All the solutions provided in **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 9 Lesson 9 Multiply Fractions by Whole Numbers **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 9 Lesson 9 Multiply Fractions by Whole Numbers

You can use models and equations to multiply a fraction by a whole number.

**Math in My World
**

**Example 1**

Each card on a trivia game has 6 questions. Each question represents \(\frac{1}{6}\) of the questions on the card. Caleb correctly answered 4 of the questions. What fraction of the questions on a card did he answer correctly?

Find 4 × \(\frac{1}{6}\).

One Way:

Use repeated addition.

Use repeated addition to write an equation.

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

= \(\frac{4}{6}\) Add like fractions.

= Simplify.

Another Way:

Use models.

The number line shows the first four multiples of \(\frac{1}{6}\).

So, 4 × \(\frac{1}{6}\) = .

Check: Use fraction tiles. 4 × \(\frac{1}{6}\) = \(\frac{4}{6}\) or .

Answer:

Fraction of the questions on a card he answer correctly = \(\frac{4}{6}\) or \(\frac{2}{3}\)

Explanation:

Number of questions on each card on a trivia game has = 6.

Number of each question on the card represents = \(\frac{1}{6}\)

Number of questions Caleb correctly answered = 4.

Fraction of the questions on a card he answer correctly = Number of questions Caleb correctly answered × Number of each question on the card represents

= 4 × \(\frac{1}{6}\)

= \(\frac{4}{6}\) ÷ \(\frac{2}{2}\)

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

1. Use repeated addition:

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

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

2. Use models.

The number line shows the first four multiples of \(\frac{1}{6}\).

So, 4 × \(\frac{1}{6}\) = \(\frac{4}{6}\)

3. Use fraction tiles.

4 × \(\frac{1}{6}\) = \(\frac{4}{6}\) ÷ \(\frac{2}{2}\) = \(\frac{2}{3}\)

You can use equations and properties to multiply a fraction by a whole number.

**Example 2
**Find 5 × \(\frac{3}{10}\) Identify the two whole numbers between which the product lies.

So, 5 × \(\frac{3}{10}\) = ______________.

The product lies between the whole numbers 1 and 2. Look at the product before it was simplified.

Answer:

Equation showing 5 × \(\frac{3}{10}\) is a multiple of \(\frac{1}{10}\) unit fraction is 15 × \(\frac{1}{10}\)

Explanation:

5 × \(\frac{3}{10}\) as unit fraction = ??

=> 5 × \(\frac{3}{10}\)

=> \(\frac{15}{10}\)

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

= 15 × \(\frac{1}{10}\)

**Talk Math
**Does 3 × \(\frac{7}{8}\) = 3\(\frac{7}{8}\)? Explain.

Answer:

Yes, 3 × \(\frac{7}{8}\) = 3\(\frac{7}{8}\) because both the product value is same.

Explanation:

3 × \(\frac{7}{8}\) = \(\frac{7}{8}\) + \(\frac{7}{8}\) + \(\frac{7}{8}\)

= \(\frac{21}{8}\)

= 3\(\frac{7}{8}\) = 3 × \(\frac{7}{8}\) = (3 × 7) ÷ 8 = \(\frac{21}{8}\)

**Guided Practice
**

**Multiply.**

Question 1.

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

Answer:

5 multiplied by \(\frac{1}{8}\), we get the product \(\frac{5}{8}\)

Explanation:

Multiplication:

5 × \(\frac{1}{8}\)

= [(5 × 1) ÷ 8]

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

Question 2.

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

Answer:

4 multiplied by \(\frac{2}{3}\), we get the product \(\frac{8}{3}\) or 2\(\frac{2}{3}\)

Explanation:

Multiplication:

4 × \(\frac{2}{3}\)

=[(4 × 2) ÷ 3]

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

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

**Practice
**

**Multiply.**

Question 1.

3 × \(\frac{2}{5}\) = ________________

Answer:

3 multiplied by \(\frac{2}{5}\), we get the product \(\frac{6}{5}\) or 1\(\frac{1}{5}\)

Explanation:

Multiplication:

3 × \(\frac{2}{5}\)

= [(3 × 2) ÷ 5]

= \(\frac{6}{5}\) or 1\(\frac{1}{5}\)

Question 2.

7 × \(\frac{3}{4}\) = ________________

Answer:

7 multiplied by \(\frac{3}{4}\), we get the product \(\frac{21}{4}\) or 5\(\frac{1}{4}\)

Explanation:

Multiplication:

7 × \(\frac{3}{4}\)

= (7 × 3) ÷ 4

= \(\frac{21}{4}\) or 5\(\frac{1}{4}\)

Question 3.

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

Answer:

5 multiplied by \(\frac{5}{6}\), we get the product \(\frac{25}{6}\) or 4\(\frac{1}{6}\)

Explanation:

Multiplication:

5 × \(\frac{5}{6}\)

= [(5 × 5) ÷ 6]

= \(\frac{25}{6}\) or 4\(\frac{1}{6}\)

Question 4.

2 × \(\frac{8}{10}\) = ________________

Answer:

2 multiplied by \(\frac{8}{10}\), we get the product \(\frac{8}{5}\) or 1\(\frac{3}{5}\)

Explanation:

Multiplication:

2 × \(\frac{8}{10}\)

= [(2 × 8) ÷ 10]

= \(\frac{16}{10}\) ÷ \(\frac{2}{2}\)

= \(\frac{8}{5}\) or 1\(\frac{3}{5}\)

Question 5.

8 × \(\frac{3}{10}\) = ________________

Answer:

8 multiplied by \(\frac{3}{10}\), we get the product \(\frac{12}{5}\) or 2\(\frac{2}{5}\)

Explanation:

Multiplication:

8 × \(\frac{3}{10}\)

= [(8 × 3) ÷ 10]

= \(\frac{24}{10}\) ÷ \(\frac{2}{2}\)

= \(\frac{12}{5}\) or 2\(\frac{2}{5}\)

Question 6.

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

Answer:

6 multiplied by \(\frac{5}{8}\), we get the product \(\frac{15}{4}\) or 3\(\frac{3}{4}\)

Explanation:

Multiplication:

6 × \(\frac{5}{8}\)

= [(6 × 5) ÷ 8]

= \(\frac{30}{8}\) ÷ \(\frac{2}{2}\)

= \(\frac{15}{4}\) or 3\(\frac{3}{4}\)

**Find each product. Identify the two whole numbers between which the product lies.
**Question 7.

5 × \(\frac{7}{10}\) = ________________

The product lies between ______________ and ______________.

Answer:

5 multiplied by \(\frac{7}{10}\), we get the product \(\frac{7}{2}\) or 3\(\frac{1}{2}\)

The product lies between 3 and 4.

Explanation:

5 × \(\frac{7}{10}\)

= [(5 × 7) ÷ 10]

= \(\frac{35}{10}\) ÷ \(\frac{5}{5}\)

= \(\frac{7}{2}\) or 3\(\frac{1}{2}\)

Question 8.

7 × \(\frac{8}{10}\) = ________________

The product lies between ______________ and ______________.

Answer:

7 multiplied by \(\frac{8}{10}\), we get the product \(\frac{28}{5\) or 5\(\frac{3}{5}\)

The product lies between 5 and 6.

Explanation:

Multiplication:

7 × \(\frac{8}{10}\)

= [(7 × 8) ÷ 10]

= \(\frac{56}{10}\) ÷ \(\frac{2}{2}\)

= \(\frac{28}{5\) or 5\(\frac{3}{5}\)

Question 9.

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

The product lies between ______________ and ______________.

Answer:

3 multiplied by \(\frac{3}{4}\), we get the product \(\frac{9}{4}\) or 2\(\frac{1}{4}\)

The product lies between 2 and 3.

Explanation:

Multiplication:

3 × \(\frac{3}{4}\)

= [(3 × 3) ÷ 4]

= \(\frac{9}{4}\) or 2\(\frac{1}{4}\)

Question 10.

6 × \(\frac{4}{5}\) = ________________

The product lies between ______________ and ______________.

Answer:

6 multiplied by \(\frac{4}{5}\), we get the product \(\frac{24}{5}\) or 4\(\frac{4}{5}\)

The product lies between 6 and 7.

Explanation:

Multiplication:

6 × \(\frac{4}{5}\)

= [(6 × 4) ÷ 5]

= \(\frac{24}{5}\) or 4\(\frac{4}{5}\)

**Problem Solving
**Question 11.

**Mathematical PRACTICE**Use Number Sense Calvin’s rug covers \(\frac{1}{8}\) of the floor space in his bedroom. How much floor space would be covered if Calvin had 4 rugs of that size? Write in simplest form.

Answer:

Length of the floor space would be covered by 4 rugs of that size = \(\frac{1}{2}\)

Explanation:

Length of the floor space in his bedroom Calvin’s rug covers = \(\frac{1}{8}\)

Number of rugs = 4.

Length of the floor space would be covered by 4 rugs of that size = Number of rugs × Length of the floor space in his bedroom Calvin’s rug covers

= 4 × \(\frac{1}{8}\)

= [(4 × 1) ÷ 8]

= \(\frac{4}{8}\) ÷ \(\frac{4}{4}\)

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

Question 12.

Amy uses \(\frac{2}{3}\) of a yard of fabric for each pillow she makes. How many yards of fabric will she need in order to make 8 pillows? Write in simplest form.

Answer:

Number of yards of fabric will she need in order to make 8 pillows = \(\frac{16}{3}\) or 5\(\frac{1}{3}\)

Explanation:

Number of a yard of fabric for each pillow she makes Amy uses = \(\frac{2}{3}\)

Number of pillows = 8.

Number of yards of fabric will she need in order to make 8 pillows = Number of pillows × Number of a yard of fabric for each pillow she makes Amy uses

= 8 × \(\frac{2}{3}\)

= [(8 × 2) ÷ 3]

= \(\frac{16}{3}\) or 5\(\frac{1}{3}\)

**Test Practice
**Question 13.

Sheila eats \(\frac{3}{4}\) of a bag of baby carrots each week. How many bags of baby carrots does she eat in 6 weeks? Write in simplest form.

(A) 4\(\frac{1}{2}\) bags

(B) 3 bags

(C) 2\(\frac{1}{4}\) bags

(D) 1\(\frac{1}{2}\) bags

Answer:

Number of bags of baby carrots she eats in 6 weeks = \(\frac{9{2}\) or 4\(\frac{1}{2}\)(A) 4\(\frac{1}{2}\) bags

Explanation:

Number of a bag of baby carrots each week Sheila eats = \(\frac{3}{4}\)

Number of weeks = 6.

Number of bags of baby carrots she eats in 6 weeks = Number of weeks × Number of a bag of baby carrots each week Sheila eats

= 6 × \(\frac{3}{4}\)

= [(6 × 3) ÷ 4]

= \(\frac{18{4}\) ÷ \(\frac{2}{2}\)

= \(\frac{9{2}\) or 4\(\frac{1}{2}\)