Resources

Resources

Identify quotients of rational numbers: word problems

George is driving at an average speed of

70

miles per hour. At this rate, how long, in minutes, will it take him to complete a

400

mile road trip?

A pink crayon is made with

12 \, \text{mL}

of red wax for every

5 \, \text{mL}

of white wax. Which of the following wax mixtures will create the same shade of pink?

Darcy harvests \\(8\)\dfrac{\(3\)}{\(4\)} acres of corn every \\dfrac{\(5\)}{\(6\)} of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?

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10

5

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9

5

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8

5

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7

5

At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red

The batting Wang Xiu Ying uses to fill quilts has a thermal conductivity rate of

\text{watts}

per meter per degree Celsius. What is the batting's thermal conductivity value in

\text{W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}

A motorboat left a harbor and traveled at an average speed of

15\,\text{mph}

toward an island. The average speed on its return trip was

10\,\text{mph}

. How far was the island from the harbor if the total trip took

5

In which story could you use the quotient

32 \div 4

to answer the question?

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(A)Ronald decided to make a movie with his friends one summer. After filming, Ronald edited the movie for

4

days. He removed

32

minutes of footage in all. On average, how much footage did Ronald remove each day?

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(B)Ronald decided to make a movie with his friends one summer. After filming, the movie was

32

minutes long. Ronald edited the movie and removed

4

minutes of footage. What was the final length of the movie?

In which story could you use the quotient

36 \div 24

to answer the question?

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(A) Sandra is making chocolate chip cookies. She gets

36

small cookies out of a

24

-ounce container of cookie dough. If each cookie is the same size, about how much cookie dough does she use for each one?

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(B) Sandra is making chocolate chip cookies. She gets

24

large cookies out of a

36

-ounce container of cookie dough. If each cookie is the same size, about how much cookie dough does she use for each one?

In which story could you use the quotient

-25,000 \div 14

to answer the question?

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(A)Ms. Erikson is filling her pool for the summer. The pool holds

25,000

gallons of water. It takes

14

hours for the pool to fill completely. On average, how much does the amount of water in the pool change per hour?

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(B)Ms. Erikson is draining her pool for the winter. The pool holds

25,000

gallons of water. It takes

14

hours for the pool to drain completely. On average, how much does the amount of water in the pool change per hour?

In which story could you use the quotient

-300 \div 45

to answer the question?

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(A)Rafi's class rented a dunk tank to raise money at their school's carnival. The tank holds

300

gallons of water. It took them

45

minutes to drain the tank at the end of the carnival. How much did the amount of water in the tank change per minute on average?

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(B)Rafi's class rented a dunk tank to raise money at their school's carnival. The tank holds

300

gallons of water. It took them

45

minutes to fill the tank with water. How much did the amount of water in the tank change per minute on average?

In which story could you use the quotient

25 \div 20

to answer the question?

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(A) Terrell is filling a

25

-cup flowerpot with soil to plant an herb garden. He uses a small shovel to scoop soil into the pot. It takes him

20

scoops to fill the pot. About how much soil does his shovel hold?

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(B) Terrell is filling a

20

-cup flowerpot with soil to plant an herb garden. He uses a small shovel to scoop soil into the pot. It takes him

25

scoops to fill the pot. About how much soil does his shovel hold?

In which story could you use the quotient

12 \div 4

to answer the question?

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(A) Harold is pickling cucumbers with his grandmother. They make

12

quarts of brine and need to pour an equal amount into

4

containers. How much brine should they pour into each container?

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(B) Harold is pickling cucumbers with his grandmother. They make

4

quarts of brine and need to pour an equal amount into

12

containers. How much brine should they pour into each container?

In which story could you use the quotient

-10 \div 2

to answer the question?

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(A)Eva is playing a monster-fighting game with her friends from the board game club. One of her abilities allows her to take away

10

strength points from a pair of monsters. If she takes away the same number of points from each monster, how much will each monster's strength change?

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(B)Eva is playing a monster-fighting game with her friends from the board game club. One of her abilities allows her to take away

10

strength points from each monster she fights. If she uses the ability while fighting a pair of monsters, what is the total change in the monsters' strength?

In which story could you use the quotient

36 \div 3

to answer the question?

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(A)Jill plays a computer game where she earns

3

points for each word she types correctly. If she ends the first round with a score of

36

points, how many words did she type correctly?

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(B)Jill plays a computer game where she earns

3

points for each word she types correctly. If she types

36

words correctly in the first round, how many points does she earn?

In which story could you use the quotient

42 \div 6

to answer the question?

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(A)Jake is making bookmarks out of ribbon for his local library. He has

42

inches of ribbon. If he cuts

6

inches of ribbon for each bookmark, how many bookmarks can he make?

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(B)Jake is making bookmarks out of ribbon for his local library. He has

42

inches of ribbon. He trims the ends of the ribbon, removing

6

inches in all. How much ribbon does he have left to make bookmarks?

In which story could you use the quotient

12 \div 24

to answer the question?

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(A) Diane is using a small shovel to fill a bucket with sand from her sandbox. It takes

24

scoops for her to fill the

12

-cup bucket. How much sand does Diane's shovel hold?

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(B) Diane is using a small shovel to fill a bucket with sand from her sandbox. It takes

12

scoops for her to fill the

24

-cup bucket. How much sand does Diane's shovel hold?

In which story could you use the quotient

-12 \div 8

to answer the question?

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(A)Jack turns on the air conditioning in his room for

8

minutes. The temperature drops a total of

12

degrees in that time. On average, how much does the temperature change per minute?

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(B)Jack turns on the air conditioning in his room for

12

minutes. The temperature drops a total of

8

degrees in that time. On average, how much does the temperature change per minute?

In which story could you use the quotient

-50 \div 6

to answer the question?

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(A)Marshall is learning to fly a drone. His remote control displays the drone's altitude in meters. As the drone takes off, its altitude increases to

50

meters. Suddenly, Marshall loses control of the drone! It drops to an altitude of

6

meters before he regains control. How much did the drone's altitude decrease?

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(B)Marshall is learning to fly a drone. His remote control displays the drone's altitude in meters. As he brings the drone in for a landing, it drops the final

50

meters to the ground in

6

seconds. On average, how much does the drone's altitude change each second?

In which story could you use the quotient

-24 \div 10

to answer the question?

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(A)Before leaving for the store, Jim turns on his air conditioning as soon as he gets into his car. In the

10

minutes it takes him to drive to the store, the temperature in the car drops

24

degrees. On average, how much did the temperature change per minute?

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(B)Before leaving for the store, Jim turns on his air conditioning as soon as he gets into his car. In the

24

minutes it takes him to drive to the store, the temperature in the car drops

10

degrees. On average, how much did the temperature change per minute?

In which story could you use the quotient

-11,000 \div 16

to answer the question?

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(A)The change in elevation from Badwater Basin to Telescope Peak in California is about

11,000

feet. The two landmarks are

16

miles apart. If Susan hikes from the Peak down to the Basin, what is her average elevation change per mile?

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(B)The change in elevation from Badwater Basin to Telescope Peak in California is about

11,000

feet. The two landmarks are

16

miles apart. If Susan hikes from the Basin up to the Peak, what is her average elevation change per mile?

In which story could you use the quotient

-30 \div 6

to answer the question?

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(A)From January to July, the average temperature at Casey Station in Antarctica drops about

30

degrees. If the average temperature in July is

6\degree F

, what is the average temperature in January?

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(B)From January to July, the average temperature at Casey Station in Antarctica drops about

30

degrees. On average, how much does the temperature change per month during that

6

-month time period?

In which story could you use the quotient

-12 \div 10

to answer the question?

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(A)The overnight temperature in Juneau, Alaska, dropped

12

10

hours. On average, how much did the temperature change per hour?

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(B)The overnight temperature in Juneau, Alaska, dropped

10

12

hours. On average, how much did the temperature change per hour?

In which story could you use the quotient

-4 \div 24

to answer the question?

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(A)Gina did a science experiment where she measured the temperature of a glass of water while adding ice cubes. After

24

minutes, the temperature of the water dropped

4

degrees. How much did the temperature change per minute?

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(B)Gina did a science experiment where she measured the temperature of a glass of water while it warmed in the sun. The temperature increased

4

24

minutes. How much did the temperature change per minute?

In which story could you use the quotient

-100 \div 6

to answer the question?

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(A)Samuel, a biologist, studies grizzly bear hibernation. Part of his research involves tracking the bears' weights. This year, one of the bears lost

100

pounds while hibernating for

6

months. About how much did the bear's weight change every month?

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(B)Samuel, a biologist, studies grizzly bear hibernation. Part of his research involves tracking the bears' weights. This year, one of the bears gained

100

6

weeks while getting ready for hibernation. About how much did the bear's weight change every week?

A local television station sells time slots for programs in

30

-minute intervals. If the station operates

24

hours per day, every day of the week, what is the total number of

30

-minute time slots the station can sell for Tuesday and Wednesday?

A frozen pepperoni pizza has

6

servings. If the pizza contains a total of

1860

calories, what is the number of calories per serving?

Charles owns a toy store. There are

8

dolls for every

5

dump trucks in his inventory. If there are

35

dump trucks, how many dolls are in the store?

\frac{4}{5}

of a can of paint covers

1

ceiling how many cans needed for

6

A French club collected the same amount from each student going on a trip to Le Cercle Molière in Winnipeg. When six students could not go, each of the remaining students was charged an extra

\$ 3

. If the total cost was

\$ 540

, how many students went on the trip?

A junior basketball player has a goal of scoring at least

1000

points during his high school career. His team plays

20

games per year, and after

2

320

points. How many points does he have to average per game over his last

2

yr to reach his goal?

2025

plants are to be planted in a garden in a such way that each row contains as many plants as the number of raws. find the number of the raws and the number of plants in each row

8

classrooms are required if each class has

33

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How many classrooms would be required if the class size has reduced to

22

60

mile trip at an average speed of

20

mph. On the return trip, the car’s average speed was

30

mph. What was the average speed of the car for the entire two-way trip?

1

table spoon per gallon of water how many table spoons do you put in to make a liter mixture?

If a boat sails

120

3

hours, how many miles will it sail in

7

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A recipe calls for

4

cups of flour for a batch of

12

cookies, how many cookies can be made with one cup of flour?

Walnuts are sold in packages that weight

3

ounces. If there is a supply of

54

ounces of walnuts, how many packages of walnuts can be made?

91

7

weeks. How many portraits can Luke paint in

4

Lian's dog eats

\frac{3}{8}

of a bag of dog food each week. Lian currently has

\frac{5}{8}

of a bag remaining. How many weeks will it take Lian's dog to finish this remaining food?

A basketball game was scheduled to last

72

minutes, including the breaks between quarters. Several timeouts were used throughout the game, resulting in the game lasting a total of

60

minutes, including breaks. If each timeout was

x

seconds, how many total timeouts were used during the game?

At a lunch stand, each hamburger has

50

more calories than each order of fries. If

2

3

orders of fries have a total of

1700

calories, how many calories does a hamburger have?

3

(c)

of flour to bake

2

loaves of bread. If

1

(lb)

of flour is equivalent to

3\frac{1}{3} c ,

how many loaves of bread can the baker make with a

10

lb

- bag of flour?

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(Round the answer to the nearest whole number.)

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A local package delivery service wants to improve the efficiency of its deliveries. As a first step, the management team decides to conduct a study to determine the average length of time from the arrival of a package at the company's mail center until its delivery at a home. Which of the following methods is most likely to produce valid results?

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1

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(A) The team selects the

1,000

heaviest packages in a one-week, non-holiday period and records how long it takes for each package to reach its destination.

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(B) The team calls

1,000

residents in their delivery area and asks them whether they have received a package from their service in the past week. They will then record how long it took for those packages to reach their destination.

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(C) The team selects a random sample of

1,000

packages arriving at the center over a one-week, non-holiday period and records how long it takes for each package to reach its destination.

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(D) None of the above

The least amount of wrapping paper needed to wrap a cube-shaped gift is

150

square inches. How long is one side of the gift?