﻿ Equivalent Fractions Worksheet - Page 9 | Problems & Solutions

# Equivalent Fractions Worksheet - Page 9

Equivalent Fractions Worksheet
• Page 9
81.
Are the fractions represented by the figures equivalent?

 a. Yes b. No

#### Solution:

In the first figure 1 out of 3 parts are shaded. So, the fraction represented by it is 1 / 3.

In the second figure 2 out of 6 parts are shaded. So, the fraction represented by it is 2 / 6 and in the third figure 3 out of 9 parts are shaded and the fraction represented by it is 3 / 9.

Simplify 2 / 6 and 3 / 9 to lowest term.

2 / 6= 2×1 / 2×3 and 3 / 9 = 3×1 / 3×3

2 / 6 = 3 / 9 = 1 / 3.

The value of the fractions in all the three situations is the same.

So, the fractions represented by the figures are equivalent.

82.
Pick the fractions equivalent to $\frac{12}{15}$.
 A B C D 4/5 40/50 8/15 400/500

 a. A, B and D b. B, C and D c. A and C d. None of the above

#### Solution:

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

A is obtained by dividing the numerator and the denominator of 12 / 15 by 3.

B is obtained by dividing the numerator and the denominator of 12 / 15 by 3 and multiplying them with 10.

Similarly, D is obtained by dividing the numerator and the denominator of 12 / 15 by 3 and multiplying them with 100.

In C the denominators are equal, but the numerators are different. So it is not an equivalent fraction of 12 / 15.

A, B and D are equivalent fractions of 12 / 15

83.
Which of the figures represent equivalent fractions?

 a. (a) A, B, C and D b. (a) A, and B (b) C, D and E c. (a) A, B and E (b) C and D d. (a) A, B and E (b) C, D and E

#### Solution:

In the picture A and B represent the fraction 2 / 4.

2 / 4 = 1 / 2
[Simplify to the lowest term.]

E represents 1 / 2.

A, B and E represent 1 / 2, and are equivalent.

In C and D, 1 out of 4 parts is shaded. So, both C and D represent 1 / 4 and are equivalent.

84.
Are the fractions represented by the figures equivalent?

 a. Yes b. No

#### Solution:

In the first figure 1 out of 2 parts are shaded. So, it represents the fraction 1 / 2.

In the second figure also 1 out of 2 parts is shaded. So, it also represent the fraction 1 / 2.

Though the figures and their sizes are different they both represent the same fraction 1 / 2.

So, the fractions represented by the figures are equivalent.

85.
Pick the fractions equivalent to $\frac{2}{3}$.
ABCD
4/910/15

#### Solution:

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

We cannot get A by multiplying the numerator and the denominator of 2 / 3 by any number.

So, A is not an equivalent fraction of the fraction.

We get B by multiplying the numerator and the denominator of 2 / 3 by 5

= 2×5 / 3×5 = 10 / 15

We cannot get C by multiplying the numerator and the denominator of 2 / 3 by any number.

So, C is not an equivalent fraction of the fraction.

We get D by multiplying the numerator and the denominator of 2 / 3 by 6

= 2×6 / 3×6 = 12 / 18

So, choice A is correct.

86.
Are $\frac{9}{12}$and $\frac{15}{20}$ equivalent?
 a. Yes b. No

#### Solution:

Divide the numerator and denominator of 9 / 12 by 3. The resultant fraction is 3 / 4.

Divide the numerator and denominator of 15 / 20 by 5. The resultant fraction is 3 / 4.

Both 9 / 12 and 15 / 20 result in the same lowest term when simplified. So, they are equivalent fractions.

87.
Find $x$ in the expression.
1 = $\frac{x}{7}$
 a. 7 b. 1 c. Cannot be determined

#### Solution:

7 / 7 = 1. So the missing numerator, x = 7.

88.
Solve $\frac{3}{4}$ = $\frac{9}{z}$.
 a. 4 b. 48 c. 12 d. 9

#### Solution:

Given, the fractions are equivalent. So, the numerator and the denominator of the first fraction are multiplied or divided by a common number to get its equivalent fraction.

The numerator in the resultant fraction is a multiple of the first fraction. 9 = 3 × 3.

As the numerator of the resultant fraction is multiplied by 3, the denominator should also be multiplied by 3.

The denominator of the resultant fraction = 4 × 3 = 12.

89.
Are $\frac{5}{6}$ and $\frac{15}{24}$ equivalent?
 a. Yes b. No

#### Solution:

In 5 / 6 and 15 / 24, the numerator 15 is a multiple of 5 and the denominator 24 is a multiple of 6.

But both the numerator and the denominator are not multiplied by the same number. 15 = 5 × 3 and the denominator 24 = 6 × 4.

5 / 65×3 / 6×4

5 / 615 / 24

So, the fractions are not equivalent.

90.
Can the fractions represented by the shaded parts of the two figures be called equivalent?

 a. Yes b. No

#### Solution:

The number of grids in the Figure 1 is 8.

The number of shaded grids in the Figure 1 is 4.

The fraction of the shaded part of the Figure 1 = The number of shaded gridsThe total number of grids.

= 48
[Substitute the values.]

= 12
[Divide.]

The number of grids in the Figure 2 is 12.

The number of shaded grids in the Figure 2 is 6.

The fraction of the shaded part of the Figure 2 = The number of shaded gridsThe total number of grids.

= 612
[Substitute the values.]

= 12
[Divide.]

The fractions of the shaded parts in both the Figures are equivalent.

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