﻿ Equivalent Fractions Worksheet - Page 2 | Problems & Solutions

# Equivalent Fractions Worksheet - Page 2

Equivalent Fractions Worksheet
• Page 2
11.
The rectangle shows $\frac{2}{10}$ shaded. Which fractional part of a rectangle is equal to $\frac{2}{10}$?

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

#### Solution:

In each of the choices, there are five equal parts.

Each part represents 1 / 5.

In Fraction 1, only one part is shaded. It represents 1 / 5.

1 / 5 is the same as 2 / 10.
[Because, when we multiply the top and the bottom numbers of 1 / 5 by the same number, 2, we get a fraction 2 / 10 that is equivalent to 1 / 5.]

So, Fraction 1 is equal to 2 / 10.

12.
Jim, Cary, Chris, and John ordered 4 pizzas of equal size. Jim ate $\frac{3}{4}$ of his pizza, Cary ate $\frac{1}{2}$ of his pizza, Chris ate $\frac{1}{4}$, and John ate $\frac{2}{4}$ of his pizza. The left portions of their pizzas are shown in the figure. Who among the four ate equal portions?

 a. Jim and Cary b. Jim and Chris c. Chris and John d. Cary and John

#### Solution:

2 / 4 is the same as 1 / 2.
[Because, 2 / 4 reduces to 1 / 2 on dividing both its top and bottom numbers by 2.]

So, John and Cary ate equal portions of pizza.

13.
Identify an equivalent fraction for the figure shown.

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

#### Solution:

The given figure represents 1 / 2.

Among the fractions listed, look for the one that reduces to 1 / 2 on dividing both its top and bottom numbers by the same number.

Among the fractions listed, only the fraction 3 / 6 reduces to 1 / 2.
[Divide both its top and bottom numbers by 3.]

So, Fraction 1 represents the equivalent fraction for the figure shown.

14.
Figure A shows a fraction of the group of stars shaded.
Which figure is shaded to represent a fraction with the same value?

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

#### Solution:

Let us first list the fractions represented by each figure.

Figure A represents the fraction 6 / 8 .
[Because, 6 out of 8 stars are shaded.]

Figure 1 represents the fraction 3 / 4 .
[Because, 3 out of 4 boxes are shaded.]

Figure 2 represents the fraction 1 / 2.
[Because, 1 out of 2 boxes are shaded.]

Figure 3 represents the fraction 2 / 3 .
[Because, 2 out of 3 boxes are shaded.]

Figure 4 represents the fraction 1 / 4 .
[Because, 1 out of 4 boxes are shaded.]

The top and the bottom numbers of the other fractions are less than that of 6 / 8 .

Now, we need to check if we can reduce 6 / 8 to one of them. Look for a number which both 6 and 8 are divisible by.

6 and 8 are both divisible by 2. So, divide them each by 2. We get 3 / 4 .

The fraction 3 / 4 corresponds to Figure 1. So, Figure 1 is shaded to represent a fraction with the same value as Figure A.

15.
Figure A shows a fraction of the group of triangles shaded.
Choose the figure that is shaded to represent a fraction with the same value.

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

#### Solution:

Let us first list the fractions represented by each figure.

Figure A represents the fraction 2 / 5.
[Since, 2 out of 5 triangles shaded.]

Figure 1 represents the fraction 2 / 8.
[Since, 2 out of 8 diamonds are shaded.]

Figure 2 represents the fraction 6 / 10.
[Since, 6 out of 10 boxes are shaded.]

Figure 3 represents the fraction 4 / 10.
[Since, 4 out of 10 stars are shaded.]

Figure 4 represents the fraction 5 / 8.
[Since, 5 out of 8 ovals are shaded.]

Now, we need to look for the number which when multiplied with 5 gives 8 or 10. There is no number which when multiplied with 5 gives 8. But 5 upon multiplication with 2 gives 10.

Multiply both the top and the bottom numbers of the fraction 2 / 5 with 2, we get 4 / 10 .

The fraction 4 / 10 corresponds to Figure 3. So, Figure 3 is shaded to represent a fraction with the same value as Figure A.

16.
Figure A shows the fraction of chocolates that Andy ate.
Identify the figure that is shaded to represent a fraction with the same value.

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

#### Solution:

Figure A represents the fraction 2 / 3.
[Because, 2 out of 3 chocolates are eaten.]

Figure 1 represents the fraction 4 / 6.

Figure 2 represents the fraction 3 / 6.

Figure 3 represents the fraction 1 / 4 .

Figure 4 represents the fraction 3 / 5.

Now, we need to check if we can reduce these fractions to that of Figure A.

Only Figure 1 on reduction gives 2 / 3.

17.
Which figure shows a fraction equivalent to the fraction represented by Figure A?

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

#### Solution:

Figure A represents the fraction 1 / 2.
[Since, 1 out of 2 parts are shaded.]

Figure 1 represents the fraction 4 / 6.
[Since, 4 out of 6 parts are shaded.]

Figure 2 represents the fraction 1 / 4.
[Since, 1 out of 4 parts are shaded.]

Figure 3 represents the fraction 3 / 6.
[Since, 3 out of 6 parts are shaded.]

Figure 4 represents the fraction 3 / 4.
[Since, 3 out of 4 parts are shaded.]

Now, we need to check if we can reduce these fractions to that of Figure A.

Only 3 / 6 on reduction gives 1 / 2. So, Figure 3 shows a fraction equivalent to the fraction represented by Figure A.
[Because, 3 / 6= 1×3 / 2×3 reduces to 1 / 2, after cancelling out the 3's and 3 / 6 corresponds to Figure 3.]

18.
Identify the figure that shows a fraction equivalent to the fraction represented by Figure A.

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

#### Solution:

Figure A represents the fraction 2 / 5.
[Since, 2 out of 5 parts are shaded.]

Figure 1 represents the fraction 3 / 5.
[Since, 3 out of 5 parts are shaded.]

Figure 2 represents the fraction 1 / 5.
[Since, 1 out of 5 parts is shaded.]

Figure 3 represents the fraction 4 / 10.
[Since, 4 out of 10 parts are shaded.]

Figure 4 represents the fraction 6 / 10.
[Since, 6 out of 10 parts are shaded.]

Since all the denominators are either 5 or 10, convert all the denominators to the same denominator 5.

6 / 10 = 3 / 5 and 4 / 10 = 2 / 5

Only Figure 3 on reduction gives 2 / 5.

19.
Figure A shows a fraction of the group of circles shaded.
Choose the figure that is shaded to represent a fraction with the same value.

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

#### Solution:

Out of 8 circles, 6 circles are shaded.

So, the fraction of circles shaded is 6 / 8.

6 / 8 = 3 / 4
[Simplify the fraction.]

Figure 4 represents the fraction 3 / 4.

20.
Fill in the missing value in the equation $\frac{4}{6}$ = $\frac{?}{3}$ .
 a. 7 b. 9 c. 2 d. 3

#### 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.