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Gemma 2B on 6.NS.B.2

Common Core Standard 6.NS.B.2

This standard covers the following:

Fluently divide multi-digit numbers using the standard algorithm.

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many seconds it takes to fill the ball, we divide the total volume of air needed by the rate at which the ball is filled.
73841 cubic centimeters / 41 cubic centimeters per second = <<73841/41=1801>>1801 seconds
### Answer: 1801 seconds

Expected answer: 1801

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many seconds it takes to fill the smaller ball, we divide the volume of air needed by the rate at which the ball is filled.
1310 cubic centimeters / 41 cubic centimeters per second = <<1310/41=32>>32 seconds
### Answer: 32 seconds

Expected answer: 1310/41

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the amount of juice in each container, we need to divide the total amount of juice by the number of containers.
Juice in each container = Total juice / Number of containers
= 73528 liters / 707 containers
= 104.28 liters
### Answer: 104.28 liters

Expected answer: 104

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of pants each store received, we need to divide the total number of pants by the number of stores.
Each store received 87780/110 = <<87780/110=798>>798 pants.
### Answer: 798

Expected answer: 798

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the number of pants each store would have received, we need to divide the new total number of pants by the number of stores.
Each store would have received 4003/110 = <<4003/110=36.39090909090909>>36.39 (rounded to two decimal places) pants.
Since it is not possible to distribute a fraction of a pant, the factory would have to distribute whole pants.
### Answer: 36 pants (if the factory produced 4003 pants, each store would receive 36 pants, with 14 stores receiving an extra pant to distribute the total number of pants produced).

Expected answer: 4003/110

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many bundles Farmer Bob will have, we need to divide the total number of carrots by the number of carrots in each bundle.
Farmer Bob will have 71820/684 = <<71820/684=105>>105 bundles of carrots.
### Answer: 105

Expected answer: 105

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many bundles Farmer Bob will have, we need to divide the total number of carrots by the new number of carrots in each bundle.
Farmer Bob will have 71820/2486 = <<71820/2486=29>>29 bundles of carrots.
### Answer: 29

Expected answer: 35910/1243

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The usage rate of the slide is constant over the 54 days. So, we can find the number of times the slide has been used per day by dividing the total number of times the slide has been used by the number of days.
Slide usage per day = Total usage / Number of days
= 85860 / 54
= 1590 times
### Answer: 1590 times

Expected answer: 1590

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The usage rate of the slide is constant over the 54 days. So, we can find the number of times the slide has been used per day by dividing the total number of times the slide has been used by the number of days.
Slide usage per day = Total usage / Number of days
= 9018 / 54
= 167 times
### Answer: 167 times 

(Note: The usage rate in this question is different from the previous question.)

Expected answer: 167

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The ski resort receives 31950/225 = <<31950/225=142.08>>142.08 inches of snowfall each day.
### Answer: 142.08 inches

Expected answer: 142

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many grams of gold will be in each ring, we need to divide the total amount of gold by the number of rings.
63802 grams / 38 rings = <<63802/38=1679>>1679 grams of gold per ring.
### Answer: 1679 grams

Expected answer: 1679

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many grams of gold will be in each ring, we need to divide the new total amount of gold by the number of rings.
5240 grams / 38 rings = <<5240/38=138>>138 grams of gold per ring.
### Answer: 138 grams 

(Note: This answer is different from the previous one because the jewelry manufacturer now has less gold available.)

Expected answer: 2620/19

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many full rings the goldsmith can make, we need to divide the total amount of gold by the amount of gold required for each ring.
60544 / 5504 = <<60544/5504=11>>11
### Answer: The goldsmith can make 11 full rings.

Expected answer: 11

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

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

The average number of animals in each cage is 10489/617 = <<10489/617=17>>17 animals.
### Answer: 17 animals

Expected answer: 17

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

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

The average number of animals in each cage is 10489/5130 = <<10489/5130=2.04>>2.04 animals.
### Answer: 2.04 animals 

(Note: This answer is rounded to two decimal places.)

Expected answer: 10489/5130

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The farmer wants to distribute 21652 grams of carrots into 5413 bags. To find out how many grams of carrots will be in each bag, we need to divide the total weight of carrots by the number of bags.
21652 grams / 5413 bags = <<21652/5413=4.00>>4.00 grams of carrots per bag.
### Answer: 4.00 grams

Expected answer: 4

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The farmer now has 5652 grams of carrots and wants to distribute them into 5413 bags. To find out how many grams of carrots will be in each bag, we need to divide the new total weight of carrots by the number of bags.
5652 grams / 5413 bags = <<5652/5413=1.044>>1.044 grams of carrots per bag.
### Answer: 1.044 grams 

(Note: The answer is approximate, as you cannot have a fraction of a gram in this scenario.)

Expected answer: 5652/5413

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The journey is divided into 5 equal stages, so the spaceship travels 38745/5 = <<38745/5=7749>>7749 miles in each stage.
### Answer: 7749 miles

Expected answer: 7749

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The spaceship now divides its total travel distance into 3113 equal stages, so it travels 38745/3113 = <<38745/3113=12.44>>12.44 miles in each stage.
### Answer: 12.44 miles 

(Note: This answer is rounded to two decimal places. In reality, the number of miles would be an exact value, not a rounded decimal.)

Expected answer: 38745/3113

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many liters each bottle contains, we need to divide the total amount of water by the number of bottles.
84,564 liters รท 261 bottles = <<84564/261=324>>324 liters per bottle.
### Answer: 324 liters

Expected answer: 324

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many liters each bottle contains, we need to divide the total amount of water by the number of bottles.
84,564 liters รท 1,779 bottles = <<84564/1779=47.49...>>47.49 liters per bottle (rounded to two decimal places).
### Answer: 47.49 liters (rounded to two decimal places)

Expected answer: 28188/593

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of pages in each volume, we divide the total number of pages by the number of volumes.
Pages per volume = Total pages / Number of volumes
= 13467 / 201
= 67
### Answer: 67 pages

Expected answer: 67

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The fireplace uses 56888 BTU of energy in 2188 hours.
To find out how many BTU of energy the fireplace uses per hour, we need to divide the total amount of energy used by the number of hours.
56888 BTU รท 2188 hours = <<56888/2188=25.986842105263157>>25.99 BTU per hour.
### Answer: 25.99 BTU of energy per hour

Expected answer: 26

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the amount of snowfall per day, we need to divide the total snowfall by the number of days.
Snowfall per day = Total snowfall / Number of days
= 36900 inches / 82 days
= 450 inches per day
### Answer: 450 inches

Expected answer: 450

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the amount of snowfall per day, we need to divide the total snowfall by the number of days.
Snowfall per day = Total snowfall / Number of days
= 36900 inches / 7138 days
= 5.17 inches per day
### Answer: 5.17 inches 

(Note: The answer is given as a decimal, which represents the average amount of snowfall per day over the course of the entire 7138-day period. The actual amount of snowfall on any given day during that period may have been more or less than 5.17 inches.)

Expected answer: 18450/3569

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the amount of space each giraffe gets, we need to divide the total area of the wildlife reserve by the number of giraffes.
71292 square kilometers / 2742 giraffes = <<71292/2742=26>>26 square kilometers per giraffe.
### Answer: Each giraffe gets 26 square kilometers of space.

Expected answer: 26

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the amount of space each giraffe gets, we need to divide the total area of the wildlife reserve by the number of giraffes.
71292 square kilometers / 8787 giraffes = <<71292/8787=8.12>>8.12 square kilometers per giraffe.
### Answer: If the wildlife reserve held 8787 giraffes, each giraffe would get 8.12 square kilometers of space.

Expected answer: 23764/2929

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The number of lions saved each year is equal to the total number of lions saved divided by the number of years.
So, the number of lions saved per year on average is 96187 / 13 = <<96187/13=7400>>7400 lions.
### Answer: 7400 lions

Expected answer: 7399

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many pearls each mermaid friend will receive, we need to divide the total number of pearls by the number of mermaid friends.
Pearls per friend = Total pearls / Number of mermaid friends
= 32812 / 631
= 52  (rounded down)
### Answer: Each mermaid friend will receive 52 pearls.

Expected answer: 52

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many pearls each mermaid friend will receive, we need to divide the total number of pearls by the number of mermaid friends.
Pearls per friend = Total pearls / Number of mermaid friends
= 32812 / 4198
= 7.82 (rounded to 2 decimal places)

Since the number of pearls must be a whole number, we can see that the mermaid cannot divide the pearls evenly among her 4198 friends.
### Answer: It is not possible to divide the 32812 pearls evenly among 4198 mermaid friends.

Expected answer: 16406/2099

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The farm produces 36,784/19 = <<36784/1

Expected answer: 1936

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the distance the train covers in a day, we need to divide the total distance by the number of days.
The train covers 63245 miles / 695 days = <<63245/695=91>>91 miles in a day.
### Answer: 91 miles.

Expected answer: 91

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the distance the train covers in a day, we need to divide the new total distance by the number of days.
The train covers 6280 miles / 695 days = <<6280/695=9>>9 miles in a day.
### Answer: 9 miles.

Expected answer: 1256/139

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The factory produced 41772/708 = <<41772/708=58.9>>58.9 dolls per day.
Since it's not possible to produce a fraction of a doll, we can say that the factory produced approximately 59 dolls per day, on average.
### Answer: 59 dolls/day

Expected answer: 59

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: If the factory produced 41772 dolls over 4664 days, then the daily production rate would be 41772/4664 = <<41772/4664=8.95>>8.95 dolls per day.
In this case, the factory would produce approximately 9 dolls per day, on average.
### Answer: 9 dolls/day 

(Note: The answer is different from the previous question because the factory is now producing dolls over a longer period of time.)

Expected answer: 10443/1166

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The drummer needs to hit the drum 61019/7 = <<61019/7=8717.0>>8717.0 times each day to meet his goal.
Since the drummer cannot hit the drum a fraction of a time, we round this number to the nearest whole number.
### Answer: 8717 times

Expected answer: 8717

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The drummer now needs to hit the drum 7454/7 = <<7454/7=1064.86>>1064.86 times each day to meet his new goal.
Since the drummer cannot hit the drum a fraction of a time, we round this number to the nearest whole number.
### Answer: 1065 times 

(Note: I rounded up because hitting the drum 1064 times would be less than the goal of 7454 hits in 7 days.)

Expected answer: 7454/7

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the distance the dolphin swims in an hour, we need to divide the total distance by the number of hours.
The dolphin can swim 98816/128 = <<98816/128=775>>775 meters in an hour.
### Answer: 775 meters

Expected answer: 772

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the average number of streams per day, we need to divide the total number of streams by the number of days.
The song was streamed 71532 times in 1987 days.
So, the average number of streams per day is 71532/1987 = <<71532/1987=35.954535954535956>>35.95 streams per day.
### Answer: 35.95 streams per day

Expected answer: 36

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many compasses each store will receive, we need to divide the total number of compasses by the number of stores.
Compasses per store = Total compasses / Number of stores
= 33046 / 1066
= 31.06
Since the number of compasses must be a whole number, we can conclude that the salesman cannot distribute the compasses equally among the stores.
### Answer: The compasses cannot be distributed equally among the stores.

Expected answer: 31

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of carrots each plot yielded, we divide the total number of carrots by the number of plots.
Carrots per plot = Total carrots / Number of plots
= 49822 / 58
= 859
### Answer: 859 carrots were yielded by each plot.

Expected answer: 859

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the number of carrots each plot yielded, we divide the total number of carrots by the number of plots.
Carrots per plot = Total carrots / Number of plots
= 9653 / 58
= 166
### Answer: 166 carrots were yielded by each plot this time.

Expected answer: 9653/58

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The revealed area is the same size as the original cloud, which is 8744 square meters.
The ratio of the revealed area to the original area is therefore 8744/8744 = <<8744/8744=1>>1.
### Answer: 1:1 or simply 1

Expected answer: 1

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many meters the scooter travels per hour, we need to divide the total distance traveled by the battery life.
97506 meters รท 18 hours = <<97506/18=5417>>5417 meters per hour.
### Answer: 5417 meters

Expected answer: 5417

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many meters the scooter travels per hour with a total distance of 7727 meters, we need to divide the new total distance traveled by the battery life.
7727 meters รท 18 hours = <<7727/18=430>>430 meters per hour.
### Answer: 430 meters 

(Note: The answer is given to the nearest whole number, as the number of meters traveled per hour is a whole number.)

Expected answer: 7727/18

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The star emits the same amount of light energy every hour. So, to find the amount of light energy emitted every hour, we can divide the total light energy emitted over the period by the number of hours in that period.
The star emits 94548/7879 = <<94548/7879=12>>12 units of light energy every hour.
### Answer: 12

Expected answer: 12

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The star emits the same amount of light energy every hour. So, to find the amount of light energy emitted every hour, we can divide the total light energy emitted over the period by the number of hours in that period.
The star emits 94548/3349 = <<94548/3349=28.25>>28.25 units of light energy every hour.
### Answer: 28.25 
(Note: The answer is expressed as a decimal number, but the actual amount of light energy emitted is still measured in whole units. This means that the star emits 28 units of light energy every hour, and emits the remaining 0.25 units of light energy by emitting slightly more light in some hours than in others.)

Expected answer: 94548/3349

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of trees in each section, we need to divide the total number of trees by the number of sections.
The number of trees in each section is 80752/412 = <<80752/412=195.762557058>>195.76 trees (rounded to two decimal places).
### Answer: 195.76 trees

Expected answer: 196

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of cucumbers harvested each day, we divide the total number of cucumbers harvested by the number of days.
44280 cucumbers รท 216 days = <<44280/216=205>>205 cucumbers per day.
### Answer: 205 cucumbers were harvested each day.

Expected answer: 205

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the number of cucumbers harvested each day with the new quantity, we divide the new total number of cucumbers harvested by the number of days.
4076 cucumbers รท 216 days = <<4076/216=18.89>>18.89 cucumbers per day.
However, since we cannot have a fraction of a cucumber, we round it to the nearest whole number.
### Answer: 19 cucumbers were harvested each day with the new quantity.

Expected answer: 1019/54

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of cookies in each package, we need to divide the total number of cookies by the number of packages.
### Answer: 77545/1193 = 65 cookies per package.

Expected answer: 65

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the number of cookies in each package, we need to divide the total number of cookies by the number of packages.
### Answer: 77545/1834 = 42 cookies per package.

Expected answer: 77545/1834

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: First, we need to find out how much light energy the star emits every second. We do this by dividing the total light energy emitted in 125 seconds by 125.
51750 / 125 = <<51750/125=414>>414 units of light energy per second.
### Answer: 414 units of light energy per second.

Expected answer: 414

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how much light energy the star emits every second, we divide the total light energy emitted in 8670 seconds by 8670.
51750 / 8670 โ‰ˆ <<51750/8670=5.96>>5.96 units of light energy per second.
### Answer: Approximately 5.96 units of light energy per second.

Expected answer: 1725/289

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The factory produced 25144/56 = <<25144/56=450>>450 candies per day.
### Answer: 450 candies

Expected answer: 449

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many loaves of bread are needed, we need to divide the total number of slices by the number of slices per loaf:
34240 slices / 10 slices per loaf = <<34240/10=3424>>3424 loaves
### Answer: 3424 loaves

Expected answer: 3424

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many loaves of bread are needed, we need to divide the total number of slices by the number of slices per loaf:
7638 slices / 10 slices per loaf = <<7638/10=763.8>>763.8 loaves
Since you can't have a fraction of a loaf, you'll need to round up to the nearest whole number.
### Answer: 764 loaves

Expected answer: 3819/5

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: If each day has the same number of new trees sprouting, then the total number of trees sprouted is the number of days times the number of trees that sprout each day.
Let x be the number of trees that sprout each day. Then, 119*x = 20111.
Solving for x, x = 20111/119 = 168.
### Answer: 168 trees sprout each day.

Expected answer: 169

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The number of cans distributed per week is equal to the total number of cans divided by the number of weeks.
So, 91,104 cans / 52 weeks = <<91104/52=1752>>1752 cans per week.
### Answer: 1752 cans

Expected answer: 1752

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The number of cans of the different brand distributed per week is equal to the total number of cans divided by the number of weeks.
So, 5,981 cans / 52 weeks = <<5981/52=115>>115 cans per week.
### Answer: 115 cans 

(Note: The distribution of cans for the two brands are independent of each other, so the distribution of the second brand is calculated separately.)

Expected answer: 5981/52

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The company uses 19944/18 = <<19944/1

Expected answer: 1108

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the average number of potatoes produced by each plant, we need to divide the total number of potatoes by the total number of plants.
### Answer: 45764/2692 = 17 
(rounded to the nearest whole number) plants produce an average of 17 potatoes.

Expected answer: 17

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the new average number of potatoes produced by each plant, we need to divide the new total number of potatoes by the total number of plants.
### Answer: 7664/2692 = 2.85 
(rounded to two decimal places) plants produce an average of 2.85 potatoes.

Expected answer: 1916/673

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The factory produced 85560/713 = <<85560/713=120>>120 marshmallows per hour.
### Answer: 120 marshmallows/hour

Expected answer: 120

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The factory produced 85560/7544 = <<85560/7544=11.34>>11.34 marshmallows per hour during this period. However, since the factory cannot produce a fraction of a marshmallow, we can conclude that the factory produced 11 marshmallows per hour during this period.
### Answer: 11 marshmallows/hour 

(Note: The factory cannot produce a fraction of a marshmallow, so the actual hourly production rate would be rounded down to the nearest whole number.)

Expected answer: 465/41

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of plots, we need to divide the total area by the area of each plot.
Number of plots = Total area / Area of each plot
= 49,928 square meters / 6,241 square meters
= 8 plots
### Answer: 8 plots

Expected answer: 8

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the number of plots, we need to divide the total area by the area of each plot.
Number of plots = Total area / Area of each plot
= 49,928 square meters / 23 square meters
= 2,166.43 plots

Since the number of plots must be a whole number, the farmer cannot subdivide the area into plots of 23 square meters.
### Answer: The farmer cannot subdivide the area into plots of 23 square meters.

Expected answer: 49928/23

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The baker used 62118/2142 = <<62118/2142=29>>29 grams of flour to make cookies each day.
### Answer: 29 grams

Expected answer: 29

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: With the correction, the baker used 62118/2755 = <<62118/2755=22.55>>22.55 grams of flour to make cookies each day.
### Answer: 22.55 grams 

(Note: The answer is an approximation, as the actual amount of flour used each day is a different value for each day.)

Expected answer: 2142/95

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The shoemaker distributes 91100 centimeters of shoelaces among 3644 pairs of shoes. Therefore, each pair gets 91100/3644 = <<91100/3644=25>>25 centimeters of shoelace.
### Answer: 25 centimeters

Expected answer: 25

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: If the shoemaker had 9498 pairs of shoes, then each pair would get 91100/9498 = <<91100/9498=9.6>>9.6 centimeters of shoelace.
### Answer: 9.6 centimeters 

(Note: This answer is slightly different from the previous one because the number of pairs of shoes has changed.)

Expected answer: 45550/4749

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The farmer distributes 505 bushels of apples into 5 bins. Therefore, each bin contains 505/5 = <<505/5=101>>101 bushels of apples.
### Answer: 101 bushels

Expected answer: 101

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The farmer distributes 7798 bushels of apples into 5 bins. Therefore, each bin contains 7798/5 = <<7798/5=1559.6>>1559.6 bushels of apples. However, since we cannot have a fraction of a bushel, we must round the number of bushels to the nearest whole number.
### Answer: 1560 bushels (when rounding to the nearest whole number)

Expected answer: 7798/5

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of confetti pieces per square foot, we need to divide the total number of confetti pieces by the total area.
Number of confetti pieces per square foot = Total number of confetti pieces / Total area
= 65325 / 5025
= 13.005 

Expected answer: 13

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of crayons in each box, we need to divide the total number of crayons by the number of boxes.
Number of crayons in each box = Total number of crayons / Number of boxes
= 26691 crayons / 123 boxes
= 217 crayons (rounded to the nearest whole number)
### Answer: 217 crayons

Expected answer: 217

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the number of crayons in each box, we need to divide the total number of crayons by the number of boxes.
Number of crayons in each box = Total number of crayons / Number of boxes
= 4521 crayons / 123 boxes
= 36.76 crayons (rounded to two decimal places)
Since it is not possible to have a fraction of a crayon, we can say that the number of crayons in each box would not be evenly distributed in this scenario.
### Answer: It is not possible to evenly distribute 4521 crayons into 123 boxes.

Expected answer: 1507/41

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The firefighter unit extinguished 45843/413 = <<45843/413=110.995>>110.995 fires per week.
Since the number of fires extinguished must be a whole number, we can conclude that the firefighter unit extinguished 111 fires per week.
### Answer: 111

Expected answer: 111

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The firefighter unit extinguished 45843/4913 = <<45843/4913=9.32>>9.32 fires per week.
Since the number of fires extinguished must be a whole number, there is a contradiction in the scenario. It is not possible for the firefighter unit to extinguish the same number of fires each week for 4913 weeks and end up with a total of 45843 fires.
### Answer: It is not possible for the firefighter unit to extinguish the same number of fires each week for 4913 weeks and end up with a total of 45843 fires.

Expected answer: 45843/4913

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the area of each section, we need to divide the total area of the park by the number of sections.
The area of each section = The total area of the park / The number of sections
The area of each section = 57546 square meters / 9591 sections
The area of each section = <<57546/9591=6>>6 square meters.
### Answer: 6 square meters.

Expected answer: 6

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the area of each section, we need to divide the total area of the park by the number of sections.
The area of each section = The total area of the park / The number of sections
The area of each section = 57546 square meters / 131 sections
The area of each section = <<57546/131=439.3588235294118>>439.36 square meters (rounded to two decimal places).
### Answer: 439.36 square meters.

Expected answer: 57546/131

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: If 4938 boxes of raw materials can produce 93822 tubes of toothpaste, then one box of raw materials can produce 93822/4938 = <<93822/4938=19>>19 tubes of toothpaste.
### Answer: 19

Expected answer: 19

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: If 4938 boxes of raw materials can produce 9206 tubes of toothpaste, then one box of raw materials can produce 9206/4938 = <<9206/4

Expected answer: 4603/2469

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The Jungle gym is used by 40740/84 = <<40740/84=487.5>>487.5 children each day.
However, since the number of children must be a whole number, we need to consider that the given number of children using the Jungle gym each day is an average.
Therefore, the actual number of children using the Jungle gym each day is 487 or 488.
### Answer: 487 or 488 children use the Jungle gym each day.

Expected answer: 485

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many cubic centimeters of snow are used for each snowman, we divide the total amount of snow used by the number of snowmen.
39482 cc / 38 = <<39482/38=1039>>1039 cc
### Answer: 1039 cc of snow are used for each snowman.

Expected answer: 1039

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the previous snowman competition, suppose that the organizers used only 5895 cc (cubic centimeters) of snow to make the same 38 identical snowmen. How many cubic centimeters of snow would be used for each snowman in this scenario?

Gemma 2B:

 Reasoning: To find out how many cubic centimeters of snow are used for each snowman in this scenario, we divide the new total amount of snow used by the number of snowmen.
5895 cc / 38 = <<5895/38=155.13157894736842>>155.13 cc
Since the amount of snow used must be a whole number, it is not possible to make 38 identical snowmen using 5895 cc of snow.
### Answer: It is not possible to make 38 identical snowmen using 5895 cc of snow.

Expected answer: 5895/38

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the area of each smaller square, we need to divide the total area of the window by the number of smaller squares.
The area of the window is 67673 square inches.
The number of smaller squares is 1147.
So, the area of each smaller square is 67673/1147 = <<67673/1147=59>>59 square inches.
### Answer: 59 square inches

Expected answer: 59

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the area of each smaller square, we need to divide the total area of the window by the number of smaller squares.
The area of the window is now 7562 square inches.
The number of smaller squares remains 1147.
So, the area of each smaller square is 7562/1147 = <<7562/1147=6.6>>6.6 square inches.
However, since the smaller squares must have a whole number area, it is not possible to divide the window into 1147 smaller squares with the given dimensions.
### Answer: It is not possible to divide the window into 1147 smaller squares with the given dimensions.

Expected answer: 7562/1147

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many oranges each tree produces, we need to divide the total number of oranges by the number of trees.
Oranges per tree = Total oranges / Number of trees
= 49,920 oranges / 195 trees
= 256 oranges
### Answer: 256 oranges

Expected answer: 256

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many oranges each of the selected trees produces, we need to divide the total number of oranges by the number of the selected trees.
Oranges per tree = Total oranges / Number of trees
= 49,920 oranges / 9,289 trees
= 5.39 oranges
Since oranges cannot be divided into fractions, we can assume that the farmer will distribute 5 oranges to each of the 9,289 trees and have 49,920 - (5 x 9,289) = 41 oranges left over.
### Answer: 5 oranges (with 41 oranges left over)

Expected answer: 49920/9289

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The total number of children who had a sandwich for lunch is 34160.
The total number of schools is 4270.
Since every school has an equal number of children, we divide the total number of children who had a sandwich for lunch by the total number of schools to find the number of children in each school who had a sandwich for lunch.
34160 / 4270 = <<34160/4270=8.014084507042253>>8.01 children per school had a sandwich for lunch.
However, the number of children must be a whole number, so we round it to the nearest whole number.
### Answer: 8 children in each school had a sandwich for lunch.

Expected answer: 8

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The total number of children who had a sandwich for lunch is still 34160.
The total number of schools is now 7823.
Since every school has an equal number of children, we divide the total number of children who had a sandwich for lunch by the total number of schools to find the number of children in each school who had a sandwich for lunch.
34160 / 7823 = <<34160/7823=4.362355746935641>>4.36 children per school had a sandwich for lunch.
However, the number of children must be a whole number, so we round it to the nearest whole number.
### Answer: 4 children in each school had a sandwich for lunch.

Expected answer: 34160/7823

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many times you can brush your teeth with this tube of toothpaste, you need to divide the total amount of toothpaste by the amount used per brushing.
3366 grams / 306 grams/brushing = <<3366/306=11>>11 brushing
### Answer: 11

Expected answer: 11

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many times you can brush your teeth with this tube of toothpaste, you need to divide the total amount of toothpaste by the amount used per brushing.
9060 grams / 306 grams/brushing = <<9060/306=29.61>>29.61 brushing
Since you can't brush your teeth a fraction of a time, you can only brush your teeth 29 times with this tube of toothpaste.
### Answer: 29 

It's important to note that the number of brushing is rounded down to the nearest whole number because you can't brush your teeth a fraction of a time.

Expected answer: 1510/51

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many towels are in each box, we need to divide the total number of towels by the number of boxes.
Towels per box = Total number of towels / Number of boxes
= 49742 towels / 1309 boxes
= 38.05 towels
However, since we cannot have a fraction of a towel in a box, we can conclude that there are 38 towels in each box and 5 towels were left over.
### Answer: 38 towels

Expected answer: 38

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many towels are in each box, we need to divide the total number of towels by the number of boxes.
Towels per box = Total number of towels / Number of boxes
= 8337 towels / 1309 boxes
= 6.37 towels
However, since we cannot have a fraction of a towel in a box, we can conclude that there are 6 towels in each box and 37 towels were left over.
### Answer: 6 towels 

(Note: The number of towels left over is different from the previous question because the total number of towels has changed.)

Expected answer: 1191/187

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The alien civilization sends the same number of messages each day. So, we divide the total number of messages by the number of days to find the number of messages sent per day.
Number of messages per day = Total number of messages / Number of days
= 43134 messages / 3318 days
= 13 messages per day
### Answer: 13

Expected answer: 13

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The alien civilization uses a different form of time measurement, where each of their "days" represents 8212 of our Earth days. So, we divide the total number of messages by the number of their "days" to find the number of messages sent per their "day".
Number of messages per their "day" = Total number of messages / Number of their "days"
= 43134 messages / (3318 Earth days / 8212)
= 43134 messages / 2655.576
= 16.23 messages per their "day"
Since they can't send a fraction of a message, we can say that they send approximately 16 messages per their "day".
### Answer: 16 
(Note: The exact number of messages sent per their "day" is 16.23, but since they can't send a fraction of a message, we can say that they send approximately 16 messages per their "day".)

Expected answer: 21567/4106

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of students per bus, we divide the total number of students by the number of buses.
Students per bus = Total students / Number of buses
= 80,011 / 31
= 2580.97 (rounded to two decimal places)

However, since the number of students must be a whole number, we can conclude that the school district has either miscounted the number of students or buses, or the students are not equally distributed.
### Answer: The number of students per bus is not provided since the numbers given do not result in an equal distribution of students.

Expected answer: 2581

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The store sold 54020/730 = <<54020/730=74>>74 cameras per day.
### Answer: 74 

(Note: This assumes that the number of cameras sold is constant each day, which is unlikely in reality but is consistent with the information provided in the problem.)

Expected answer: 74

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The store sold 54020/5546 = <<54020/5546=9.75>>9.75 cameras per day.
### Answer: 10 (rounded to the nearest whole number)

(Note: This assumes that the number of cameras sold is constant each day, which is unlikely in reality but is consistent with the information provided in the problem. Also, note that the answer is rounded to the nearest whole number, as it is not possible to sell a fraction of a camera.)

Expected answer: 27010/2773

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many liters of ice cream each container can accommodate, we need to divide the total amount of ice cream by the number of containers.
25774 liters / 526 containers = <<25774/526=49>>49 liters per container.
### Answer: 49 liters

Expected answer: 49

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many liters of ice cream each container can accommodate now, we need to divide the total amount of ice cream by the new number of containers.
25774 liters / 418 containers = <<25774/418=61.68>>61.68 liters per container.
### Answer: 61.68 liters 

(Note: This answer is approximate, as it is not possible to divide 25774 liters exactly among 418 containers.)

Expected answer: 12887/209

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the distance driven by each bus, we divide the total distance driven by the number of buses.

The calculation is: 85300 miles / 3412 buses = <<85300/3412=25>>25 miles per bus.
### Answer: 25 miles.

Expected answer: 25

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the distance driven by each bus, we divide the total distance driven by the number of buses.

The calculation is: 3940 miles / 3412 buses = <<3940/3412=1.157>>1.16 miles per bus (rounded to two decimal places).
### Answer: 1.16 miles.

Expected answer: 985/853

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the energy produced per hour, we need to divide the total energy produced by the number of hours.
Energy per hour = Total energy / Number of hours
= 92250 kilowatts / 75 hours
= 1230 kilowatts
### Answer: 1230 kilowatts/hour

Expected answer: 1230

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the energy produced per hour, we need to divide the total energy produced by the number of hours.
Energy per hour = Total energy / Number of hours
= 5837 kilowatts / 75 hours
= 77.8266666667 kilowatts
### Answer: 77.83 kilowatts/hour (rounded to two decimal places) 

(Note: I rounded the answer to two decimal places as is typical for this type of calculation, but the exact answer is 77.8266666667 kilowatts/hour.)

Expected answer: 5837/75

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the average daily weight gain, we need to divide the total weight gained by the number of days.
The baby gained 3734 grams in 1867 days.
So, the baby gained 3734/1867 = <<3734/1867=2.00>>2.00 grams per day on average.
### Answer: 2.00 grams

Expected answer: 2

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the average daily weight gain over a span of 1651 days, we need to divide the total weight gained by the number of days.
The baby gained 3734 grams in 1651 days.
So, the baby gained 3734/1651 = <<3734/1651=2.26>>2.26 grams per day on average.
### Answer: 2.26 grams 

(Note: The average daily weight gain has increased because the same total weight gain is spread over a shorter period of time.)

Expected answer: 3734/1651

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The hose releases 33,532/8,383 = <<33532/8383=4>>4 liters of water per minute.
### Answer: 4 liters of water are released per minute.

Expected answer: 4

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The hose releases 33,532/7,845 = <<33532/7845=4.26>>4.26 liters of water per minute.
### Answer: 4.26 liters of water are released per minute. 

(Note: The answer is an approximation, as the number of liters released per minute is not a whole number.)

Expected answer: 33532/7845

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The farmer collects 96,120/20 = <<96120/20=4806>>4,806 eggs from each chicken.
### Answer: 4,806 eggs

Expected answer: 4806

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: Each chicken contributes 96,120/9,046 = <<96120/9046=10.6344>>10.6344 eggs.
### Answer: 10.6344 eggs 
(Note: This answer is rounded to four decimal places. The actual number of eggs contributed by each chicken is an irrational number, and so it cannot be expressed exactly as a fraction or as a decimal number with a finite number of digits.)

Expected answer: 48060/4523

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the amount of rain each day, we divide the total amount of rain by the number of days.
Rain per day = Total rain / Number of days
Rain per day = 11458 mm / 17 days
Rain per day = 674 mm (rounded to the nearest whole number)
### Answer: 674 mm

Expected answer: 674

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the amount of rain each day, we divide the total amount of rain by the number of days.
Rain per day = Total rain / Number of days
Rain per day = 11458 mm / 8513 days
Rain per day = 1.34 mm (rounded to two decimal places)
### Answer: 1.34 mm

Expected answer: 11458/8513

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of pens produced per hour, we need to divide the total number of pens produced by the total number of hours.
The calculation is: 2526 pens / 842 hours = <<2526/842=3>>3 pens per hour.
### Answer: 3 pens per hour.

Expected answer: 3

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find the number of pens produced per hour, we need to divide the total number of pens produced by the total number of hours.
The calculation is: 2526 pens / 547 hours = <<2526/547=4.62>>4.62 pens per hour.
### Answer: 4.62 pens per hour.

Expected answer: 2526/547

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find out how many erasers each classroom gets, we need to divide the total number of erasers by the number of classrooms.
Each classroom gets 285/19 = <<285/19=15>>15 erasers.
### Answer: 15 

(Note: The answer is a whole number, so no eraser is left out or divided.)

Expected answer: 15

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: To find out how many erasers each classroom gets now, we need to divide the new total number of erasers by the number of classrooms.
Each classroom gets 4681/19 = <<4681/19=246.37>>246.37 erasers.
Since it's not possible to distribute a fraction of an eraser, the school needs to round the number of erasers each classroom gets.
### Answer: Each classroom gets 246 erasers or is given a few extra erasers to make the number a whole number.

Expected answer: 4681/19

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The penguin's speed is the distance it covers divided by the time it takes to cover that distance.
So, the penguin's speed is 41020/5 = <<41020/5=8204>>8204 feet per hour.
### Answer: 8204 feet per hour

Expected answer: 8204

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: The penguin's speed is the distance it covers divided by the time it takes to cover that distance.
So, the penguin's speed in this new scenario is 4325/5 = <<4325/5=865>>865 feet per hour.
### Answer: 865 feet per hour 

(Note: The penguin's speed changes with the distance it covers.)

Expected answer: 865

Correct? Yes

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: The reservoir is divided into 576 equal sections, so each section holds 63360/576 = <<63360/576=110>>110 gallons of water.
### Answer: 110 gallons

Expected answer: 110

Correct? Yes

๐Ÿ”— Follow-up

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

Gemma 2B:

 Reasoning: Each section holds 63360/9999 = <<63360/9999=6.34>>6.34 gallons of water. However, since the reservoir holds a whole number of gallons, it is not possible for the reservoir to be divided into 9999 equal sections with each section holding a whole number of gallons.
### Answer: It is not possible for the reservoir to be divided into 9999 equal sections with each section holding a whole number of gallons.

Expected answer: 640/101

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

 Reasoning: To find the number of skirts each store got, we divide the total number of skirts by the number of stores.
Number of skirts per store = Total number of skirts / Number of stores
= 21868 / 77
= 283
### Answer: 283 skirts

Expected answer: 284

Correct? No

๐Ÿ”— Problem

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

Gemma 2B:

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

Minutes of advertisements per day = Total minutes of advertisements / Number of days
= 56109 minutes / 59 days
= 951 minutes (rounded to the nearest whole number)

Therefore, on average, the TV channel broadcasts 951 minutes of advertisements each day.
### Answer: 951 minutes

Expected answer: 951

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the TV channel decided to reduce the total minutes of advertisements. Now, over a 59-day period, they only broadcast a total of 5352 minutes of advertisements. What is the new average of advertisement minutes shown each day?

Gemma 2B:

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

New minutes of advertisements per day = New total minutes of advertisements / Number of days
= 5352 minutes / 59 days
= 90.71 minutes (rounded to two decimal places)

Therefore, with the new total, the TV channel now broadcasts an average of approximately 90.71 minutes of advertisements each day.
### Answer: 90.71 minutes 

Note: The answer is rounded to two decimal places, but in practice, the actual average may be slightly different due to rounding.

Expected answer: 5352/59

Correct? No

๐Ÿ”— Problem

Problem: A teacher marks a total of 59748 marks distributed evenly over 1149 exam papers. How many marks are in each exam paper?

Gemma 2B:

 Reasoning: To find the number of marks in each exam paper, we divide the total number of marks by the number of exam papers.
Marks per paper = Total marks / Number of papers
= 59748 / 1149
= 52.14 (rounded to two decimal places)

However, it doesn't make sense to have a fraction of a mark on an exam paper, so the teacher must have made a mistake when calculating the average marks per paper. The total number of marks must be a multiple of the number of exam papers.

### Answer: It is not possible to determine the number of marks in each exam paper based on the given information.

Expected answer: 52

Correct? No

๐Ÿ”— Problem

Problem: A reservoir holds 44840 liters of water. If this water is equally distributed across 76 houses in a village, how many liters of water will each house get?

Gemma 2B:

 Reasoning: To find out how many liters of water each house gets, we need to divide the total amount of water by the number of houses.
Water per house = 44840 liters / 76 houses = <<44840/76=590>>590 liters per house.
### Answer: 590 liters

Expected answer: 590

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the reservoir now has 6614 houses to supply. If the reservoir still holds 44840 liters of water, how many liters can be distributed to each house?

Gemma 2B:

 Reasoning: To find out how many liters of water each house can get, we need to divide the total amount of water by the number of houses.
Water per house = 44840 liters / 6614 houses = <<44840/6614=6.78>>6.78 liters per house.
### Answer: 6.78 liters 
(Note: This answer is approximate, as the total amount of water is not enough to give every house an equal amount.)

Expected answer: 22420/3307

Correct? No

๐Ÿ”— Problem

Problem: A butterfly during its lifetime lay 5385 eggs, and she spread these eggs evenly across 359 flowers. How many eggs did she lay on each flower?

Gemma 2B:

 Reasoning: The butterfly lays 5385/359 = <<5385/359=15>>15 eggs on each flower.
### Answer: 15

Expected answer: 15

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose the butterfly had instead spread a total of 9710 eggs across the same 359 flowers. How many eggs did she lay on each flower in this case?

Gemma 2B:

 Reasoning: The butterfly lays 9710/359 = <<9710/3

Expected answer: 9710/359

Correct? Yes

๐Ÿ”— Problem

Problem: A camera has a total of 95038 pixels divided evenly into 61 rows. How many pixels are there in each row?

Gemma 2B:

 Reasoning: To find the number of pixels in each row, we divide the total number of pixels by the number of rows.
Number of pixels in each row = Total pixels / Number of rows
= 95038 pixels / 61 rows
= 1558 pixels (approximately)
### Answer: 1558 pixels

Expected answer: 1558

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead of 95038 pixels, the camera has only 2122 pixels and still divides them evenly into 61 rows. How many pixels would there be in each row now?

Gemma 2B:

 Reasoning: To find the number of pixels in each row, we divide the total number of pixels by the number of rows.
Number of pixels in each row = Total pixels / Number of rows
= 2122 pixels / 61 rows
= 34.8 pixels (approximately)
Since the number of pixels must be a whole number, this camera cannot have 61 rows of pixels.
### Answer: It is not possible for the camera to have 61 rows of pixels with only 2122 pixels.

Expected answer: 2122/61

Correct? No

๐Ÿ”— Problem

Problem: An ice cream factory produces a total of 45580 cones of ice cream over a period of 53 days. If the ice cream cones are produced uniformly across these days, how many ice cream cones are made each day?

Gemma 2B:

 Reasoning: If the production of ice cream cones is uniform over the 53 days, then the factory produces 45580/53 = <<45580/53=860>>860 ice cream cones per day.
### Answer: 860 

(Note: The answer is expressed as a whole number because it is assumed that the question is asking for the average number of cones produced each day over the 53-day period.)

Expected answer: 860

Correct? Yes

๐Ÿ”— Follow-up

Problem: The same ice cream factory has adjusted their volume and now makes a total of 4660 cones over the same 53 day period. If production is still uniform, how many ice cream cones are they making each day now?

Gemma 2B:

 Reasoning: If the production of ice cream cones is still uniform over the 53 days, then the factory now produces 4660/53 = <<4660/53=88>>88 ice cream cones per day.
### Answer: 88

Expected answer: 4660/53

Correct? No

๐Ÿ”— Problem

Problem: A textile factory produces 36135 square inches of towel fabric that is divided evenly among 219 towels. How many square inches of fabric is each towel?

Gemma 2B:

 Reasoning: To find the area of fabric for each towel, we divide the total area of fabric produced by the number of towels.
Area of fabric per towel = Total area of fabric / Number of towels
= 36135 square inches / 219 towels
= 164.95 square inches
### Answer: 164.95 square inches

Expected answer: 165

Correct? No

๐Ÿ”— Problem

Problem: A fireplace burns 36300 kilojoules of energy in 4 hours. How much energy does it burn in one hour?

Gemma 2B:

 Reasoning: To find the amount of energy burned in one hour, we need to divide the total energy burned by the number of hours.
Energy burned in 1 hour = Total energy burned / Number of hours
= 36300 kilojoules / 4 hours
= 9075 kilojoules
### Answer: 9075 kilojoules

Expected answer: 9075

Correct? Yes

๐Ÿ”— Follow-up

Problem: In another scenario, a different fireplace burns 8712 kilojoules of energy in 4 hours. Assuming it also burns energy at a constant rate, how much energy does this fireplace burn in one hour?

Gemma 2B:

 Reasoning: To find the amount of energy burned in one hour, we need to divide the total energy burned by the number of hours.
Energy burned in 1 hour = Total energy burned / Number of hours
= 8712 kilojoules / 4 hours
= 2178 kilojoules
### Answer: 2178 kilojoules

Expected answer: 2178

Correct? Yes

๐Ÿ”— Problem

Problem: A snowman-making competition has 9 teams, each of them was provided an equal amount of snow weighing up to 51156 kilograms in total. How much snow, in kilograms, did each team get to make their snowman?

Gemma 2B:

 Reasoning: If there are 9 teams and they all get an equal amount of snow, we can find the amount of snow each team gets by dividing the total amount of snow by the number of teams.
51156 kg รท 9 = <<51156/9=5684>>5684 kg
### Answer: Each team got 5684 kilograms of snow.

Expected answer: 5684

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead of 51156 kilograms of snow, only 6407 kilograms of snow was available for the same 9 teams in the snowman-making competition. How much snow, in kilograms, would each team get to make their snowman now?

Gemma 2B:

 Reasoning: If there are 9 teams and they all get an equal amount of snow, we can find the amount of snow each team gets by dividing the total amount of snow by the number of teams.
6407 kg รท 9 = <<6407/9=711.89 (rounded to two decimal places)>>711.89 kg
### Answer: Each team would get 711.89 kilograms of snow (rounded to two decimal places). 

Note: In practice, it might not be possible to divide the snow into exactly equal parts for each team, but this is the amount each team would be entitled to if the snow was divided equally.

Expected answer: 6407/9

Correct? No

๐Ÿ”— Problem

Problem: An apple orchard yielded a total of 56250 apples. Over the course of 30 days, they managed to harvest the same number of apples every day. How many apples were harvested each day?

Gemma 2B:

 Reasoning: The orchard harvested 56250/30 = <<56250/30=1875>>1875 apples each day.
### Answer: 1875 apples

Expected answer: 1875

Correct? Yes

๐Ÿ”— Follow-up

Problem: Instead of the original 30 days, the workers actually took 3028 days to harvest a total of 56250 apples, harvesting the same number of apples every day. In light of this new information, how many apples were actually harvested each day?

Gemma 2B:

 Reasoning: The orchard harvested 56250/3028 = <<56250/3028=18.57>>18.57 (rounded to two decimal places) apples each day.
### Answer: Approximately 18.57 apples 

(Note: This answer is rounded to two decimal places, but the actual number of apples harvested each day is an irrational number, meaning it goes on indefinitely without repeating. In real-world scenarios, it's impossible to harvest an irrational number of apples, but I'm providing the exact answer based on the information given.)

Expected answer: 28125/1514

Correct? No

๐Ÿ”— Problem

Problem: A baby spoke her first word after 82992 seconds of being awake in her life. If one day is considered 1729 seconds, after how many days did she speak her first word?

Gemma 2B:

 Reasoning: To find out how many days it took for the baby to speak her first word, we need to divide the total number of seconds by the number of seconds in a day.

72992 / 1729 = 42.2 days

Since a baby cannot speak a fraction of a day, we round up to the nearest whole day.

### Answer: 43 days

Expected answer: 48

Correct? No

๐Ÿ”— Problem

Problem: A map has a scale of 91368 centimeters representing 216 kilometers. How many centimeters on the map represent 1 kilometer in real life?

Gemma 2B:

 Reasoning: First, we need to convert the distance on the map from centimeters to kilometers.
91368 centimeters = 91368/100000 = 0.91368 kilometers (on the map)

Now, we can find out how many centimeters on the map represent 1 kilometer in real life.
1 kilometer = 0.91368 kilometers (on the map)

Therefore, 1 kilometer = 0.91368 \* 100000 = 91368 centimeters (on the map)
### Answer: 91368 centimeters on the map represent 1 kilometer in real life.

Expected answer: 423

Correct? No

๐Ÿ”— Problem

Problem: A fashion designer plans to use 33536 beads to embellish a dress uniformly across 131 different sections. How many beads will be used for each section?

Gemma 2B:

 Reasoning: To find the number of beads used for each section, we need to divide the total number of beads by the number of sections.
Beads per section = Total beads / Number of sections
= 33536 / 131
= 256
### Answer: 256 beads will be used for each section.

Expected answer: 256

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now, imagine that the fashion designer decides to use the same total number of 33536 beads, but wants to distribute them uniformly over a larger number of sections. If they decides to spread these beads over 3206 different sections on the dress, how many beads will there be in each section?

Gemma 2B:

 Reasoning: To find the number of beads used for each section, we need to divide the total number of beads by the number of sections.
Beads per section = Total beads / Number of sections
= 33536 / 3206
= 10.46
Since it's not possible to have a fraction of a bead, the designer cannot distribute the beads uniformly over 3206 sections. They need to use fewer beads or fewer sections.
### Answer: It is not possible to distribute 33536 beads uniformly over 3206 sections.

Expected answer: 16768/1603

Correct? No

๐Ÿ”— Problem

Problem: A firefighter sprays 69966 gallons of water on a fire in 299 minutes. If the firefighter sprays the same amount of water every minute, how many gallons does he spray each minute?

Gemma 2B:

 Reasoning: The firefighter sprays 69966/299 = <<69966/299=234>>234 gallons of water each minute.
### Answer: 234

Expected answer: 234

Correct? Yes

๐Ÿ”— Follow-up

Problem: After the fire is controlled, a firefighter continues to spray 8749 gallons of water to cool down the area over the next 299 minutes. If the firefighter sprays the same amount of water every minute as before, how many gallons does he spray each minute now?

Gemma 2B:

 Reasoning: The firefighter sprays 8749/299 = <<8749/299=29.23>>29.23 gallons of water each minute now.
### Answer: 29.23 (This answer has 2 decimal places because the result is a decimal number.)

Expected answer: 673/23

Correct? No

๐Ÿ”— Problem

Problem: The latest model of window that a company has designed will require 6354 square inches of glass material. The manufacturer's current stock can cover 2118 same-sized windows. How many square inches of glass are required for a single window?

Gemma 2B:

 Reasoning: The manufacturer's current stock can cover 2118 \* x square inches (where x is the area of a single window), so 6354 = 2118 \* x.
Solving for x, we get x = 6354 / 2118 = <<6354/2118=3.0>>3.0 square inches.
### Answer: 3.0 square inches

Expected answer: 3

Correct? Yes

๐Ÿ”— Follow-up

Problem: After revising their design slightly, the company now finds that they will only need 6354 square inches of glass material to produce 6122 of the new model of windows. How many square inches of glass are now required for each of the new model windows?

Gemma 2B:

 Reasoning: The new model of windows requires 6354 square inches of glass material to produce 6122 windows, so the area of a single window is 6354 / 6122 = <<6354/6122=1.04>>1.04 square inches.
### Answer: 1.04 square inches 

(Note: The answer is approximate because 6354 is not an exact multiple of 6122.)

Expected answer: 3177/3061

Correct? No

๐Ÿ”— Problem

Problem: A frog jumps a total of 12288 centimeters in 512 jumps. If the frog jumps the same distance each time, how many centimeters does the frog jump per jump?

Gemma 2B:

 Reasoning: The frog jumps 12288/512 = <<12288/512=24>>24 centimeters per jump.
### Answer: 24 centimeters

Expected answer: 24

Correct? Yes

๐Ÿ”— Follow-up

Problem: After practicing for a while, the frog now jumps a total of 9064 centimeters in the same 512 jumps. If the frog jumps the same distance each time, how many centimeters does the frog now jump per jump?

Gemma 2B:

 Reasoning: The frog jumps 9064/512 = <<9064/512=17.7>>17.7 centimeters per jump. However, the problem states that the frog jumps the same distance each time, and 17.7 is not a whole number. This means that the frog cannot jump the same distance each time and reach a total of 9064 centimeters in 512 jumps.
### Answer: It is not possible for the frog to jump the same distance each time and reach a total of 9064 centimeters in 512 jumps.

Expected answer: 1133/64

Correct? No

๐Ÿ”— Problem

Problem: A gardener planted a total of 1392 flowers evenly into 116 pots. How many flowers are there in each pot?

Gemma 2B:

 Reasoning: To find the number of flowers in each pot, we need to divide the total number of flowers by the number of pots.
Number of flowers in each pot = Total number of flowers / Number of pots
= 1392 / 116
= 12
### Answer: 12 flowers

Expected answer: 12

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of planting a total of 1392 flowers, the gardener planted a total of 7275 flowers evenly into the 116 pots, then how many flowers would there be in each pot now?

Gemma 2B:

 Reasoning: To find the number of flowers in each pot, we need to divide the total number of flowers by the number of pots.
Number of flowers in each pot = Total number of flowers / Number of pots
= 7275 / 116
= 62.77 (rounded to two decimal places)

However, since it is not possible to have a fraction of a flower in a pot, we need to round the number of flowers to the nearest whole number.

### Answer: There would be 63 flowers in each pot (rounded to the nearest whole number).

Expected answer: 7275/116

Correct? No

๐Ÿ”— Problem

Problem: An ice cream shop sold a total of 31,176 scoops of ice cream over 9 weeks. How many scoops of ice cream did they sell each week?

Gemma 2B:

 Reasoning: To find the number of scoops of ice cream sold each week, we divide the total number of scoops by the number of weeks.
Scoops per week = Total scoops / Number of weeks
= 31,176 scoops / 9 weeks
= 3,464 scoops
### Answer: 3,464 scoops

Expected answer: 3464

Correct? Yes

๐Ÿ”— Follow-up

Problem: Suppose instead of 9 weeks, it took the ice cream shop 4035 days to sell a total of 31,176 scoops of ice cream. How many scoops of ice cream did they sell each day?

Gemma 2B:

 Reasoning: To find the number of scoops of ice cream sold each day, we divide the total number of scoops by the number of days.
Scoops per day = Total scoops / Number of days
= 31,176 scoops / 4,035 days
= 7.72 scoops
### Answer: 7.72 scoops 

(Note: This answer is in decimal form, as it is not possible to sell a fraction of a scoop of ice cream.)

Expected answer: 10392/1345

Correct? No

๐Ÿ”— Problem

Problem: A very active mouse runs 14824 meters in 4 hours. If he runs at a constant rate, how many meters per hour does he run?

Gemma 2B:

 Reasoning: The mouse runs 14824/4 = <<14824/4=3706>>3706 meters per hour.
### Answer: 3706

Expected answer: 3706

Correct? Yes

๐Ÿ”— Problem

Problem: In a large monkey sanctuary, there are 88,508 bananas to be split evenly among 406 monkeys. If every monkey will receive an equal number of bananas, how many bananas would each monkey get?

Gemma 2B:

 Reasoning: To find out how many bananas each monkey gets, we divide the total number of bananas by the number of monkeys.
Each monkey gets 88,508/406 = <<88508/406=218>>218 bananas.
### Answer: 218 bananas

Expected answer: 218

Correct? Yes

๐Ÿ”— Follow-up

Problem: What if the sanctuary in the previous problem had only 9,073 bananas instead of 88,508? How many bananas would each monkey get then, if they still had to be split evenly among the 406 monkeys?

Gemma 2B:

 Reasoning: To find out how many bananas each monkey gets, we divide the total number of bananas by the number of monkeys.
Each monkey gets 9,073/406 = <<9073/406=22>>22 bananas.
### Answer: 22 bananas 

(Note: This answer is different from the previous one because the total number of bananas has changed.)

Expected answer: 9073/406

Correct? No

๐Ÿ”— Problem

Problem: A furniture maker has a large order placed by a hotel owner for tables. The order is for 15110 table legs, making the assumption that each table will have 2 legs. How many tables is the hotel owner ordering?

Gemma 2B:

 Reasoning: If each table has 2 legs, then the number of tables is the number of legs divided by 2.
So, the hotel owner is ordering 15110/2 = <<15110/2=7555>>7555 tables.
### Answer: 7555 

(Note: This answer assumes that all table legs are used and that there are no extra legs. If that's not the case, the number of tables may be different.)

Expected answer: 7555

Correct? Yes

๐Ÿ”— Follow-up

Problem: The furniture maker later realizes that there was a mistake in the initial order, and the hotel owner actually only wanted 3774 table legs, with each table having 2 legs. With this corrected order, how many tables is the hotel owner actually ordering?

Gemma 2B:

 Reasoning: If each table has 2 legs, then the number of tables is the number of legs divided by 2.
So, the hotel owner is ordering 3774/2 = <<3774/2=1887>>1887 tables.
### Answer: 1887 

(Note: This answer assumes that all table legs are used and that there are no extra legs. If that's not the case, the number of tables may be different.)

Expected answer: 1887

Correct? Yes

๐Ÿ”— Problem

Problem: A hat maker has 3560 feathers which will be used to decorate hats. If each hat will have 890 feathers, how many hats can be made?

Gemma 2B:

 Reasoning: To find out how many hats can be made, we need to divide the total number of feathers by the number of feathers per hat.
Number of hats = Total feathers / Feathers per hat
= 3560 / 890
= 4
So, the hat maker can make 4 hats.
### Answer: 4 hats

Expected answer: 4

Correct? Yes

๐Ÿ”— Follow-up

Problem: In the previous scenario, suppose the hat maker did not have 3560 feathers, but only had 1416 feathers instead. If each hat will still have 890 feathers, how many hats can be produced now?

Gemma 2B:

 Reasoning: To find out how many hats can be made, we need to divide the total number of feathers by the number of feathers per hat.
Number of hats = Total feathers / Feathers per hat
= 1416 / 890
Since 1416 is not a multiple of 890, we cannot divide 1416 evenly by 890.
Therefore, the hat maker can make 1 hat with 890 feathers and the remaining 526 feathers will not be enough to make another hat.
### Answer: 1 hat 

Note: The remaining 526 feathers can be used to decorate other items or saved for future use.

Expected answer: 708/445

Correct? No

๐Ÿ”— Problem

Problem: A card game involves a total of 17394 points distributed equally over 3 players. How many points does each player have?

Gemma 2B:

 Reasoning: To find the number of points each player has, we divide the total number of points by the number of players.
Each player has 17394/3 = <<17394/3=5798>>5798 points.
### Answer: 5798 

(Note: If the number of points is not evenly divisible by 3, the problem would need to be restated or reconsidered.)

Expected answer: 5798

Correct? Yes

๐Ÿ”— Follow-up

Problem: Now, consider a similar game where the total of 17394 points is now distributed evenly among 7489 players instead. In this case, how many points would each player have?

Gemma 2B:

 Reasoning: To find the number of points each player has, we divide the total number of points by the number of players.
However, in this case, the number of points is not evenly divisible by the number of players.
Therefore, it is not possible for the total of 17394 points to be distributed evenly among 7489 players.
### Answer: It is not possible for the total of 17394 points to be distributed evenly among 7489 players.

Expected answer: 17394/7489

Correct? No

๐Ÿ”— Problem

Problem: The central park covers a big land area of 3276 acres divided into 126 identical sections. How many acres does each section have?

Gemma 2B:

 Reasoning: To find the number of acres in each section, we need to divide the total acreage of the park by the number of identical sections.
Each section has 3276/126 = <<3276/126=26>>26 acres.
### Answer: 26 acres.

Expected answer: 26

Correct? Yes

๐Ÿ”— Follow-up

Problem: If instead of the original size, the park was smaller, covering only 139 acres, but the sections remained the same, each with an equal area, how many acres would each section cover?

Gemma 2B:

 Reasoning: To find the number of acres in each section, we need to divide the new total acreage of the park by the number of identical sections.
Each section would cover 139/126 = <<139/126=1.1031746031746032>>1.103 acres (rounded to five decimal places).
### Answer: Approximately 1.10317 acres.

Expected answer: 139/126

Correct? No

๐Ÿ”— Problem

Problem: A pants manufacturer has 54736 yards of fabric. If they are planning to make each pair of pants using the same amount of fabric and each will consume an equal portion of the total fabric, how many yards of fabric are needed for each pair if they intend to produce 11 pairs?

Gemma 2B:

 Reasoning: To find the number of yards of fabric needed for each pair, we need to divide the total amount of fabric by the number of pairs they intend to produce.
So, 54736/11 = <<54736/1

Expected answer: 4976

Correct? No

๐Ÿ”— Problem

Problem: The minute hand of a clock rotates 49716 degrees throughout 18 hours. If the rotation is uniform, how many degrees does it rotate each hour?

Gemma 2B:

 Reasoning: The minute hand of a clock completes one full rotation (360 degrees) in 60 minutes or 1 hour.
Therefore, in 18 hours, the minute hand would complete 18 times the number of degrees it completes in 1 hour.
So, the number of degrees it rotates in 1 hour is 360 / 18 = <<360/18=20>>20 degrees.
### Answer: 20 degrees.

Expected answer: 2762

Correct? No

๐Ÿ”— Problem

Problem: A toy company has made 1865 stuffed animals spread over 373 different designs. If each design has the same number of stuffed animals, how many stuffed animals are there for each design?

Gemma 2B:

 Reasoning: Each design has 1865/373 = <<1865/373=5>>5 stuffed animals.
### Answer: 5 stuffed animals for each design.

Expected answer: 5

Correct? Yes

๐Ÿ”— Follow-up

Problem: In an alternate scenario, the toy company made 2542 stuffed animals, still spread over 373 different designs. If each design had the same number of stuffed animals in this scenario, how many stuffed animals would there be for each design?

Gemma 2B:

 Reasoning: Each design would have 2542/373 = <<2542/373~6.81>>7 stuffed animals. However, since the number of stuffed animals must be a whole number, the scenario is not possible with the given numbers.
### Answer: The scenario is not possible with the given numbers.

Expected answer: 2542/373

Correct? No

๐Ÿ”— Problem

Problem: A bear travels a total of 31470 feet in 30 days. If the bear travels the same distance each day, how many feet does it travel each day?

Gemma 2B:

 Reasoning: The bear travels a total of 31470 feet in 30 days. To find out how many feet the bear travels each day, we divide the total distance by the number of days.
### Answer: 31470 / 30 = 1049 feet

Expected answer: 1049

Correct? Yes

๐Ÿ”— Follow-up

Problem: Considering our previous calculation, if a bear travels a total of 31470 feet but this time over 1406 days instead of 30 days and still travels the same distance each day, how many feet does it travel each day now?

Gemma 2B:

 Reasoning: The bear travels a total of 31470 feet in 1406 days. To find out how many feet the bear travels each day, we divide the total distance by the number of days.
### Answer: 31470 / 1406 โ‰ˆ 22.4 feet 
(Note: The bear travels approximately 22.4 feet each day.)

Expected answer: 15735/703

Correct? Yes

๐Ÿ”— Problem

Problem: A pen manufacturer produced 9636 pen units and distributed them equally among its 44 retailers. How many pen units did each retailer receive?

Gemma 2B:

 Reasoning: To find out how many pen units each retailer received, we need to divide the total number of pen units by the number of retailers.
Pen units per retailer = Total pen units / Number of retailers
Pen units per retailer = 9636 / 44
Pen units per retailer = 220
### Answer: 220 pen units per retailer.

Expected answer: 219

Correct? No