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

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 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 . 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 × $$\frac{1}{6}$$
= $$\frac{4}{6}$$ ÷ $$\frac{2}{2}$$
= $$\frac{2}{3}$$

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.  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. 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 × $$\frac{1}{8}$$ = ________________
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 × $$\frac{2}{3}$$ = ________________
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 × $$\frac{2}{5}$$ = ________________
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 × $$\frac{3}{4}$$ = ________________
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 × $$\frac{5}{6}$$ = ________________
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 × $$\frac{8}{10}$$ = ________________
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 × $$\frac{3}{10}$$ = ________________
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 × $$\frac{5}{8}$$ = ________________
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 ______________.
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 ______________.
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 ______________.
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 ______________.
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.
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.
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
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
Number of a bag of baby carrots each week Sheila eats = $$\frac{3}{4}$$
= 6 × $$\frac{3}{4}$$
= $$\frac{18{4}$$ ÷ $$\frac{2}{2}$$
= $$\frac{9{2}$$ or 4$$\frac{1}{2}$$