# Spectrum Math Grade 4 Chapter 6 Lesson 15 Answer Key Multiplying Fractions and Whole Numbers

This handy Spectrum Math Grade 4 Answer Key Chapter 6 Lesson 6.15 Multiplying Fractions and Whole Numbers provides detailed answers for the workbook questions.

## Spectrum Math Grade 4 Chapter 6 Lesson 6.15 Multiplying Fractions and Whole Numbers Answers Key

Rewrite the whole number as a fraction.
Multiply the numerators.
Multiply the denominators.
Reduce to simplest form.

$$\frac{2}{3}$$ × 6 = $$\frac{2}{3}$$ × $$\frac{6}{1}$$
= $$\frac{2 \times 6}{3 \times 1}$$
= $$\frac{12}{3}$$
= 4

7 × $$\frac{1}{2}$$ = $$\frac{7}{1}$$ × $$\frac{1}{2}$$
= $$\frac{7 \times 1}{1 \times 2}$$
= $$\frac{7}{2}$$
= 3 $$\frac{1}{2}$$

Multiply. Write answers in simplest form.

Question 1.
a. 3 × $$\frac{1}{8}$$ = _______________
$$\frac{3}{8}$$

Explanation:
Given,
3 × $$\frac{1}{8}$$
= $$\frac{3}{1}$$ × $$\frac{1}{8}$$
= $$\frac{3 \times 1}{1 \times 8}$$
= $$\frac{3}{8}$$

b. 5 × $$\frac{2}{3}$$ = ______________
3 $$\frac{1}{3}$$

Explanation:
Given,
5 × $$\frac{2}{3}$$
= $$\frac{5}{1}$$ × $$\frac{2}{3}$$
= $$\frac{5 \times 1}{2 \times 3}$$
= $$\frac{10}{3}$$
= 3 $$\frac{1}{3}$$

c. $$\frac{2}{9}$$ × 8 = ______________
1 $$\frac{7}{9}$$

Explanation:
Given,
$$\frac{2}{9}$$ × 8
= $$\frac{2}{9}$$ × $$\frac{8}{1}$$
= $$\frac{2 \times 8}{9 \times 1}$$
= $$\frac{16}{9}$$
= 1 $$\frac{7}{9}$$

d. $$\frac{4}{7}$$ × 2 = ______________
1 $$\frac{1}{7}$$

Explanation:
Given,
$$\frac{4}{7}$$ × 2
= $$\frac{4}{7}$$ × $$\frac{2}{1}$$
= $$\frac{4 \times 2}{7 \times 1}$$
= $$\frac{8}{7}$$
= 1 $$\frac{1}{7}$$

Question 2.
a. 6 × $$\frac{3}{5}$$ = _______________
3 $$\frac{3}{5}$$

Explanation:
Given,
6 × $$\frac{3}{5}$$
= $$\frac{6}{1}$$ × $$\frac{3}{5}$$
= $$\frac{6 \times 1}{3 \times 5}$$
= $$\frac{18}{5}$$
= 3 $$\frac{3}{5}$$

b. 2 × $$\frac{5}{9}$$ = _______________
1 $$\frac{1}{9}$$

Explanation:
Given,
2 x $$\frac{5}{9}$$
= $$\frac{2}{1}$$ × $$\frac{5}{9}$$
= $$\frac{2 \times 1}{5 \times 9}$$
= $$\frac{10}{9}$$
= 1 $$\frac{1}{9}$$

c. $$\frac{2}{7}$$ × 3 = _______________
$$\frac{6}{7}$$

Explanation:
Given,
$$\frac{2}{7}$$ × 3
= $$\frac{2}{7}$$ × $$\frac{3}{1}$$
= $$\frac{2 \times 3}{7 \times 1}$$
= $$\frac{6}{7}$$

d. 7 × $$\frac{3}{4}$$ = _______________
5 $$\frac{1}{4}$$

Explanation:
Given,
7 × $$\frac{3}{4}$$
= $$\frac{7}{1}$$ × $$\frac{3}{4}$$
= $$\frac{7 \times 1}{3 \times 4}$$
= $$\frac{21}{4}$$
= 5 $$\frac{1}{4}$$

Question 3.
a. $$\frac{8}{9}$$ × 4 = ________________
3 $$\frac{5}{9}$$

Explanation:
Given,
$$\frac{8}{9}$$ × 4
= $$\frac{8}{9}$$ × $$\frac{4}{1}$$
= $$\frac{8 \times 4}{9 \times 1}$$
= $$\frac{32}{9}$$
= 3 $$\frac{5}{9}$$

b. $$\frac{1}{2}$$ × 8 = _______________
4

Explanation:
Given,
$$\frac{1}{2}$$ × 8
= $$\frac{1}{2}$$ × $$\frac{8}{1}$$
= $$\frac{1 \times 8}{2\times 1}$$
= $$\frac{8}{2}$$
= 4

c. $$\frac{4}{5}$$ × 6 = ________________
4 $$\frac{4}{5}$$

Explanation:
Given,
$$\frac{4}{5}$$ × 6
= $$\frac{4}{5}$$ × $$\frac{6}{1}$$
= $$\frac{4 \times 6}{5 \times 1}$$
= $$\frac{24}{5}$$
= 4 $$\frac{4}{5}$$

d. 9 × $$\frac{1}{3}$$ = ________________
3

Explanation:
Given,
9 × $$\frac{1}{3}$$
= $$\frac{9}{1}$$ × $$\frac{1}{3}$$
= $$\frac{9 \times 1}{1 \times 3}$$
= $$\frac{9}{3}$$
= 3

Question 4.
a. 5 × $$\frac{3}{10}$$ = ________________
1 $$\frac{1}{2}$$

Explanation:
Given,
5 × $$\frac{3}{10}$$
= $$\frac{5}{1}$$ × $$\frac{3}{10}$$
= $$\frac{5 \times 1}{3 \times 10}$$
= $$\frac{15}{10}$$
= $$\frac{3}{2}$$
= 1 $$\frac{1}{2}$$

b. $$\frac{2}{3}$$ × 3 = ________________
2

Explanation:
Given,
$$\frac{2}{3}$$ × 3
= $$\frac{2}{3}$$ × $$\frac{3}{1}$$
= $$\frac{2 \times 3}{3 \times 1}$$
= $$\frac{6}{3}$$
= 2

c. 9 × $$\frac{7}{8}$$ = _________________
7 $$\frac{7}{8}$$

Explanation:
Given,
9 × $$\frac{7}{8}$$
= $$\frac{9}{1}$$ × $$\frac{7}{8}$$
= $$\frac{9 \times 1}{7 \times 8}$$
= $$\frac{63}{8}$$
= 7 $$\frac{7}{8}$$

d. $$\frac{6}{11}$$ × 7 = _________________
3 $$\frac{9}{11}$$

Explanation:
Given,
$$\frac{6}{11}$$ × 7
= $$\frac{6}{11}$$ × $$\frac{7}{1}$$
= $$\frac{6 \times 7}{11 \times 1}$$
= $$\frac{42}{11}$$
= 3 $$\frac{9}{11}$$

Question 5.
a. $$\frac{4}{9}$$ × 7 = _________________
3 $$\frac{1}{9}$$

Explanation:
Given,
$$\frac{4}{9}$$ × 7
= $$\frac{4}{9}$$ × $$\frac{7}{1}$$
= $$\frac{4 \times 7}{9 \times 1}$$
= $$\frac{28}{9}$$
= 3 $$\frac{1}{9}$$

b. 9 × $$\frac{3}{10}$$ = _________________
2 $$\frac{7}{10}$$

Explanation:
Given,
9 × $$\frac{3}{10}$$
= $$\frac{9}{1}$$ × $$\frac{3}{10}$$
= $$\frac{9 \times 1}{3 \times 10}$$
= $$\frac{27}{10}$$
= 2 $$\frac{7}{10}$$

c. 2 × $$\frac{7}{12}$$ = _________________
1 $$\frac{1}{6}$$

Explanation:
Given,
2 × $$\frac{7}{12}$$
= $$\frac{2}{1}$$ × $$\frac{7}{12}$$
= $$\frac{2 \times 1}{7 \times 12}$$
= $$\frac{14}{12}$$
= $$\frac{7}{6}$$
= 1 $$\frac{1}{6}$$

d. $$\frac{5}{7}$$ × 8 = _________________
5 $$\frac{5}{7}$$

Explanation:
Given,
$$\frac{5}{7}$$ × 8
= $$\frac{5}{7}$$ × $$\frac{8}{1}$$
= $$\frac{5 \times 8}{7 \times 1}$$
= $$\frac{40}{7}$$
= 5 $$\frac{5}{7}$$

Multiply. Write answers in simplest form.

Question 1.
a. 5 × $$\frac{2}{7}$$ = _______________
1 $$\frac{3}{7}$$

Explanation:
Given,
5 × $$\frac{2}{7}$$
= $$\frac{5}{1}$$ × $$\frac{2}{7}$$
= $$\frac{5 \times 1}{2 \times 7}$$
= $$\frac{10}{7}$$
= 1 $$\frac{3}{7}$$

b. 3 × $$\frac{4}{5}$$ = _______________
2 $$\frac{2}{5}$$

Explanation:
Given,
3 × $$\frac{4}{5}$$
= $$\frac{3}{1}$$ × $$\frac{4}{5}$$
= $$\frac{3 \times 1}{4 \times 5}$$
= $$\frac{12}{5}$$
= 2 $$\frac{2}{5}$$

c. 7 × $$\frac{6}{8}$$ = _______________
5 $$\frac{1}{4}$$

Explanation:
Given,
7 × $$\frac{6}{8}$$
= $$\frac{7}{1}$$ × $$\frac{6}{8}$$
= $$\frac{7 \times 1}{6 \times 8}$$
= $$\frac{42}{8}$$
= 5 $$\frac{1}{4}$$

d. 2 × $$\frac{3}{4}$$ = ______________
1 $$\frac{1}{2}$$

Explanation:
Given,
2 × $$\frac{3}{4}$$
= $$\frac{2}{1}$$ × $$\frac{3}{4}$$
= $$\frac{2 \times 1}{3 \times 4}$$
= $$\frac{6}{4}$$
= $$\frac{3}{2}$$
= 1 $$\frac{1}{2}$$

Question 2.
a. 4 × $$\frac{2}{7}$$ = ______________
1 $$\frac{1}{7}$$

Explanation:
Given,
4 × $$\frac{2}{7}$$
= $$\frac{4}{1}$$ × $$\frac{2}{7}$$
= $$\frac{4 \times 1}{2 \times 7}$$
= $$\frac{8}{7}$$
= 7 $$\frac{1}{7}$$

b. 6 × $$\frac{1}{8}$$ = _______________
$$\frac{3}{4}$$

Explanation:
Given,
6 × $$\frac{1}{8}$$
= $$\frac{6}{1}$$ × $$\frac{1}{8}$$
= $$\frac{6 \times 1}{1 \times 8}$$
= $$\frac{6}{8}$$
= $$\frac{3}{4}$$

c. 8 × $$\frac{1}{3}$$ = ______________
2 $$\frac{2}{3}$$

Explanation:
Given,
8 × $$\frac{1}{3}$$
= $$\frac{8}{1}$$ × $$\frac{1}{3}$$
= $$\frac{8 \times 1}{1\times 3}$$
= $$\frac{8}{3}$$
= 6 $$\frac{2}{3}$$

d. 2 × $$\frac{3}{10}$$ = ______________
$$\frac{3}{5}$$

Explanation:
Given,
2 × $$\frac{3}{10}$$
= $$\frac{2}{1}$$ × $$\frac{3}{10}$$
= $$\frac{2 \times 1}{3 \times 10}$$
= $$\frac{6}{10}$$
= $$\frac{3}{5}$$

Question 3.
a. $$\frac{8}{9}$$ × 3 = _____________
2 $$\frac{2}{3}$$

Explanation:
Given,
$$\frac{8}{9}$$ × 3
= $$\frac{8}{9}$$ × $$\frac{3}{1}$$
= $$\frac{8 \times 3}{9 \times 1}$$
= $$\frac{24}{9}$$
= $$\frac{8}{3}$$
= 2 $$\frac{2}{3}$$

b. $$\frac{2}{5}$$ × 5 = ______________
2

Explanation:
Given,
$$\frac{2}{5}$$ × 5
= $$\frac{2}{5}$$ × $$\frac{5}{1}$$
= $$\frac{2 \times 5}{5 \times 1}$$
= $$\frac{10}{5}$$
= 2

c. 4 × $$\frac{3}{8}$$ = ______________
1 $$\frac{1}{2}$$

Explanation:
Given,
4 × $$\frac{3}{8}$$
= $$\frac{4}{1}$$ × $$\frac{3}{8}$$
= $$\frac{4 \times 1}{3 \times 8}$$
= $$\frac{12}{8}$$
= $$\frac{3}{2}$$
= 1 $$\frac{1}{2}$$

d. 6 × $$\frac{1}{8}$$ = ______________
$$\frac{3}{4}$$

Explanation:
Given,
6 × $$\frac{1}{8}$$
= $$\frac{6}{1}$$ × $$\frac{1}{8}$$
= $$\frac{6 \times 1}{1 \times 8}$$
= $$\frac{6}{8}$$
= $$\frac{3}{4}$$

Question 4.
a. 3 × $$\frac{5}{8}$$ = ______________
1 $$\frac{7}{8}$$

Explanation:
Given,
3 × $$\frac{5}{8}$$
= $$\frac{3}{1}$$ × $$\frac{5}{8}$$
= $$\frac{3 \times 1}{5 \times 8}$$
= $$\frac{15}{8}$$
= 1 $$\frac{7}{8}$$

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

Explanation:
Given,
4 × $$\frac{1}{6}$$
= $$\frac{4}{1}$$ × $$\frac{1}{6}$$
= $$\frac{4 \times 1}{1 \times 6}$$
= $$\frac{4}{6}$$
= $$\frac{2}{3}$$

c. $$\frac{1}{3}$$ × 9 = ______________
3

Explanation:
Given,
$$\frac{1}{3}$$ × 9
= $$\frac{1}{3}$$ × $$\frac{9}{1}$$
= $$\frac{1 \times 3}{9 \times 1}$$
= $$\frac{3}{9}$$
= 3

d. $$\frac{5}{9}$$ × 7 = ______________
3 $$\frac{8}{9}$$

Explanation:
Given,
$$\frac{5}{9}$$ × 7
= $$\frac{5}{9}$$ × $$\frac{7}{1}$$
= $$\frac{5 \times 7}{9 \times 1}$$
= $$\frac{35}{9}$$
= 3 $$\frac{8}{9}$$

Question 5.
a. $$\frac{7}{12}$$ × 2 = ______________
1 $$\frac{1}{6}$$

Explanation:
Given,
$$\frac{7}{12}$$ × 2
= $$\frac{7}{12}$$ × $$\frac{2}{1}$$
= $$\frac{7 \times 2}{12 \times 1}$$
= $$\frac{14}{12}$$
= $$\frac{7}{6}$$
= 1 $$\frac{1}{6}$$

b. 3 × $$\frac{6}{7}$$ = ______________
2 $$\frac{4}{7}$$

Explanation:
Given,
3 × $$\frac{6}{7}$$
= $$\frac{3}{1}$$ × $$\frac{6}{7}$$
= $$\frac{3 \times 1}{6 \times 7}$$
= $$\frac{18}{7}$$
= 2 $$\frac{4}{7}$$

c. $$\frac{1}{2}$$ × 5 = ______________
2 $$\frac{1}{2}$$

Explanation:
Given,
$$\frac{1}{2}$$ × 5
= $$\frac{1}{2}$$ × $$\frac{5}{1}$$
= $$\frac{1 \times 5}{2 \times 1}$$
= $$\frac{5}{2}$$
= 2 $$\frac{1}{2}$$

d. 6 × $$\frac{2}{3}$$ = ______________
4

Explanation:
Given,
6 × $$\frac{2}{3}$$
= $$\frac{6}{1}$$ × $$\frac{2}{3}$$
= $$\frac{6 \times 1}{2 \times 3}$$
= $$\frac{12}{3}$$
= 4

Question 6.
a. $$\frac{1}{5}$$ × 4 = ______________
$$\frac{4}{5}$$

Explanation:
Given,
$$\frac{1}{5}$$ × 4
= $$\frac{1}{5}$$ × $$\frac{4}{1}$$
= $$\frac{1 \times 4}{5 \times 1}$$
= $$\frac{4}{5}$$

b. 5 × $$\frac{2}{3}$$ = ______________
3 $$\frac{1}{3}$$

Explanation:
Given,
5 × $$\frac{2}{3}$$
= $$\frac{5}{1}$$ × $$\frac{2}{3}$$
= $$\frac{5 \times 1}{2 \times 3}$$
= $$\frac{10}{3}$$
= 3 $$\frac{1}{3}$$

c. $$\frac{2}{7}$$ × 6 = ______________
1 $$\frac{5}{7}$$

Explanation:
Given,
$$\frac{2}{7}$$ × 6
= $$\frac{2}{7}$$ × $$\frac{6}{1}$$
= $$\frac{2 \times 6}{7 \times 1}$$
= $$\frac{12}{7}$$
= 1 $$\frac{5}{7}$$

d. 3 × $$\frac{2}{5}$$ = ______________
1 $$\frac{1}{5}$$
3 × $$\frac{2}{5}$$
= $$\frac{3}{1}$$ × $$\frac{2}{5}$$
= $$\frac{3 \times 1}{2 \times 5}$$
= $$\frac{6}{5}$$
= 1 $$\frac{1}{5}$$