# Equivalent Fractions Worksheet - Page 11

Equivalent Fractions Worksheet
• Page 11
101.
Choose the number sentence that is true about the figure shown.

 a. $\frac{1}{2}$ > $\frac{2}{4}$ b. $\frac{1}{2}$ = $\frac{2}{4}$ c. $\frac{1}{2}$ < $\frac{2}{4}$ d. $\frac{1}{2}$ = $\frac{4}{2}$

#### Solution:

The fraction represented by the first square is 1 / 2 .
[1 out of 2 parts is shaded.]

The fraction represented by the second square is 2 / 4 .
[2 out of 4 parts are shaded.]

Also, we notice that the squares are of the same size and the same amount is shaded in both the squares.

So the number sentence '1 / 2 = 2 / 4' is true about the figure shown.

102.
Identify the figure that shows a pair of equivalent fractions.

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

#### Solution:

Among the four figures shown, only the pair in Figure 1 have the same amount shaded.

So, Figure 1 shows a pair of equivalent fractions.

103.
Which model is shaded to show a fraction equivalent to $\frac{5}{15}$?

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

#### Solution:

Model 1 represents the fraction 1 / 3.
[1 out of 3 parts is shaded.]

Model 2 represents the fraction 5 / 8.
[5 out of 8 parts are shaded.]

Model 3 represents the fraction 3 / 4.
[3 out of 4 parts are shaded.]

Model 4 represents the fraction 5 / 10.
[5 out of 10 parts are shaded.]

The given fraction 5 / 15 reduces to 1 / 3.
[Divide both the top and the bottom numbers by 5, because they both are multiples of 5.]

So, among the models shown, only Model 1 is shaded to show a fraction equivalent to 5 / 15.
[Because, 5 / 15 = 1 / 3.]

104.
Identify the two figures that have an equivalent fraction shaded.

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

#### Solution:

Figure 1 represents the fraction 6 / 8.
[6 out of 8 parts are shaded.]

Figure 2 represents the fraction 3 / 4.
[3 out of 4 parts are shaded.]

Figure 3 represents the fraction 1 / 4.
[1 out of 4 parts is shaded.]

Figure 4 represents the fraction 1 / 2.
[1 out of 2 parts is shaded.]

Make all the denominators (bottom numbers) the same, preferably 8. Figure 1 already shows a fraction with 8 in the denominator.

Consider 3 / 4. It becomes 6 / 8.
[Multiply the top and the bottom numbers by 2.]

Consider 1 / 4. It becomes 2 / 8.
[Multiply the top and the bottom numbers by 2.]

Consider 1 / 2. It becomes 4 / 8.
[Multiply the top and the bottom numbers by 4.]

So, Figure 1 and Figure 2 have an equivalent fraction shaded.

105.
John and Amy are arranging books in shelves. They have completed $\frac{3}{5}$ of the job so far. Identify the fraction that is equivalent to $\frac{3}{5}$.
 a. $\frac{6}{10}$ b. $\frac{3}{10}$ c. $\frac{6}{5}$ d. $\frac{9}{8}$

#### Solution:

Let us use skip counting to find a fraction equivalent to 3 / 5.

Skip count the top number by 3′s and the bottom number by 5′s.

3 / 5 , 6 / 10 , 9 / 15 , 12 / 20, and so on.
[All these fractions are equivalent to each other, because we added as many 5′s as 3′s to each fraction.]

So, among the fractions listed, 6 / 10 is the right answer.

106.
Use the figure shown to choose the number that replaces the ? to make the fractions equivalent.

 a. 6 b. 3 c. 12

#### Solution:

In the first rectangle, 6 out of 12 parts are shaded.

In the second rectangle, 3 out of 6 parts are shaded.

So, 6 / 12 = 3 / 6.
[Because, both the rectangles shown are the same size and the same amount is shaded in both the rectangles.]

So, 3 replaces the ? to make the fractions equivalent.

107.
Are the pair of fractions $\frac{2}{5}$ and $\frac{3}{10}$ equivalent ?
 a. Yes b. No

#### Solution:

Fractions that represent the same amount are called equivalent fractions.

Represent 2 / 5 using two 1 / 5 strips and represent 3 / 10 using three 1 / 10 strips and line up three 1 / 10 strips below the two 1 / 5 strips as below.

From the above figure, 2 / 5 and 3 / 10 does not represent same amount.

So, the fractions 2 / 5 and 3 / 10 are not equivalent fractions.

108.
Compare the two figures. Are the fractions equivalent?

 a. No b. Yes

#### Solution:

The fraction represented by the first circle is 1 / 2 and the fraction represented by the second circle is 3 / 8.

Fractions that represent same amount are called equivalent fractions.

In fraction 1 / 2, multiplying the numerator and the denominator by 3 gives 3 / 6.

As 3 / 6 is not equal to 3 / 8, the fractions 1 / 2 and 3 / 8 are not equivalent fractions.

So, the fractions represented by the figures are not equivalent.

109.
Find an equivalent fraction of $\frac{6}{8}$ .
 a. $\frac{1}{2}$ b. $\frac{3}{4}$ c. $\frac{3}{2}$ d. $\frac{8}{6}$

#### Solution:

Fractions that represent same amount are called equivalent fractions.

Represent the fraction 6 / 8 by using six 1 / 8 strips as below.

Line up 1 / 4 strips below 1 / 8 strips.

As three 1 / 4 strips form the same amount as six 1 / 8 strips, 6 / 8 and 3 / 4 are equivalent fractions.

So, the equivalent fraction of 6 / 8 is 3 / 4 .

110.
Find the fraction equivalent to $\frac{2}{3}$ .
 a. $\frac{4}{6}$ b. $\frac{1}{3}$ c. $\frac{13}{6}$ d. $\frac{2}{4}$

#### Solution:

Fractions that represent same amount are called equivalent fractions.

Represent the fraction 2 / 3 using two 1 / 3 strips as below.

Line up 1 / 6 strips below 1 / 3 strips.

As four 1 / 6 strips form the same amount as two 1 / 3 strips, 2 / 3 and 4 / 6 are equivalent fractions.

So, the equivalent fraction of 2 / 3 is 4 / 6 .