This handy **Spectrum Math Grade 4 Answer Key Chapter 6 Lesson 6.1 Finding Equivalent Fractions** provides detailed answers for the workbook questions.

## Spectrum Math Grade 4 Chapter 6 Lesson 6.1 Finding Equivalent Fractions Answers Key

\(\frac{3}{4}\) To find an equivalent fraction, multiply both the numerator and 4 denominators by the same number.

\(\frac{3}{4}\) = \(\frac{9}{12}\)

\(\frac{3}{4}\) and \(\frac{9}{12}\) are equivalent fractions.

**To find an equivalent fraction, multiply the numerator and the denominator by the number in the circle.**

Question 1.

a.

Answer:

\(\frac{9}{12}\)

Explanation:

Given,

\(\frac{3}{4}\)

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 3.

\(\frac{3 × 3}{4 × 3}\) = \(\frac{9}{12}\)

So, \(\frac{3}{4}\) and \(\frac{9}{12}\) are equivalent fractions.

b.

Answer:

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

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 4.

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

So, \(\frac{1}{4}\) and \(\frac{4}{16}\) are equivalent fractions.

c.

Answer:

\(\frac{10}{15}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 5.

\(\frac{2 × 5}{3 × 5}\) = \(\frac{10}{15}\)

So, \(\frac{2}{3}\) and \(\frac{10}{15}\) are equivalent fractions.

d.

Answer:

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

Explanation:

Given,

\(\frac{1}{2}\)

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 2.

\(\frac{1 × 2}{2 × 2}\) = \(\frac{2}{4}\)

So, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.

Question 2.

a.

Answer:

\(\frac{6}{18}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 6.

\(\frac{1 × 6}{3 × 6}\) = \(\frac{6}{18}\)

So, \(\frac{1}{3}\) and \(\frac{6}{18}\) are equivalent fractions.

b.

Answer:

\(\frac{6}{24}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 2.

\(\frac{3 × 2}{12 × 2}\) = \(\frac{6}{24}\)

So, \(\frac{3}{12}\) and \(\frac{6}{24}\) are equivalent fractions.

c.

Answer:

\(\frac{3}{15}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 3.

\(\frac{1 × 3}{5 × 3}\) = \(\frac{3}{15}\)

So, \(\frac{1}{5}\) and \(\frac{3}{15}\) are equivalent fractions.

d.

Answer:

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

Explanation:

Given,

\(\frac{2}{10}\)

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 4.

\(\frac{2 × 4}{10 × 4}\) = \(\frac{8}{40}\)

So, \(\frac{2}{10}\) and \(\frac{8}{40}\) are equivalent fractions.

Question 3.

a.

Answer:

\(\frac{10}{14}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 2.

\(\frac{5 × 2}{7 × 2}\) = \(\frac{10}{14}\)

So, \(\frac{3}{4}\) and \(\frac{9}{12}\) are equivalent fractions.

b.

Answer:

\(\frac{12}{24}\)

Explanation:

Given,

\(\frac{3}{6}\)

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 4.

\(\frac{3 × 4}{6 × 4}\) = \(\frac{12}{24}\)

So, \(\frac{3}{6}\) and \(\frac{12}{24}\) are equivalent fractions.

c.

Answer:

\(\frac{8}{32}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 4.

\(\frac{2 × 4}{8 × 4}\) = \(\frac{8}{32}\)

So, \(\frac{2}{8}\) and \(\frac{8}{32}\) are equivalent fractions.

d.

Answer:

\(\frac{6}{36}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 6.

\(\frac{1 × 6}{6 × 6}\) = \(\frac{6}{36}\)

So, \(\frac{1}{6}\) and \(\frac{6}{36}\) are equivalent fractions.

Question 4.

a.

Answer:

\(\frac{9}{27}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number .

\(\frac{1 × 9}{3 × 9}\) = \(\frac{9}{27}\)

So, \(\frac{1}{9}\) and \(\frac{9}{27}\) are equivalent fractions.

b.

Answer:

\(\frac{20}{30}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 10.

\(\frac{2 × 10}{3 × 10}\) = \(\frac{20}{30}\)

So, \(\frac{2}{3}\) and \(\frac{20}{30}\) are equivalent fractions.

c.

Answer:

\(\frac{10}{25}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 5.

\(\frac{2 × 5}{5 × 5}\) = \(\frac{10}{25}\)

So, \(\frac{2}{5}\) and \(\frac{10}{25}\) are equivalent fractions.

d.

Answer:

\(\frac{2}{16}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 2.

\(\frac{1 × 2}{8 × 2}\) = \(\frac{2}{16}\)

So, \(\frac{1}{8}\) and \(\frac{2}{16}\) are equivalent fractions.

**Use multiplication to find each equivalent fraction.**

Question 5.

a. \(\frac{1}{5}\) = \(\frac{3}{}\)

Answer:

15

Explanation:

Given,

\(\frac{1}{5}\) = \(\frac{3}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{5 × 3}{1 × x}\) = \(\frac{15}{1}\)

Therefore, the unknown number of equivalent number is 15.

b. \(\frac{1}{10}\) = \(\frac{}{20}\)

Answer:

2

Explanation:

Given,

\(\frac{1}{10}\) = \(\frac{}{20}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{1 × 20}{x × 10}\) = \(\frac{20}{10}\)

Therefore, the unknown number of equivalent number is 2.

c. \(\frac{3}{4}\) = \(\frac{9}{}\)

Answer:

12

Explanation:

Given,

\(\frac{3}{4}\) = \(\frac{9}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{9 × 4}{3 × x}\) = \(\frac{36}{3x}\)

x = \(\frac{36}{3}\)

x = 12

Therefore, the unknown number of equivalent number is 12.

d. \(\frac{1}{2}\) = \(\frac{9}{}\)

Answer:

18

Explanation:

Given,

\(\frac{1}{2}\) = \(\frac{9}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{2 × 9}{1 × x}\) = \(\frac{18}{1}\)

Therefore, the unknown number of equivalent number is 15.

Question 6.

a. \(\frac{1}{3}\) = \(\frac{}{12}\)

Answer:

4

Explanation:

Given,

\(\frac{1}{3}\) = \(\frac{}{12}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{1 × 12}{3 × x}\) = \(\frac{12}{3x}\)

x = \(\frac{12}{3}\)

x = 4

Therefore, the unknown number of equivalent number is 4.

b. \(\frac{2}{4}\) = \(\frac{8}{}\)

Answer:

16

Explanation:

Given,

\(\frac{2}{4}\) = \(\frac{8}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{4 × 8}{2 × x}\) = \(\frac{32}{2x}\)

x = \(\frac{32}{2}\)

x = 16

Therefore, the unknown number of equivalent number is 16.

c. \(\frac{1}{12}\) = \(\frac{2}{}\)

Answer:

24

Explanation:

Given,

\(\frac{1}{12}\) = \(\frac{2}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{12 × 2}{1 × x}\) = \(\frac{24}{1}\)

Therefore, the unknown number of equivalent number is 24.

d. \(\frac{2}{6}\) = \(\frac{}{18}\)

Answer:

6

Explanation:

Given,

\(\frac{2}{6}\) = \(\frac{}{18}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{2 × 18}{6 × x}\) = \(\frac{36}{6x}\)

x = \(\frac{36}{6}\)

x = 6

Therefore, the unknown number of equivalent number is 6.

Question 7.

a. \(\frac{2}{8}\) = \(\frac{10}{}\)

Answer:

40

Explanation:

Given,

\(\frac{2}{8}\) = \(\frac{10}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{8 × 10}{2 × x}\) = \(\frac{80}{2x}\)

x = \(\frac{80}{2}\)

x = 40

Therefore, the unknown number of equivalent number is 40.

b. \(\frac{3}{5}\) = \(\frac{}{25}\)

Answer:

15

Explanation:

Given,

\(\frac{3}{5}\) = \(\frac{}{25}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{3 × 25}{5 × x}\) = \(\frac{75}{5x}\)

x = \(\frac{75}{5}\)

Therefore, the unknown number of equivalent number is 15.

c. \(\frac{3}{7}\) = \(\frac{9}{}\)

Answer:

21

Explanation:

Given,

\(\frac{3}{7}\) = \(\frac{9}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{7 × 9}{3 × x}\) = \(\frac{63}{3x}\)

x = \(\frac{63}{3}\)

Therefore, the unknown number of equivalent number is 21.

d. \(\frac{1}{2}\) = \(\frac{}{20}\)

Answer:

10

Explanation:

Given,

\(\frac{1}{2}\) = \(\frac{}{20}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{1 × 20}{2 × x}\) = \(\frac{20}{2x}\)

x = \(\frac{20}{2}\)

x = 10

Therefore, the unknown number of equivalent number is 10.

Question 8.

a. \(\frac{4}{12}\) = \(\frac{}{24}\)

Answer:

8

Explanation:

Given,

\(\frac{4}{12}\) = \(\frac{}{24}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{4 × 24}{12 × x}\) = \(\frac{96}{12x}\)

x = \(\frac{96}{12}\)

x = 8

Therefore, the unknown number of equivalent number is 8.

b. \(\frac{5}{6}\) = \(\frac{}{24}\)

Answer:

20

Explanation:

Given,

\(\frac{5}{6}\) = \(\frac{}{24}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{5 × 24}{6 × x}\) = \(\frac{120}{6x}\)

x = \(\frac{120}{6}\)

x = 20

Therefore, the unknown number of equivalent number is 20.

c. \(\frac{1}{3}\) = \(\frac{9}{}\)

Answer:

27

Explanation:

Given,

\(\frac{1}{3}\) = \(\frac{9}{}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{3 × 9}{1 × x}\) = \(\frac{27}{1}\)

Therefore, the unknown number of equivalent number is 27.

d. \(\frac{1}{2}\) = \(\frac{}{18}\)

Answer:

9

Explanation:

Given,

\(\frac{1}{2}\) = \(\frac{}{18}\)

Let the unknown number be x.

To find the unknown equivalent fraction,

cross multiply the numerator and denominator of the given fractions.

\(\frac{1 × 18}{2 × x}\) = \(\frac{18}{2x}\)

x = \(\frac{18}{2}\)

x = 9

Therefore, the unknown number of equivalent number is 9.