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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 1
\(\frac{3}{4}\) = \(\frac{9}{12}\)
\(\frac{3}{4}\) 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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 2
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 3
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 4
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 5
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 6
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 7
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 8
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 9
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 10
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 11
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 12
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 13
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 14
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 15
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 16
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.
Spectrum Math Grade 4 Chapter 6 Lesson 1 Answer Key Finding Equivalent Fractions 17
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.

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