We included **H****MH Into Math Grade 6 Answer Key**** PDF** **Module 3 Lesson 4 Practice and Apply Division of Fractions and Mixed Numbers** to make students experts in learning maths.

## HMH Into Math Grade 6 Module 3 Lesson 4 Answer Key Practice and Apply Division of Fractions and Mixed Numbers

I Can divide mixed numbers and fractions to solve problems.

**Step It Out**

1. Kevin is making hamburgers for a cookout. He bought 10\(\frac{1}{4}\) pounds of ground meat. How many \(\frac{1}{4}\)-pound hamburger patties can he make?

A. Complete the division problem that answers this question.

B. He can make ____ \(\frac{1}{4}\)-pound patties.

Answer:

A.

B. He can make 41 number of \(\frac{1}{4}\)-pound patties,

Explanation:

Given Kevin is making hamburgers for a cookout.

He bought 10\(\frac{1}{4}\) pounds of ground meat, how many \(\frac{1}{4}\)-pound hamburger patties can he make,

A. Completed the division problem that answers this question above,

B. Kevin can make 41 number of \(\frac{1}{4}\)-pound patties.

2. Kevin’s friend Justin is bringing juice to the cookout. If he brings 43\(\frac{3}{4}\) pints of juice, then how many 2\(\frac{1}{2}\)-pint bottles can be filled?

A. Complete the division problem that answers this question.

Explanation:

Given Kevin’s friend Justin is bringing juice to the cookout. If he brings 43\(\frac{3}{4}\) pints of juice, so 2\(\frac{1}{2}\)-pint bottles can be filled

completed the division problem that answers this question above as 17\(\frac{1}{2}\)-pint bottles can be filled.

**Turn and Talk** If Kevin made \(\frac{1}{2}\)-pound patties, how many could he make? How does this compare to the number of \(\frac{1}{4}\)-pound patties? Explain.

Answer:

Quantity of number of pound patties changes from 41 number of \(\frac{1}{4}\)-pound patties to 82 number of \(\frac{1}{2}\)-pound patties,

ground meat quantity will be the same,

Explanation:

If Kevin made \(\frac{1}{2}\)-pound patties, he can make 82 number of \(\frac{1}{2}\)-pound patties, Comparing to the number of \(\frac{1}{4}\)-pound patties it is only quantity of number of pound patties changes from

41 number of \(\frac{1}{4}\)-pound patties to 82 number of \(\frac{1}{2}\)-pound patties ground meat quantity will be the same.

**Step It Out**

3. Cedric finished a 4-mile race. If he ran each mile at the same pace, how many minutes did he average for each mile?

A. Write an expression to represent this situation.

___________________

B. Evaluate the division expression using the reciprocal of the divisor. Show your work.

C. How many minutes did Cedric take to run each mile?

___________________

Answer:

A. m = 38 \(\frac{1}{2}\) ÷ 4,

B.

C. 9\(\frac{5}{8}\) minutes,

Explanation:

Given Cedric finished a 4-mile race. If he ran each mile at the same pace, let m be number of

minutes did he average for each mile so

A. An expression to represent this situation is m = 38 \(\frac{1}{2}\) ÷ 4,

B. Evaluated the division expression using the reciprocal of the divisor. Shown my work above,

C. Number of minutes did Cedric take to run each mile is 9\(\frac{5}{8}\) minutes.

**Turn and Talk** How could you use a model to find how many minutes Cedric used to run each mile?

**Check Understanding**

Question 1.

Yousef is cutting pieces of construction paper so he can make cards for his family. Each piece of paper is 11\(\frac{1}{2}\) inches wide. If he cuts that width so he would have two equal-sized smaller pieces, how wide will each smaller piece be?

___________________

Answer:

\(\frac{23}{4}\) inches wide or 5\(\frac{3}{4}\) inches wide,

Explanation:

Given Yousef is cutting pieces of construction paper so he can make cards for his family. Each piece of paper is 11\(\frac{1}{2}\) inches wide. If he cuts that width, so he would have two equal-sized smaller pieces, therefore wide will each smaller piece be 11\(\frac{1}{2}\) ÷ 2 solving

\(\frac{23}{2}\) X \(\frac{1}{2}\) = \(\frac{23 X 1}{2 X 2}\) = \(\frac{23}{4}\) inches wide or \(\frac{5 X 4 + 3}{4}\) = 5 \(\frac{3}{4}\) inches wide.

Question 2.

Marisol has 4\(\frac{1}{2}\) cups of flour. A biscuit recipe she wants to try requires \(\frac{3}{4}\) cup of flour for a single batch of biscuits. How many batches of biscuits can Marisol make?

Answer:

6 batches of biscuits can Marisol can make,

Explanation:

Given Marisol has 4\(\frac{1}{2}\) cups of flour.

A biscuit recipe she wants to try requires \(\frac{3}{4}\) cup of flour for a single batch of biscuits. Number of batches of biscuits can Marisol make are 4\(\frac{1}{2}\) ÷ \(\frac{3}{4}\) solving \(\frac{9}{2}\) X \(\frac{4}{3}\) = \(\frac{9 X 4}{2 X 3}\) = \(\frac{36}{6}\) = 6. Therefore, Marisol can make 6 batches of biscuits.

**For Problems 3-8, divide the mixed numbers or fractions.**

Question 3.

3\(\frac{1}{8}\) ÷ \(\frac{1}{8}\) ___________________

Answer:

25,

Explanation:

Given to find 3\(\frac{1}{8}\) ÷ \(\frac{1}{8}\) = \(\frac{3 X 8 + 1}{8}\) X \(\frac{8}{1}\) = \(\frac{25}{8}\) X \(\frac{8}{1}\) as 8 and 8 goes we get 25.

Question 4.

6\(\frac{2}{5}\) ÷ 4\(\frac{1}{10}\) _______

Answer:

\(\frac{64}{41}\) or 1\(\frac{23}{41}\),

Explanation:

Given to find 6\(\frac{2}{5}\) ÷ 4\(\frac{1}{10}\) = \(\frac{6 X 5 + 2}{5}\) ÷ \(\frac{4 X 10 + 1}{10}\) = \(\frac{32}{5}\) X \(\frac{10}{41}\)

\(\frac{32 X 10}{5 X 41}\) = \(\frac{64}{41}\) as numerator is greater we write in

mixed fraction as 1\(\frac{23}{41}\).

Question 5.

4\(\frac{1}{2}\) ÷ 3\(\frac{2}{3}\) ___________________

Answer:

\(\frac{27}{22}\) or 1\(\frac{5}{22}\),

Explanation:

Given to find 4\(\frac{1}{2}\) ÷ 3\(\frac{2}{3}\) = \(\frac{4 X 2 + 1}{2}\) ÷ \(\frac{3 X 3 + 2}{3}\) = \(\frac{9}{2}\) X \(\frac{3}{11}\) = \(\frac{9 X 3}{2 X 11}\) = \(\frac{27}{22}\) as numerator is greater we write in mixed fraction as 1\(\frac{5}{22}\).

Question 6.

2\(\frac{5}{8}\) ÷ 1\(\frac{3}{4}\) ___________________

Answer:

\(\frac{77}{36}\) or 2\(\frac{5}{36}\),

Explanation:

Given to find 2\(\frac{5}{8}\) ÷ 1\(\frac{5}{22}\) = \(\frac{2 X 8 + 5}{8}\) ÷ \(\frac{1 X 22 + 5}{22}\) = \(\frac{21}{8}\) X \(\frac{22}{27}\) = \(\frac{21 X 22}{8 X 27}\) = \(\frac{7 X 11}{4 X 9}\) = \(\frac{77}{36}\) as numerator is greater we write in mixed fraction as 2\(\frac{5}{36}\).

Question 7.

5\(\frac{3}{4}\) ÷ \(\frac{1}{2}\) ___________________

Answer:

\(\frac{23}{2}\) or 11\(\frac{1}{2}\),

Explanation:

Given to find 5\(\frac{3}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{5 X 4 + 3}{4}\) X 2 = \(\frac{23 X 2}{4}\) = \(\frac{23}{2}\) as numeratore is greater we write in

mixed fraction as 11\(\frac{1}{2}\).

Question 8.

7\(\frac{5}{6}\) ÷ 2\(\frac{1}{3}\) ___________________

Answer:

\(\frac{47}{16}\) or 2\(\frac{15}{16}\),

Explanation:

Given to find 7\(\frac{5}{6}\) ÷ 2\(\frac{2}{3}\) = \(\frac{7 X 6 + 5}{6}\) ÷ \(\frac{2 X 3 + 2}{3}\) = \(\frac{47}{6}\) X \(\frac{3}{8}\) = \(\frac{47 X 3}{6 X 8}\) = \(\frac{47 X 1}{2 X 8}\) = \(\frac{47}{16}\) as numerator is greater we write in mixed fraction as 2\(\frac{15}{16}\).

**On Your Own**

Question 9.

To paint a bedroom, Jade estimates she will need to buy 3\(\frac{1}{4}\) gallons of paint. How many \(\frac{1}{2}\)-gallon cans of paint should she buy? Explain.

Answer:

Jade buys \(\frac{13}{2}\) or 6\(\frac{1}{2}\) gallon cans of paint,

Explanation:

Given to paint a bedroom, Jade estimates she will need to buy 3\(\frac{1}{4}\) gallons of paint. Number of \(\frac{1}{2}\)-gallon cans of paint should she buy are 3\(\frac{1}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{3 X 4 + 1}{4}\) X 2 = \(\frac{13}{4}\) X 2 = \(\frac{13 X 2}{4}\) = \(\frac{13}{2}\) as numerator is greater we write in

mixed fraction as 6\(\frac{1}{2}\).

Question 10.

**Critique Reasoning** Jefferson shows the following work for a division problem. What mistake did Jefferson make? What is the correct answer to his original division problem?

5\(\frac{2}{5}\) ÷ 2\(\frac{1}{3}\) = \(\frac{27}{5}\) ÷ \(\frac{6}{3}\) = \(\frac{27}{5}\) × \(\frac{3}{6}\)

= \(\frac{81}{30}\) = 2\(\frac{21}{30}\) = 2\(\frac{7}{10}\)

Answer:

2\(\frac{1}{3}\) not equal to \(\frac{6}{3}\),

but \(\frac{7}{3}\) correct answer is 2\(\frac{11}{35}\),

Explanation:

Given Jefferson shows the following work for a division problem. Mistake did Jefferson made are

2\(\frac{1}{3}\) is not \(\frac{6}{3}\) but \(\frac{7}{3}\) solving for correct answe 5\(\frac{2}{5}\) ÷ 2\(\frac{1}{3}\) = \(\frac{27}{5}\) ÷ \(\frac{7}{3}\) = \(\frac{27}{5}\) X \(\frac{3}{7}\) = \(\frac{81}{35}\) = 2\(\frac{11}{35}\).

Question 11.

A cube has a surface area of 253\(\frac{1}{2}\) square inches. What is the area of one face of the cube in square inches? How do you know?

___________________

Answer:

42\(\frac{1}{4}\) square inches,

Explanation:

Given a cube has a surface area of 253\(\frac{1}{2}\) square inches.

as surface area is 6 a^{2}, The area of one face of the cube in square inches is

253\(\frac{1}{2}\) ÷ 6 = \(\frac{253 X 2 + 1}{2}\) X \(\frac{1}{6}\) =

\(\frac{507}{12}\) as both goes in 3, 3 X 169 = 507 and 3 x 4 = 12 , so \(\frac{169}{4}\) as numerator is greater, we write in mixed fraction as 42\(\frac{1}{4}\) square inches.

Question 12.

Darlene has 6\(\frac{3}{4}\) gallons of gasoline. Every time she mows a lawn, she uses \(\frac{3}{8}\) gallon. How many times can she mow a lawn before she needs more gas?

Answer:

18 times Darlene can mow a lawn before she needs more gas,

Explanation:

Given Darlene has 6\(\frac{3}{4}\) gallons of gasoline.

Every time she mows a lawn, she uses \(\frac{3}{8}\) gallon.

Number of times can she mow a lawn before she needs more gas 6\(\frac{3}{4}\) ÷ \(\frac{3}{8}\) = \(\frac{6 X 4 + 3}{4}\) X \(\frac{8}{3}\) =

\(\frac{27}{4}\) X \(\frac{8}{3}\) = \(\frac{27 X 8}{4 X 3}\) = \(\frac{9 X 2}{1 X 1}\) = 18. Therefore 18 times Darlene can mow a lawn before she needs more gas.

Question 13.

A rectangle has an area of 24\(\frac{1}{2}\) square feet. If the length of the rectangle is 4\(\frac{3}{8}\) feet, what is the width in feet?

___________________

Answer:

The width is 5\(\frac{3}{5}\) feet,

Explanation:

Given a rectangle has an area of 24\(\frac{1}{2}\) square feet.

If the length of the rectangle is 4\(\frac{3}{8}\) feet, so width is 24\(\frac{1}{2}\) ÷ \(\frac{35}{8}\) = \(\frac{24 X 2 + 1}{2}\) X \(\frac{8}{35}\) =

\(\frac{49}{2}\) X \(\frac{8}{35}\) = \(\frac{49 X 8}{2 X 35}\) = \(\frac{7 X 4}{1 X 5}\) = \(\frac{28}{5}\) as numerator is greater we write in mixed fraction as 5\(\frac{3}{5}\) feet.

**On Your Own**

Question 14.

**Open Ended** Write a story problem that is modeled by the expression 10\(\frac{1}{2}\) ÷ 5\(\frac{1}{2}\). What is the answer to your problem?

___________________

___________________

___________________

Answer:

Story:

“Benjamin have 10\(\frac{1}{2}\) feet of ribbon he has cut them into 5\(\frac{1}{2}\) feets how many bows can he make?”, 1\(\frac{10}{11}\) bow,

Explanation:

Asking to write a story problem that is modeled by the expression 10\(\frac{1}{2}\) ÷ 5\(\frac{1}{2}\).

So Story:

“Benjamin have 10\(\frac{1}{2}\) feets of ribbon he has cut them into 5\(\frac{1}{2}\) feets how many bows can he make?”, solving 10\(\frac{1}{2}\) ÷ 5\(\frac{1}{2}\) = \(\frac{10 X 2 + 1}{2}\) ÷ \(\frac{5 X 2 + 1}{2}\) = \(\frac{21}{2}\) X \(\frac{2}{11}\) = \(\frac{21 X 2}{2 X 11}\) = \(\frac{21}{11}\)

as numerator is greater we write in mixed fraction as 1\(\frac{10}{11}\) bow.

Question 15.

Jack mails 10 packages that each weigh the same amount. If the combined weight of all 10 packages is 67\(\frac{1}{2}\) pounds, how much does one package weigh? Show your work.

Answer:

6\(\frac{3}{4}\) each one package weigh,

Explanation:

Given Jack mails 10 packages that each weigh the same amount.

If the combined weight of all 10 packages is 67\(\frac{1}{2}\) pounds, So does one package weigh is 67\(\frac{1}{2}\) ÷ 10 = \(\frac{67 X 2 + 1}{2}\) X \(\frac{1}{10}\) = \(\frac{135}{2}\) X \(\frac{1}{10}\) = \(\frac{135 X 1}{2 X 10}\) = \(\frac{27}{4}\) as numerator is greater we write in mixed fraction as 6\(\frac{3}{4}\) each one package weigh.

Question 16.

Peter is building a fence. If each section is 4\(\frac{1}{2}\) feet long, how many sections will there be in the finished fence shown?

Answer:

8 \(\frac{1}{2}\) sections will there be in the finished fence,

Explanation:

Given Peter is building a fence. If each section is 4\(\frac{1}{2}\) feet long, Number of sections will there be in the finished fence shown are 38\(\frac{1}{4}\) ÷ 4\(\frac{1}{2}\) = \(\frac{38 X 4 + 1}{4}\) ÷ \(\frac{4 X 2 + 1}{2}\) = \(\frac{153}{4}\) X \(\frac{2}{9}\) = \(\frac{3 X 3 X 17 X 2}{2 X 2 X 3 x 3}\) = \(\frac{17}{2}\) as numerator is greater we write in mixed fraction as 8\(\frac{1}{2}\) sections will there be in the finished fence.

Question 17.

Jill has a pail of water that holds 6\(\frac{1}{2}\) quarts. She needs to give some plants \(\frac{1}{8}\) quart each. How many plants can she water?

_____________________

_____________________

Answer:

52 plants she can water,

Explanation:

Given Jill has a pail of water that holds 6\(\frac{1}{2}\) quarts. She needs to give

some plants \(\frac{1}{8}\) quart each. Number of plants can she water are 6\(\frac{1}{2}\) ÷ \(\frac{1}{8}\) = \(\frac{6 X 2 + 1}{2}\) X 8 = \(\frac{13}{2}\) X 8 = \(\frac{13 X 8}{2}\) = 52, 52 plants.

**For Problems 18-23, divide.**

Question 18.

1\(\frac{1}{2}\) ÷ \(\frac{1}{2}\) ___________________

Answer:

3,

Explanation:

Given 1\(\frac{1}{2}\) ÷ \(\frac{1}{2}\) = \(\frac{1 X 2 + 1}{2}\) X 2 =

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

Question 19.

6\(\frac{1}{5}\) ÷ 2 ___________________

Answer:

3\(\frac{1}{10}\),

Explanation:

Given 6\(\frac{1}{5}\) ÷ 2 solving \(\frac{6 X 5 + 1}{5}\) X \(\frac{1}{2}\) =

\(\frac{31}{5}\) X \(\frac{1}{2}\) = \(\frac{31 X 1}{5 x 2}\) = \(\frac{31}{10}\) as numerator is greater we write in mixed fraction as 3\(\frac{1}{10}\).

Question 20.

3\(\frac{2}{5}\) ÷ \(\frac{1}{4}\) ___________________

Answer:

13\(\frac{3}{5}\),

Explanation:

Given 3\(\frac{2}{5}\) ÷ \(\frac{1}{4}\) solving \(\frac{3 X 5 + 2}{5}\) X 4 =

\(\frac{17 X 4}{5}\) = \(\frac{68}{5}\) as numerator is greater we write in mixed fraction as 13\(\frac{3}{5}\).

Question 21.

\(\frac{6}{5}\) ÷ \(\frac{1}{5}\) ___________________

Answer:

6,

Explanation:

Given \(\frac{6}{5}\) ÷ \(\frac{1}{5}\) solving \(\frac{6}{5}\) X 5 =

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

Question 22.

1\(\frac{4}{8}\) ÷ \(\frac{2}{3}\) ___________________

Answer:

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

Explanation:

Given 1\(\frac{4}{8}\) ÷ \(\frac{2}{3}\) solving \(\frac{1 X 8 + 4}{8}\) X \(\frac{3}{2}\) = \(\frac{12}{8}\) X \(\frac{3}{2}\) = \(\frac{12 X 3}{8 x 2}\) = \(\frac{9}{4}\) as numerator is greater we write in mixed fraction as

2\(\frac{1}{4}\).

Question 23.

10\(\frac{1}{5}\) ÷ 3\(\frac{3}{10}\) ___________________

Answer:

3\(\frac{1}{11}\),

Explanation:

Given 10\(\frac{1}{5}\) ÷ 3\(\frac{3}{10}\) = \(\frac{10 X 5 + 1}{5}\) ÷ \(\frac{3 X 10 + 3}{10}\) = \(\frac{51}{5}\) X \(\frac{10}{33}\) =\(\frac{51 X 10}{5 X 33}\) = \(\frac{34}{11}\) as numerator is greater we write in mixed fraction as 3\(\frac{1}{11}\).

**Lesson 3.4 More Practice/Homework**

**Practice and Apply Division of Fraction and Mixed Numbers**

Question 1.

Andy works at a grocery store. The manager of the store would like Andy to set up a display of apples. Part of the display will include bags of apples. Each bag of apples has the same weight as shown. If there are 39 pounds of apples in the back of the store, how many bags of apples can Andy make for the display?

Answer:

Andy can make for the display 58 \(\frac{1}{2}\) bags,

Explanation:

Given Andy works at a grocery store. The manager of the store would like Andy to set up a display of apples. Part of the display will include bags of apples. Each bag of apples has the same weight as

1\(\frac{1}{2}\) pounds of bags.

If there are 39 pounds of apples in the back of the store number of bags of apples can Andy make for the display are 39 ÷ 1\(\frac{1}{2}\) = 39 ÷ \(\frac{1 X 2 + 1}{2}\) = 39 X \(\frac{3}{2}\) = \(\frac{39 X 3}{2}\) = \(\frac{117}{2}\)

as numerator is greater we write in mixed fraction as 58 \(\frac{1}{2}\) bags of apples.

Question 2.

**Attend to Precision** Gilbert needs to move 20\(\frac{3}{4}\) pounds of soil from a truck to a garden. His wheelbarrow can move 6 pounds at one time. How many loads of Explain.

Answer:

3\(\frac{11}{24}\) loads,

Explanation:

Given Gilbert needs to move 20\(\frac{3}{4}\) pounds of soil from a truck to a garden. His wheelbarrow can move 6 pounds at one time number of loads he can move are

20 \(\frac{3}{4}\) ÷ 6 = \(\frac{20 X 4 + 3}{4}\) X \(\frac{1}{6}\) =

\(\frac{83}{4}\) X \(\frac{1}{6}\) = \(\frac{83}{4 x 6}\) = \(\frac{83}{24}\) as numerator is greater we write in mixed fraction as 3\(\frac{11}{24}\).

Question 3.

**Math on the Spot** The area of a rectangular garden is 53\(\frac{5}{6}\) square feet. The length of the garden is 9\(\frac{1}{2}\) feet. What is the width?

___________________

Answer:

Width is 5\(\frac{2}{3}\) feet,

Explanation:

Given the area of a rectangular garden is 53\(\frac{5}{6}\) square feet. The length of the garden is 9\(\frac{1}{2}\) feet. So the width is 53\(\frac{5}{6}\) ÷ 9\(\frac{1}{2}\) = \(\frac{53 X 6 + 5}{6}\) ÷ \(\frac{9 X 2 + 1}{2}\) = \(\frac{323}{6}\) X \(\frac{2}{19}\) = \(\frac{323 X 2}{6 X 19}\) = \(\frac{17}{3}\)

as numerator is greater we write in mixed fraction as 5\(\frac{2}{3}\).

Question 4.

Ramon is making book shelves. He bought a board that is \(\frac{4}{5}\) meter long. He needs 5 shelves. If he cuts 5 equal-sized pieces from the board, how long is each piece?

___________________

Answer:

Each long piece \(\frac{4}{25}\) meter,

Explanation:

Given Ramon is making book shelves. He bought a board that is \(\frac{4}{5}\) meter long.

He needs 5 shelves. If he cuts 5 equal-sized pieces from the board, long is each piece \(\frac{4}{5}\) ÷ 5, \(\frac{4}{5}\) X \(\frac{1}{5}\) = \(\frac{4 X 1}{5 X 5}\) = \(\frac{4}{25}\).

**For Problems 5-10, divide.**

Question 5.

\(\frac{5}{4}\) ÷ \(\frac{1}{10}\)

Answer:

12\(\frac{1}{2}\),

Explanation:

Given \(\frac{5}{4}\) ÷ \(\frac{1}{10}\) = \(\frac{5}{4}\) X \(\frac{10}{1}\) = \(\frac{5 X 10}{4 X 1}\) = \(\frac{25}{2}\) as numerator is greater we write in mixed fraction as 12\(\frac{1}{2}\).

Question 6.

1\(\frac{1}{2}\) ÷ 8

Answer:

\(\frac{3}{16}\),

Explanation:

Given 1\(\frac{1}{2}\) ÷ 8 solving \(\frac{1 X 2 + 1}{2}\) X \(\frac{1}{8}\) =

\(\frac{3}{2}\) X \(\frac{1}{8}\) = \(\frac{3 X 1}{2 x 8}\) = \(\frac{3}{16}\).

Question 7.

4\(\frac{1}{10}\) ÷ \(\frac{2}{5}\)

Answer:

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

Explanation:

Given 4\(\frac{1}{10}\) ÷ \(\frac{2}{5}\) solving \(\frac{4 X 10 + 1}{10}\) X \(\frac{5}{2}\) = \(\frac{41 X 5}{10 X 2}\) = \(\frac{41}{4}\)

as numerator is greater we write in mixed fraction as 10\(\frac{1}{4}\).

Question 8.

5\(\frac{1}{2}\) ÷ 6\(\frac{1}{3}\)

Answer:

\(\frac{33}{38}\),

Explanation:

Given 5\(\frac{1}{2}\) ÷ 6\(\frac{1}{3}\) = \(\frac{5 X 2 + 1}{2}\) ÷ \(\frac{6 X 3 + 1}{3}\) = \(\frac{11}{2}\) X \(\frac{3}{19}\) =

\(\frac{11 X 3}{2 X 19}\) = \(\frac{33}{38}\).

Question 9.

10 ÷ 3\(\frac{3}{4}\)

Answer:

\(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Explanation:

Given 10 ÷ 3\(\frac{3}{4}\) = 10 ÷ \(\frac{3 X 4 + 3}{4}\) = 10 X \(\frac{4}{15}\) = \(\frac{10 X 4}{15}\) = \(\frac{8}{3}\) as numerator is greater we write in mixed fraction as 2\(\frac{2}{3}\).

Question 10.

9\(\frac{1}{5}\) ÷ \(\frac{1}{10}\)

Answer:

92,

Explanation:

Given 9\(\frac{1}{5}\) ÷ \(\frac{1}{10}\) solving \(\frac{9 X 5 + 1}{5}\) X \(\frac{10}{1}\) = \(\frac{46 X 10}{5 X 1}\) = 92.

**Test Prep**

Question 11.

Which two expressions are equivalent to 4\(\frac{1}{2}\) ÷ 2\(\frac{1}{4}\)?

A. 4\(\frac{1}{2}\) × 2\(\frac{4}{1}\)

B. \(\frac{9}{2}\) ÷ \(\frac{9}{4}\)

C. \(\frac{8}{2}\) × \(\frac{8}{4}\)

D. \(\frac{9}{2}\) × \(\frac{4}{9}\)

E. \(\frac{8}{2}\) × \(\frac{4}{9}\)

Answer:

B. \(\frac{9}{2}\) ÷ \(\frac{9}{4}\) and

D. \(\frac{9}{2}\) × \(\frac{4}{9}\),

Explanation:

First evaluating 4\(\frac{1}{2}\) ÷ 2\(\frac{1}{4}\) = \(\frac{4 X 2 + 1}{2}\) ÷ \(\frac{2 X 4 + 1}{4}\) = \(\frac{9}{2}\) X \(\frac{4}{9}\) = \(\frac{9 X 4}{2 X 9}\) = 2 now checking with bits

Bit A. 4\(\frac{1}{2}\) X 2\(\frac{4}{1}\) = \(\frac{4 x 2 + 1}{2}\) X \(\frac{2 X 1 + 4}{1}\) = \(\frac{9}{2}\) X \(\frac{4}{1}\) = \(\frac{9 x 4}{2 X 1}\) = 18 which will ot match with 2,

Bit B. \(\frac{9}{2}\) ÷ \(\frac{9}{4}\) = \(\frac{9}{2}\) X \(\frac{4}{9}\) = \(\frac{9 X 4}{2 X 9}\) = 2 matches,

Bit C. \(\frac{8}{2}\) X \(\frac{8}{4}\) = \(\frac{8 X 8}{2 X 4}\) = \(\frac{64}{8}\) = 8 which will not match with 2.

Bit D. \(\frac{9}{2}\) X \(\frac{4}{9}\) = \(\frac{9 X 4}{2 X 9}\) = \(\frac{4}{2}\) = 2 which will match with 2,

Bit E. \(\frac{8}{2}\) X \(\frac{4}{9}\) = \(\frac{8 X 4}{2 X 9}\) = \(\frac{16}{9}\) which will not match with 2,

The expressions which are equivalent to 4\(\frac{1}{2}\) ÷ 2\(\frac{1}{4}\) are

B. \(\frac{9}{2}\) ÷ \(\frac{9}{4}\) and D. \(\frac{9}{2}\) × \(\frac{4}{9}\).

Question 12.

An expression is shown.

3\(\frac{1}{8}\) ÷ 2\(\frac{3}{4}\)

What is the value of the expression?

___________________

Answer:

The value of the expression is 1\(\frac{3}{22}\),

Explanation:

Given expression 3\(\frac{1}{8}\) ÷ 2\(\frac{3}{4}\)

solving \(\frac{3 X 8 + 1}{8}\) ÷ \(\frac{2 X 4 + 3}{4}\) = \(\frac{25}{8}\) X \(\frac{4}{11}\) = \(\frac{25 X 4}{8 X 11}\) = \(\frac{25}{22}\)

as numerator is greater we write in mixed fraction as 1\(\frac{3}{22}\).

Question 13.

Tara made 2\(\frac{3}{4}\) cups of white rice for a dinner party. She has 3 friends coming to the party and will give each person, including herself, the same amount of rice. How many cups of rice will she serve each friend and herself?

A. \(\frac{7}{20}\) cup

B. \(\frac{11}{16}\) cup

C. 1\(\frac{7}{20}\) cups

D. 1\(\frac{11}{16}\) cups

Answer:

B. \(\frac{11}{16}\) cup,

Explanation:

Given Tara made 2\(\frac{3}{4}\) cups of white rice for a dinner party. She has 3 friends

coming to the party and will give each person, including herself, the same amount of rice.

Number of cups of rice will she serve each friend and herself are 2\(\frac{3}{4}\) ÷ 4 solving

\(\frac{2 X 4 + 3}{4}\) X \(\frac{1}{4}\) = \(\frac{11}{4}\) X \(\frac{1}{4}\) = \(\frac{11 X 1}{4 X 4}\) = \(\frac{11}{16}\) matches with B.

Question 14.

Foster needs to divide a plot of land covering 5\(\frac{3}{8}\) acres into plots covering \(\frac{3}{4}\) acre each. How many whole plots can he make?

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Answer:

7 whole plots Foster can make,

Explanation:

Given Foster needs to divide a plot of land covering 5\(\frac{3}{8}\) acres into plots covering

\(\frac{3}{4}\) acre each. Number of whole plots can he make are 5\(\frac{3}{8}\) ÷ \(\frac{3}{4}\) solving \(\frac{5 X 8 + 3}{8}\) ÷ \(\frac{3}{4}\) =

\(\frac{43}{8}\) X \(\frac{4}{3}\) = \(\frac{43 X 4}{8 X 3}\) = \(\frac{43}{6}\) as numerator is greater we write in mixed fraction as 7\(\frac{1}{6}\) therefore Foster can make 7 whole plots.

Question 15.

An alligator is 11\(\frac{3}{4}\) feet long. Its tail is 5\(\frac{7}{8}\) feet long. What fraction of the alligator’s total length is its tail?

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Answer:

The fraction of 2 is the alligator’s total length is its tail,

Explanation:

Given an alligator is 11\(\frac{3}{4}\) feet long.

Its tail is 5\(\frac{7}{8}\) feet long. The fraction of the alligator’s total length is its tail is

11\(\frac{3}{4}\) ÷ 5\(\frac{7}{8}\) solving \(\frac{11 X 4 + 3}{4}\) ÷ \(\frac{5 X 8 + 7}{8}\) = \(\frac{47}{4}\) X \(\frac{8}{47}\) =

\(\frac{47 X 8}{4 X 47}\) = 2, therefore the fraction of 2 is the alligator’s total length is its tail.

**Spiral Review**

Question 16.

Write the numbers in order from least to greatest: -5, 0, -10, 1, -18.

Answer:

-18, -10, -5, 0 , 1,

Explanation:

The given numbers are -5, 0, -10, 1, -18 numbers in

order from least to greatest are as the least among all is

– 18 next -10 next -5 then 0 and 1 so the order is

-18, -10, -5, 0 , 1.

Question 17.

Add the fractions: \(\frac{1}{5}\) + \(\frac{1}{10}\).

Answer:

\(\frac{3}{10}\),

Explanation:

Given to add the fractions: \(\frac{1}{5}\) + \(\frac{1}{10}\),

when both denominators are same we take it as common and add numerator so we make common denominator by multiplying numerator and denominator of \(\frac{1}{5}\) by 2

so \(\frac{1 X 2}{5 X 2}\) = \(\frac{2}{10}\) now both have common denominator 10 so now we add numerators \(\frac{2}{10}\) + \(\frac{1}{10}\) = \(\frac{2 + 1}{10}\) = \(\frac{3}{10}\).