We included **H****MH Into Math Grade 6 Answer Key**** PDF** **Module 3 Lesson 1 Understand Fraction Division** to make students experts in learning maths.

## HMH Into Math Grade 6 Module 3 Lesson 1 Answer Key Understand Fraction Division

I Can divide fractions with like denominators with and without models.

**Spark Your Learning**

Jayson is making sushi rolls. He has \(\frac{5}{6}\) cup of rice and will use \(\frac{2}{6}\) cup for each sushi roll. How many whole sushi rolls can he make?

Answer:

2 whole sushi rolls,

Explanation:

Given Jayson is making sushi rolls. He has 5/6 cup of

rice and will use 2/6 cup for each sushi roll.

2 whole sushi rolls can he make.

**Turn and Talk** How many sushi rolls can Jayson make if he uses up all the rice? Explain.

Answer:

2 1/2 sushi rolls,

Explanation:

Given Jayson is making sushi rolls. He has

5/6 cup of rice and will use

\(\frac{2}{6}\) cup for each sushi roll,

Number of sushi rolls can Jayson make if he uses

up all the rice is \(\frac{5}{6}\) ÷ \(\frac{2}{6}\) =

\(\frac{5}{6}\) X \(\frac{6}{2}\) =

\(\frac{5 X 6}{6 X 2}\) = \(\frac{5}{2}\)

as numerator is greater than denominator we write in

mixed fraction as 2\(\frac{1}{2}\).

Therefore sushi rolls can Jayson make if he uses up all the rice are

2\(\frac{1}{2}\).

**Build Understanding**

1. Malik is making eggrolls to share with Jayson. Malik has \(\frac{4}{5}\) pound of chicken and will use the amount shown per batch. How many batches of eggrolls can Malik make?

A. Write an expression to show how you would divide a fraction by a fraction to solve this problem.

_____ ÷ _____

B. Explain how you can use a model to find how many groups of \(\frac{2}{5}\) are in \(\frac{4}{5}\). Then make a model.

C. How many groups of \(\frac{2}{5}\) are there in \(\frac{4}{5}\) ? How many batches of eggrolls can Malik make?

Answer:

A. Expression:

4/5 ÷ 2/5,

B. 2 groups, Area Model,

C. 2 groups and 2 batches of eggrolls can Malik make,

Explanation:

Given Malik is making eggrolls to share with Jayson.

Malik has \(\frac{4}{5}\) pound of chicken and

will use the amount \(\frac{2}{5}\) pound per batch

A. An expression to show how I would divide a fraction

by a fraction to solve this problem is

\(\frac{4}{5}\) ÷ \(\frac{2}{5}\).

B. Drawn a area model with \(\frac{4}{5}\)

and in that there are 2 groups of \(\frac{2}{5}\).

Then made a model as shown above circled 2 groups of

\(\frac{2}{5}\).

C. Number of groups of \(\frac{2}{5}\) are

there in \(\frac{4}{5}\) are

\(\frac{4}{5}\) ÷ \(\frac{2}{5}\) =

\(\frac{4}{5}\) X \(\frac{5}{2}\) =

\(\frac{4 X 5}{5 X 2}\) = 2, 2 batches of eggrolls

can Malik make.

2. Suppose Malik had \(\frac{3}{4}\) pound of chicken and uses \(\frac{3}{8}\) pound to make one batch of eggrolls. How many batches of eggrolls could he make?

A. Draw the fraction strip you could use to begin to find the solution.

B. Will the fraction strip you drew in Part A help you to make groups of \(\frac{3}{8}\)? If not, what other fraction strip could help? Explain why.

________________________

C. Draw the fraction strip you chose in Part B in the answer box in Part A. How many groups of \(\frac{3}{8}\) are in \(\frac{3}{4}\)? Explain.

D. How many batches of eggrolls can Malik make?

________________________

Answer:

A.

B. Yes, the fraction strip I drew in Part A will help me

to make groups of 3/8,

C.

2 groups,

D. 2 batches,

Explanation:

Given Malik had \(\frac{3}{4}\) pound of

chicken and uses \(\frac{3}{8}\) pound to

make one batch of eggrolls.

A. Drawn the fraction strip I could use to begin

to find the solution as \(\frac{3}{4}\),

B. The fraction strip I drew in Part A will help me

to make groups of \(\frac{3}{8}\),

C. Drawn the fraction strip that I chose in

Part B in the answer box in Part A.

Two groups of \(\frac{3}{8}\)

are in \(\frac{3}{4}\) as shown above

circled with red color.

D. Number of batches of eggrolls could he make are

\(\frac{3}{4}\) ÷ \(\frac{3}{8}\) =

\(\frac{3}{4}\) X \(\frac{8}{3}\) =

\(\frac{3 X 8}{4 X 2}\) = 2, 2 batches of eggrolls

can Malik make.

3. Suyin is making a dog house. She needs to cut a board that is \(\frac{5}{9}\) yard long into smaller pieces. How many pieces can she cut if each piece needs to be \(\frac{2}{9}\) yard long?

A. Complete the following to express the problem in words. Suyin needs to find how many groups of ____ are in ____.

B. What division expression can you use to answer this question?

_________________

C. Complete the bar model to show the division problem in Part B.

D. Write an explanation of how the bar model represents the quotient in Part B.

E. What is the number of pieces of board, each \(\frac{2}{9}\) yard long, that Suyin an cut? Did Suyln use up all the wood? If not, how long Is the leftover piece of board?

Answer:

A. Suyin needs to find how many groups of

\(\frac{2}{9}\) are in \(\frac{5}{9}\),

B. Division expression:

\(\frac{5}{9}\) ÷ \(\frac{2}{9}\),

C.

D.

E. The number of pieces of board each

\(\frac{2}{9}\) yard long that Suyin can cut is 2,

No Suyin has not used up all the wood

\(\frac{1}{2}\) is the leftover piece of board,

Explanation:

Given Suyin is making a dog house. She needs to cut a

board that is \(\frac{5}{9}\) yard long into smaller pieces.

If each piece needs to be \(\frac{2}{9}\) yard long

A. Completed the following to express the problem in words as

Suyin needs to find how many groups of

\(\frac{2}{9}\) are in \(\frac{5}{9}\),

B. Division expression I can use to answer this question is

Division expression:

\(\frac{5}{9}\) ÷ \(\frac{2}{9}\).

C. Completed the bar model to show the division

problem in Part B above.

D. Wrote an explanation of how the bar model

represents the quotient in Part B.

E. The number of pieces of board, each

\(\frac{2}{9}\) yard long, that Suyin can cut is 2,

No Suyin has not used up all the wood

\(\frac{1}{2}\) is the leftover piece of board.

**Turn and Talk** What fraction of another piece an Suyin make with what is left over?

Answer:

\(\frac{1}{2}\) fraction of another piece

Suyin can make with the leftover piece,

Explanation:

Given \(\frac{5}{9}\) ÷ \(\frac{2}{9}\) solving

\(\frac{5}{9}\) X \(\frac{9}{2}\) =

\(\frac{5 X 9}{9 X 2}\) = \(\frac{5}{2}\)

as numerator is greater than denominator we write in

mixed fraction as 2\(\frac{1}{2}\) therefore

\(\frac{1}{2}\) fraction of another piece

Suyin can make with the leftover piece.

4. The diagram shows part of a road that is \(\frac{9}{10}\) mile long. Consider the expression \(\frac{9}{10}\) ÷ \(\frac{2}{10}\).

A. Write a problem that can be modeled with the given expression and that uses the information in the diagram.

B. Show or describe how to find the quotient.

C. Recall that the dividend is the number to be divided in a division problem. The divisor is the number you are dividing by. In your problem, what do the dividend and divisor represent?

_________________________

_________________________

D. How does the answer to the question in Part A compare to the quotient in Part B? Explain.

_________________________

Answer:

A. “A road is \(\frac{9}{10}\) mile long there are trees

each at a distance of \(\frac{2}{10}\) mile long,

how many trees are along the road side”,

B.

C. The dividend is \(\frac{9}{10}\) and

divisor is \(\frac{2}{10}\),

D. Part A question results are shown in part B,

Explanation:

Given the diagram shows part of a road that is

\(\frac{9}{10}\) mile long.

Considering the expression \(\frac{9}{10}\) ÷ \(\frac{2}{10}\)

A. Wrote a problem that can be modeled with the given

expression and that uses the information in the diagram as

“A road is \(\frac{9}{10}\) mile long there are trees

each at a distance of \(\frac{2}{10}\) mile long,

how many trees are along the road side”.

B. Described how to find the quotient as 4\(\frac{1}{2}\) above,

C. Recalled that the dividend is the number to be divided

in a division problem. The divisor is the number

we are dividing by. In my problem, the dividend is

\(\frac{9}{10}\) and divisor is \(\frac{2}{10}\).

D. The answer to the question in Part A compared to the

quotient in Part B is the question of Part A is how many trees are

along the road side and the result is shown in Part B.

**Check Understanding**

Question 1.

Hana is organizing a \(\frac{3}{4}\)-mile fun run. There will be a water station every \(\frac{1}{4}\) mile after the start.

A. How many groups of \(\frac{1}{4}\) are in \(\frac{3}{4}\)? ___________

Answer:

3 groups,

Explanation:

Given Hana is organizing a \(\frac{3}{4}\)-mile fun run.

There will be a water station every \(\frac{1}{4}\) mile after the start,

number of groups of \(\frac{1}{4}\) are in \(\frac{3}{4}\) are

\(\frac{3}{4}\) ÷ \(\frac{1}{4}\) solving

\(\frac{3}{4}\) X \(\frac{4}{1}\) = 3 groups.

B. How many water stations will there be? ___________________

Answer:

3 water stations,

Explanation:

Given Hana is organizing a \(\frac{3}{4}\)-mile fun run.

There will be a water station every \(\frac{1}{4}\) mile after the start,

number of water stations are \(\frac{3}{4}\) ÷ \(\frac{1}{4}\),

solving \(\frac{3}{4}\) X \(\frac{4}{1}\) = 3 water stations.

Question 2.

Janice is cutting ribbon to decorate a present. She has \(\frac{7}{8}\) foot of ribbon. She needs to make pieces that are \(\frac{3}{8}\) foot each. How many \(\frac{3}{8}\)-foot pieces will she get from the \(\frac{7}{8}\)-foot ribbon? ___________

Answer:

Janice will get 2\(\frac{1}{3}\) pieces of

\(\frac{3}{8}\)-foot pieces will she get from the

\(\frac{7}{8}\)-foot ribbon,

Explanation:

Given Janice is cutting ribbon to decorate a present.

She has \(\frac{7}{8}\) foot of ribbon.

She needs to make pieces that are \(\frac{3}{8}\) foot each.

Number of \(\frac{3}{8}\)-foot pieces will she

get from the \(\frac{7}{8}\)-foot ribbon are

\(\frac{7}{8}\) ÷ \(\frac{3}{8}\) solving

\(\frac{7}{8}\) X \(\frac{8}{3}\) =

\(\frac{7 X 8}{8 X 3}\) = \(\frac{7}{3}\)

as numerator is greater than denominator we write in

mixed fraction as 2\(\frac{1}{3}\).

**On Your Own**

Question 3.

Jasmine has \(\frac{4}{5}\) pound of fertilizer. She wants to store the fertilizer in

separate containers, each with \(\frac{1}{5}\) pound of fertilizer. How many containers

will she need? ___________

Answer:

Jasmine needs 4 containers,

Explanation:

Given Jasmine has \(\frac{4}{5}\) pound of fertilizer.

She wants to store the fertilizer in separate containers,

each with \(\frac{1}{5}\) pound of fertilizer.

Number of containers will she need are

\(\frac{4}{5}\) ÷ \(\frac{1}{5}\) solving

\(\frac{4}{5}\) X \(\frac{5}{1}\) =

\(\frac{4 X 5}{5 X 1}\) = 4.

Question 4.

**Reason** A city places street lights at equal intervals along a city street beginning \(\frac{3}{8}\) mile from one end of the street. If the street is \(\frac{7}{8}\) mile long, how many street lights will the city use? Explain.

Answer:

2 street lights,

Explanation:

Given a city places street lights at equal intervals along a

city street beginning \(\frac{3}{8}\) mile from

one end of the street. If the street is \(\frac{7}{8}\) mile long,

Number of street lights will the city use is

\(\frac{7}{8}\) ÷ \(\frac{3}{8}\) solving

\(\frac{7}{8}\) X \(\frac{8}{3}\) =

\(\frac{7 X 8}{8 X 3}\) = \(\frac{7}{3}\)

as numerator is greater than denominator we write in

mixed fraction as 2\(\frac{1}{3}\). Therefore

2 street lights will the city use.

Question 5.

Eric has \(\frac{9}{16}\) pound of bird feed left. If he feeds his bird \(\frac{1}{8}\) pound each day, how many days can he feed the bird before he needs to buy more food?

Answer:

4\(\frac{1}{2}\) days can he feed the bird

before he needs to buy more food,

Explaantion:

Given Eric has \(\frac{9}{16}\) pound of bird feed left.

If he feeds his bird \(\frac{1}{8}\) pound each day,

Number of days can he feed the bird before he

needs to buy more food are

\(\frac{9}{16}\) ÷ \(\frac{1}{8}\) solving

\(\frac{9}{16}\) X \(\frac{8}{1}\) =

\(\frac{9 X 8}{16 X 1}\) = \(\frac{9}{2}\)

as numerator is greater than denominator we write in

mixed fraction as 4\(\frac{1}{2}\), Therefore

4\(\frac{1}{2}\) days can he feed the bird

before he needs to buy more food.

Question 6.

Daryl has \(\frac{2}{8}\) of a bag of dog food. His dog eats \(\frac{4}{9}\) of a bag per week.

A. How many weeks will the dog food last? __________

Answer:

Number of weeks will the dog food last is

\(\frac{9}{16}\),

Explanation:

Given Daryl has \(\frac{2}{8}\) of a bag of dog food.

His dog eats \(\frac{4}{9}\) of a bag per week.

Number of weeks will the dog food last is

\(\frac{2}{8}\) ÷ \(\frac{4}{9}\) solving

\(\frac{2}{8}\) X \(\frac{9}{4}\) =

\(\frac{2 X 9}{8 X 4}\) = \(\frac{9}{16}\) weeks.

B. What fraction strip could you use to solve this problem? Explain why.

________________________

________________________

Answer:

Area model,

Explanation:

By using the area model because it shows

a rectangular diagram for division problems,

in which the factors or the quotient and divisor

define the length and width of the rectangle.

Question 7.

How long will it take Sarah to paint \(\frac{11}{12}\) of a fence if she paints \(\frac{2}{12}\) of the fence each day?

___________________

Answer:

5\(\frac{1}{2}\) days it will take,

Explanation:

Given it will take Sarah to paint \(\frac{11}{12}\) of

a fence if she paints \(\frac{2}{12}\) of the fence each day

it will take \(\frac{11}{12}\) ÷ \(\frac{2}{12}\) solving

\(\frac{11}{12}\) X \(\frac{12}{2}\) =

\(\frac{11 X 12}{12 X 2}\) = \(\frac{11}{2}\)

as numerator is greater than denominator we write in

mixed fraction as 5\(\frac{1}{2}\), Therefore

it will take 5\(\frac{1}{2}\) days to paint the fence.

Question 8.

How many \(\frac{1}{3}\)-cup servings are there in \(\frac{10}{3}\) cups of dried beans?

___________________

Answer:

There are 10 servings of \(\frac{1}{3}\)-cup in

Explanation:

Asking to find number of \(\frac{1}{3}\)-cup

servings are there in \(\frac{10}{3}\) cups of dried beans,

So it is \(\frac{10}{3}\) ÷ \(\frac{1}{3}\),

\(\frac{10}{3}\) X \(\frac{3}{1}\) =

\(\frac{10 X 3}{3 X 1}\) = 10 servings.

Question 9.

Tressa’s home is \(\frac{4}{5}\) mile from school. Anton’s home is \(\frac{3}{5}\) mile from school. How many times the distance from Anton’s home to school is the distance from Tressa’s home to school?

Answer:

1\(\frac{1}{3}\) times the distance from Anton’s home to

school is the distance from Tressa’s home to school,

Explanation:

Given Tressa’s home is \(\frac{4}{5}\) mile from school.

Anton’s home is \(\frac{3}{5}\) mile from school.

So number of times the distance from Anton’s home to school is

the distance from Tressa’s home to school is

\(\frac{4}{5}\) ÷ \(\frac{3}{5}\),

\(\frac{4}{5}\) X \(\frac{5}{3}\) =

\(\frac{4 X 5}{5 X 3}\) = \(\frac{4}{3}\)

as numerator is greater than denominator we write in

mixed fraction as 1\(\frac{1}{3}\) times.

Question 10.

**Model with Mathematics** Tom is pouring \(\frac{3}{32}\)-gallon servings from a bottle that contains \(\frac{15}{32}\) gallon of tomato juice. Write and evaluate a division expression to find the number of servings in the bottle.

Answer:

Division expression : \(\frac{15}{32}\) ÷ \(\frac{3}{32}\),

5 number of servings in the bottel,

Explanation:

Given Tom is pouring \(\frac{3}{32}\)-gallon servings

from a bottle that contains \(\frac{15}{32}\) gallon of

tomato juice.The division expression to find the

number of servings in the bottle is

\(\frac{15}{32}\) ÷ \(\frac{3}{32}\),

\(\frac{15}{32}\) X \(\frac{32}{3}\) =

\(\frac{15 X 32}{32 X 3}\) = 5 servings.

Question 11.

**Model with Mathematics** It takes \(\frac{1}{3}\) pint of paint to cover a birdhouse. There are 12\(\frac{1}{3}\) pints of paint in a can. Write and evaluate a division expression to find the number of birdhouses that can be painted.

Answer:

Division expression:

12\(\frac{1}{3}\) ÷ \(\frac{1}{3}\),

Number of birdhouses that can be painted are 37,

Explanation:

Given it takes \(\frac{1}{3}\) pint of paint to

cover a birdhouse. There are 12\(\frac{1}{3}\) pints of

paint in a can. Division expression to find the number of

birdhouses that can be painted is

12\(\frac{1}{3}\) ÷ \(\frac{1}{3}\) =

\(\frac{12 X 3 + 1}{3}\) X \(\frac{3}{1}\) =

\(\frac{37}{3}\) X 3 = 37.

Question 12.

Juan has \(\frac{5}{8}\) pound of beef. He wants to make burgers using the meat. If the meat in each burger weighs \(\frac{1}{8}\) pound, how many burgers can he make?

_________________

Answer:

5 burgers he can make,

Explanation:

Given Juan has \(\frac{5}{8}\) pound of beef.

He wants to make burgers using the meat. If the meat in

each burger weighs \(\frac{1}{8}\) pound,

Number of many burgers can he make are

\(\frac{5}{8}\) ÷ \(\frac{1}{8}\) =

\(\frac{5 X 1}{8}\) X 8 = 5.

Question 13.

Felice lives \(\frac{9}{10}\) mile from a park. She needs to stop several times while walking her new puppy to the park, including her final stop when she reaches the park. How many times will she stop when walking to the park?

Answer:

3 times Felice should stopwhen walking to park,

Explanation:

Given Felice lives \(\frac{9}{10}\) mile from a park.

She needs to stop several times while walking her new puppy

to the park, including her final stop when she reaches the park.

Number of times will she stop when walking to the park are

\(\frac{9}{10}\) ÷ \(\frac{3}{10}\) =

\(\frac{9}{10}\) X \(\frac{10}{3}\) =

\(\frac{9 X 10}{10 X 3}\) = 3 times.

Question 14.

**Critique Reasoning** Darius says that \(\frac{1}{3}\) ÷ \(\frac{2}{3}\) is 2, because you can’t make groups of \(\frac{2}{3}\) from \(\frac{1}{3}\). so you need to make groups of \(\frac{1}{3}\) from \(\frac{2}{3}\). Darius’ answer is not correct. What mistake did he make? What is the correct answer?

Answer:

\(\frac{1}{2}\) is the correct answer,

Explanation:

Given Darius says that \(\frac{1}{3}\) ÷ \(\frac{2}{3}\) is 2,

because you can’t make groups of \(\frac{2}{3}\)

from \(\frac{1}{3}\). so I need to make groups of

\(\frac{1}{3}\) from \(\frac{2}{3}\).

Darius’ answer is not correct. He made mistake in calculations

\(\frac{1}{3}\) ÷ \(\frac{2}{3}\) =

\(\frac{1}{3}\) X \(\frac{3}{2}\) =

\(\frac{1 X 3}{3 X 2}\) = \(\frac{1}{2}\).

So the correct answer is \(\frac{1}{2}\) not 2.

Question 15.

Write and solve a real-world problem that can be modeled by the diagram shown and the division expression \(\frac{3}{6}\) ÷ \(\frac{4}{6}\).

Answer:

Explanation:

World problem:”Nancy has \(\frac{3}{6}\) flour,

She needs \(\frac{4}{6}\) flour to make cake how much

part can she prepare the cake”,

Nancy can prepare \(\frac{3}{4}\) portion,

Explanation:

Asking to write and solve a real-world problem that

can be modeled by the diagram shown and the division

expression \(\frac{3}{6}\) ÷ \(\frac{4}{6}\) is

World problem: “Nancy has \(\frac{3}{6}\) flour,

She needs \(\frac{4}{6}\) flour to make cake how much

part can she prepare the cake”, solving

\(\frac{3}{6}\) ÷ \(\frac{4}{6}\) =

\(\frac{3}{6}\) X \(\frac{6}{4}\) =

\(\frac{3 X 6}{6 X 4}\) = \(\frac{3}{4}\) part.

**I’m in a Learning Mindset!**

Is using a model to divide fractions an effective strategy? Why or why not?

___________________________

___________________________

Answer:

Yes it is effective strategy,

Explanation:

As division is an essential foundation for fractions.

We can divide objects into equal groups,

We can begin to grasp dividing a whole into equal parts.

Dividing fractions using models makes this tricky topic

easier to visualize and find results.

**Lesson 3.1 More Practice/Homework**

**Understand Fraction Division**

Question 1.

Yu has a part of an hour for his workout. He would like to do a different exercise each \(\frac{1}{4}\) hour. How many different exercises does he have time for?

Answer:

3 different exercises,

Explanation:

Given Yu has \(\frac{3}{4}\) an hour for his workout.

He would like to do a different exercise each

\(\frac{1}{4}\) hour. Number of

different exercises does he have time for is

\(\frac{3}{4}\) ÷ \(\frac{1}{4}\) =

\(\frac{3}{4}\) X \(\frac{4}{1}\) =

\(\frac{3 X 4}{4 X 1}\) = 3.

Question 2.

A phone has \(\frac{5}{8}\) of its battery charge left. If the battery loses \(\frac{3}{8}\) of its full charge every hour, how many hours will the battery last?

_________________

Answer:

1\(\frac{2}{3}\) hours will the battery last,

Explanation:

Given a phone has \(\frac{5}{8}\) of its battery

charge left. If the battery loses \(\frac{3}{8}\) of

its full charge every hour, Number of hours will the battery last is

\(\frac{5}{8}\) ÷ \(\frac{3}{8}\) =

\(\frac{5}{8}\) X \(\frac{8}{3}\) =

\(\frac{5 X 8}{8 X 3}\) = \(\frac{5}{3}\)

as numerator is greater than denominator we write in

mixed fraction as 1\(\frac{2}{3}\) hours.

Question 3.

Sonia takes a \(\frac{4}{5}\)-mile walk every day. What part of her walk has she completed once she has walked \(\frac{3}{5}\) mile?

Answer:

1\(\frac{1}{3}\) part of her walk,

Explanation:

Given Sonia takes a \(\frac{4}{5}\)-mile walk every day.

The part of her walk has she completed once she has

walked \(\frac{3}{5}\) mile is

\(\frac{4}{5}\) ÷ \(\frac{3}{5}\) =

\(\frac{4}{5}\) X \(\frac{5}{3}\) =

\(\frac{4 X 5}{5 X 3}\) = \(\frac{4}{3}\)

as numerator is greater than denominator we write in

mixed fraction as 1\(\frac{1}{3}\) part.

Question 4.

**Reason** A bread recipe requires that \(\frac{5}{8}\) teaspoon of yeast be added to flour and water. Alejandro only has a \(\frac{1}{8}\)-teaspoon measuring spoon. How many measuring spoons of yeast will he need to add to the flour and water? Explain your reasoning.

________________________

________________________

Answer:

5 spoons,

Explanation:

Given a bread recipe requires that \(\frac{5}{8}\)

teaspoon of yeast be added to flour and water.

Alejandro only has a \(\frac{1}{8}\)-teaspoon

measuring spoon. Number of measuring spoons of yeast

will he need to add to the flour and water are

\(\frac{5}{8}\) ÷ \(\frac{1}{8}\) =

\(\frac{5}{8}\) X \(\frac{8}{1}\) =

\(\frac{5 X 8}{8 X 1}\) = 5 spoons.

Question 5.

**Open Ended** Write and solve a real-world problem that can be modeled by the division expression \(\frac{8}{12}\) ÷ \(\frac{9}{12}\). Identify what the dividend, divisor, and

quotient represent in your problem. Show your work.

Answer:

World problem:

“Joy has \(\frac{8}{12}\) candies and

Nancy has \(\frac{9}{12}\) more candies than Joy,

how many more candies does Nancy has than Joy”,

Dividend: \(\frac{8}{12}\),

Divisor : \(\frac{9}{12}\),

Quotient : \(\frac{8}{9}\),

Nancy has \(\frac{8}{9}\) more candies than Joy,

Explanation:

Wrote and solved a real-world problem that can be

modeled by the division expression

\(\frac{8}{12}\) ÷ \(\frac{9}{12}\).

Identified the dividend, divisor and quotient represented

in the problem as world problem –

“Joy has \(\frac{8}{12}\) candies and

Nancy has \(\frac{9}{12}\) more candies than Joy,

how much more does Nancy has more than Joy”,

more candies does

Dividend: \(\frac{8}{12}\),

Divisor : \(\frac{9}{12}\),

Quotient : \(\frac{8}{9}\), Now solving

\(\frac{8}{12}\) ÷ \(\frac{9}{12}\) =

\(\frac{8}{12}\) X \(\frac{12}{9}\) =

\(\frac{8 X 12}{12 X 9}\) = \(\frac{8}{9}\),

therefore Nancy has \(\frac{8}{9}\)

more candies than Joy.

**Test Prep**

Question 6.

Jolene is cutting a strip of yarn that is \(\frac{11}{12}\) inch long into pieces that are \(\frac{2}{12}\) inch long for a collage. How many complete pieces can she make?

Answer:

5 complete pieces Jolene can make,

Explanation:

Given Jolene is cutting a strip of yarn that is

\(\frac{11}{12}\) inch long into pieces

that are \(\frac{2}{12}\) inch long for a collage.

Number of complete pieces can she make are

\(\frac{11}{12}\) ÷ \(\frac{2}{12}\) =

\(\frac{11}{12}\) X \(\frac{12}{2}\) =

\(\frac{11 X 12}{12 X 2}\) = \(\frac{11}{2}\),

as numerator is greater than denominator we write in

mixed fraction as 5\(\frac{1}{2}\) therefore

5 complete pieces Jolene can make.

Question 7.

Sinh has \(\frac{14}{16}\) pound of nuts. He separates them into \(\frac{2}{16}\)-pound servings. How many servings can he make? Which expression models the situation?

A. \(\frac{2}{16}\) ÷ \(\frac{14}{16}\)

B. \(\frac{2}{16}\) × \(\frac{14}{16}\)

C. \(\frac{14}{16}\) ÷ \(\frac{2}{16}\)

D. \(\frac{14}{16}\) – \(\frac{2}{16}\)

Answer:

C. \(\frac{14}{16}\) ÷ \(\frac{2}{16}\),

Explanation:

Given Sinh has \(\frac{14}{16}\) pound of nuts.

He separates them into \(\frac{2}{16}\)-pound

servings. Number of servings can he make is the

expression models the situation is

\(\frac{14}{16}\) ÷ \(\frac{2}{16}\)

so matches with bit C. \(\frac{14}{16}\) ÷ \(\frac{2}{16}\).

Question 8.

Which question can be answered using the expression \(\frac{3}{8}\) ÷ \(\frac{5}{8}\) ?

A. How many \(\frac{5}{8}\)-cup servings of apple cider are in \(\frac{3}{8}\) cup of cider?

B. How many \(\frac{3}{8}\)-cup servings of apple cider are in \(\frac{5}{8}\) cup of cider?

C. Dan drank \(\frac{3}{8}\) of a \(\frac{5}{8}\)-cup serving of apple cider. How much did he drink?

D. Dan drank \(\frac{5}{8}\) of a \(\frac{3}{8}\)-cup serving of apple cider. How much did he drink?

Answer:

Bits B and D,

Explanation:

Given to find questions can be answered using the expression

\(\frac{3}{8}\) ÷ \(\frac{5}{8}\) are

bit A. How many \(\frac{5}{8}\)-cup servings of

apple cider are in \(\frac{3}{8}\) cup of cider? and

bit D. Dan drank \(\frac{5}{8}\) of a

\(\frac{3}{8}\)-cup serving of apple cider. How much did he drink?.

Question 9.

Terell is cutting a piece of trimming that is \(\frac{15}{18}\) foot long into pieces that are \(\frac{3}{18}\) foot long. How many pieces will Terell have?

A. 3 pieces

B. 5 pieces

C. 6 pieces

D. 8 pieces

Answer:

B. 5 pieces,

Explanation:

Given Terell is cutting a piece of trimming that is

\(\frac{15}{18}\) foot long into pieces that are

\(\frac{3}{18}\) foot long. Number of pieces will

Terell have \(\frac{15}{18}\) ÷ \(\frac{3}{18}\) =

\(\frac{15}{18}\) X \(\frac{18}{3}\) =

\(\frac{15 X 18}{18 X 3}\) = 5, Matches with bit

B. 5 pieces.

**Spiral Review**

Question 10.

What is the absolute value of -8?

_________________

Answer:

8,

Explanation:

The absolute value is the non-negative value of a

real number without regard for its sign so the

absolute value of -8 is 8.

Question 11.

Write an inequality to compare the integers -5 and -6.

_________________

Answer:

-5 > -6,

Explanation:

As – 5 is greater than -6 so an inequality to

compare the integers -5 and -6 is -5 > -6.

Question 12.

Find the product: \(\frac{2}{3}\) × \(\frac{3}{8}\).

Answer:

\(\frac{1}{4}\),

Explanation:

Given to find the product

\(\frac{2}{3}\) X \(\frac{3}{8}\) so it is

\(\frac{2 X 3}{3 X 8}\) = \(\frac{1}{4}\).