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 × \(\frac{1}{8}\) = _______________
Answer:
\(\frac{3}{8}\)
Explanation:
Given,
3 × \(\frac{1}{8}\)
= \(\frac{3}{1}\) × \(\frac{1}{8}\)
= \(\frac{3 \times 1}{1 \times 8}\)
= \(\frac{3}{8}\)
b. 5 × \(\frac{2}{3}\) = ______________
Answer:
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 = ______________
Answer:
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 = ______________
Answer:
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 × \(\frac{3}{5}\) = _______________
Answer:
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 × \(\frac{5}{9}\) = _______________
Answer:
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 = _______________
Answer:
\(\frac{6}{7}\)
Explanation:
Given,
\(\frac{2}{7}\) × 3
= \(\frac{2}{7}\) × \(\frac{3}{1}\)
= \(\frac{2 \times 3}{7 \times 1}\)
= \(\frac{6}{7}\)
d. 7 × \(\frac{3}{4}\) = _______________
Answer:
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 = ________________
Answer:
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 = _______________
Answer:
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 = ________________
Answer:
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 × \(\frac{1}{3}\) = ________________
Answer:
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 × \(\frac{3}{10}\) = ________________
Answer:
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 = ________________
Answer:
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 × \(\frac{7}{8}\) = _________________
Answer:
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 = _________________
Answer:
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 = _________________
Answer:
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 × \(\frac{3}{10}\) = _________________
Answer:
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 × \(\frac{7}{12}\) = _________________
Answer:
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 = _________________
Answer:
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 × \(\frac{2}{7}\) = _______________
Answer:
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 × \(\frac{4}{5}\) = _______________
Answer:
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 × \(\frac{6}{8}\) = _______________
Answer:
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 × \(\frac{3}{4}\) = ______________
Answer:
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 × \(\frac{2}{7}\) = ______________
Answer:
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 × \(\frac{1}{8}\) = _______________
Answer:
\(\frac{3}{4}\)
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 × \(\frac{1}{3}\) = ______________
Answer:
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 × \(\frac{3}{10}\) = ______________
Answer:
\(\frac{3}{5}\)
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 = _____________
Answer:
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 = ______________
Answer:
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 × \(\frac{3}{8}\) = ______________
Answer:
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 × \(\frac{1}{8}\) = ______________
Answer:
\(\frac{3}{4}\)
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 × \(\frac{5}{8}\) = ______________
Answer:
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 × \(\frac{1}{6}\) = ______________
Answer:
\(\frac{2}{3}\)
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 = ______________
Answer:
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 = ______________
Answer:
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 = ______________
Answer:
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 × \(\frac{6}{7}\) = ______________
Answer:
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 = ______________
Answer:
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 × \(\frac{2}{3}\) = ______________
Answer:
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 = ______________
Answer:
\(\frac{4}{5}\)
Explanation:
Given,
\(\frac{1}{5}\) × 4
= \(\frac{1}{5}\) × \(\frac{4}{1}\)
= \(\frac{1 \times 4}{5 \times 1}\)
= \(\frac{4}{5}\)
b. 5 × \(\frac{2}{3}\) = ______________
Answer:
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 = ______________
Answer:
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 × \(\frac{2}{5}\) = ______________
Answer:
1 \(\frac{1}{5}\)
Explanation:
Given,
3 × \(\frac{2}{5}\)
= \(\frac{3}{1}\) × \(\frac{2}{5}\)
= \(\frac{3 \times 1}{2 \times 5}\)
= \(\frac{6}{5}\)
= 1 \(\frac{1}{5}\)