Equivalent Fractions Worksheet - Page 3

Equivalent Fractions Worksheet
• Page 3
21.
Identify a figure that represents the equivalent fraction for the fraction shown.

 a. Figure-2 b. Figure-3 c. Figure-4 d. Figure-1

Solution:

In the given figure, 2 out of 4 boxes are shaded. So the fraction is 1 / 2.

In Figure-1, 4 out of 8 boxes are shaded. So, the fraction is 4 / 8 , which is equal to 1 / 2.

In Figure-2, 6 out of 8 boxes are shaded. So, the fraction is 6 / 8 = 3 / 4.

In the Figure-3, 5 out of 8 boxes are shaded. So, the fraction is 5 / 8.

In Figure-4, 3 out of 8 boxes are shaded. So, the fraction is 3 / 8.

So, Figure-1 represents the equivalent fraction to the given figure.

22.
State whether the fractions shown are equivalent or not.

 a. Yes b. No

Solution:

In Figure-1, 1 out of 2 parts is shaded.

So, the fraction is 1 / 2.

In Figure-2, 4 out of 8 parts are shaded.

So, the fraction for Figure-2 is 4 / 8 = 1 / 2
[Simplify.]

So, both the fractions shown are equivalent.

23.
Which fraction is equivalent to $\frac{5}{10}$?

 a. Figure-2 b. Figure-3 c. Figure-1 d. Figure-4

Solution:

Given fraction is 5 / 10 = 1 / 2
[Simplify.]

In Figure-1, 5 out of 8 parts are shaded. So, the fraction is 5 / 8.

In Figure-2, 1 out of 2 parts is shaded. So, the fraction is 1 / 2.

In Figure-3, 3 out of 8 parts are shaded. So, the fraction is 3 / 8.

In Figure-4, 4 out of 6 parts are shaded. So, the fraction is 4 / 6.

So, Figure-2 shows the fraction equivalent to 5 / 10.

24.
Which fraction represents an equivalent fraction of the fraction shown?

 a. Figure 2 b. Figure 1 c. Figure 4 d. Figure 3

Solution:

In the given figure, 2 out of 3 parts are shaded. So the fraction is 2 / 3.

In Figure-1, 1 out of 3 parts are shaded. So, the fraction is 1 / 3.

In Figure-2, 4out of 6 parts are shaded. So, the fraction is 4 / 6 = 2 / 3.

In the Figure-3, 2 out of 4 parts are shaded. So, the fraction is 2 / 4 = 1 / 2.

In Figure- 4, 1 out of 5 parts are shaded. So, the fraction is 1 / 5.

So, Figure-2 represents the equivalent fraction to the given figure.

25.
Which figure models an equivalent fraction of $\frac{3}{5}$?

 a. Figure 1 b. Figure 2 c. Figure 3 d. None of the above

Solution:

The fraction modeled in Figure 1 is 6 / 10.

GCF of 6 and 10 is 2
[The greatest factor which is common for 6 and 10 is 2.]

610 = 6÷210÷2
[Divide numerator and denominator by the GCF 2.]

= 35
[Simplify.]

The fraction modeled in the Figure 2 is 2 / 5 and the fraction modeled in Figure 3 is 7 / 15.

So, Figure 1 models an equivalent fraction of 3 / 5.

26.
What is the number by which the numerator and the denominator of the fraction $\frac{7}{8}$ should be multiplied with to get $\frac{105}{120}$?
 a. 30 b. 14 c. 12 d. 15

Solution:

105 = 7 × 15 and 120 = 8 × 15
[Express 105 as a multiple of 7 and 120 as a multiple of 8.]

The numerator and denominator of 7 / 8 should be multiplied by 15 to get 105 / 120.

27.
Express $\frac{6}{9}$ in its simplest form.
 a. $\frac{1}{4}$ b. $\frac{2}{5}$ c. $\frac{3}{5}$ d. $\frac{2}{3}$

Solution:

Factors of 6 are 1, 2, 3, 6
[Write factors for numerator.]

Factors of 9 are 1, 3, 9
[Write factors for denominator.]

GCF of 6 and 9 is 3.
[Select the greatest factor which is common to both the numbers.]

6 ÷ 39 ÷ 3 = 2 / 3
[Divide numerator and denominator by the GCF 3.]

So, the simplest form of the fraction 6 / 9 is 2 / 3.

28.
Select the figure that is an equivalent fraction of the model given.

 a. Figure 1 b. Figure 2 c. Figure 3 d. None of the above

Solution:

The figure models the fraction 4 / 8.

Factors of 4 are 1, 2, 4
[Write factors of the numerator.]

Factors of 8 are 1, 2, 4, 8
[Write factors of the denominator.]

GCF of 4 and 8 is 4
[Select the common factors and find GCF.]

4÷4 / 8÷4 = 1 / 2
[Divide numerator and denominator by the GCF 4.]

Figure 1 models the fraction, 3 / 4.

Figure 2 models the fraction, 1 / 4.

Figure 3 models the fraction, 2 / 4.

Factors of 2 are 1, 2
[Write factors of the numerator.]

Factors of 4 are 1, 2, 4
[Write factors of the denominator.]

GCF of 2 and 4 is 2.
[Select the common factors and find GCF.]

2÷2 / 4÷2 = 1 / 2
[Divide numerator and denominator by the GCF 2.]

Figure 3 models the equivalent fraction of the model.

29.
Find the value of $x$, if $\frac{5}{10}$ and $\frac{x}{50}$ are equivalent fractions.
 a. 25 b. 24 c. 27 d. 26

Solution:

50 = 10 x 5
[Write 50 as a factor of 10.]

5x510x5 = x50
[Multiply numerator and denominator of 5 / 10 by 5.]

2550 = x50

So, x = 25
[If two equal fractions have equal denominators, their numerators are also equal.]

30.
What is the equivalent fraction for the model?

 a. $\frac{5}{8}$ b. $\frac{3}{4}$ c. $\frac{4}{3}$ d. None of the above

Solution:

In the model, 9 divisions are shaded out of 12 divisions.

The model represents a fraction of 9 / 12.

9÷312÷3 = 34
[Divide 9 and 12 by their GCF 3.]

The equivalent fraction for the model is 3 / 4.