# Spectrum Math Grade 5 Chapter 4 Lesson 5 Answer Key Finding Common Denominators

Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 4 Lesson 4.5 Finding Common Denominators regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 4 Lesson 4.5 Finding Common Denominators Answers Key

The two fractions $$\frac{1}{5}$$ and $$\frac{3}{5}$$ have common denominators. However ana do not have common denominators. Rename these fractions so that they have common denominators by finding the least common multiple of their denominators.
Multiples of 4 are 4, 8, 12, 16, 20, 24,…
Multiples of 5 are 5, 10, 15, 20,. . .
The smallest number that is a multiple of 4 and 5 is 20.
Rename each fraction with a denominator of 20.
$$\frac{1}{4}$$ = $$\frac{1 \times 5}{4 \times 5}$$ = $$\frac{5}{20}$$; $$\frac{3}{5}$$ = $$\frac{3 \times 4}{5 \times 4}$$ = $$\frac{12}{20}$$
$$\frac{5}{20}$$ and $$\frac{12}{20}$$ have common denominators.

Rename each pair of fractions with common denominators.

Question 1.
a. $$\frac{1}{4}$$ and $$\frac{2}{3}$$ ______
$$\frac{1}{4}$$ and $$\frac{2}{3}$$ have common denominators by $$\frac{3}{12}$$  and $$\frac{8}{12}$$.

Explanation:
$$\frac{1}{4}$$ and $$\frac{2}{3}$$
Common multiple of 4 and 3 is 12.
=> $$\frac{1}{4}$$ × $$\frac{3}{3}$$ = $$\frac{3}{12}$$
$$\frac{2}{3}$$ × $$\frac{4}{4}$$ = $$\frac{8}{12}$$

b. $$\frac{3}{8}$$ and $$\frac{7}{10}$$ ______
$$\frac{3}{8}$$ and $$\frac{7}{10}$$ have common denominators by $$\frac{15}{40}$$ and $$\frac{28}{40}$$.

Explanation:
$$\frac{3}{8}$$ and $$\frac{7}{10}$$
Common multiple of 8 and 10 is 40.
=> $$\frac{3}{8}$$ × $$\frac{5}{5}$$  = $$\frac{15}{40}$$
$$\frac{7}{10}$$ × $$\frac{4}{4}$$  = $$\frac{28}{40}$$

c. $$\frac{4}{7}$$ and $$\frac{2}{3}$$ ______
$$\frac{4}{7}$$ and $$\frac{2}{3}$$ have common denominators by $$\frac{12}{21}$$ and $$\frac{14}{21}$$.

Explanation:
$$\frac{4}{7}$$ and $$\frac{2}{3}$$
Common multiple of 7 and 3 = 21.
=> $$\frac{4}{7}$$ × $$\frac{3}{3}$$ = $$\frac{12}{21}$$
$$\frac{2}{3}$$ × $$\frac{7}{7}$$ = $$\frac{14}{21}$$

Question 2.
a. $$\frac{3}{8}$$ and $$\frac{1}{6}$$ ______
$$\frac{3}{8}$$ and $$\frac{1}{6}$$ have common denominators by $$\frac{9}{24}$$ and $$\frac{4}{24}$$.

Explanation:
$$\frac{3}{8}$$ and $$\frac{1}{6}$$
Common multiple of 8 and 6 is 24.
=> $$\frac{3}{8}$$ × $$\frac{3}{3}$$ = $$\frac{9}{24}$$
$$\frac{1}{6}$$ ×  $$\frac{4}{4}$$= $$\frac{4}{24}$$

b. $$\frac{2}{3}$$ and $$\frac{1}{2}$$ ______
$$\frac{2}{3}$$ and $$\frac{1}{2}$$ have common denominators by $$\frac{4}{6}$$  and $$\frac{3}{6}$$.

Explanation:
$$\frac{2}{3}$$ and $$\frac{1}{2}$$
=> Common multiple of 3 and 2 is 6.
$$\frac{2}{3}$$ × $$\frac{2}{2}$$  = $$\frac{4}{6}$$
$$\frac{1}{2}$$ × $$\frac{3}{3}$$ = $$\frac{3}{6}$$

c. $$\frac{3}{8}$$ and $$\frac{5}{6}$$ ______
$$\frac{3}{8}$$ and $$\frac{5}{6}$$ have common denominators by $$\frac{9}{24}$$ and $$\frac{20}{24}$$.

Explanation:
$$\frac{3}{8}$$ and $$\frac{5}{6}$$
=> Common multiple of 8 and 6 is 24.
$$\frac{3}{8}$$ × $$\frac{3}{3}$$ = $$\frac{9}{24}$$
$$\frac{5}{6}$$ × $$\frac{4}{4}$$ = $$\frac{20}{24}$$

Question 3.
a. $$\frac{2}{5}$$ and $$\frac{1}{3}$$ ______
$$\frac{2}{5}$$ and $$\frac{1}{3}$$ have common denominators by $$\frac{6}{15}$$ and $$\frac{5}{15}$$.

Explanation:
$$\frac{2}{5}$$ and $$\frac{1}{3}$$
=> Common multiple of 5 and 3 is 15.
$$\frac{2}{5}$$ × $$\frac{3}{3}$$ = $$\frac{6}{15}$$
$$\frac{1}{3}$$ × $$\frac{5}{5}$$ = $$\frac{5}{15}$$

b. $$\frac{5}{16}$$ and $$\frac{3}{8}$$ ______
$$\frac{5}{16}$$ and $$\frac{3}{8}$$ have common denominators by $$\frac{5}{16}$$ and $$\frac{6}{16}$$.

Explanation:
$$\frac{5}{16}$$ and $$\frac{3}{8}$$
=> Common multiple of 16 and 8 is 16.
$$\frac{5}{16}$$ × $$\frac{1}{1}$$ = $$\frac{5}{16}$$
$$\frac{3}{8}$$ × $$\frac{2}{2}$$ = $$\frac{6}{16}$$

c. $$\frac{1}{2}$$ and $$\frac{1}{3}$$ ______
$$\frac{1}{2}$$ and $$\frac{1}{3}$$ have common denominators by $$\frac{3}{6}$$ and $$\frac{2}{6}$$.

Explanation:
$$\frac{1}{2}$$ and $$\frac{1}{3}$$
=> Common multiple of 2 and 3 is 6.
$$\frac{1}{2}$$ × $$\frac{3}{3}$$ = $$\frac{3}{6}$$
$$\frac{1}{3}$$ × $$\frac{2}{2}$$ = $$\frac{2}{6}$$

Question 4.
a. $$\frac{5}{8}$$ and $$\frac{3}{16}$$ ______
$$\frac{5}{8}$$ and $$\frac{3}{16}$$ have common denominators by $$\frac{10}{16}$$ and $$\frac{3}{16}$$.

Explanation:
$$\frac{5}{8}$$ and $$\frac{3}{16}$$
=> Common multiple of 8 and 16 is 16.
$$\frac{5}{8}$$ × $$\frac{2}{2}$$ = $$\frac{10}{16}$$
$$\frac{3}{16}$$ × $$\frac{1}{1}$$ = $$\frac{3}{16}$$

b. $$\frac{2}{5}$$ and $$\frac{3}{4}$$ ______
$$\frac{2}{5}$$ and $$\frac{3}{4}$$ have common denominators by $$\frac{8}{20}$$ and $$\frac{15}{20}$$.

Explanation:
$$\frac{2}{5}$$ and $$\frac{3}{4}$$
=> Common multiple of 5 and 4 is 20.
$$\frac{2}{5}$$ × $$\frac{4}{4}$$ = $$\frac{8}{20}$$
$$\frac{3}{4}$$ × $$\frac{5}{5}$$ = $$\frac{15}{20}$$

c. $$\frac{5}{12}$$ and $$\frac{4}{5}$$ ______
$$\frac{5}{12}$$ and $$\frac{4}{5}$$ have common denominators by $$\frac{25}{60}$$ and $$\frac{48}{60}$$.

Explanation:
$$\frac{5}{12}$$ and $$\frac{4}{5}$$
=> Common multiple of 12 and 5 is 60.
$$\frac{5}{12}$$ × $$\frac{5}{5}$$ = $$\frac{25}{60}$$
$$\frac{4}{5}$$ × $$\frac{12}{12}$$ = $$\frac{48}{60}$$

Question 5.
a. $$\frac{5}{9}$$ and $$\frac{1}{2}$$ ______
$$\frac{5}{9}$$ and $$\frac{1}{2}$$ have common denominators by $$\frac{10}{18}$$  and $$\frac{9}{18}$$.

Explanation:
$$\frac{5}{9}$$ and $$\frac{1}{2}$$
=> Common multiple of 9 and 2 is 18.
$$\frac{5}{9}$$ × $$\frac{2}{2}$$ = $$\frac{10}{18}$$
$$\frac{1}{2}$$ × $$\frac{9}{9}$$ = $$\frac{9}{18}$$

b. $$\frac{7}{8}$$ and $$\frac{7}{12}$$ ______
$$\frac{7}{8}$$ and $$\frac{7}{12}$$ have common denominators by $$\frac{21}{24}$$ and $$\frac{14}{24}$$.

Explanation:
$$\frac{7}{8}$$ and $$\frac{7}{12}$$
=> Common multiple of 8 and 12 is 24.
$$\frac{7}{8}$$ × $$\frac{3}{3}$$ = $$\frac{21}{24}$$
$$\frac{7}{12}$$ × $$\frac{2}{2}$$ = $$\frac{14}{24}$$

c. $$\frac{1}{9}$$ and $$\frac{2}{3}$$ ______
$$\frac{1}{9}$$ and $$\frac{2}{3}$$ have common denominators by $$\frac{1}{9}$$  and $$\frac{6}{9}$$.
$$\frac{1}{9}$$ and $$\frac{2}{3}$$
$$\frac{1}{9}$$ × $$\frac{1}{1}$$ = $$\frac{1}{9}$$
$$\frac{2}{3}$$ × $$\frac{3}{3}$$ = $$\frac{6}{9}$$