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 \(\frac{2}{3}\) ______

Answer:

\(\frac{1}{4}\) 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 \(\frac{7}{10}\) ______

Answer:

\(\frac{3}{8}\) 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 \(\frac{2}{3}\) ______

Answer:

\(\frac{4}{7}\) 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 \(\frac{1}{6}\) ______

Answer:

\(\frac{3}{8}\) 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 \(\frac{1}{2}\) ______

Answer:

\(\frac{2}{3}\) 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 \(\frac{5}{6}\) ______

Answer:

\(\frac{3}{8}\) 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 \(\frac{1}{3}\) ______

Answer:

\(\frac{2}{5}\) 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 \(\frac{3}{8}\) ______

Answer:

\(\frac{5}{16}\) 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 \(\frac{1}{3}\) ______

Answer:

\(\frac{1}{2}\) 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 \(\frac{3}{16}\) ______

Answer:

\(\frac{5}{8}\) 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 \(\frac{3}{4}\) ______

Answer:

\(\frac{2}{5}\) 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 \(\frac{4}{5}\) ______

Answer:

\(\frac{5}{12}\) 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 \(\frac{1}{2}\) ______

Answer:

\(\frac{5}{9}\) 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 \(\frac{7}{12}\) ______

Answer:

\(\frac{7}{8}\) 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 \(\frac{2}{3}\) ______

Answer:

\(\frac{1}{9}\) and \(\frac{2}{3}\) have common denominators by \(\frac{1}{9}\) and \(\frac{6}{9}\).

Explanation:

\(\frac{1}{9}\) and \(\frac{2}{3}\)

=> Common multiple of 9 and 3 is 9.

\(\frac{1}{9}\) × \(\frac{1}{1}\) = \(\frac{1}{9}\)

\(\frac{2}{3}\) × \(\frac{3}{3}\) = \(\frac{6}{9}\)