﻿ Equivalent Fractions Worksheet - Page 8 | Problems & Solutions
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Equivalent Fractions Worksheet
• Page 8
71.
Are $\frac{15}{18}$ and $\frac{20}{24}$ equivalent? a. Yes b. No

#### Solution:

Divide the numerator and denominator of 15 / 18 by 3. The resultant fraction is 5 / 6.

Divide the numerator and denominator of 20 / 24 by 4. The resultant fraction is 5 / 6.

Both 15 / 18 and 20 / 24 result in the same lowest term when simplified. So, they are equivalent fractions.

Correct answer : (1)
72.
Find $x$ in the expression.
1 = $\frac{x}{9}$ a. 9 b. 1 c. 10

#### Solution:

9 / 9 = 1. So the missing numerator, x = 9.

Correct answer : (1)
73.
Are $\frac{4}{5}$ and $\frac{8}{15}$ equivalent? a. No b. Yes

#### Solution:

In 4 / 5 and 8 / 15, the numerator 8 is a multiple of 4 and the denominator 15 is a multiple of 5.

But both the numerator and the denominator are not multiplied by the same number. 8 = 4 × 2 and the denominator 15 = 5 × 3.

4 / 54×2 / 5×3

4 / 58 / 15

So, the fractions are not equivalent.

Correct answer : (1)
74.
Fill in the missing numerator in the given equivalent fractions.
$\frac{12}{15}$ = $\frac{?}{5}$ a. 4 b. 5 c. 12 d. none of these

#### Solution:

Given, the fractions in the problem are equivalent.

An equivalent of a fraction is obtained by multiplying or dividing the numerator and the denominator of a given fraction with a common number.

The denominator in the first fraction is a multiple of the denominator in the resultant fraction. So, the denominator should be divided by some number to get the resultant denominator.

15 / 3 = 5

The numerator of the fraction should be divided by 3 to get the missing numerator. The missing numerator = 12 ÷ 3.

The missing numerator = 4.

Correct answer : (1)
75.
Pick fractions equivalent to $\frac{10}{12}$.
 $f$1 $f$2 $f$3 $f$4 5/6 50/60 10/11 500/600 a. $f$1, $f$2, and $f$4 b. $f$1 and $f$3 c. $f$2, $f$3 and $f$4 d. none of these

#### Solution:

An equivalent of the fraction is obtained by multiplying or dividing the numerator and the denominator of the fraction with a common number.

f1 is obtained by dividing the numerator and the denominator of 10 / 12 by 2.

f2 is obtained by dividing the numerator and the denominator of 10 / 12 by 2 and multiplying them with 10.

Similarly, f4 is obtained by dividing the numerator and the denominator of 10 / 12 by 2 and multiplying them with 100.

In f3, the numerator of the fraction is equal to the numerator of the given fraction, but the denominators are different. So it is not an equivalent fraction of 10 / 12.

f1, f2, and f4 are equivalent fractions of 10 / 12 .

Correct answer : (1)
76.
Identify the sentence that describes the fractions.  a. $\frac{1}{2}$ is greater than $\frac{2}{4}$ b. $\frac{1}{2}$ is equivalent to $\frac{2}{4}$ c. $\frac{1}{2}$ is less than $\frac{2}{4}$ d. $\frac{1}{2}$ is equivalent to $\frac{2}{3}$

#### Solution:

The circles in the figure are of the same size and the same amount is shaded in both the circles.

So, the sentence '1 / 2 is equivalent to 2 / 4' describes the fractions.

Correct answer : (2)
77.
Complete:
$\frac{1}{2}$ = $\frac{?}{4}$  a. $\frac{1}{2}$ = $\frac{2}{4}$ b. $\frac{1}{2}$ = $\frac{1}{4}$ c. $\frac{1}{2}$ = $\frac{2}{8}$ d. $\frac{1}{2}$ = $\frac{2}{2}$

#### Solution:

Two fraction strips of 1 / 4 match one strip of 1 / 2.

Hence, the missing number is 2.

Hence, 1 / 2 = 2 / 4 .

Correct answer : (1)
78.
Which number sentence is true? a. $\frac{9}{18}$ > $\frac{6}{12}$ b. $\frac{9}{18}$ < $\frac{6}{12}$ c. $\frac{9}{18}$ = $\frac{1}{12}$ d. $\frac{9}{18}$ = $\frac{6}{12}$

#### Solution:

Consider the fractions 9 / 18 and 6 / 12.

For each fraction, check whether the top and the bottom numbers are both multiples of the same number.

Consider 9 / 18. In this fraction, both 9 and 18 are multiples of 9.

So, dividing the top and bottom numbers by 9 will reduce the fraction to 1 / 2 .

Proceeding the same way, we find that the other fraction 6 / 12 also reduces to 1 / 2 .
[Divide the top and the bottom numbers of the fraction 6 / 12 by 6, because they both are multiples of 6.]

So, among the number sentences listed only '9 / 18 = 6 / 12' is true.

Correct answer : (4)
79.
Valerie used $\frac{6}{10}$ cup of chocolate chips to make cookies. Nina used $\frac{9}{15}$ cup of chocolate chips to make cookies. Which sentence is true about the amount of chocolate chips used by both Valerie and Nina? a. Both used the same amount of chocolate chips. b. The amount of chocolate chips that Valerie used is greater than what Nina used. c. The amount of chocolate chips that Valerie used is less than what Nina used. d. The amount of chocolate chips that Nina used is greater than what Valerie used.

#### Solution:

Consider the fractions 6 / 10 and 9 / 15.

For each fraction, check whether the top and the bottom numbers are both multiples of the same number.

Consider 6 / 10. In this fraction, both 6 and 10 are multiples of 2.

So, dividing the top and bottom numbers by 2 will reduce the fraction to 3 / 5 .

Proceeding the same way, we find that the other fraction 9 / 15 also reduces to 3 / 5.
[Divide the top and the bottom numbers of the fraction 9 / 15 by 3, because they both are multiples of 3.]

So, Valerie and Nina both used the same amount of chocolate chips.
[Because, the two fractions are equivalent.]

Correct answer : (1)
80.
Fill in the missing value in the equation $\frac{4}{6}$ = $\frac{?}{3}$ . a. 2 b. 3 c. 4 d. None of the above

#### Solution:

Given, the fractions in the problem are equivalent.

An equivalent of a fraction is obtained by multiplying or dividing the numerator and the denominator of a given fraction with a common number.

The denominator in the first fraction is a multiple of the denominator in the resultant fraction. So, the denominator should be divided by some number to get the resultant denominator.

6 / 2 = 3

The numerator of the fraction should be divided by 2 to get the missing numerator. The missing numerator = 4 ÷ 2 .

The missing value = 2.

Correct answer : (1)

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