Equivalent Fractions Worksheet - Page 14

Equivalent Fractions Worksheet
• Page 14
131.
Choose the figures which represent equivalent fractions.

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

Solution:

The fraction that represents the shaded part of figure 1 is 11 / 14 .

The fraction that represents the shaded part of figure 2 is 11 / 14 .

The fraction that represents the shaded part of figure 3 is 14 / 21 .

The fraction that represents the shaded part of figure 4 is 11 / 12 .

So, the fractions given by the figures 1 and 2 are equivalent.

132.
If the fractions $\frac{8}{26}$ and $\frac{x}{13}$ are equivalent, then find the value of $x$.
 a. 4 b. 6 c. 5 d. 3

Solution:

The two given fractions are equivalent.

So, the numerator and the denominator of the first fraction are multiplied or divided by a common number, to give the second fraction.

262 = 13
The denominator of the second fraction is obtained by dividing the denominator of the first fraction by 2.

So, the numerator of the first fraction should also be divided by the same number, 2.

The numerator of the second fraction = 8 / 2 = 4 .

So, the missing value x = 4.

133.
Say whether the fractions represented by the figures are equivalent or not.

 a. Yes b. No

Solution:

The total number of parts in the first figure is 15 and 10 of them are shaded.

So, the fraction represented by this figure is 10 / 15 .

The total number of parts in the second figure is 15 and the shaded parts in it are 10.

So, the fraction represented by this figure is 10 / 15 .

So, the fractions represented by the two figures are equivalent.

134.
Are the fractions represented by the figures equivalent?

 a. Yes b. No

Solution:

The total number of parts in the first figure is 8 and 4 of them are shaded.

So, the fraction represented by this figure is 4 / 8 .

The total number of parts in the second figure is 8 and the shaded parts in it are 6.

So, the fraction represented by this figure is 6 / 8 .

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

135.
Choose the figures which represent equivalent fractions.

 a. Figures 1, 2 and 3 b. Figures 1 and 2 c. Figures 1, 2 and 4 d. Figures 1 and 3

Solution:

The fraction that represents the shaded part of figure 1 is 3 / 4 .

The fraction that represents the shaded part of figure 2 is 3 / 4 .

The fraction that represents the shaded part of figure 3 is 6 / 8 = 3 / 4 .

The fraction that represents the shaded part of figure 4 is 7 / 8 .

So, the fractions given by the figures 1, 2 and 3 are equivalent.

136.
Which of the following is an equivalent of $\frac{18}{24}$?
 a. $\frac{4}{3}$ b. $\frac{1}{3}$ c. $\frac{3}{4}$ d. $\frac{1}{4}$

Solution:

18 / 24
[Given fraction.]

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

18 / 24 = (3×6) / (4×6) = 3 / 4
[Divide out the common factor 6.]

So, 18 / 24 = 3 / 4.

137.
The greatest number that is a factor of each of two numbers is called the _________.
 a. Greatest common factor (GCF) b. Least common denominator (LCD)

Solution:

The greatest number that is a factor of each of two numbers is called the greatest common factor.

138.
Can we simplify the fraction $\frac{9}{8}$?
 a. Yes b. No

Solution:

A fraction is in simplest form when the greatest common factor of the numerator and the denominator is 1.

The fraction 9 / 8 is already in its simplest form.

So, the fraction cannot be further simplified.

139.
Fractions that name the same region, part of a set, and part of a segment are called _________.
 a. Improper fractions b. Proper fractions c. Simple fractions d. Equivalent fractions

Solution:

Fractions that name the same region, part of a set, and part of a segment are called equivalent fractions.