All the solutions provided in **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 9 Lesson 8 Model Fractions and Multiplication **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 9 Lesson 8 Model Fractions and Multiplication

You have learned to write a fraction as a sum of unit fractions. For example, \(\frac{4}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\).

You can also write a fraction as a multiple of a unit fraction.

**Build It
**Use an equation to write \(\frac{4}{5}\) as a multiple of a unit fraction.

One Way:

Use fraction tiles.

Model \(\frac{4}{5}\) using fraction tiles. Draw your result below.

How many \(\frac{1}{5}\)-tiles did you use?

Another Way:

Use repeated addition.

You know that \(\frac{4}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)

How many times is added to equal \(\frac{4}{5}\)?

So, \(\frac{4}{5}\) = ________________ × \(\frac{1}{5}\).

Answer:

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

Explanation:

\(\frac{4}{5}\) as a multiple of a unit fraction = ??

1. Use fraction tiles:

2. Use repeated addition:

You know that \(\frac{4}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)

=> 4 times \(\frac{1}{5}\) is added to equal \(\frac{4}{5}\).

You know that 6 is a multiple of 2. Any multiples of 6, such as 12, 18, and 24, are also multiples of 2. The same is true for fractions. A multiple of a fraction can also be written as a multiple of a unit fraction.

**Try It
**Use an equation to write 2 × \(\frac{4}{5}\) as a multiple of a unit fraction.

Use repeated addition to write 2 × \(\frac{4}{5}\) as \(\frac{4}{5}\) + \(\frac{4}{5}\).

\(\frac{4}{5}\) + \(\frac{4}{5}\) = \(\frac{8}{5}\) Add like fractions.

Model \(\frac{8}{5}\) using fraction tiles. Draw your result below.

How many \(\frac{1}{5}\)-tiles did you use? ______________

So, \(\frac{8}{5}\) is a multiple of \(\frac{4}{5}\). It is also a multiple of \(\frac{1}{5}\).

\(\frac{8}{5}\) = ________________ × \(\frac{1}{5}\)

Write an equation showing that \(\frac{8}{5}\) is a multiple of the unit fraction \(\frac{1}{5}\).

\(\frac{8}{5}\) = ________________ × \(\frac{1}{5}\)

So, 2 × \(\frac{4}{5}\) = ________________ × \(\frac{1}{5}\).

Answer:

Equation showing that \(\frac{8}{5}\) is a multiple of the unit fraction \(\frac{1}{5}\) is

2 × \(\frac{4}{5}\) = 8 × \(\frac{1}{5}\).

Explanation:

2 × \(\frac{4}{5}\) as a multiple of a unit fraction = ??

1. Use fraction tiles:

2 × \(\frac{4}{5}\) = \(\frac{4}{5}\) + \(\frac{4}{5}\) = \(\frac{8}{5}\)

2. Use repeated addition:

2 × \(\frac{4}{5}\) = \(\frac{4}{5}\) + \(\frac{4}{5}\).

=> \(\frac{4}{5}\) + \(\frac{4}{5}\) = \(\frac{8}{5}\)

So, \(\frac{8}{5}\) is a multiple of \(\frac{4}{5}\). It is also a multiple of \(\frac{1}{5}\).

\(\frac{8}{5}\) = 8 × \(\frac{1}{5}\)

**Talk About It
**Question 1.

**Mathematical PRACTICE**Identify Structure Write an equation showing how \(\frac{3}{8}\) is a multiple of \(\frac{1}{8}\).

Answer:

Equation showing \(\frac{3}{8}\) is a multiple of \(\frac{1}{8}\) is \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)

Explanation:

\(\frac{3}{8}\) is a multiple of \(\frac{1}{8}\):

=> \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)

=> (1 + 1 + 1) ÷ 8

=> \(\frac{3}{8}\)

Question 2.

Write equations showing how \(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\) and \(\frac{1}{8}\).

Answer:

Equations showing \(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\) and \(\frac{1}{8}\) is 2 × \(\frac{3}{8}\) = 6 × \(\frac{1}{8}\)

Explanation:

\(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\) and \(\frac{1}{8}\):

1. \(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\)

=> \(\frac{3}{8}\) + \(\frac{3}{8}\)

=> (3 + 3) ÷ 8

=> \(\frac{6}{8}\)

2. \(\frac{6}{8}\) is a multiple of \(\frac{1}{8}\):

=> \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)+ \(\frac{1}{8}\)+\(\frac{1}{8}\) + \(\frac{1}{8}\)

=> (1 + 1 + 1 + 1 + 1 + 1) ÷ 8

=> \(\frac{6}{8}\)

**Practice It
**

**Algebra Use an equation to write each fraction or product as a multiple of a unit fraction.**

Question 3.

\(\frac{3}{4}\) ________________

Answer:

Equation showing \(\frac{3}{4}\) as a multiple of a \(\frac{1}{4}\) unit fraction is

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

Explanation:

\(\frac{3}{4}\) as a multiple of a unit fraction:

=> \(\frac{1}{4}\) + \(\frac{1}{4}\)+ \(\frac{1}{4}\)

=> (1 + 1 +1) ÷ 4

=> \(\frac{3}{4}\)

Question 4.

\(\frac{7}{8}\) ________________

Answer:

Equation showing \(\frac{7}{8}\) as a multiple of a \(\frac{1}{8}\) unit fraction is 7 × \(\frac{1}{8}\)

Explanation:

\(\frac{7}{8}\) as a multiple of a unit fraction:

=> \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)+ \(\frac{1}{8}\)+ \(\frac{1}{8}\)+ \(\frac{1}{8}\)+ \(\frac{1}{8}\)

=> (1 + 1 + 1 + 1 + 1 + 1 + 1) ÷ 8

=> \(\frac{7}{8}\)

Question 5.

\(\frac{5}{12}\) ________________

Answer:

Equation showing \(\frac{5}{12}\) as a multiple of a \(\frac{1}{12}\) unit fraction is 5 × \(\frac{1}{12}\)

Explanation:

\(\frac{5}{12}\) as a multiple of a unit fraction:

=> \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\)+ \(\frac{1}{12}\)+ \(\frac{1}{12}\)

=> (1 + 1 + 1 + 1 + 1) ÷ 12

=> \(\frac{5}{12}\)

Question 6.

\(\frac{5}{6}\) ________________

Answer:

Equation showing \(\frac{5}{6}\) as a multiple of a \(\frac{1}{6}\) unit fraction is 5 × \(\frac{1}{6}\)

Explanation:

Equation showing \(\frac{5}{6}\) as a multiple of a unit fraction:

=> \(\frac{1}{6}\) + \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+\(\frac{1}{6}\)

=> (1 + 1 + 1 + 1 + 1) ÷ 6

=> \(\frac{5}{6}\)

Question 7.

2 × \(\frac{2}{3}\) ________________

Answer:

Equation showing 2 × \(\frac{2}{3}\) as a multiple of a \(\frac{1}{3}\) and \(\frac{2}{3}\) unit fraction is 4 × \(\frac{1}{3}\) = 2 × \(\frac{2}{3}\)

Explanation:

2 × \(\frac{2}{3}\) as a multiple of a unit fraction:

=> \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\)

=> 4 × \(\frac{1}{3}\) or 2 × \(\frac{2}{3}\)

Question 8.

2 × \(\frac{5}{6}\) ________________

Answer:

Equation showing 2 × \(\frac{5}{6}\) as a multiple of a \(\frac{5}{6}\) and \(\frac{1}{6}\) is \(\frac{5}{6}\) + \(\frac{5}{6}\) = 10 × \(\frac{1}{6}\)

Explanation:

2 × \(\frac{5}{6}\) as a multiple of a unit fraction:

=> \(\frac{5}{6}\)+ \(\frac{5}{6}\)

=> \(\frac{10}{6}\)

= \(\frac{1}{6}\) + \(\frac{1}{6}\)+\(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\) + \(\frac{1}{6}\)

=> 10 × \(\frac{1}{6}\)

=> 10\(\frac{1}{6}\)

Question 9.

4 × \(\frac{3}{4}\) ________________

Answer:

Equation showing 4 × \(\frac{3}{4}\) as a multiple of a \(\frac{3}{4}\) unit fraction is \(\frac{3}{4}\) + \(\frac{3}{4}\)+ \(\frac{3}{4}\)+\(\frac{3}{4}\)

Explanation:

4 × \(\frac{3}{4}\) as a multiple of a unit fraction:

=>\(\frac{3}{4}\) + \(\frac{3}{4}\)+ \(\frac{3}{4}\)+\(\frac{3}{4}\)

=> (3 + 3 + 3 + 3) ÷ 4

=> 12 ÷ 4 or \(\frac{12}{4}\)

Question 10.

3 × \(\frac{7}{8}\) ________________

Answer:

Equation showing 3 × \(\frac{7}{8}\) as a multiple of a \(\frac{7}{8}\) unit fraction is \(\frac{7}{8}\) + \(\frac{7}{8}\) + \(\frac{7}{8}\)

Explanation:

3 × \(\frac{7}{8}\) as a multiple of a unit fraction:

=> \(\frac{7}{8}\) + \(\frac{7}{8}\) + \(\frac{7}{8}\)

=> (7 + 7 + 7) ÷ 8

=> 21 ÷ 8 or \(\frac{21}{8}\)

Question 11.

5 × \(\frac{3}{5}\) ________________

Answer:

Equation showing 5 × \(\frac{3}{5}\) as a multiple of a \(\frac{3}{5}\) unit fraction is \(\frac{3}{5}\) + \(\frac{3}{5}\) + \(\frac{3}{5}\)+ \(\frac{3}{5}\)+ \(\frac{3}{5}\)

Explanation:

5 × \(\frac{3}{5}\) as a multiple of a unit fraction:

=> \(\frac{3}{5}\) + \(\frac{3}{5}\) + \(\frac{3}{5}\)+ \(\frac{3}{5}\)+ \(\frac{3}{5}\)

=> (3 + 3 + 3 + 3 + 3) ÷ 5

=\(\frac{15}{5}\)

Question 12.

6 × \(\frac{7}{12}\) ________________

Answer:

Equation showing 6 × \(\frac{7}{12}\) as a multiple of a \(\frac{7}{12}\) unit fraction is \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) +\(\frac{7}{12}\) + \(\frac{7}{12}\)

Explanation:

6 × \(\frac{7}{12}\) as a multiple of a unit fraction:

=> \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) +\(\frac{7}{12}\) + \(\frac{7}{12}\)

=> (7 + 7 + 7 + 7 + 7 + 7) ÷ 12

=> \(\frac{42}{12}\)

**Apply It
**Question 13.

**Mathematical PRACTICE**Model Math Use fraction tiles and repeated addition to write 3 × \(\frac{3}{4}\) as a multiple of a unit fraction. Draw your result below.

Answer:

Equation showing 3 × \(\frac{3}{4}\) as a multiple of a \(\frac{1}{4}\) unit fraction is 9 × \(\frac{1}{4}\)

Explanation:

3 × \(\frac{3}{4}\) as a multiple of a unit fraction.

=> \(\frac{1}{4}\) + \(\frac{1}{4}\)+ \(\frac{1}{4}\)+ \(\frac{1}{4}\)+ \(\frac{1}{4}\)+ \(\frac{1}{4}\)+ \(\frac{1}{4}\)+\(\frac{1}{4}\) + \(\frac{1}{4}\)

=> (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) ÷ 4

=> \(\frac{9}{4}\)

Question 14.

Gracie and Jackson each bought \(\frac{2}{3}\) pound of blackberries. Circle the correct equation that represents 2 × \(\frac{2}{3}\) as a multiple of a unit fraction.

2 × \(\frac{2}{3}\) = 4 × \(\frac{1}{3}\)

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

Answer:

2 × \(\frac{2}{3}\) as a multiple of a \(\frac{1}{3}\) unit fraction is 4 × \(\frac{1}{3}\).

Explanation:

Number of pound of blackberries Gracie and Jackson each bought = \(\frac{2}{3}\) .

2 × \(\frac{2}{3}\) as a multiple of a unit fraction = ??

=> \(\frac{2}{3}\) + \(\frac{2}{3}\)

=> (2 + 2) ÷ 3

=> \(\frac{4}{3}\)

=> \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) +\(\frac{1}{3}\)

=> 4 × \(\frac{1}{3}\)

Question 15.

**Mathematical PRACTICE** Use Algebra Find the unknown in the equation

m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\).

Answer:

Unknown in the equation m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) is 5.

Explanation:

Equation given:

m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\).

=> m = ??

=> m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\)

=> m × \(\frac{1}{6}\) = (1 + 1 + 1 + 1 + 1) ÷ 6

=> m × \(\frac{1}{6}\) = 5 × \(\frac{1}{6}\)

=> m = {5 × \(\frac{1}{6}\)} ÷ 5 × \(\frac{1}{6}\)

=> m = 5.

**Write About It
**Question 16.

How can any fraction \(\frac{a}{b}\) be written as a multiple of a unit fraction?

Answer:

Any fraction \(\frac{a}{b}\) be written as a multiple of a unit fraction by using the number of times the unit fraction holds to express the given fraction.

### McGraw Hill My Math Grade 4 Chapter 9 Lesson 8 My Homework Answer Key

**Practice
**

**Algebra Use an equation to write each fraction as a multiple of a unit fraction.**

Question 1.

Answer:

Equation showing \(\frac{5}{6}\) as a multiple of a \(\frac{1}{6}\) unit fraction is 5 × \(\frac{1}{6}\)

Explanation:

Equation showing to the above fraction tiles:

\(\frac{1}{6}\) + \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)

=> (1 + 1 + 1 + 1 + 1) ÷ 6

=> 5 × \(\frac{1}{6}\)

Question 2.

Answer:

Equation showing \(\frac{8}{10}\) as a multiple of a \(\frac{1}{10}\) unit fraction is 8 × \(\frac{1}{10}\)

Explanation:

Equation showing to the above fraction tiles:

\(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)

=> (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 ) ÷ 10

=> 8 × \(\frac{1}{10}\)

**Algebra Use an equation to write each fraction or product as a multiple of a unit fraction.
**Question 3.

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

Answer:

Equation showing \(\frac{3}{8}\) as a multiple of a \(\frac{1}{8}\) unit fraction is 3 × \(\frac{1}{8}\)

Explanation:

\(\frac{3}{8}\) = \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)

= 3 × \(\frac{1}{8}\)

Question 4.

\(\frac{7}{12}\) ___________________

Answer:

Equation showing \(\frac{7}{12}\) as a multiple of a \(\frac{1}{12}\) unit fraction is 7 × \(\frac{1}{12}\)

Explanation:

\(\frac{7}{12}\) = \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\)

= (1 + 1 + 1 + 1 + 1 + 1 + 1) ÷ 12

= 7 × \(\frac{1}{12}\)

Question 5.

\(\frac{6}{10}\) ___________________

Answer:

Equation showing \(\frac{6}{10}\) as a multiple of a \(\frac{1}{10}\) unit fraction is 6 × \(\frac{1}{10}\)

Explanation:

\(\frac{6}{10}\) = \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)

= (1 + 1 + 1 + 1 + 1 + 1) ÷ 10

= 6 × \(\frac{1}{10}\)

Question 6.

\(\frac{4}{5}\) ___________________

Answer:

Equation showing \(\frac{4}{5}\) as a multiple of a \(\frac{1}{5}\) unit fraction is 4 × \(\frac{1}{5}\)

Explanation:

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

= (1 + 1 + 1 + 1) ÷ 5

= 4 × \(\frac{1}{5}\)

Question 7.

3 × \(\frac{4}{5}\) ___________________

Answer:

Equation showing 3 × \(\frac{4}{5}\) as a multiple of a \(\frac{1}{5}\) unit fraction is 12 × \(\frac{1}{5}\)

Explanation:

3 × \(\frac{4}{5}\) = \(\frac{12}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)

= 12 × \(\frac{1}{5}\)

Question 8.

5 × \(\frac{2}{5}\) ___________________

Answer:

Equation showing 5 × \(\frac{2}{5}\) as a multiple of a \(\frac{1}{5}\) unit fraction is 10 × \(\frac{1}{5}\)

Explanation:

5 × \(\frac{2}{5}\) = \(\frac{10}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)

= 10 × \(\frac{1}{5}\)

Question 9.

8 × \(\frac{6}{10}\) ___________________

Answer:

Equation showing 8 × \(\frac{6}{10}\) as a multiple of a \(\frac{8}{10}\) unit fraction is 6 × \(\frac{8}{10}\)

Explanation:

8 × \(\frac{6}{10}\) = \(\frac{48}{10}\) = \(\frac{8}{10}\) + \(\frac{8}{10}\) + \(\frac{8}{10}\)+ \(\frac{8}{10}\) + \(\frac{8}{10}\)+ \(\frac{8}{10}\)

= 6 × \(\frac{8}{10}\)

Question 10.

7 × \(\frac{8}{12}\) ___________________

Answer:

Equation showing 7 × \(\frac{8}{12}\) as a multiple of a \(\frac{7}{12}\) unit fraction is 8 × \(\frac{7}{12}\)

Explanation:

7 × \(\frac{8}{12}\) = \(\frac{56}{12}\) = \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\)

= 8 × \(\frac{7}{12}\)

**Problem Solving
**Question 11.

**Mathematical PRACTICE**Model Math Marcia has one cup of tea each day for 7 days. She puts \(\frac{2}{3}\) tablespoons of honey in each cup of tea. Write an equation that represents 7 × \(\frac{2}{3}\) as a multiple of a unit fraction.

Answer:

Equation that represents 7 × \(\frac{2}{3}\) as a multiple of a \(\frac{1}{3}\) unit fraction is 14 × \(\frac{1}{3}\)

Explanation:

Number of days Marcia has one cup of tea = 7.

Number of cups of tea he has each day = 1.

Number of tablespoons of honey in each cup of tea she puts = \(\frac{2}{3}\).

Total number of tea with tablespoons of honey he has = Number of days Marcia has one cup of tea × Number of cups of tea he has each day × Number of tablespoons of honey in each cup of tea she puts

= 7 × 1 × \(\frac{2}{3}\)

= \(\frac{14}{3}\)

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

= 14 × \(\frac{1}{3}\)

Question 12.

Sam buys 4 tropical fish. Each fish is \(\frac{5}{8}\) of an inch long. Write an equation that represents 4 × \(\frac{5}{8}\) as a multiple of a unit fraction.

Answer:

Equation that represents 4 × \(\frac{5}{8}\) as a multiple of a \(\frac{5}{8}\) unit fraction is \(\frac{5}{8}\) + \(\frac{5}{8}\)+ \(\frac{5}{8}\)+ \(\frac{5}{8}\)

Explanation:

Number of tropical fish Sam buys = 4.

Number of inches each fish = \(\frac{5}{8}\)

Total number of inches all fishes = Number of tropical fish Sam buys × Number of inches each fish

= 4 × \(\frac{5}{8}\)

=> \(\frac{20}{8}\)