# Equivalent Fractions Worksheet - Page 10

Equivalent Fractions Worksheet
• Page 10
91.
Which of the given fractions is equivalent to $\frac{2}{3}$?
 a. $\frac{6}{9}$ b. $\frac{4}{3}$ c. $\frac{3}{2}$ d. $\frac{4}{9}$

#### Solution:

To find an equivalent fraction, we have to multiply or divide the numerator and denominator by the same number.

To compare 2 / 3 and 4 / 3, we would multiply 2 / 3 by 2 / 2 to produce 4 / 6.
[2 × 23 × 2 = 4 / 6]

4 / 6 and 4 / 3 are not equivalent fractions. Since, 4 / 6 is not the same as 4 / 3.

To compare 2 / 3 and 4 / 9, we would multiply 2 / 3 by 2 / 2 to produce 4 / 6.
[2 × 23 × 2 = 4 / 6]

4 / 6 and 4 / 9 are not equivalent fractions. Since, 4 / 6 is not the same as 4 / 9.

2 / 3 is not same as 3 / 2. Since 2 / 3 and 3 / 2 are not equivalent fractions .

To compare 2 / 3 and 6 / 9, we would multiply 2 / 3 by 3 / 3 to produce 6 / 9.
[2 × 33 × 3 = 6 / 9]

2 / 3 and 6 / 9 are equivalent fractions.

92.
Use the figure shown to identify the number that replaces the ? to make the fractions equivalent.

 a. 2 b. 4 c. 8 d. 6

#### Solution:

In the first circle, 2 out of 4 parts are shaded.

In the second circle, 4 out of 8 parts are shaded.

2 / 4 = 4 / 8
[Because, both the circles shown are the same size and the same amount is shaded in both the circles.]

So, 4 replaces the ? to make the fractions equivalent.

93.
Write three equivalent fractions of $\frac{18}{30}$ using the common factors.
 a. 3/6, 6/10 and 3/5 b. 6/15, 6/10 and 3/5 c. 3/15, 6/10 and 3/5 d. 9/15, 6/10 and 3/5

#### Solution:

Factors of the numerator, 18 are 1, 2, 3, 6, 9, 18.

Factors of the denominator, 30 are 1, 2, 3, 5, 6, 10, 15, 30.

The common factors of 18 and 30 are 1, 2, 3 and 6.

18 / 30 = 18÷2 / 30÷2 = 9 / 15
[Divide the numerator and the denominator by 2.]

18 / 30 = 18÷3 / 30÷3 = 6 / 10
[Divide the numerator and the denominator by 3.]

18 / 30 = 18÷6 / 30÷6 = 3 / 5
[Divide the numerator and the denominator by 6.]

The three equivalent fractions of 18 / 30 are 9 / 15, 6 / 10 and 3 / 5.

94.
Andrew has 4 red and 6 blue marbles. Write an equivalent fraction for the fraction of blue marbles Andrew has.
 a. $\frac{2}{5}$ b. $\frac{3}{5}$ c. $\frac{1}{3}$ d. $\frac{1}{5}$

#### Solution:

Total marbles = 4 + 6 = 10

Fraction of blue marbles Andrew has = (Blue marbles) / (Total marbles)

= 610
[Substitute the values.]

Factors of 6 are 1, 2, 3, 6.

Factors of 10 are 1, 2, 5, 10.

The common factor of 6 and 10 is 2.

= 6÷210÷2 = 35
[Divide the numerator and denominator by the common factor.]

So, the equivalent fraction for the fraction of blue marbles Andrew has is 3 / 5.

95.
A manufacturing company produces 172 cycles per month. If 60 of them are yellow-colored cycles and 40 of them are pink-colored, then what fraction of cycles are pink-colored when compared to the yellow-colored cycles?
 a. $\frac{4}{5}$ b. $\frac{3}{4}$ c. $\frac{5}{6}$ d. $\frac{2}{3}$

#### Solution:

The fraction of pink colored cycles to the yellow colored cycles = 40 / 60

40 = 1, 2, 4, 5, 8, 10, 20, 40 and
60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
[Write factors of the numerator and the denominator.]

GCF of 40 and 60 is 20
[Select the greatest common factor.]

40÷2060÷20 = 23
[Divide numerator and denominator by GCF 20.]

The fraction of pink colored cycles to the yellow colored cycles is 2 / 3 .

96.
What would you call different fractions that represent the same amount?
 a. like fractions b. equivalent fractions c. unlike fractions d. unequal fractions

#### Solution:

Fractions that name the same amount are called equivalent fractions.

97.
Which of the figures is equivalent to the figure?

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

#### Solution:

Amount shaded in the figure and Figure 3 is equal.

Amounts shaded in Figure 1, Figure 2, and Figure 4 are more than that shaded in the figure.

So, only Figure 3 is equivalent to the figure.

98.
Matt has 8 pens and he gave 3 of them to Danielle. Choose an equivalent fraction to the fraction of the pens left with Matt.
 a. $\frac{11}{17}$ b. $\frac{10}{16}$ c. $\frac{16}{10}$ d. None of the above

#### Solution:

The number of pens left with Matt = 8 - 3 = 5

The fraction of the pens left with Matt = Remaining pensTotal pens = 5 / 8

The equivalent fraction for this is, 5×28×2 = 10 / 16
[Multiply numerator and denominator by same non-zero number.]

The equivalent fraction is 10 / 16.

99.
In a game of 25 matches, Joe lost 10 matches. What fraction of the matches did Joe lose? Identify equivalent fractions of this fraction.
 a. $\frac{10}{25}$, $\frac{25}{50}$ and $\frac{5}{20}$ b. $\frac{10}{25}$, $\frac{20}{50}$ and $\frac{2}{5}$ c. $\frac{10}{25}$, $\frac{2}{50}$ and $\frac{5}{20}$ d. None of the above

#### Solution:

The fraction of matches Joe lost = Number of matches lostTotal number of matches = 10 / 25

The equivalent fractions for this is, 10×225×2 = 20 / 50
[Multiply numerator and denominator by the same nonzero number.]

10÷5 / 25÷5 = 2 / 5
[Divide numerator and denominator by GCF 5.]

The two equivalent fractions of 10 / 25 are 20 / 50 and 2 / 5

100.
In a family of 16, 7 are males and the remaining are females. Choose two equivalent fractions of the fraction representing the males in the family.
 a. $\frac{14}{48}$ and $\frac{21}{32}$ b. $\frac{14}{32}$ and $\frac{21}{48}$ c. $\frac{21}{48}$ and $\frac{14}{48}$ d. None of the above

#### Solution:

Fraction of males = Number of malesTotal number of persons in the family = 7 / 16

7 / 16 = 7×216×2 = 14 / 32
[Multiply the numerator and the denominator by the same nonzero number.]

7 / 16 = 7×316×3 = 21 / 48
[Multiply the numerator and the denominator by the same nonzero number.]

The two equivalent fractions for the fraction of males in the family are 14 / 32 and 21 / 48.