand will there be at each station?

Gemma 2B:

To determine how much sand each competitor station will receive with the new total amount of sand, we need to divide the new total amount of sand by the number of stations.

Given:
- Total sand = 1120 pounds
- Number of stations = 80

We perform the division:
\[ \frac{1120 \text{ pounds}}{80 \text{ stations}} = 14 \text{ pounds per station} \]

### Answer: 14 pounds per station.

Expected answer: 14

Correct? Yes

๐Ÿ”— Problem

Problem: A jewellery store received a shipment of 2520 colourful bracelets and decided to divide them evenly amongst 56 display cases. How many bracelets would be in each display case?

Gemma 2B:

To determine how many bracelets would be in each display case, we need to divide the total number of bracelets by the number of display cases.

Given:
- Total number of bracelets = 2520
- Number of display cases = 56

We perform the division:
\[ \frac{2520}{56} \]

First, simplify the division:
\[ 2520 \div 56 = 45 \]

So, each display case would contain 45 bracelets.

### Answer: 45

Expected answer: 45

Correct? Yes

๐Ÿ”— Follow-up

Problem: After the jewellery store's successful sale, they decided to bring in a fresh shipment of 5311 new bracelets. If they distributed these new bracelets equally amongst the same 56 display cases as before, how many bracelets would be in each display case now?

Gemma 2B:

To determine how many bracelets would be in each display case, we need to divide the total number of new bracelets by the number of display cases.

Given:
- Total number of new bracelets = 5311
- Number of display cases = 56

We perform the division:
\[ \frac{5311}{56} \]

Let's calculate this step-by-step:

1. Divide 5311 by 56:
\[ 5311 \div 56 \approx 94.8393 \]

Since we are distributing the bracelets equally, we take the integer part of the division result, which is 94.

So, each display case would contain 94 bracelets, with some remaining.

To find the exact number of remaining bracelets:
\[ 5311 - (94 \times 56) = 5311 - 5264 = 47 \]

Thus, each display case would contain 94 bracelets, and there would be 47 bracelets left over.

### Answer: 94

Expected answer: 5311/56

Correct? No

๐Ÿ”— Problem

Problem: A tiger travels a total distance of 4104 miles over 54 days. If the tiger traveled an equal number of miles each day, how many miles does the tiger travel in one day?

Gemma 2B:

To determine how many miles the tiger travels in one day, we need to divide the total distance by the number of days.

Total distance traveled: 4104 miles
Number of days: 54 days

We perform the division:

\[ \frac{4104 \text{ miles}}{54 \text{ days}} \]

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

1. Divide 4104 by 54:
\[ 4104 \div 54 = 76 \]

So, the tiger travels 76 miles each day.

### Answer: 76 miles

Expected answer: 76

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now suppose that the tiger traveled a shorter distance of 2498 miles over the same period of 54 days. If the tiger still travelled an equal number of miles each day, how many miles would the tiger travel in one day now?

Gemma 2B:

To determine how many miles the tiger travels in one day with the new total distance, we need to divide the total distance by the number of days.

Total distance traveled: 2498 miles
Number of days: 54 days

We perform the division:

\[ \frac{2498 \text{ miles}}{54 \text{ days}} \]

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

1. Divide 2498 by 54:
\[ 2498 \div 54 \approx 46.259 \]

So, the tiger travels approximately 46.259 miles each day.

### Answer: 46.259 miles

Expected answer: 1249/27

Correct? No

๐Ÿ”— Problem

Problem: A host baked cookies for a party and made a total of 2460 cookies. The baking process is evenly distributed over 60 batches. How many cookies are there in each batch?

Gemma 2B:

To determine the number of cookies in each batch, we need to divide the total number of cookies by the number of batches.

Total number of cookies = 2460
Number of batches = 60

We perform the division:

\[
\frac{2460}{60} = 41
\]

So, there are 41 cookies in each batch.

### Answer: 41

Expected answer: 41

Correct? Yes

๐Ÿ”— Follow-up

Problem: The host now realized he miscalculated and actually baked 2460 cookies over 554 batches not 60. How many cookies are in each batch now?

Gemma 2B:

To find the number of cookies in each batch, we need to divide the total number of cookies by the number of batches.

Total number of cookies = 2460
Number of batches = 554

We perform the division:

\[
\frac{2460}{554} \approx 4.44
\]

So, there are approximately 4.44 cookies in each batch.

### Answer: 4.44

Expected answer: 1230/277

Correct? No

๐Ÿ”— Problem

Problem: If you divide 156 evenly into 6 sets, how many numbers will be in each set?

Gemma 2B:

To determine how many numbers will be in each set when 156 is divided evenly into 6 sets, we need to perform the division:

\[
\frac{156}{6}
\]

Performing the division:

\[
156 \div 6 = 26
\]

So, each set will contain 26 numbers.

### Answer: 26

Expected answer: 26

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of splitting 156 items, you had to divide a larger number of items, like 2347, into the same 6 groups, how many items would be in each group now?

Gemma 2B:

To determine how many items will be in each group when 2347 items are divided evenly into 6 groups, we need to perform the division:

\[
\frac{2347}{6}
\]

Performing the division:

\[
2347 \div 6 = 391.1667
\]

Since we are dividing items, we typically consider whole items. Therefore, each group would have 391 items, with a remainder of 1 item (since \( 2347 - 6 \times 391 = 1 \)).

### Answer: 391

Expected answer: 2347/6

Correct? No

๐Ÿ”— Problem

Problem: A bubble machine produces a total of 888 bubbles over a period of 24 minutes. How many bubbles does it produce in a minute?

Gemma 2B:

To determine how many bubbles the machine produces in a minute, we need to divide the total number of bubbles by the total number of minutes.

Given:
- Total bubbles produced = 888
- Total time in minutes = 24

We perform the division:
\[ \frac{888 \text{ bubbles}}{24 \text{ minutes}} = 37 \text{ bubbles per minute} \]

### Answer: 37

Expected answer: 37

Correct? Yes

๐Ÿ”— Follow-up

Problem: The bubble machine's performance improved and it now produces a total of 6080 bubbles over the same period of 24 minutes. How many bubbles does it produce in a minute now?

Gemma 2B:

To find out how many bubbles the machine produces in a minute with the improved performance, we need to divide the total number of bubbles by the total number of minutes.

Given:
- Total bubbles produced = 6080
- Total time in minutes = 24

We perform the division:
\[ \frac{6080 \text{ bubbles}}{24 \text{ minutes}} = 253.33 \text{ bubbles per minute} \]

### Answer: 253.33

Expected answer: 760/3

Correct? No

๐Ÿ”— Problem

Problem: A rainbow appears after a rainstorm and lasts for 680 seconds. It cycles through its complete range of colors 8 times during its appearance. How many seconds does it spend on each cycle?

Gemma 2B:

To determine how many seconds the rainbow spends on each cycle, we need to divide the total duration of the rainbow's appearance by the number of cycles it completes.

The total duration of the rainbow's appearance is 680 seconds, and it cycles through its complete range of colors 8 times.

We perform the division:
\[ \frac{680 \text{ seconds}}{8 \text{ cycles}} = 85 \text{ seconds per cycle} \]

### Answer: 85 seconds per cycle.

Expected answer: 85

Correct? Yes

๐Ÿ”— Follow-up

Problem: In an unusual display, a different rainbow after a subsequent rainstorm lasts for 8713 seconds while still cycling through its complete range of colors 8 times. How many seconds does this rainbow spend on each cycle?

Gemma 2B:

To determine how many seconds the rainbow spends on each cycle, we need to divide the total duration of the rainbow's appearance by the number of cycles it completes.

The total duration of the rainbow's appearance is 8713 seconds, and it cycles through its complete range of colors 8 times.

We perform the division:
\[ \frac{8713 \text{ seconds}}{8 \text{ cycles}} = 1089.125 \text{ seconds per cycle} \]

### Answer: 1089.125 seconds per cycle.

Expected answer: 8713/8

Correct? No

๐Ÿ”— Problem

Problem: A ball recycler has a total of 3864 balls that he wants to evenly distribute into 42 recycling bins. How many balls will there be in each bin?

Gemma 2B:

To determine how many balls will be in each recycling bin, we need to divide the total number of balls by the number of bins.

First, we set up the division:
\[ \frac{3864}{42} \]

Next, we perform the division:
1. Divide 3864 by 42.
2. 3864 divided by 42 equals 92.

So, each recycling bin will contain 92 balls.

### Answer: 92

Expected answer: 92

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the ball recycler instead had a total of 4934 balls that he wanted to evenly distribute into 42 recycling bins, how many balls would there be in each bin?

Gemma 2B:

To determine how many balls will be in each recycling bin, we need to divide the total number of balls by the number of bins.

First, we set up the division:
\[ \frac{4934}{42} \]

Next, we perform the division:
1. Divide 4934 by 42.
2. 4934 divided by 42 equals approximately 117.48.

Since we are distributing whole balls, we typically round down to the nearest whole number, as you can't have a fraction of a ball in each bin.

So, each recycling bin will contain 117 balls.

### Answer: 117

Expected answer: 2467/21

Correct? No

๐Ÿ”— Problem

Problem: A metalsmith is making rings. He has 1610 grams of silver and decides to use 70 grams of silver for each ring. How many rings can the metalsmith create?

Gemma 2B:

To determine how many rings the metalsmith can create, we need to divide the total amount of silver by the amount of silver used for each ring.

Given:
- Total silver: 1610 grams
- Silver per ring: 70 grams

We perform the division:
\[ \frac{1610 \text{ grams}}{70 \text{ grams/ring}} \]

First, simplify the division:
\[ \frac{1610}{70} = \frac{1610 \div 10}{70 \div 10} = \frac{161}{7} \]

Now, perform the division:
\[ 161 \div 7 = 23 \]

So, the metalsmith can create 23 rings.

### Answer: 23

Expected answer: 23

Correct? Yes

๐Ÿ”— Follow-up

Problem: The metalsmith decided to melt more silver from the warehouse and now he has a total of 5312 grams of silver. If he continues using the same amount of 70 grams of silver for each ring, how many rings can the metalsmith create now?

Gemma 2B:

To determine how many rings the metalsmith can create with 5312 grams of silver, we need to divide the total amount of silver by the amount of silver used for each ring.

Given:
- Total silver: 5312 grams
- Silver per ring: 70 grams

We perform the division:
\[ \frac{5312 \text{ grams}}{70 \text{ grams/ring}} \]

First, simplify the division:
\[ \frac{5312}{70} = \frac{5312 \div 10}{70 \div 10} = \frac{531.2}{7} \]

Now, perform the division:
\[ 531.2 \div 7 = 75.8857 \]

Since the metalsmith can only create whole rings, we take the integer part of the result:
\[ 75 \]

So, the metalsmith can create 75 rings.

### Answer: 75

Expected answer: 2656/35

Correct? No

๐Ÿ”— Problem

Problem: A crate contains 88 apples. If the apples are equally distributed into 44 bags, how many apples does each bag contain?

Gemma 2B:

To determine how many apples each bag contains, we need to divide the total number of apples by the number of bags.

Given:
- Total number of apples = 88
- Number of bags = 44

We perform the division:
\[ \frac{88}{44} = 2 \]

So, each bag contains 2 apples.

### Answer: 2

Expected answer: 2

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose we reconsider the number of apples and there are actually 8840 apples in the crate instead of 88. If these apples are still equally distributed into 44 bags, how many apples would each bag contain now?

Gemma 2B:

To find out how many apples each bag contains when there are 8840 apples distributed into 44 bags, we need to divide the total number of apples by the number of bags.

Given:
- Total number of apples = 8840
- Number of bags = 44

We perform the division:
\[ \frac{8840}{44} = 200 \]

So, each bag contains 200 apples.

### Answer: 200

Expected answer: 2210/11

Correct? No

๐Ÿ”— Problem

Problem: A jewelry maker uses 87 precious stones to create a bracelet that consists of 29 identical parts. How many stones are there in each part of the bracelet?

Gemma 2B:

To determine how many stones are in each part of the bracelet, we need to divide the total number of precious stones by the number of identical parts.

Given:
- Total number of precious stones = 87
- Number of identical parts = 29

We perform the division:
\[ \frac{87}{29} = 3 \]

So, there are 3 precious stones in each part of the bracelet.

### Answer: 3

Expected answer: 3

Correct? Yes

๐Ÿ”— Follow-up

Problem: The jewelry maker now uses 8017 precious stones to create the bracelet still keeping the same structure of 29 identical parts. How many stones are there in each part of the new bracelet?

Gemma 2B:

To determine how many stones are in each part of the new bracelet, we need to divide the total number of precious stones by the number of identical parts.

Given:
- Total number of precious stones = 8017
- Number of identical parts = 29

We perform the division:
\[ \frac{8017}{29} \]

Let's calculate this step-by-step:

1. Divide 8017 by 29:
\[ 8017 \div 29 \approx 276.448 \]

Since we are dealing with whole stones, we round to the nearest whole number:
\[ 276.448 \approx 276 \]

So, there are approximately 276 precious stones in each part of the new bracelet.

### Answer: 276

Expected answer: 8017/29

Correct? No

๐Ÿ”— Problem

Problem: A beverage company has set a target of filling 1320 bottles with juice evenly spread over 88 hours. How many bottles are filled per hour?

Gemma 2B:

To determine how many bottles are filled per hour, we need to divide the total number of bottles by the total number of hours.

Given:
- Total number of bottles = 1320
- Total number of hours = 88

We perform the division:
\[ \frac{1320 \text{ bottles}}{88 \text{ hours}} = 15 \text{ bottles per hour} \]

### Answer: 15

Expected answer: 15

Correct? Yes

๐Ÿ”— Follow-up

Problem: The beverage company has now set a new target of filling 8607 bottles with juice, maintaining the same 88 hours of operation. How many bottles are filled per hour under this new target?

Gemma 2B:

To determine how many bottles are filled per hour under the new target, we need to divide the total number of bottles by the total number of hours.

Given:
- Total number of bottles = 8607
- Total number of hours = 88

We perform the division:
\[ \frac{8607 \text{ bottles}}{88 \text{ hours}} \approx 97.8068 \text{ bottles per hour} \]

Since we typically round to the nearest whole number when dealing with bottles, we round 97.8068 to 98.

### Answer: 98

Expected answer: 8607/88

Correct? No

๐Ÿ”— Problem

Problem: Annapurna is an avid gardener and plans to plant 3520 tulips in 40 equal rows. How many tulips will she plant in each row?

Gemma 2B:

To determine how many tulips Annapurna will plant in each row, we need to divide the total number of tulips by the number of rows.

Given:
- Total number of tulips = 3520
- Number of rows = 40

We perform the division:
\[ \frac{3520}{40} = 88 \]

So, Annapurna will plant 88 tulips in each row.

### Answer: 88

Expected answer: 88

Correct? Yes

๐Ÿ”— Follow-up

Problem: Anna now realized she made a mistake earlier. Instead of 40 rows, she remembered that she actually only has 3052 spaces to plant her tulips. If she wants to split the 3520 tulips evenly, how many tulips will she plant in each space?

Gemma 2B:

To determine how many tulips Anna will plant in each space, we need to divide the total number of tulips by the number of spaces.

Given:
- Total number of tulips = 3520
- Number of spaces = 3052

We perform the division:
\[ \frac{3520}{3052} \approx 1.153 \]

Since we cannot plant a fraction of a tulip, we need to consider the practical approach. Anna can plant 1 tulip in each space and will have some tulips left over. To find out how many tulips will be left over, we calculate:
\[ 3520 - 3052 = 468 \]

So, Anna can plant 1 tulip in each of the 3052 spaces and will have 468 tulips left over.

### Answer: 1 tulip per space, with 468 tulips left over.

Expected answer: 880/763

Correct? No

๐Ÿ”— Problem

Problem: A toy shop produced 3306 doll clothes and distributed them evenly among 58 dolls. How many pieces of clothing did each doll get?

Gemma 2B:

To determine how many pieces of clothing each doll received, we need to divide the total number of doll clothes by the number of dolls.

Given:
- Total doll clothes = 3306
- Number of dolls = 58

We perform the division:

\[ \frac{3306}{58} \]

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

1. 3306 รท 58
2. 58 goes into 330 six times (since 58 * 6 = 348, which is too high, we use 5 times).
3. 58 * 5 = 290
4. Subtract 290 from 330 to get 40.
5. Bring down the next digit (6), making it 406.
6. 58 goes into 406 seven times (since 58 * 7 = 406).

So, 3306 รท 58 = 57.

Each doll gets 57 pieces of clothing.

### Answer: 57

Expected answer: 57

Correct? Yes

๐Ÿ”— Follow-up

Problem: After another production run, the toy shop produced an additional 9115 doll clothes and distributed them evenly among the same 58 dolls. How many pieces of clothing did each doll get this time?

Gemma 2B:

To determine how many pieces of clothing each doll received in the second production run, we need to divide the total number of doll clothes by the number of dolls.

Given:
- Total doll clothes = 9115
- Number of dolls = 58

We perform the division:

\[ \frac{9115}{58} \]

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

1. 9115 รท 58
2. 58 goes into 91 one time (since 58 * 1 = 58).
3. Subtract 58 from 91 to get 33.
4. Bring down the next digit (1), making it 331.
5. 58 goes into 331 five times (since 58 * 5 = 290).
6. Subtract 290 from 331 to get 41.
7. Bring down the next digit (5), making it 415.
8. 58 goes into 415 seven times (since 58 * 7 = 406).

So, 9115 รท 58 = 157.

Each doll gets 157 pieces of clothing.

### Answer: 157

Expected answer: 9115/58

Correct? No

๐Ÿ”— Problem

Problem: A bear consumes 1881 pounds of food over a 19-day hibernation period. On average, how many pounds of food does the bear consume per day during this period?

Gemma 2B:

To find the average amount of food the bear consumes per day, we need to divide the total amount of food by the number of days.

Total food consumed: 1881 pounds
Number of days: 19 days

Average consumption per day = Total food consumed / Number of days
\[ \text{Average consumption per day} = \frac{1881 \text{ pounds}}{19 \text{ days}} \]

Now, we perform the division:
\[ 1881 \div 19 = 99 \]

So, the bear consumes 99 pounds of food per day on average.

### Answer: 99 pounds

Expected answer: 99

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the same bear were to consume 7207 pounds of food over the same 19-day hibernation period instead, how many pounds of food would the bear consume per day during this period in that case?

Gemma 2B:

To find the average amount of food the bear consumes per day, we need to divide the total amount of food by the number of days.

Total food consumed: 7207 pounds
Number of days: 19 days

Average consumption per day = Total food consumed / Number of days
\[ \text{Average consumption per day} = \frac{7207 \text{ pounds}}{19 \text{ days}} \]

Now, we perform the division:
\[ 7207 \div 19 = 379 \]

So, the bear consumes 379 pounds of food per day on average in this case.

### Answer: 379 pounds

Expected answer: 7207/19

Correct? No

๐Ÿ”— Problem

Problem: A plane flew 1720 miles in 86 hours. How many miles did the plane fly per hour?

Gemma 2B:

To determine how many miles the plane flew per hour, we need to divide the total distance flown by the total time taken.

Given:
- Total distance flown = 1720 miles
- Total time taken = 86 hours

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

Substituting the given values:
\[ \text{Speed} = \frac{1720 \text{ miles}}{86 \text{ hours}} \]

Now, perform the division:
\[ \text{Speed} = 20 \text{ miles per hour} \]

### Answer: 20 miles per hour

Expected answer: 20

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the same plane had flown 1990 miles instead of 1720 miles in the same 86 hours, how many miles did the plane fly per hour then?

Gemma 2B:

To determine how many miles the plane flew per hour when it flew 1990 miles in 86 hours, we use the same formula for speed:

\[ \text{Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Given:
- Total distance flown = 1990 miles
- Total time taken = 86 hours

Substituting the given values:
\[ \text{Speed} = \frac{1990 \text{ miles}}{86 \text{ hours}} \]

Now, perform the division:
\[ \text{Speed} = \frac{1990}{86} \approx 23.14 \text{ miles per hour} \]

### Answer: 23.14 miles per hour

Expected answer: 995/43

Correct? No

๐Ÿ”— Problem

Problem: A pencil factory manufactured 4950 pencils over a period of 90 hours. If the factory produced the same number of pencils every hour, how many pencils did it produce each hour?

Gemma 2B:

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

The total number of pencils manufactured is 4950, and the total number of hours is 90.

We perform the division:
\[ \frac{4950}{90} \]

First, simplify the division by canceling out common factors. Both 4950 and 90 are divisible by 10:
\[ \frac{4950 \div 10}{90 \div 10} = \frac{495}{9} \]

Next, perform the division:
\[ 495 \div 9 = 55 \]

So, the factory produced 55 pencils each hour.

### Answer: 55

Expected answer: 55

Correct? Yes

๐Ÿ”— Follow-up

Problem: The pencil factory revised its production records and found out that it actually produced 3487 pencils over a period of 90 hours, not 4950 pencils. If this new total amount was produced evenly over the same period, how many pencils did the factory actually produce each hour?

Gemma 2B:

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

The revised total number of pencils manufactured is 3487, and the total number of hours is 90.

We perform the division:
\[ \frac{3487}{90} \]

Perform the division step-by-step:

1. Divide 3487 by 90:
\[ 3487 \div 90 \approx 38.7444 \]

Since we are looking for the number of pencils produced each hour, we can round this to the nearest whole number if necessary. However, in this context, it is more precise to keep the decimal value.

So, the factory produced approximately 38.7444 pencils each hour.

### Answer: 38.7444

Expected answer: 3487/90

Correct? No

๐Ÿ”— Problem

Problem: During a certain season, a garden produces a total of 780 tomatoes. If this output is evenly distributed over 52 weeks, how many tomatoes does the garden produce each week?

Gemma 2B:

To determine how many tomatoes the garden produces each week, we need to divide the total number of tomatoes by the number of weeks.

Given:
- Total tomatoes = 780
- Number of weeks = 52

We perform the division:
\[ \frac{780}{52} \]

First, simplify the fraction:
\[ \frac{780 \div 4}{52 \div 4} = \frac{195}{13} \]

Now, perform the division:
\[ 195 \div 13 = 15 \]

So, the garden produces 15 tomatoes each week.

### Answer: 15

Expected answer: 15

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the following season, conditions improve in the garden and it produces a total of 2502 tomatoes. If this greater output is distributed evenly across 52 weeks like before, how many tomatoes does the garden produce each week now?

Gemma 2B:

To find out how many tomatoes the garden produces each week, we need to divide the total number of tomatoes by the number of weeks.

Given:
- Total tomatoes = 2502
- Number of weeks = 52

We perform the division:
\[ \frac{2502}{52} \]

First, perform the division directly:
\[ 2502 \div 52 \approx 48.115 \]

Since we are looking for the number of tomatoes produced each week, we typically round to the nearest whole number:
\[ 48.115 \approx 48 \]

So, the garden produces approximately 48 tomatoes each week.

### Answer: 48

Expected answer: 1251/26

Correct? No

๐Ÿ”— Problem

Problem: A tiger travels a total distance of 1679 km evenly over a period of 73 days. How many kilometers does the tiger cover each day?

Gemma 2B:

To determine how many kilometers the tiger covers each day, we need to divide the total distance by the number of days.

Total distance: 1679 km
Number of days: 73

We perform the division:

\[ \frac{1679 \text{ km}}{73 \text{ days}} \approx 23 \text{ km/day} \]

### Answer: 23 km/day

Expected answer: 23

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the same tiger were to travel a total distance of 7008 km, instead of 1679 km, evenly over the SAME period of 73 days, how many kilometers would the tiger cover each day now?

Gemma 2B:

To determine how many kilometers the tiger covers each day when traveling a total distance of 7008 km over 73 days, we need to divide the total distance by the number of days.

Total distance: 7008 km
Number of days: 73

We perform the division:

\[ \frac{7008 \text{ km}}{73 \text{ days}} \approx 96 \text{ km/day} \]

### Answer: 96 km/day

Expected answer: 96

Correct? Yes

๐Ÿ”— Problem

Problem: A popular sporting goods store just got a shipment of 2280 new ice skates. They plan on distributing them equally among their 38 store locations. How many ice skates will each store receive?

Gemma 2B:

To determine how many ice skates each store will receive, we need to divide the total number of ice skates by the number of store locations.

Given:
- Total number of ice skates = 2280
- Number of store locations = 38

We perform the division:

\[ \frac{2280}{38} \]

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

1. Divide 2280 by 38:
\[ 2280 \div 38 \approx 60 \]

To verify, we can multiply 60 by 38 to ensure it matches the original number of ice skates:
\[ 60 \times 38 = 2280 \]

Since the multiplication confirms our division, each store will receive 60 ice skates.

### Answer: 60

Expected answer: 60

Correct? Yes

๐Ÿ”— Follow-up

Problem: The sporting goods store unexpectedly received an additional shipment, bringing the total number of new ice skates to 3887. If they still plan on distributing them equally among their 38 store locations, how many ice skates will each store receive now?

Gemma 2B:

To determine how many ice skates each store will receive after the additional shipment, we need to divide the new total number of ice skates by the number of store locations.

Given:
- New total number of ice skates = 3887
- Number of store locations = 38

We perform the division:

\[ \frac{3887}{38} \]

Let's carry out the division step-by-step:

1. Divide 3887 by 38:
\[ 3887 \div 38 \approx 102.289 \]

Since we are distributing physical items (ice skates), we need to consider the integer part of the division result, as we cannot distribute a fraction of an ice skate.

Thus, each store will receive 102 ice skates, and there will be some remainder.

To find the remainder:
\[ 3887 - (38 \times 102) = 3887 - 3876 = 11 \]

So, each store will receive 102 ice skates, and there will be 11 ice skates left over.

### Answer: 102

Expected answer: 3887/38

Correct? No

๐Ÿ”— Problem

Problem: You've embarked on reading an epic novel of 4606 pages. You decide to split the reading evenly over 47 days. How many pages do you need to read each day to achieve this?

Gemma 2B:

To determine how many pages you need to read each day, you divide the total number of pages by the number of days.

Total number of pages: 4606
Number of days: 47

We perform the division:

\[ \frac{4606}{47} \]

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

1. 47 goes into 4606 approximately 98 times (since \( 47 \times 98 = 4606 \)).

Thus, you need to read:

\[ \frac{4606}{47} = 98 \]

### Answer: 98 pages per day.

Expected answer: 98

Correct? Yes

๐Ÿ”— Follow-up

Problem: Following your initial reading plan, imagine if instead of a 4606 pages epic novel, you chose a different tome with a total of 5982 pages. If you still want to finish reading in 47 days, how many pages would you now need to read each day?

Gemma 2B:

To determine how many pages you need to read each day for the new tome, you divide the total number of pages by the number of days.

Total number of pages: 5982
Number of days: 47

We perform the division:

\[ \frac{5982}{47} \]

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

1. 47 goes into 5982 approximately 127 times (since \( 47 \times 127 = 5982 \)).

Thus, you need to read:

\[ \frac{5982}{47} = 127 \]

### Answer: 127 pages per day.

Expected answer: 5982/47

Correct? No

๐Ÿ”— Problem

Problem: A dressmaking company has 3234 centimeters of fabric. If they used 33 centimeters of fabric to make each skirt, how many skirts can they make in total?

Gemma 2B:

To determine how many skirts the dressmaking company can make, we need to divide the total amount of fabric by the amount of fabric used for each skirt.

Given:
- Total fabric = 3234 centimeters
- Fabric per skirt = 33 centimeters

We perform the division:
\[ \frac{3234 \text{ cm}}{33 \text{ cm/skirt}} \]

First, let's do the division:
\[ 3234 \div 33 = 98 \]

So, the dressmaking company can make 98 skirts with the available fabric.

### Answer: 98

Expected answer: 98

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the dressmaking company decides to create a more elaborate skirt design that requires 158 centimeters of fabric per skirt instead of 33 centimeters, how many skirts can they make now with the 3234 centimeters of fabric they have?

Gemma 2B:

To determine how many skirts the dressmaking company can make with the new design, we need to divide the total amount of fabric by the amount of fabric required for each skirt.

Given:
- Total fabric = 3234 centimeters
- Fabric per skirt (new design) = 158 centimeters

We perform the division:
\[ \frac{3234 \text{ cm}}{158 \text{ cm/skirt}} \]

First, let's do the division:
\[ 3234 \div 158 \approx 20.47 \]

Since the company cannot make a fraction of a skirt, we take the integer part of the result:
\[ 20 \]

So, the dressmaking company can make 20 skirts with the available fabric using the new design.

### Answer: 20

Expected answer: 1617/79

Correct? No

๐Ÿ”— Problem

Problem: A doctor has spent a total of 4424 minutes talking with patients over the past 56 days. If the doctor spends the same amount of time talking with patients each day, how many minutes does he spend each day?

Gemma 2B:

To determine how many minutes the doctor spends talking with patients each day, we need to divide the total number of minutes by the number of days.

Total minutes spent talking with patients: 4424 minutes
Number of days: 56 days

We perform the division:

\[ \frac{4424 \text{ minutes}}{56 \text{ days}} \]

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

1. Divide 4424 by 56:
\[ 4424 \div 56 = 79 \]

So, the doctor spends 79 minutes each day talking with patients.

### Answer: 79 minutes

Expected answer: 79

Correct? Yes

๐Ÿ”— Follow-up

Problem: On further reflection, the doctor realized that over the past 56 days, he actually only spent 1047 minutes talking with patients. If he spent the same amount of time each day, how many minutes does he actually spend talking with patients daily?

Gemma 2B:

To determine how many minutes the doctor actually spends talking with patients each day, we need to divide the total number of minutes by the number of days.

Total minutes spent talking with patients: 1047 minutes
Number of days: 56 days

We perform the division:

\[ \frac{1047 \text{ minutes}}{56 \text{ days}} \]

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

1. Divide 1047 by 56:
\[ 1047 \div 56 \approx 18.6964 \]

Since we are looking for the number of minutes per day, we round to the nearest whole number:

\[ 18.6964 \approx 19 \]

So, the doctor spends approximately 19 minutes each day talking with patients.

### Answer: 19 minutes

Expected answer: 1047/56

Correct? No

๐Ÿ”— Problem

Problem: Sam has a total of 3025 marshmallows which he wants to package into bags of 55. How many marshmallows will be in each bag?

Gemma 2B:

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

Given:
- Total marshmallows = 3025
- Marshmallows per bag = 55

We perform the division:

\[ 3025 \div 55 \]

First, let's estimate how many times 55 goes into 3025. We can start by simplifying the division:

\[ 3025 \div 55 \approx 55 \times 55 = 3025 \]

So, we can see that:

\[ 3025 \div 55 = 55 \]

Therefore, each bag will contain 55 marshmallows.

### Answer: 55

Expected answer: 55

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead, Sam wants to divide his 3025 marshmallows evenly into 2011 bags, how many marshmallows will be in each bag then?

Gemma 2B:

To determine how many marshmallows will be in each bag when Sam divides his 3025 marshmallows into 2011 bags, we need to perform the division:

\[ 3025 \div 2011 \]

Let's calculate this:

\[ 3025 \div 2011 \approx 1.503 \]

Since we are looking for an integer number of marshmallows per bag, we take the integer part of the division, which is 1. This means each bag will contain 1 marshmallow, and there will be some marshmallows left over.

To find the exact number of marshmallows left over, we can calculate the remainder:

\[ 3025 \mod 2011 = 3025 - (2011 \times 1) = 3025 - 2011 = 1014 \]

So, each of the 2011 bags will contain 1 marshmallow, and there will be 1014 marshmallows left over.

### Answer: 1

Expected answer: 3025/2011

Correct? No

๐Ÿ”— Problem

Problem: A jeweler has 1944 pieces of beads and wants to create bracelets using an equal number of beads in each bracelet. If the jeweler ends up making 72 bracelets, how many beads does each bracelet have?

Gemma 2B:

To determine how many beads each bracelet has, we need to divide the total number of beads by the number of bracelets.

Given:
- Total number of beads = 1944
- Number of bracelets = 72

We perform the division:
\[ \frac{1944}{72} \]

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

1. Divide 1944 by 72:
\[ 1944 \div 72 = 27 \]

So, each bracelet will have 27 beads.

### Answer: 27

Expected answer: 27

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the jeweler decided instead to make 495 bracelets using the same 1944 beads, how many beads would each bracelet have then?

Gemma 2B:

To determine how many beads each bracelet would have if the jeweler made 495 bracelets, we need to divide the total number of beads by the number of bracelets.

Given:
- Total number of beads = 1944
- Number of bracelets = 495

We perform the division:
\[ \frac{1944}{495} \]

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

1. Simplify the fraction \(\frac{1944}{495}\) by finding the greatest common divisor (GCD) of 1944 and 495.

The prime factorization of 1944 is:
\[ 1944 = 2^3 \times 3^5 \]

The prime factorization of 495 is:
\[ 495 = 3^2 \times 5 \times 11 \]

The common prime factors are \(3^2\).

So, the GCD is:
\[ 3^2 = 9 \]

Now, divide both the numerator and the denominator by the GCD (9):
\[ \frac{1944 \div 9}{495 \div 9} = \frac{216}{55} \]

Since 216 and 55 have no common factors other than 1, the fraction \(\frac{216}{55}\) cannot be simplified further. Therefore, each bracelet will have:
\[ \frac{216}{55} \approx 3.927 \]

Since the number of beads must be an integer, it is not possible to evenly distribute 1944 beads into 495 bracelets.

### Answer: It is not possible to evenly distribute 1944 beads into 495 bracelets.

Expected answer: 216/55

Correct? No

๐Ÿ”— Problem

Problem: A farmer has 272 carrots and he wants to evenly divide them into 17 bunches for the market. How many carrots will there be in each bunch?

Gemma 2B:

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

\[ \text{Number of carrots per bunch} = \frac{272 \text{ carrots}}{17 \text{ bunches}} \]

Performing the division:

\[ 272 \div 17 = 16 \]

So, there will be 16 carrots in each bunch.

### Answer: 16

Expected answer: 16

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the previous scenario, if the farmer instead had 3176 carrots and still wanted to divide them evenly into 17 bunches, how many carrots would there then be in each bunch?

Gemma 2B:

To find out how many carrots will be in each bunch, we need to divide the total number of carrots by the number of bunches.

\[ \text{Number of carrots per bunch} = \frac{3176 \text{ carrots}}{17 \text{ bunches}} \]

Performing the division:

\[ 3176 \div 17 = 187 \]

So, there will be 187 carrots in each bunch.

### Answer: 187

Expected answer: 3176/17

Correct? No

๐Ÿ”— Problem

Problem: During a winter season, 1740 inches of snow fell over the course of 87 days. On average, how many inches of snow fell each day?

Gemma 2B:

To find the average number of inches of snow that fell each day, we need to divide the total amount of snow by the number of days.

Given:
- Total snow: 1740 inches
- Number of days: 87 days

We perform the division:
\[ \text{Average inches per day} = \frac{1740 \text{ inches}}{87 \text{ days}} \]

Now, let's calculate:
\[ \frac{1740}{87} = 20 \]

So, on average, 20 inches of snow fell each day.

### Answer: 20 inches

Expected answer: 20

Correct? Yes

๐Ÿ”— Problem

Problem: A carpenter has 80 inches of wood to create a door that requires exactly 80 inches. How many doors can he make?

Gemma 2B:

To determine how many doors the carpenter can make, we need to see if the total amount of wood he has is sufficient for one door.

The carpenter has 80 inches of wood, and each door requires exactly 80 inches.

We can calculate the number of doors by dividing the total amount of wood by the amount required for one door:
\[ \text{Number of doors} = \frac{\text{Total wood}}{\text{Wood per door}} \]
\[ \text{Number of doors} = \frac{80 \text{ inches}}{80 \text{ inches/door}} \]
\[ \text{Number of doors} = 1 \]

Thus, the carpenter can make exactly one door.

### Answer: 1

Expected answer: 1

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the carpenter now has 4322 inches of wood instead of 80, how many doors can he make if each door still requires exactly 80 inches of wood?

Gemma 2B:

To determine how many doors the carpenter can make with 4322 inches of wood, we need to divide the total amount of wood by the amount required for one door.

Each door requires 80 inches of wood.

We can calculate the number of doors as follows:
\[ \text{Number of doors} = \frac{\text{Total wood}}{\text{Wood per door}} \]
\[ \text{Number of doors} = \frac{4322 \text{ inches}}{80 \text{ inches/door}} \]

Perform the division:
\[ \text{Number of doors} = 54.025 \]

Since the carpenter cannot make a fraction of a door, we take the integer part of the result:
\[ \text{Number of doors} = 54 \]

Thus, the carpenter can make 54 doors with 4322 inches of wood.

### Answer: 54

Expected answer: 2161/40

Correct? No

๐Ÿ”— Problem

Problem: A doctor, in the course of her career, has treated a total of 2691 patients. If this was achieved over a period of 39 years of active service, how many patients did she attend to in each year on average?

Gemma 2B:

To find the average number of patients the doctor treated each year, we need to divide the total number of patients by the number of years of active service.

Total number of patients = 2691
Number of years of active service = 39

Average number of patients per year = Total number of patients / Number of years of active service
\[ \text{Average number of patients per year} = \frac{2691}{39} \]

Now, we perform the division:
\[ 2691 \div 39 = 69 \]

### Answer: 69

Expected answer: 69

Correct? Yes

๐Ÿ”— Follow-up

Problem: Continuing from the previous problem, considering that over her career, the doctor treated a total of 9447 patients, rather than 2691, how many patients did she attend to in each year on average now?

Gemma 2B:

To find the new average number of patients the doctor treated each year, we need to divide the updated total number of patients by the number of years of active service.

Total number of patients = 9447
Number of years of active service = 39

Average number of patients per year = Total number of patients / Number of years of active service
\[ \text{Average number of patients per year} = \frac{9447}{39} \]

Now, we perform the division:
\[ 9447 \div 39 = 242 \]

### Answer: 242

Expected answer: 3149/13

Correct? No

๐Ÿ”— Problem

Problem: A farmer harvested 936 cucumbers from his 52 plants. If he got the same number of cucumbers from each plant, how many cucumbers did he get from each plant?

Gemma 2B:

To determine how many cucumbers the farmer got from each plant, we need to divide the total number of cucumbers by the number of plants.

The total number of cucumbers is 936, and the number of plants is 52.

We perform the division:
\[ 936 \div 52 \]

First, let's see how many times 52 fits into 936. We can use long division for this:

1. 52 goes into 93 once (since 52 * 1 = 52).
2. Subtract 52 from 93 to get 41.
3. Bring down the next digit, which is 6, making it 416.
4. 52 goes into 416 eight times (since 52 * 8 = 416).

So, 936 divided by 52 is 18.

### Answer: 18

Expected answer: 18

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the next season, the same farmer harvested a larger crop of 8539 cucumbers from his 52 plants. If he harvested the same number of cucumbers from each plant as in the previous season, how many cucumbers did he get from each plant this time around?

Gemma 2B:

To determine how many cucumbers the farmer got from each plant in the next season, we need to divide the total number of cucumbers by the number of plants.

The total number of cucumbers is 8539, and the number of plants is 52.

We perform the division:
\[ 8539 \div 52 \]

First, let's see how many times 52 fits into 8539. We can use long division for this:

1. 52 goes into 85 once (since 52 * 1 = 52).
2. Subtract 52 from 85 to get 33.
3. Bring down the next digit, which is 3, making it 333.
4. 52 goes into 333 six times (since 52 * 6 = 312).
5. Subtract 312 from 333 to get 21.
6. Bring down the next digit, which is 9, making it 219.
7. 52 goes into 219 four times (since 52 * 4 = 208).
8. Subtract 208 from 219 to get 11.

So, 8539 divided by 52 is 164 with a remainder of 11.

This means the farmer harvested 164 cucumbers from each plant, with 11 cucumbers left over.

### Answer: 164

Expected answer: 8539/52

Correct? No

๐Ÿ”— Problem

Problem: A party organizer has 2470 balloons to be equally distributed over 26 parties. How many balloons does each party get?

Gemma 2B:

To determine how many balloons each party gets, we need to divide the total number of balloons by the number of parties.

First, we perform the division:
\[ 2470 \div 26 \]

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

1. Divide 247 by 26:
   - 26 goes into 247 approximately 9 times (since \( 26 \times 9 = 234 \)).
   - Subtract 234 from 247 to get the remainder: \( 247 - 234 = 13 \).

2. Bring down the next digit (0) to make it 130.

3. Divide 130 by 26:
   - 26 goes into 130 exactly 5 times (since \( 26 \times 5 = 130 \)).
   - Subtract 130 from 130 to get the remainder: \( 130 - 130 = 0 \).

So, the quotient is 95, and there is no remainder.

Therefore, each party gets 95 balloons.

### Answer: 95

Expected answer: 95

Correct? Yes

๐Ÿ”— Follow-up

Problem: The party organizer recently received another batch of balloons, increasing the total quantity to 8421. If these are to be equally distributed over the same 26 parties, how many balloons does each party now get?

Gemma 2B:

To determine how many balloons each party gets with the new total of 8421 balloons, we need to divide the total number of balloons by the number of parties.

First, we perform the division:
\[ 8421 \div 26 \]

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

1. Divide 84 by 26:
   - 26 goes into 84 approximately 3 times (since \( 26 \times 3 = 78 \)).
   - Subtract 78 from 84 to get the remainder: \( 84 - 78 = 6 \).

2. Bring down the next digit (2) to make it 62.

3. Divide 62 by 26:
   - 26 goes into 62 approximately 2 times (since \( 26 \times 2 = 52 \)).
   - Subtract 52 from 62 to get the remainder: \( 62 - 52 = 10 \).

4. Bring down the next digit (1) to make it 101.

5. Divide 101 by 26:
   - 26 goes into 101 approximately 3 times (since \( 26 \times 3 = 78 \)).
   - Subtract 78 from 101 to get the remainder: \( 101 - 78 = 23 \).

So, the quotient is 323, and the remainder is 23.

Therefore, each party gets 323 balloons, with 23 balloons left over.

### Answer: 323

Expected answer: 8421/26

Correct? No

๐Ÿ”— Problem

Problem: A manufacturer makes a large batch of 858 milliliters of juice. It plans to distribute this juice equally into 13 bottles. How much juice will each bottle contain?

Gemma 2B:

To determine how much juice each bottle will contain, we need to divide the total amount of juice by the number of bottles.

Given:
- Total juice = 858 milliliters
- Number of bottles = 13

We perform the division:

\[ \frac{858 \text{ milliliters}}{13 \text{ bottles}} \]

First, we perform the division:

\[ 858 \div 13 = 66 \]

So, each bottle will contain 66 milliliters of juice.

### Answer: 66 milliliters

Expected answer: 66

Correct? Yes

๐Ÿ”— Follow-up

Problem: Given the same situation as before, what if the manufacturer makes a larger batch of 1192 milliliters of juice instead, and still plans to distribute this juice equally into 13 bottles. How much juice will each bottle contain now?

Gemma 2B:

To determine how much juice each bottle will contain in this new scenario, we need to divide the total amount of juice by the number of bottles.

Given:
- Total juice = 1192 milliliters
- Number of bottles = 13

We perform the division:

\[ \frac{1192 \text{ milliliters}}{13 \text{ bottles}} \]

First, we perform the division:

\[ 1192 \div 13 = 91.6923076923077 \]

Since we typically round to a reasonable number of decimal places for practical purposes, we can round this to two decimal places:

\[ 91.69 \]

So, each bottle will contain approximately 91.69 milliliters of juice.

### Answer: 91.69 milliliters

Expected answer: 1192/13

Correct? No

๐Ÿ”— Problem

Problem: A scooter travels a total of 1600 feet in 64 seconds. How many feet does the scooter travel in each second?

Gemma 2B:

To determine how many feet the scooter travels in each second, we need to divide the total distance by the total time.

Given:
- Total distance = 1600 feet
- Total time = 64 seconds

We use the formula:
\[ \text{Distance per second} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Distance per second} = \frac{1600 \text{ feet}}{64 \text{ seconds}} \]

Perform the division:
\[ \text{Distance per second} = 25 \text{ feet/second} \]

### Answer: 25 feet/second

Expected answer: 25

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of traveling 1600 feet in 64 seconds, let's assume that the scooter traveled 3984 feet in the same amount of time. How many feet would the scooter travel in each second under this new scenario?

Gemma 2B:

To determine how many feet the scooter travels in each second under the new scenario, we need to divide the total distance by the total time.

Given:
- Total distance = 3984 feet
- Total time = 64 seconds

We use the formula:
\[ \text{Distance per second} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Distance per second} = \frac{3984 \text{ feet}}{64 \text{ seconds}} \]

Perform the division:
\[ \text{Distance per second} = 62.25 \text{ feet/second} \]

### Answer: 62.25 feet/second

Expected answer: 249/4

Correct? No

๐Ÿ”— Problem

Problem: A company has manufactured a total of 2907 lamps that are to be divided equally among 51 stores. How many lamps will each store receive?

Gemma 2B:

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

\[
\text{Total number of lamps} = 2907
\]
\[
\text{Number of stores} = 51
\]

We perform the division:

\[
2907 \div 51
\]

First, we estimate how many times 51 goes into 2907. We can start by checking how many times 51 goes into the first few digits of 2907.

1. 51 goes into 290 (the first three digits of 2907) approximately 5 times because \(51 \times 5 = 255\).
2. Subtract 255 from 290 to get the remainder: \(290 - 255 = 35\).
3. Bring down the next digit (7), making it 357.
4. 51 goes into 357 approximately 7 times because \(51 \times 7 = 357\).

Thus, 51 goes into 2907 exactly 57 times.

\[
2907 \div 51 = 57
\]

So, each store will receive 57 lamps.

### Answer: 57

Expected answer: 57

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the company instead manufactured a total of 4753 lamps that are to be divided equally among the 51 stores. How many lamps will each store receive now?

Gemma 2B:

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

\[
\text{Total number of lamps} = 4753
\]
\[
\text{Number of stores} = 51
\]

We perform the division:

\[
4753 \div 51
\]

First, we estimate how many times 51 goes into 4753. We can start by checking how many times 51 goes into the first few digits of 4753.

1. 51 goes into 475 (the first three digits of 4753) approximately 9 times because \(51 \times 9 = 459\).
2. Subtract 459 from 475 to get the remainder: \(475 - 459 = 16\).
3. Bring down the next digit (3), making it 163.
4. 51 goes into 163 approximately 3 times because \(51 \times 3 = 153\).
5. Subtract 153 from 163 to get the remainder: \(163 - 153 = 10\).

Thus, 51 goes into 4753 approximately 93 times with a remainder of 10.

\[
4753 \div 51 = 93 \text{ R } 10
\]

So, each store will receive 93 lamps, and there will be 10 lamps left over.

### Answer: 93

Expected answer: 4753/51

Correct? No

๐Ÿ”— Problem

Problem: A clock ticks 756 times in 18 minutes. How many times does it tick in one minute?

Gemma 2B:

To determine how many times the clock ticks in one minute, we need to divide the total number of ticks by the total number of minutes.

Given:
- Total ticks = 756
- Total minutes = 18

We perform the division:
\[ \text{Ticks per minute} = \frac{756}{18} \]

Now, we calculate:
\[ \frac{756}{18} = 42 \]

So, the clock ticks 42 times in one minute.

### Answer: 42

Expected answer: 42

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead the clock ticks a total of 3788 times in the same 18-minute period, how many times would it tick in one minute?

Gemma 2B:

To determine how many times the clock ticks in one minute, we need to divide the total number of ticks by the total number of minutes.

Given:
- Total ticks = 3788
- Total minutes = 18

We perform the division:
\[ \text{Ticks per minute} = \frac{3788}{18} \]

Now, we calculate:
\[ \frac{3788}{18} = 210.4444\ldots \]

Since we are looking for the number of ticks per minute, we can round to the nearest whole number if necessary. However, in this context, it is more precise to keep the exact value.

### Answer: 210.4444

Expected answer: 1894/9

Correct? No

๐Ÿ”— Problem

Problem: A pillow factory has 930 feathers available to fill their pillows. If they put the same amount of feathers into each pillow and are able to fill 15 pillows, how many feathers are in each pillow?

Gemma 2B:

To determine how many feathers are in each pillow, we need to divide the total number of feathers by the number of pillows.

Given:
- Total feathers = 930
- Number of pillows = 15

We perform the division:
\[ \frac{930}{15} = 62 \]

So, each pillow contains 62 feathers.

### Answer: 62

Expected answer: 62

Correct? Yes

๐Ÿ”— Follow-up

Problem: An additional pillow factory comes into play where they have 5881 feathers available to fill their pillows. If they also put the same amount of feathers into each pillow and are able to fill 15 pillows just like the first factory, how many feathers would be in each of their pillows?

Gemma 2B:

To determine how many feathers are in each pillow at the additional pillow factory, we need to divide the total number of feathers by the number of pillows.

Given:
- Total feathers = 5881
- Number of pillows = 15

We perform the division:
\[ \frac{5881}{15} \approx 392.0667 \]

Since the number of feathers must be a whole number, we round to the nearest whole number:
\[ 392.0667 \approx 392 \]

So, each pillow contains approximately 392 feathers.

### Answer: 392

Expected answer: 5881/15

Correct? No

๐Ÿ”— Problem

Problem: A pair of binoculars cost $702. If the cost is divided equally amongst a birdwatching group of 54 people, how much does each person have to contribute?

Gemma 2B:

To determine how much each person in the birdwatching group has to contribute, we need to divide the total cost of the binoculars by the number of people in the group.

The total cost of the binoculars is $702, and the number of people in the group is 54.

We perform the division:
\[ \frac{702}{54} \]

First, we simplify the division:
\[ 702 \div 54 = 13 \]

So, each person has to contribute $13.

### Answer: $13

Expected answer: 13

Correct? Yes

๐Ÿ”— Follow-up

Problem: After the birdwatching group purchased the binoculars, they found a different pair costing $446 and decided to return the previous set to buy the cheaper set. If the cost is divided equally amongst the 54 people again, how much does each person have to pay now?

Gemma 2B:

To determine how much each person in the birdwatching group has to contribute for the new pair of binoculars costing $446, we need to divide the total cost of the new binoculars by the number of people in the group.

The total cost of the new binoculars is $446, and the number of people in the group is 54.

We perform the division:
\[ \frac{446}{54} \]

First, we simplify the division:
\[ 446 \div 54 \approx 8.26 \]

So, each person has to contribute approximately $8.26.

### Answer: $8.26

Expected answer: 223/27

Correct? No

๐Ÿ”— Problem

Problem: A rope is 510 cm long. If it's divided into 30 equal pieces, how long is each piece?

Gemma 2B:

To determine the length of each piece, we need to divide the total length of the rope by the number of pieces.

Given:
- Total length of the rope = 510 cm
- Number of pieces = 30

We perform the division:
\[ \frac{510 \text{ cm}}{30} = 17 \text{ cm} \]

So, each piece of the rope is 17 cm long.

### Answer: 17 cm

Expected answer: 17

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the rope was actually 9650 cm long instead of 510 cm, and we still want to divide it into 30 equal parts. How long would each piece be now?

Gemma 2B:

To find the length of each piece when the rope is 9650 cm long and divided into 30 equal parts, we need to divide the total length of the rope by the number of pieces.

Given:
- Total length of the rope = 9650 cm
- Number of pieces = 30

We perform the division:
\[ \frac{9650 \text{ cm}}{30} = 321.67 \text{ cm} \]

So, each piece of the rope would be 321.67 cm long.

### Answer: 321.67 cm

Expected answer: 965/3

Correct? No

๐Ÿ”— Problem

Problem: A pirate ship has a total of 6097 gold coins stowed away, evenly distributed among its 91 chests. How many coins are in each chest?

Gemma 2B:

To determine how many gold coins are in each chest, we need to divide the total number of gold coins by the number of chests.

Total gold coins: 6097
Number of chests: 91

We perform the division:

\[ \frac{6097}{91} \]

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

1. 6097 divided by 91.
2. 6097 รท 91 โ‰ˆ 67 (since 91 * 67 = 6097).

Thus, each chest contains 67 gold coins.

### Answer: 67

Expected answer: 67

Correct? Yes

๐Ÿ”— Follow-up

Problem: Let's reconsider our previous scenario, but this time the pirate ship stashes a total of 6097 gold coins evenly distributed among not 91, but 2910 chests. How many gold coins are now in each chest?

Gemma 2B:

To determine how many gold coins are in each chest, we need to divide the total number of gold coins by the number of chests.

Total gold coins: 6097
Number of chests: 2910

We perform the division:

\[ \frac{6097}{2910} \]

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

1. 6097 divided by 2910.
2. This can be approximated as:

\[ 6097 \div 2910 \approx 2.094 \]

Since we are dealing with whole gold coins, we need to round to the nearest whole number. However, in this case, the exact division is:

\[ \frac{6097}{2910} \approx 2.094 \]

So, each chest contains approximately 2 gold coins, with some chests possibly containing 3 coins to account for the remainder.

### Answer: 2

Expected answer: 6097/2910

Correct? No

๐Ÿ”— Problem

Problem: A treasure chest contains 2425 gold coins. The coins are to be divided evenly among 97 pirates. How many coins does each pirate receive?

Gemma 2B:

To determine how many coins each pirate receives, we need to divide the total number of gold coins by the number of pirates.

We start with the division:
\[ 2425 \div 97 \]

First, we estimate how many times 97 fits into 2425. We can use long division for this:

1. 97 goes into 242 (the first three digits of 2425) approximately 2 times (since \( 97 \times 2 = 194 \)).
2. Subtract 194 from 242 to get the remainder:
\[ 242 - 194 = 48 \]
3. Bring down the next digit (5), making it 485.
4. 97 goes into 485 approximately 5 times (since \( 97 \times 5 = 485 \)).

So, the division is exact:
\[ 2425 \div 97 = 25 \]

Each pirate receives 25 coins.

### Answer: 25

Expected answer: 25

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the treasure chest actually contained 5005 gold coins instead of 2425. If these coins are to be divided evenly among the same 97 pirates, how many coins would each pirate receive now?

Gemma 2B:

To determine how many coins each pirate receives when the treasure chest contains 5005 gold coins, we need to divide the total number of gold coins by the number of pirates.

We start with the division:
\[ 5005 \div 97 \]

We can use long division for this:

1. 97 goes into 500 (the first three digits of 5005) approximately 5 times (since \( 97 \times 5 = 485 \)).
2. Subtract 485 from 500 to get the remainder:
\[ 500 - 485 = 15 \]
3. Bring down the next digit (5), making it 155.
4. 97 goes into 155 approximately 1 time (since \( 97 \times 1 = 97 \)).
5. Subtract 97 from 155 to get the remainder:
\[ 155 - 97 = 58 \]

So, the division is:
\[ 5005 \div 97 = 51 \text{ R } 58 \]

Each pirate receives 51 coins, with a remainder of 58 coins.

### Answer: 51

Expected answer: 5005/97

Correct? No

๐Ÿ”— Problem

Problem: A boat consumes 204 liters of fuel during a journey of 51 hours. How many liters of fuel does the boat consume in one hour?

Gemma 2B:

To determine the fuel consumption per hour, we need to divide the total fuel consumed by the total number of hours.

Given:
- Total fuel consumed = 204 liters
- Total time = 51 hours

We calculate the fuel consumption per hour as follows:

\[
\text{Fuel consumption per hour} = \frac{\text{Total fuel consumed}}{\text{Total time}} = \frac{204 \text{ liters}}{51 \text{ hours}}
\]

Perform the division:

\[
\frac{204}{51} = 4
\]

So, the boat consumes 4 liters of fuel per hour.

### Answer: 4 liters per hour

Expected answer: 4

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the boat only had 100 liters of fuel to start with instead of 204 liters for the same 51-hour journey, how much fuel would the boat consume per hour now?

Gemma 2B:

The fuel consumption per hour is determined by the rate at which the boat uses fuel, which is independent of the initial amount of fuel. The rate of fuel consumption per hour remains the same regardless of the total amount of fuel available.

From the previous calculation, we know that the boat consumes 4 liters of fuel per hour.

Therefore, even if the boat starts with 100 liters of fuel, the fuel consumption per hour remains:

### Answer: 4 liters per hour

Expected answer: 100/51

Correct? No

๐Ÿ”— Problem

Problem: A map's scale is such that 8448 kilometers are represented as 96 centimeters. How many kilometers does each centimeter represent on this map?

Gemma 2B:

To determine how many kilometers each centimeter represents on the map, we need to divide the total number of kilometers by the total number of centimeters.

Given:
- 8448 kilometers are represented by 96 centimeters.

We calculate the number of kilometers per centimeter as follows:
\[ \text{Kilometers per centimeter} = \frac{8448 \text{ kilometers}}{96 \text{ centimeters}} \]

Perform the division:
\[ \frac{8448}{96} = 88 \]

So, each centimeter on the map represents 88 kilometers.

### Answer: 88 kilometers

Expected answer: 88

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose that on another map, a larger area of 8448 kilometers is represented by a length of 4759 centimeters. In this scenario, how many kilometers would each centimeter represent?

Gemma 2B:

To determine how many kilometers each centimeter represents on this new map, we need to divide the total number of kilometers by the total number of centimeters.

Given:
- 8448 kilometers are represented by 4759 centimeters.

We calculate the number of kilometers per centimeter as follows:
\[ \text{Kilometers per centimeter} = \frac{8448 \text{ kilometers}}{4759 \text{ centimeters}} \]

Perform the division:
\[ \frac{8448}{4759} \approx 1.775 \]

So, each centimeter on the map represents approximately 1.775 kilometers.

### Answer: 1.775 kilometers

Expected answer: 8448/4759

Correct? No

๐Ÿ”— Problem

Problem: A train travels a total of 584 kms evenly over 73 hours. How many kms does it travel each hour?

Gemma 2B:

To determine how many kilometers the train travels each hour, we need to divide the total distance traveled by the total time taken.

Given:
- Total distance = 584 kilometers
- Total time = 73 hours

We perform the division:
\[ \frac{584 \text{ km}}{73 \text{ hours}} = 8 \text{ km/hour} \]

### Answer: 8 km/hour

Expected answer: 8

Correct? Yes

๐Ÿ”— Follow-up

Problem: A train travels a total of 584 kms evenly over 71 hours instead of 73. How many kms does it travel each hour now?

Gemma 2B:

To determine how many kilometers the train travels each hour, we need to divide the total distance traveled by the total time taken.

Given:
- Total distance = 584 kilometers
- Total time = 71 hours

We perform the division:
\[ \frac{584 \text{ km}}{71 \text{ hours}} = 8.225352112676056 \text{ km/hour} \]

Rounding to two decimal places:
\[ 8.23 \text{ km/hour} \]

### Answer: 8.23 km/hour

Expected answer: 584/71

Correct? No

๐Ÿ”— Problem

Problem: A teacher assigns a total of 3612 pages of reading over 86 days of school. If the teacher assigns an equal number of pages for every day, how many pages does each student need to read daily?

Gemma 2B:

To determine how many pages each student needs to read daily, we need to divide the total number of pages by the total number of days.

Given:
- Total pages = 3612
- Total days = 86

We perform the division:

\[ \frac{3612}{86} \]

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

1. 3612 divided by 86:
   - 86 goes into 361 approximately 4 times (since \( 86 \times 4 = 344 \)).
   - Subtract 344 from 361 to get the remainder: \( 361 - 344 = 17 \).
   - Bring down the next digit (2), making it 172.
   - 86 goes into 172 exactly 2 times (since \( 86 \times 2 = 172 \)).

So, \( 3612 \div 86 = 42 \).

Therefore, each student needs to read 42 pages daily.

### Answer: 42

Expected answer: 42

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the teacher realizes that the reading load is too much and reduces the total number of pages to be read to 3612, but spreads them over 328 days instead of 86 days, how many pages would each student need to read daily then?

Gemma 2B:

To determine the new daily reading load, we need to divide the total number of pages by the new total number of days.

Given:
- Total pages = 3612
- Total days = 328

We perform the division:

\[ \frac{3612}{328} \]

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

1. 3612 divided by 328:
   - 328 goes into 361 approximately 1 time (since \( 328 \times 1 = 328 \)).
   - Subtract 328 from 361 to get the remainder: \( 361 - 328 = 33 \).
   - Bring down the next digit (2), making it 332.
   - 328 goes into 332 exactly 1 time (since \( 328 \times 1 = 328 \)).

So, \( 3612 \div 328 = 11 \).

Therefore, each student needs to read 11 pages daily.

### Answer: 11

Expected answer: 903/82

Correct? No

๐Ÿ”— Problem

Problem: A hat maker makes 1083 hats throughout 57 weeks. If the hat maker makes the same amount of hats every week, how many hats does the hat maker produce weekly?

Gemma 2B:

To determine how many hats the hat maker produces weekly, we need to divide the total number of hats by the number of weeks.

Given:
- Total number of hats = 1083
- Number of weeks = 57

We perform the division:

\[ \frac{1083}{57} \]

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

1. 1083 divided by 57.
2. 57 goes into 108 once (since 57 * 1 = 57).
3. Subtract 57 from 108 to get 51.
4. Bring down the next digit, which is 3, making it 513.
5. 57 goes into 513 exactly 9 times (since 57 * 9 = 513).

So, the hat maker produces:

\[ 1083 \div 57 = 19 \]

### Answer: 19

Expected answer: 19

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the following year, the hat maker manages to produce a total of 7678 hats over 57 weeks. Maintaining the same pace of production every week as the previous year, how many hats does the hat maker now produce weekly?

Gemma 2B:

To determine how many hats the hat maker produces weekly in the following year, we need to divide the total number of hats by the number of weeks.

Given:
- Total number of hats = 7678
- Number of weeks = 57

We perform the division:

\[ \frac{7678}{57} \]

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

1. 57 goes into 76 once (since 57 * 1 = 57).
2. Subtract 57 from 76 to get 19.
3. Bring down the next digit, which is 7, making it 197.
4. 57 goes into 197 three times (since 57 * 3 = 171).
5. Subtract 171 from 197 to get 26.
6. Bring down the next digit, which is 8, making it 268.
7. 57 goes into 268 four times (since 57 * 4 = 228).
8. Subtract 228 from 268 to get 40.
9. Bring down the next digit, which is 0, making it 400.
10. 57 goes into 400 seven times (since 57 * 7 = 399).
11. Subtract 399 from 400 to get 1.

So, the hat maker produces:

\[ 7678 \div 57 = 134 \]

### Answer: 134

Expected answer: 7678/57

Correct? No

๐Ÿ”— Problem

Problem: A sock manufacturer produced 4218 pairs of socks over 74 days. If they produced the same number of socks each day, how many pairs of socks did they make daily?

Gemma 2B:

To determine the number of pairs of socks produced daily, we need to divide the total number of pairs of socks by the number of days.

Given:
- Total pairs of socks = 4218
- Number of days = 74

We perform the division:

\[ \frac{4218}{74} \]

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

1. 4218 divided by 74:
   - 4218 รท 74 โ‰ˆ 57

To verify, we multiply 57 by 74:

\[ 57 \times 74 = 4218 \]

Since the multiplication confirms our division, the manufacturer produced 57 pairs of socks each day.

### Answer: 57

Expected answer: 57

Correct? Yes

๐Ÿ”— Follow-up

Problem: After a reassessment, it was found that the sock manufacturer actually produced a total of 4055 pairs of socks over the same 74 days. With this new information, how many pairs of socks did they make daily?

Gemma 2B:

To determine the number of pairs of socks produced daily with the new total, we need to divide the total number of pairs of socks by the number of days.

Given:
- Total pairs of socks = 4055
- Number of days = 74

We perform the division:

\[ \frac{4055}{74} \]

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

1. 4055 divided by 74:
   - 4055 รท 74 โ‰ˆ 54.8

Since we are dealing with pairs of socks, we should round to the nearest whole number. Therefore, the manufacturer produced approximately 55 pairs of socks each day.

### Answer: 55

Expected answer: 4055/74

Correct? No

๐Ÿ”— Problem

Problem: A jewellery shop makes bracelets, each using 69 small pearls. From 3657 pearls, how many full bracelets can be made?

Gemma 2B:

To determine how many full bracelets can be made, we need to divide the total number of pearls by the number of pearls required for each bracelet.

First, we perform the division:
\[ \frac{3657}{69} \]

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

1. Divide 3657 by 69:
\[ 3657 \div 69 = 53 \]

So, 53 full bracelets can be made from 3657 pearls.

### Answer: 53

Expected answer: 53

Correct? Yes

๐Ÿ”— Problem

Problem: A scooter travelled a total distance of 4000 meters in 80 minutes. How many meters did the scooter travel per minute?

Gemma 2B:

To find out how many meters the scooter traveled per minute, we need to divide the total distance by the total time.

The total distance traveled is 4000 meters, and the total time taken is 80 minutes.

We use the formula:
\[ \text{Distance per minute} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Distance per minute} = \frac{4000 \text{ meters}}{80 \text{ minutes}} \]

Perform the division:
\[ \text{Distance per minute} = 50 \text{ meters per minute} \]

### Answer: 50 meters per minute.

Expected answer: 50

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the following week, the same scooter travelled a longer total distance of 5391 meters in the same time period of 80 minutes. How many meters did the scooter travel per minute now?

Gemma 2B:

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

The total distance traveled is 5391 meters, and the total time taken is 80 minutes.

We use the formula:
\[ \text{Distance per minute} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting the given values:
\[ \text{Distance per minute} = \frac{5391 \text{ meters}}{80 \text{ minutes}} \]

Perform the division:
\[ \text{Distance per minute} = 67.3875 \text{ meters per minute} \]

### Answer: 67.3875 meters per minute.

Expected answer: 5391/80

Correct? No

๐Ÿ”— Problem

Problem: A toy factory makes 364 toys in a week. If the factory operates the same number of hours each day for 4 days a week, how many toys are made per day?

Gemma 2B:

To determine how many toys are made per day, we need to divide the total number of toys made in a week by the number of days the factory operates.

The factory makes 364 toys in a week and operates for 4 days a week.

First, we divide the total number of toys by the number of days:
\[ \frac{364 \text{ toys}}{4 \text{ days}} = 91 \text{ toys/day} \]

### Answer: 91 toys/day

Expected answer: 91

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the toy factory changes its operations and now makes 571 toys in a week over the same 4 days, how many toys are now made per day?

Gemma 2B:

To determine the new number of toys made per day, we need to divide the total number of toys made in a week by the number of days the factory operates.

The factory now makes 571 toys in a week and operates for 4 days a week.

First, we divide the total number of toys by the number of days:
\[ \frac{571 \text{ toys}}{4 \text{ days}} = 142.75 \text{ toys/day} \]

### Answer: 142.75 toys/day

Expected answer: 571/4

Correct? No

๐Ÿ”— Problem

Problem: A slide that is 4950 millimeters long is divided into 66 equal sections. How many millimeters long is each section?

Gemma 2B:

To determine the length of each section, we need to divide the total length of the slide by the number of sections.

Given:
- Total length of the slide = 4950 millimeters
- Number of sections = 66

We perform the division:
\[ \frac{4950 \text{ mm}}{66} \]

First, simplify the division:
\[ 4950 \div 66 = 75 \]

So, each section is 75 millimeters long.

### Answer: 75 millimeters

Expected answer: 75

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the slide was instead 9823 millimeters long but still divided into 66 equal sections, how many millimeters long would each section be now?

Gemma 2B:

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

Given:
- Total length of the slide = 9823 millimeters
- Number of sections = 66

We perform the division:
\[ \frac{9823 \text{ mm}}{66} \]

First, perform the division:
\[ 9823 \div 66 \approx 148.8333 \]

So, each section is approximately 148.8333 millimeters long.

### Answer: 148.8333 millimeters

Expected answer: 893/6

Correct? No

๐Ÿ”— Problem

Problem: A dragon hoards 726 gold coins in his cave spread evenly among 66 small chests. How many gold coins are there in each chest?

Gemma 2B:

To determine how many gold coins are in each chest, we need to divide the total number of gold coins by the number of chests.

Given:
- Total gold coins = 726
- Number of chests = 66

We perform the division:

\[ \frac{726}{66} \]

First, simplify the fraction if possible. Both 726 and 66 are divisible by 6:

\[ \frac{726 \div 6}{66 \div 6} = \frac{121}{11} \]

Now, divide 121 by 11:

\[ 121 \div 11 = 11 \]

So, there are 11 gold coins in each chest.

### Answer: 11

Expected answer: 11

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering the same dragon's hoard from the previous problem, suppose that the dragon actually had 3453 gold coins instead of 726. If the dragon still spread the gold evenly among the 66 chests, how many gold coins would be in each chest now?

Gemma 2B:

To determine how many gold coins are in each chest, we need to divide the total number of gold coins by the number of chests.

Given:
- Total gold coins = 3453
- Number of chests = 66

We perform the division:

\[ \frac{3453}{66} \]

First, perform the division directly:

\[ 3453 \div 66 \approx 52.318 \]

Since we are dealing with gold coins, we need the result to be a whole number. Therefore, we round down to the nearest whole number:

\[ 52 \]

So, there are 52 gold coins in each chest.

### Answer: 52

Expected answer: 1151/22

Correct? No

๐Ÿ”— Problem

Problem: A group of marine biologists count a total of 702 limbs on a group of starfish. If each starfish has 9 limbs, how many starfish are there in the group?

Gemma 2B:

To determine the number of starfish in the group, we need to divide the total number of limbs by the number of limbs each starfish has.

Given:
- Total number of limbs = 702
- Number of limbs per starfish = 9

We perform the division:
\[ \text{Number of starfish} = \frac{702}{9} \]

Now, let's calculate:
\[ \frac{702}{9} = 78 \]

So, there are 78 starfish in the group.

### Answer: 78

Expected answer: 78

Correct? Yes

๐Ÿ”— Follow-up

Problem: Continuing from the previous problem, the marine biologists later noticed that they made a mistake and there were actually only 278 limbs counted. If each starfish still has 9 limbs, how many starfish are there in the group now?

Gemma 2B:

To determine the number of starfish in the group with the corrected count of limbs, we need to divide the total number of limbs by the number of limbs each starfish has.

Given:
- Corrected total number of limbs = 278
- Number of limbs per starfish = 9

We perform the division:
\[ \text{Number of starfish} = \frac{278}{9} \]

Now, let's calculate:
\[ \frac{278}{9} \approx 30.89 \]

Since the number of starfish must be a whole number, we round down to the nearest whole number because you can't have a fraction of a starfish.

So, there are 30 starfish in the group.

### Answer: 30

Expected answer: 278/9

Correct? No

๐Ÿ”— Problem

Problem: The city park covers an area of 1927 acres. The area is divided into 47 equal sections for various activities and recreational facilities. If each section is of equal size, how large is each section in acres?

Gemma 2B:

To determine the size of each section in acres, we need to divide the total area of the city park by the number of sections.

Given:
- Total area of the city park = 1927 acres
- Number of sections = 47

We perform the division:

\[ \text{Size of each section} = \frac{1927 \text{ acres}}{47} \]

Now, we calculate:

\[ \frac{1927}{47} = 41 \]

Thus, each section is 41 acres in size.

### Answer: 41 acres

Expected answer: 41

Correct? Yes

๐Ÿ”— Follow-up

Problem: The city decides to reconfigure the park by further dividing the 1927 acre park into 411 equal sections instead to accommodate more activities and recreational facilities. If each new section is of equal size, how large is each section in acres now?

Gemma 2B:

To determine the size of each new section in acres, we need to divide the total area of the city park by the new number of sections.

Given:
- Total area of the city park = 1927 acres
- Number of new sections = 411

We perform the division:

\[ \text{Size of each new section} = \frac{1927 \text{ acres}}{411} \]

Now, we calculate:

\[ \frac{1927}{411} \approx 4.69 \]

Thus, each new section is approximately 4.69 acres in size.

### Answer: 4.69 acres

Expected answer: 1927/411

Correct? No

๐Ÿ”— Problem

Problem: A truck rental company has a total of 744 trucks distributed evenly among 24 branches. How many trucks does each branch have?

Gemma 2B:

To determine how many trucks each branch has, we need to divide the total number of trucks by the number of branches.

Given:
- Total number of trucks = 744
- Number of branches = 24

We perform the division:
\[ \frac{744}{24} \]

First, we can simplify the division by breaking it down:
\[ 744 \div 24 = 31 \]

Thus, each branch has 31 trucks.

### Answer: 31

Expected answer: 31

Correct? Yes

๐Ÿ”— Follow-up

Problem: The truck rental company decides to add more trucks and now has a total of 6028 trucks. If they are still distributed evenly among the 24 branches, how many trucks does each branch now have?

Gemma 2B:

To find out how many trucks each branch has after the increase, we need to divide the new total number of trucks by the number of branches.

Given:
- New total number of trucks = 6028
- Number of branches = 24

We perform the division:
\[ \frac{6028}{24} \]

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

1. Divide 6028 by 24:
\[ 6028 \div 24 \approx 251.1667 \]

Since we are dealing with trucks, we should round to the nearest whole number. Therefore, each branch has approximately 251 trucks.

### Answer: 251

Expected answer: 1507/6

Correct? No

๐Ÿ”— Problem

Problem: A farmer has 2820 oranges that he wants to distribute equally into 60 boxes. How many oranges will be in each box?

Gemma 2B:

To determine how many oranges will be in each box, we need to divide the total number of oranges by the number of boxes.

\[
\text{Number of oranges per box} = \frac{2820 \text{ oranges}}{60 \text{ boxes}}
\]

Perform the division:

\[
\frac{2820}{60} = 47
\]

So, each box will contain 47 oranges.

### Answer: 47

Expected answer: 47

Correct? Yes

๐Ÿ”— Problem

Problem: A treasure chest contains 7280 gold coins. The coins are evenly distributed in 91 bags. How many gold coins are there in each bag?

Gemma 2B:

To determine how many gold coins are in each bag, we need to divide the total number of gold coins by the number of bags.

Given:
- Total gold coins = 7280
- Number of bags = 91

We perform the division:
\[ \frac{7280}{91} \]

First, let's set up the division:
\[ 7280 \div 91 \]

Performing the division step-by-step:
1. 91 goes into 7280 approximately 80 times (since \( 91 \times 80 = 7280 \)).

Thus, each bag contains:
\[ 7280 \div 91 = 80 \]

### Answer: 80

Expected answer: 80

Correct? Yes

๐Ÿ”— Follow-up

Problem: What if instead of 7280 gold coins, the treasure chest contained 5857 gold coins, still distributed evenly among the 91 bags? How many gold coins would each bag hold now?

Gemma 2B:

To determine how many gold coins are in each bag when the treasure chest contains 5857 gold coins distributed evenly among 91 bags, we need to divide the total number of gold coins by the number of bags.

Given:
- Total gold coins = 5857
- Number of bags = 91

We perform the division:
\[ \frac{5857}{91} \]

First, let's set up the division:
\[ 5857 \div 91 \]

Performing the division step-by-step:
1. 91 goes into 5857 approximately 64 times (since \( 91 \times 64 = 5824 \)).
2. Subtracting 5824 from 5857 gives a remainder of 33.

Thus, each bag contains:
\[ 5857 \div 91 = 64 \text{ remainder } 33 \]

Since we are looking for the number of gold coins in each bag, we consider only the quotient:
\[ 5857 \div 91 = 64 \]

### Answer: 64

Expected answer: 5857/91

Correct? No

๐Ÿ”— Problem

Problem: A soap factory produced 1980 bars of soap by using 20 equal-sized molds. What is the number of soap bars produced by each mold?

Gemma 2B:

To determine the number of soap bars produced by each mold, we need to divide the total number of soap bars by the number of molds.

Given:
- Total number of soap bars = 1980
- Number of molds = 20

We perform the division:
\[ \frac{1980}{20} = 99 \]

So, each mold produces 99 bars of soap.

### Answer: 99

Expected answer: 99

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the following month, the same soap factory now produced 9741 bars of soap using the same 20 equal-sized molds. How many soap bars are now produced by each mold?

Gemma 2B:

To find the number of soap bars produced by each mold, we need to divide the total number of soap bars by the number of molds.

Given:
- Total number of soap bars = 9741
- Number of molds = 20

We perform the division:
\[ \frac{9741}{20} = 487.05 \]

So, each mold produces 487.05 bars of soap.

### Answer: 487.05

Expected answer: 9741/20

Correct? Yes

๐Ÿ”— Problem

Problem: A mountain is 1457 meters high and consists of 47 equally tall layers of rock. How tall is each layer of rock?

Gemma 2B:

To find the height of each layer of rock, we need to divide the total height of the mountain by the number of layers.

Given:
- Total height of the mountain = 1457 meters
- Number of layers = 47

We perform the division:

\[ \text{Height of each layer} = \frac{1457 \text{ meters}}{47} \]

Let's calculate this:

\[ 1457 \div 47 = 31 \]

So, each layer of rock is 31 meters tall.

### Answer: 31 meters

Expected answer: 31

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now imagine the mountain's height is adjusted to 8729 meters and it still has the same 47 equally tall layers of rock. How tall would each layer of rock be in this scenario?

Gemma 2B:

To find the height of each layer of rock with the new total height, we need to divide the new total height of the mountain by the number of layers.

Given:
- New total height of the mountain = 8729 meters
- Number of layers = 47

We perform the division:

\[ \text{Height of each layer} = \frac{8729 \text{ meters}}{47} \]

Let's calculate this:

\[ 8729 \div 47 = 185.72340425531915 \]

Rounding to a reasonable number of decimal places, we get:

\[ 8729 \div 47 \approx 185.72 \]

So, each layer of rock would be approximately 185.72 meters tall.

### Answer: 185.72 meters

Expected answer: 8729/47

Correct? No

๐Ÿ”— Problem

Problem: A 4230 meter long rope gets divided evenly into 90 pieces. How long is each piece of rope?

Gemma 2B:

To determine the length of each piece of rope, we need to divide the total length of the rope by the number of pieces.

Given:
- Total length of the rope = 4230 meters
- Number of pieces = 90

We perform the division:
\[ \frac{4230 \text{ meters}}{90} = 47 \text{ meters} \]

So, each piece of rope is 47 meters long.

### Answer: 47 meters

Expected answer: 47

Correct? Yes

๐Ÿ”— Problem

Problem: A forest contains 2508 trees evenly distributed over 38 hectares of land. How many trees are there per hectare?

Gemma 2B:

To find the number of trees per hectare, we need to divide the total number of trees by the total number of hectares.

\[
\text{Number of trees per hectare} = \frac{\text{Total number of trees}}{\text{Total number of hectares}}
\]

Given:
- Total number of trees = 2508
- Total number of hectares = 38

\[
\text{Number of trees per hectare} = \frac{2508}{38}
\]

Perform the division:

\[
2508 \div 38 = 66
\]

So, there are 66 trees per hectare.

### Answer: 66

Expected answer: 66

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the same forest, there are 2508 animals living on a 1417-hectares terrain. If the animals are evenly dispersed throughout the forest, how many animals would you expect to encounter in each hectare?

Gemma 2B:

To determine the number of animals per hectare, we need to divide the total number of animals by the total number of hectares.

\[
\text{Number of animals per hectare} = \frac{\text{Total number of animals}}{\text{Total number of hectares}}
\]

Given:
- Total number of animals = 2508
- Total number of hectares = 1417

\[
\text{Number of animals per hectare} = \frac{2508}{1417}
\]

Perform the division:

\[
2508 \div 1417 \approx 1.77
\]

So, there are approximately 1.77 animals per hectare.

### Answer: 1.77

Expected answer: 2508/1417

Correct? No

๐Ÿ”— Problem

Problem: A backpacker plans a thru-hike of 4526 miles, intending to walk the same distance each day for 62 days. What is the distance, in miles, that the backpacker walks each day?

Gemma 2B:

To find the distance the backpacker walks each day, we need to divide the total distance by the number of days.

Total distance: 4526 miles
Number of days: 62

We perform the division:

\[ \frac{4526}{62} \]

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

1. Divide 4526 by 62:
   \[ 4526 \div 62 = 73 \]

So, the backpacker walks 73 miles each day.

### Answer: 73 miles

Expected answer: 73

Correct? Yes

๐Ÿ”— Follow-up

Problem: After finishing his first thru-hike, the backpacker decides to undertake a shorter journey of 2714 miles, still planning to cover an equal distance every day for 62 days. What is the new distance, in miles, that the backpacker plans to walk each day now?

Gemma 2B:

To find the new distance the backpacker plans to walk each day, we need to divide the total distance of the new journey by the number of days.

Total distance: 2714 miles
Number of days: 62

We perform the division:

\[ \frac{2714}{62} \]

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

1. Divide 2714 by 62:
   \[ 2714 \div 62 = 43.8 \]

So, the backpacker plans to walk approximately 43.8 miles each day.

### Answer: 43.8 miles

Expected answer: 1357/31

Correct? No

๐Ÿ”— Problem

Problem: An alien sends a pulsating signal every 925 seconds. If the signal is organized into 37 equal pulses, how long is each pulse?

Gemma 2B:

To determine the duration of each pulse, we need to divide the total time by the number of pulses.

Given:
- Total time for all pulses = 925 seconds
- Number of pulses = 37

We calculate the duration of each pulse as follows:
\[ \text{Duration of each pulse} = \frac{\text{Total time}}{\text{Number of pulses}} \]
\[ \text{Duration of each pulse} = \frac{925 \text{ seconds}}{37} \]

Now, we perform the division:
\[ 925 \div 37 = 25 \]

So, each pulse lasts 25 seconds.

### Answer: 25 seconds

Expected answer: 25

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of sending a pulsating signal every 925 seconds, the alien sends it every 9094 seconds, how long would each pulse be if the signal is still organized into 37 equal pulses?

Gemma 2B:

To determine the duration of each pulse when the total time is 9094 seconds and the number of pulses is 37, we use the same method as before.

Given:
- Total time for all pulses = 9094 seconds
- Number of pulses = 37

We calculate the duration of each pulse as follows:
\[ \text{Duration of each pulse} = \frac{\text{Total time}}{\text{Number of pulses}} \]
\[ \text{Duration of each pulse} = \frac{9094 \text{ seconds}}{37} \]

Now, we perform the division:
\[ 9094 \div 37 = 246 \]

So, each pulse lasts 246 seconds.

### Answer: 246 seconds

Expected answer: 9094/37

Correct? No

๐Ÿ”— Problem

Problem: A dragon had collected a hoard of 3010 jewels over a period of 43 years. If he collected evenly throughout these years, how many jewels did he collect each year?

Gemma 2B:

To determine how many jewels the dragon collected each year, we need to divide the total number of jewels by the number of years.

Total number of jewels: 3010
Number of years: 43

We perform the division:

\[ \frac{3010}{43} \]

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

1. 3010 divided by 43 gives approximately 70 (since \( 43 \times 70 = 3010 \)).

Thus, the dragon collected 70 jewels each year.

### Answer: 70

Expected answer: 70

Correct? Yes

๐Ÿ”— Follow-up

Problem: Let's consider that our dragon, instead of collecting 3010 jewels over 43 years, increased his hoard to 6402 jewels over the same period. If the dragon collected at an even pace throughout these years, how many jewels did he collect each year now?

Gemma 2B:

To determine how many jewels the dragon collected each year, we need to divide the total number of jewels by the number of years.

Total number of jewels: 6402
Number of years: 43

We perform the division:

\[ \frac{6402}{43} \]

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

1. 6402 divided by 43 gives approximately 148.88.

Since we are looking for the number of jewels collected each year, we round to the nearest whole number:

\[ \frac{6402}{43} \approx 149 \]

Thus, the dragon collected 149 jewels each year.

### Answer: 149

Expected answer: 6402/43

Correct? No

๐Ÿ”— Problem

Problem: An alien spaceship sends out a pattern of 6699 signals over the course of 87 Earth days. If the spaceship sends the same number of signals each day, how many signals does it send daily?

Gemma 2B:

To determine how many signals the alien spaceship sends daily, we need to divide the total number of signals by the number of days.

Total number of signals: 6699
Number of days: 87

We perform the division:

\[ \frac{6699}{87} \]

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

1. 87 goes into 6699 approximately 77 times (since \( 87 \times 77 = 6699 \)).

Thus, the spaceship sends:

\[ \frac{6699}{87} = 77 \]

### Answer: 77

Expected answer: 77

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the alien spaceship from the previous problem actually sent out the same pattern of 6699 signals over the course of 2715 Earth days instead of 87 days, how many signals does it now send daily?

Gemma 2B:

To determine how many signals the alien spaceship sends daily over 2715 Earth days, we need to divide the total number of signals by the number of days.

Total number of signals: 6699
Number of days: 2715

We perform the division:

\[ \frac{6699}{2715} \]

First, let's simplify the fraction by finding the greatest common divisor (GCD) of 6699 and 2715. We can use the Euclidean algorithm to find the GCD.

1. Divide 6699 by 2715 and find the remainder:
   \[ 6699 \div 2715 \approx 2 \]
   \[ 6699 - (2715 \times 2) = 6699 - 5430 = 1269 \]

2. Now, divide 2715 by 1269 and find the remainder:
   \[ 2715 \div 1269 \approx 2 \]
   \[ 2715 - (1269 \times 2) = 2715 - 2538 = 177 \]

3. Next, divide 1269 by 177 and find the remainder:
   \[ 1269 \div 177 \approx 7 \]
   \[ 1269 - (177 \times 7) = 1269 - 1239 = 30 \]

4. Now, divide 177 by 30 and find the remainder:
   \[ 177 \div 30 \approx 5 \]
   \[ 177 - (30 \times 5) = 177 - 150 = 27 \]

5. Next, divide 30 by 27 and find the remainder:
   \[ 30 \div 27 \approx 1 \]
   \[ 30 - (27 \times 1) = 30 - 27 = 3 \]

6. Finally, divide 27 by 3 and find the remainder:
   \[ 27 \div 3 \approx 9 \]
   \[ 27 - (3 \times 9) = 27 - 27 = 0 \]

The GCD of 6699 and 2715 is 3.

Now, we simplify the fraction:

\[ \frac{6699 \div 3}{2715 \div 3} = \frac{2233}{905} \]

Next, we perform the division:

\[ 2233 \div 905 \approx 2.467 \]

So, the spaceship sends approximately 2.467 signals daily.

### Answer: 2.467

Expected answer: 2233/905

Correct? No

๐Ÿ”— Problem

Problem: A water tank contains 2016 liters of water. It is designed to provide enough water for 28 days without replenishment. How much water does the tank provide per day?

Gemma 2B:

To determine how much water the tank provides per day, we need to divide the total amount of water by the number of days it is designed to last.

Given:
- Total water in the tank = 2016 liters
- Number of days = 28 days

We perform the division:

\[ \text{Water per day} = \frac{2016 \text{ liters}}{28 \text{ days}} \]

Now, we calculate:

\[ \frac{2016}{28} = 72 \]

So, the tank provides 72 liters of water per day.

### Answer: 72 liters per day

Expected answer: 72

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering the water tank from the previous problem, suppose it was filled with 8329 liters of water instead of 2016 liters. Without changing the duration of usage, how much water would the tank provide per day now?

Gemma 2B:

To determine how much water the tank provides per day with the new amount of water, we need to divide the new total amount of water by the same number of days (28 days).

Given:
- New total water in the tank = 8329 liters
- Number of days = 28 days

We perform the division:

\[ \text{Water per day} = \frac{8329 \text{ liters}}{28 \text{ days}} \]

Now, we calculate:

\[ \frac{8329}{28} \approx 297.4643 \]

Rounding to the nearest whole number, the tank provides approximately 297 liters of water per day.

### Answer: 297 liters per day

Expected answer: 8329/28

Correct? No

๐Ÿ”— Problem

Problem: A toy company produced 4686 stuffed animals which were evenly distributed among 66 stores. If each store received the same number of stuffed toys, how many stuffed animals did each store receive?

Gemma 2B:

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

Given:
- Total number of stuffed animals = 4686
- Number of stores = 66

We perform the division:

\[ \frac{4686}{66} \]

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

1. Divide 4686 by 66:
\[ 4686 \div 66 = 71 \]

So, each store received 71 stuffed animals.

### Answer: 71

Expected answer: 71

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now, imagine if the toy company had to distribute the same 4686 stuffed animals among 1023 stores instead of 66. If they still had to distribute them evenly, how many stuffed animals would each store receive now?

Gemma 2B:

To determine how many stuffed animals each store would receive if the 4686 stuffed animals were distributed among 1023 stores, we need to divide the total number of stuffed animals by the number of stores.

Given:
- Total number of stuffed animals = 4686
- Number of stores = 1023

We perform the division:

\[ \frac{4686}{1023} \]

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

1. Divide 4686 by 1023:
\[ 4686 \div 1023 \approx 4.58 \]

Since we are distributing whole stuffed animals, each store would receive 4 stuffed animals, and there would be some remainder.

To find the exact number of stuffed animals each store receives without considering the remainder:
\[ 4686 \div 1023 = 4 \]

### Answer: 4

Expected answer: 142/31

Correct? No

๐Ÿ”— Problem

Problem: A toy car company has 910 toy cars ready for selling and they want to pack them in boxes of 10. How many boxes will they need to pack all the toy cars?

Gemma 2B:

To determine how many boxes are needed to pack all the toy cars, we need to divide the total number of toy cars by the number of toy cars that can fit in each box.

Given:
- Total number of toy cars = 910
- Number of toy cars per box = 10

We perform the division:
\[ \frac{910}{10} = 91 \]

So, the company will need 91 boxes to pack all the toy cars.

### Answer: 91

Expected answer: 91

Correct? Yes

๐Ÿ”— Follow-up

Problem: The toy car company now decides to package the 910 toy cars in larger boxes that can hold 538 cars each. How many boxes will they need now to pack all the toy cars?

Gemma 2B:

To determine how many larger boxes are needed to pack all the toy cars, we need to divide the total number of toy cars by the number of toy cars that can fit in each larger box and then round up to the nearest whole number since any remaining cars will still require a box.

Given:
- Total number of toy cars = 910
- Number of toy cars per larger box = 538

We perform the division:
\[ \frac{910}{538} \approx 1.691 \]

Since we cannot have a fraction of a box, we round up to the nearest whole number:
\[ \lceil 1.691 \rceil = 2 \]

So, the company will need 2 larger boxes to pack all the toy cars.

### Answer: 2

Expected answer: 455/269

Correct? No

๐Ÿ”— Problem

Problem: A juice factory produces 1333 bottles of juice and packs them evenly into 43 boxes. How many bottles of juice are there in each box?

Gemma 2B:

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

\[
\text{Number of bottles per box} = \frac{1333}{43}
\]

Performing the division:

\[
1333 \div 43 \approx 31
\]

To verify, we can multiply 31 by 43:

\[
31 \times 43 = 1333
\]

Thus, each box contains exactly 31 bottles of juice.

### Answer: 31

Expected answer: 31

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the juice factory decides to make less juice and only produces 423 bottles instead, still distributed evenly across the 43 boxes, how many bottles of juice would now be in each box?

Gemma 2B:

To determine how many bottles of juice are in each box when the factory produces 423 bottles and distributes them evenly across 43 boxes, we need to divide the total number of bottles by the number of boxes.

\[
\text{Number of bottles per box} = \frac{423}{43}
\]

Performing the division:

\[
423 \div 43 = 9.8372 \approx 9
\]

Since we are distributing bottles evenly, we need to consider the integer part of the division. Therefore, each box will contain 9 bottles of juice, with some bottles left over.

To verify, we can multiply 9 by 43:

\[
9 \times 43 = 387
\]

This means 387 bottles are evenly distributed, and the remainder is:

\[
423 - 387 = 36
\]

So, each box will contain 9 bottles, and there will be 36 bottles left over.

### Answer: 9

Expected answer: 423/43

Correct? No

๐Ÿ”— Problem

Problem: A generous benefactor donated 741 gifts to a local charity. These gifts were evenly divided between 13 shelters. How many gifts did each shelter receive?

Gemma 2B:

To determine how many gifts each shelter received, we need to divide the total number of gifts by the number of shelters.

\[ \text{Total gifts} = 741 \]
\[ \text{Number of shelters} = 13 \]

We perform the division:

\[ 741 \div 13 \]

First, we see how many times 13 fits into 74 (the first two digits of 741):

\[ 74 \div 13 \approx 5 \]

So, 13 goes into 74 approximately 5 times. We multiply to check:

\[ 13 \times 5 = 65 \]

Subtract 65 from 74:

\[ 74 - 65 = 9 \]

Now, bring down the next digit (1) to get 91. Next, we see how many times 13 fits into 91:

\[ 91 \div 13 \approx 7 \]

So, 13 goes into 91 approximately 7 times. We multiply to check:

\[ 13 \times 7 = 91 \]

Subtract 91 from 91:

\[ 91 - 91 = 0 \]

Thus, the division is exact, and each shelter receives:

\[ 741 \div 13 = 57 \]

### Answer: 57

Expected answer: 57

Correct? Yes

๐Ÿ”— Follow-up

Problem: The benefactor decided to be even more generous and increased the number of gifts to 3697. If these additional gifts were also evenly divided between the 13 shelters, then how many gifts did each shelter receive now?

Gemma 2B:

To determine how many gifts each shelter received after the increase, we need to divide the new total number of gifts by the number of shelters.

\[ \text{Total gifts} = 3697 \]
\[ \text{Number of shelters} = 13 \]

We perform the division:

\[ 3697 \div 13 \]

First, we see how many times 13 fits into 36 (the first two digits of 3697):

\[ 36 \div 13 \approx 2 \]

So, 13 goes into 36 approximately 2 times. We multiply to check:

\[ 13 \times 2 = 26 \]

Subtract 26 from 36:

\[ 36 - 26 = 10 \]

Now, bring down the next digit (9) to get 109. Next, we see how many times 13 fits into 109:

\[ 109 \div 13 \approx 8 \]

So, 13 goes into 109 approximately 8 times. We multiply to check:

\[ 13 \times 8 = 104 \]

Subtract 104 from 109:

\[ 109 - 104 = 5 \]

Now, bring down the next digit (7) to get 57. Next, we see how many times 13 fits into 57:

\[ 57 \div 13 \approx 4 \]

So, 13 goes into 57 approximately 4 times. We multiply to check:

\[ 13 \times 4 = 52 \]

Subtract 52 from 57:

\[ 57 - 52 = 5 \]

Thus, the division is not exact, and we have a remainder. Each shelter receives:

\[ 3697 \div 13 = 284 \text{ with a remainder of } 5 \]

### Answer: 284

Expected answer: 3697/13

Correct? No

๐Ÿ”— Problem

Problem: A child makes a giant snowball with a volume of 528 cubic feet. The child uses the same amount of snow to make each of 16 smaller snowballs. What is the volume of each smaller snowball in cubic feet?

Gemma 2B:

To find the volume of each smaller snowball, we need to divide the total volume of the giant snowball by the number of smaller snowballs.

The total volume of the giant snowball is 528 cubic feet, and there are 16 smaller snowballs.

We perform the division:
\[ \frac{528 \text{ cubic feet}}{16} = 33 \text{ cubic feet} \]

So, the volume of each smaller snowball is 33 cubic feet.

### Answer: 33 cubic feet

Expected answer: 33

Correct? Yes

๐Ÿ”— Follow-up

Problem: If the child decided to make a different giant snowball, this time using a total of 3327 cubic feet of snow, and again divides it to make 16 smaller snowballs, what would be the volume of each smaller snowball in cubic feet?

Gemma 2B:

To find the volume of each smaller snowball, we need to divide the total volume of the new giant snowball by the number of smaller snowballs.

The total volume of the new giant snowball is 3327 cubic feet, and there are 16 smaller snowballs.

We perform the division:
\[ \frac{3327 \text{ cubic feet}}{16} = 207.9375 \text{ cubic feet} \]

So, the volume of each smaller snowball is 207.9375 cubic feet.

### Answer: 207.9375 cubic feet

Expected answer: 3327/16

Correct? No

๐Ÿ”— Problem

Problem: A slide is 728 inches long and has evenly spaced waves every 56 inches. How many waves are there on the slide?

Gemma 2B:

To determine the number of waves on the slide, we need to divide the total length of the slide by the length of each wave.

Given:
- Total length of the slide = 728 inches
- Length of each wave = 56 inches

We perform the division:
\[ \frac{728 \text{ inches}}{56 \text{ inches/wave}} \]

First, we simplify the division:
\[ 728 \div 56 \]

To make the division easier, we can use long division:

1. 56 goes into 72 once (1 time), because \( 56 \times 1 = 56 \).
2. Subtract 56 from 72 to get 16.
3. Bring down the next digit, which is 8, making it 168.
4. 56 goes into 168 exactly three times (3 times), because \( 56 \times 3 = 168 \).

So, the division is:
\[ 728 \div 56 = 13 \]

Therefore, there are 13 waves on the slide.

### Answer: 13

Expected answer: 13

Correct? Yes

๐Ÿ”— Follow-up

Problem: The slide in the amusement park is being redesigned, and its new length is 3769 inches. The waves are still placed every 56 inches. How many waves will the redesigned slide have now?

Gemma 2B:

To determine the number of waves on the redesigned slide, we need to divide the total length of the slide by the length of each wave.

Given:
- Total length of the redesigned slide = 3769 inches
- Length of each wave = 56 inches

We perform the division:
\[ \frac{3769 \text{ inches}}{56 \text{ inches/wave}} \]

First, we simplify the division:
\[ 3769 \div 56 \]

To make the division easier, we can use long division:

1. 56 goes into 376 six times (6 times), because \( 56 \times 6 = 336 \).
2. Subtract 336 from 376 to get 40.
3. Bring down the next digit, which is 9, making it 409.
4. 56 goes into 409 seven times (7 times), because \( 56 \times 7 = 392 \).
5. Subtract 392 from 409 to get 17.

So, the division is:
\[ 3769 \div 56 = 67 \text{ remainder } 17 \]

Since we are only interested in the number of complete waves, we ignore the remainder.

Therefore, the number of waves on the redesigned slide is 67.

### Answer: 67

Expected answer: 3769/56

Correct? No