# Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions

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.

$$\frac{9}{12}$$

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.

$$\frac{4}{16}$$

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.

$$\frac{10}{15}$$

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.

$$\frac{2}{4}$$

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.

$$\frac{6}{18}$$

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.

$$\frac{6}{24}$$

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.

$$\frac{3}{15}$$

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.

$$\frac{8}{40}$$

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.

$$\frac{10}{14}$$

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.

$$\frac{12}{24}$$

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.

$$\frac{8}{32}$$

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.

$$\frac{6}{36}$$

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.

$$\frac{9}{27}$$

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.

$$\frac{20}{30}$$

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.

$$\frac{10}{25}$$

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.

$$\frac{2}{16}$$

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. $$\frac{1}{5}$$ = $$\frac{3}{}$$
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. $$\frac{1}{10}$$ = $$\frac{}{20}$$
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. $$\frac{3}{4}$$ = $$\frac{9}{}$$
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. $$\frac{1}{2}$$ = $$\frac{9}{}$$
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. $$\frac{1}{3}$$ = $$\frac{}{12}$$
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. $$\frac{2}{4}$$ = $$\frac{8}{}$$
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. $$\frac{1}{12}$$ = $$\frac{2}{}$$
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. $$\frac{2}{6}$$ = $$\frac{}{18}$$
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. $$\frac{2}{8}$$ = $$\frac{10}{}$$
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. $$\frac{3}{5}$$ = $$\frac{}{25}$$
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. $$\frac{3}{7}$$ = $$\frac{9}{}$$
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. $$\frac{1}{2}$$ = $$\frac{}{20}$$
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. $$\frac{4}{12}$$ = $$\frac{}{24}$$
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. $$\frac{5}{6}$$ = $$\frac{}{24}$$
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. $$\frac{1}{3}$$ = $$\frac{9}{}$$
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. $$\frac{1}{2}$$ = $$\frac{}{18}$$
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.

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