Practice with the help of **Spectrum Math Grade 5 Answer Key Chapter 6 Lesson 6.3 Multiplying Mixed Numbers **regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 6 Lesson 6.3 Multiplying Mixed Numbers Answers Key

2\(\frac{1}{5}\) × 1\(\frac{1}{4}\) = \(\frac{11}{5}\) × \(\frac{5}{4}\) Rewrite the mixed numbers as improper fractions.

= \(\frac{55}{20}\) Multiply the fractions.

= 2\(\frac{15}{20}\) = 2\(\frac{3}{4}\) Write the answer in simplest form.

**Multiply. Write answers in simplest form.**

Question 1.

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

Answer:

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

Explanation:

Given,

2\(\frac{1}{4}\) × 2\(\frac{1}{3}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{9}{4}\) × \(\frac{7}{3}\)

Multiply the fractions.

\(\frac{9 \times 7}{4 \times 3}\) = \(\frac{63}{12}\)

Write the answer in simplest form.

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

b. 5\(\frac{1}{2}\) × 1\(\frac{1}{6}\) = ________________

Answer:

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

Explanation:

Given,

5\(\frac{1}{2}\) × 1\(\frac{1}{6}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{11}{2}\) × \(\frac{7}{6}\)

Multiply the fractions.

\(\frac{11 \times 7}{2 \times 6}\) = \(\frac{77}{12}\)

Write the answer in simplest form.

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

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

Answer:

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

Explanation:

Given,

3\(\frac{1}{4}\) × 4\(\frac{2}{3}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{13}{4}\) × \(\frac{14}{3}\)

Multiply the fractions.

\(\frac{13 \times 14}{4 \times 3}\) = \(\frac{182}{12}\)

Write the answer in simplest form.

\(\frac{91}{6}\) = 15\(\frac{1}{6}\)

d. 1\(\frac{6}{7}\) × 2\(\frac{2}{3}\) = ________________

Answer:

4\(\frac{20}{21}\)

Explanation:

Given,

1\(\frac{6}{7}\) × 2\(\frac{2}{3}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{13}{7}\) × \(\frac{8}{3}\)

Multiply the fractions.

\(\frac{13 \times 8}{7 \times 3}\) = \(\frac{104}{21}\)

Write the answer in simplest form.

4\(\frac{20}{21}\)

Question 2.

a. 1\(\frac{7}{10}\) × 4\(\frac{3}{4}\) = ________________

Answer:

8\(\frac{3}{40}\)

Explanation:

Given,

1\(\frac{7}{10}\) × 4\(\frac{3}{4}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{17}{10}\) × \(\frac{19}{4}\)

Multiply the fractions.

\(\frac{17 \times 19}{10 \times 4}\) = \(\frac{323}{40}\)

Write the answer in simplest form.

8\(\frac{3}{40}\)

b. 3\(\frac{3}{5}\) × 4\(\frac{1}{7}\) = ________________

Answer:

14\(\frac{32}{35}\)

Explanation:

Given,

3\(\frac{3}{5}\) × 4\(\frac{1}{7}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{18}{5}\) × \(\frac{29}{7}\)

Multiply the fractions.

\(\frac{18 \times 29}{5 \times 7}\) = \(\frac{522}{35}\)

Write the answer in simplest form.

14\(\frac{32}{35}\)

c. 1\(\frac{5}{9}\) × 3\(\frac{1}{2}\) = ________________

Answer:

5\(\frac{4}{9}\)

Explanation:

Given,

1\(\frac{5}{9}\) × 3\(\frac{1}{2}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{14}{9}\) × \(\frac{7}{2}\)

Multiply the fractions.

\(\frac{14 \times 7}{9 \times 2}\) = \(\frac{98}{18}\)

Write the answer in simplest form.

\(\frac{49}{9}\) = 5\(\frac{4}{9}\)

d. 6\(\frac{2}{3}\) × 2\(\frac{1}{9}\) = ________________

Answer:

14\(\frac{2}{27}\)

Explanation:

Given,

6\(\frac{2}{3}\) × 2\(\frac{1}{9}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{20}{3}\) × \(\frac{19}{9}\)

Multiply the fractions.

\(\frac{20 \times 19}{3 \times 9}\) = \(\frac{380}{27}\)

Write the answer in simplest form.

14\(\frac{2}{27}\)

Question 3.

a. 5\(\frac{3}{5}\) × 2\(\frac{1}{4}\) = ________________

Answer:

12\(\frac{3}{5}\)

Explanation:

Given,

5\(\frac{3}{5}\) × 2\(\frac{1}{4}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{28}{5}\) × \(\frac{9}{4}\)

Multiply the fractions.

\(\frac{28 \times 9}{5 \times 4}\) = \(\frac{252}{20}\)

Write the answer in simplest form.

\(\frac{63}{5}\) = 12\(\frac{3}{5}\)

b. 6\(\frac{1}{3}\) × 1\(\frac{2}{5}\) = ________________

Answer:

8\(\frac{13}{15}\)

Explanation:

Given,

6\(\frac{1}{3}\) × 1\(\frac{2}{5}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{19}{3}\) × \(\frac{7}{5}\)

Multiply the fractions.

\(\frac{19 \times 7}{3 \times 5}\) = \(\frac{133}{15}\)

Write the answer in simplest form.

8\(\frac{13}{15}\)

c. 9\(\frac{1}{2}\) × 2\(\frac{2}{7}\) = ________________

Answer:

21\(\frac{5}{7}\)

Explanation:

Given,

9\(\frac{1}{2}\) × 2\(\frac{2}{7}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{19}{2}\) × \(\frac{16}{7}\)

Multiply the fractions.

\(\frac{19 \times 16}{2 \times 7}\) = \(\frac{304}{14}\)

Write the answer in simplest form.

\(\frac{152}{7}\) = 21\(\frac{5}{7}\)

d. 2\(\frac{6}{7}\) × 5\(\frac{1}{7}\) = ________________

Answer:

14\(\frac{34}{49}\)

Explanation:

Given,

2\(\frac{6}{7}\) × 5\(\frac{1}{7}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{20}{7}\) × \(\frac{36}{7}\)

Multiply the fractions.

\(\frac{20 \times 36}{7 \times 7}\) = \(\frac{720}{49}\)

Write the answer in simplest form.

14\(\frac{34}{49}\)

Question 4.

a. 8\(\frac{1}{6}\) × 2\(\frac{1}{2}\) = ________________

Answer:

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

Explanation:

Given,

8\(\frac{1}{6}\) × 2\(\frac{1}{2}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{49}{6}\) × \(\frac{5}{2}\)

Multiply the fractions.

\(\frac{49 \times 5}{6 \times 2}\) = \(\frac{245}{12}\)

Write the answer in simplest form.

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

b. 3\(\frac{1}{8}\) × 1\(\frac{5}{8}\) = ________________

Answer:

5\(\frac{5}{64}\)

Explanation:

Given,

3\(\frac{1}{8}\) × 1\(\frac{5}{8}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{25}{8}\) × \(\frac{13}{8}\)

Multiply the fractions.

\(\frac{25 \times 13}{8 \times 8}\) = \(\frac{325}{64}\)

Write the answer in simplest form.

5\(\frac{5}{64}\)

c. 7\(\frac{1}{2}\) × 1\(\frac{1}{5}\) = ________________

Answer:

9

Explanation:

Given,

7\(\frac{1}{2}\) × 1\(\frac{1}{5}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{15}{2}\) × \(\frac{6}{5}\)

Multiply the fractions.

\(\frac{15 \times 6}{2 \times 5}\) = \(\frac{90}{10}\) = 9

d. 3\(\frac{5}{6}\) × 3\(\frac{1}{5}\) = ________________

Answer:

12\(\frac{4}{15}\)

Explanation:

Given,

3\(\frac{5}{6}\) × 3\(\frac{1}{5}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{23}{6}\) × \(\frac{16}{5}\)

Multiply the fractions.

\(\frac{23 \times 16}{6 \times 5}\) = \(\frac{368}{30}\)

Write the answer in simplest form.

\(\frac{184}{15}\) = 12\(\frac{4}{15}\)

Question 5.

a. 1\(\frac{7}{12}\) × 2\(\frac{5}{6}\) = ________________

Answer:

4\(\frac{35}{72}\)

Explanation:

Given,

1\(\frac{7}{12}\) × 2\(\frac{5}{6}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{19}{12}\) × \(\frac{17}{6}\)

Multiply the fractions.

\(\frac{19 \times 17}{12 \times 6}\) = \(\frac{228}{72}\)

Write the answer in simplest form.

4\(\frac{35}{72}\)

b. 2\(\frac{1}{6}\) × 7\(\frac{1}{2}\) = ________________

Answer:

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

Explanation:

Given,

2\(\frac{1}{6}\) × 7\(\frac{1}{2}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{13}{6}\) × \(\frac{15}{2}\)

Multiply the fractions.

\(\frac{13 \times 15}{6 \times 2}\) = \(\frac{195}{12}\)

Write the answer in simplest form.

\(\frac{65}{4}\) = 16\(\frac{1}{4}\)

c. 2\(\frac{1}{8}\) × 3\(\frac{1}{4}\) = ________________

Answer:

6\(\frac{29}{32}\)

Explanation:

Given,

2\(\frac{1}{8}\) × 3\(\frac{1}{4}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{17}{8}\) × \(\frac{13}{4}\)

Multiply the fractions.

\(\frac{17 \times 13}{8 \times 4}\) = \(\frac{221}{32}\)

Write the answer in simplest form.

6\(\frac{29}{32}\)

d. 8\(\frac{2}{3}\) × 4\(\frac{1}{2}\) = ________________

Answer:

39

Explanation:

Given,

8\(\frac{2}{3}\) × 4\(\frac{1}{2}\)

Rewrite the mixed numbers as improper fractions.

\(\frac{26}{3}\) × \(\frac{9}{2}\)

Multiply the fractions.

\(\frac{26 \times 9}{3 \times 2}\) = \(\frac{234}{6}\) = 39