# Spectrum Math Grade 5 Chapter 6 Lesson 3 Answer Key Multiplying Mixed Numbers

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$$\frac{1}{3}$$ = ________________
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$$\frac{1}{6}$$ = ________________
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$$\frac{2}{3}$$ = ________________
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$$\frac{2}{3}$$ = ________________
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$$\frac{3}{4}$$ = ________________
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$$\frac{1}{7}$$ = ________________
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$$\frac{1}{2}$$ = ________________
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$$\frac{1}{9}$$ = ________________
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$$\frac{1}{4}$$ = ________________
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$$\frac{2}{5}$$ = ________________
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$$\frac{2}{7}$$ = ________________
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$$\frac{1}{7}$$ = ________________
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$$\frac{1}{2}$$ = ________________
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$$\frac{5}{8}$$ = ________________
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$$\frac{1}{5}$$ = ________________
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$$\frac{1}{5}$$ = ________________
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$$\frac{5}{6}$$ = ________________
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$$\frac{1}{2}$$ = ________________
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$$\frac{1}{4}$$ = ________________
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$$\frac{1}{2}$$ = ________________
8$$\frac{2}{3}$$ × 4$$\frac{1}{2}$$
$$\frac{26}{3}$$ × $$\frac{9}{2}$$
$$\frac{26 \times 9}{3 \times 2}$$ = $$\frac{234}{6}$$ = 39