﻿ Equivalent Fractions Worksheet - Page 15 | Problems & Solutions
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Equivalent Fractions Worksheet
• Page 15
141.
Which of the following fractions is in its simplest form? a. $\frac{7}{7}$ b. $\frac{9}{3}$ c. $\frac{5}{9}$ d. $\frac{5}{10}$

#### Solution:

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

Among the choices, the fraction 5 / 9 is in its simplest form as the GCF of the numerator and the denominator is 1.

Correct answer : (3)
142.
Which of the following fractions is not in its simplest form? a. $\frac{6}{4}$ b. $\frac{3}{4}$ c. $\frac{3}{7}$ d. $\frac{5}{3}$

#### Solution:

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

Among the choices, the fraction 6 / 4 can be still simplified into 3 / 2.

The fractions in all the other choices are already in their simplest form.

So, the fraction 6 / 4 is not in the simplified form among the choices.

Correct answer : (1)
143.
Which of the following fractions is in its simplest form? a. $\frac{3}{6}$ b. $\frac{2}{4}$ c. $\frac{1}{7}$ d. $\frac{6}{4}$

#### Solution:

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

Among the choices, the fraction 1 / 7 is in its simplest form as the GCF of the numerator and the denominator is 1.

The fractions in all the other choices can be further simplified.

Correct answer : (3)
144.
Find the simplest form of the fraction. $\frac{24}{32}$ a. $\frac{1}{4}$ b. $\frac{4}{5}$ c. $\frac{1}{3}$ d. $\frac{3}{4}$

#### Solution:

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

2432 = 2 × 2 × 2 × 332× 2 × 2 × 3D=2 × 2 × 2 × 2 × 2
[Write the factors of 24 and 32.]

= 34
[Divide out the common factors.]

The fraction 3 / 4 is in the simplest form. So, the simplest form of the fraction 24 / 32 is 3 / 4.

Correct answer : (4)
145.
Pick the simplest form of the fraction. $\frac{14}{35}$ a. $\frac{2}{5}$ b. $\frac{1}{2}$ c. $\frac{1}{5}$ d. $\frac{2}{6}$

#### Solution:

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

1435 = 2 × 735× 7D=5 × 7
[Write the factors of 14 and 35.]

= 25
[Divide out the common factor, 7.]

The fraction 2 / 5 is in the simplest form.

So, the simplest form of the fraction 14 / 35 is 2 / 5.

Correct answer : (1)
146.
Which of the following fractions is in its simplest form? a. $\frac{9}{3}$ b. $\frac{3}{11}$ c. $\frac{6}{2}$ d. $\frac{12}{8}$

#### Solution:

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

Among the choices, the fraction 3 / 11 is in its simplest form as the GCF of the numerator and the denominator is 1.

The fractions in all the other choices can be further simplified.

Correct answer : (2)
147.
Which of the following fractions is not in its simplest form? a. $\frac{2}{3}$ b. $\frac{1}{3}$ c. $\frac{8}{12}$ d. $\frac{1}{12}$

#### Solution:

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

Among the choices, the fraction 8 / 12 can be still simplified into 2 / 3.

The fractions in all the other choices are already in their simplest form.

Correct answer : (3)
148.
Find the value of $b$ if $\frac{b}{3}$ = $1\frac{1}{7}$. a. $4\frac{3}{8}$ b. $3\frac{3}{7}$ c. $3\frac{3}{8}$ d. $4\frac{3}{7}$

#### Solution:

b / 3 = 11 / 7
[Original expression.]

b / 3 = 8 / 7
[Convert the mixed number into improper fractions.]

b = 3 × 8 / 7
[Multiply each side by 3.]

b = (3×8) / (1×7)
[Group the numerators and denominators.]

b = 24 / 7
[Simplify.]

b = 33 / 7
[Convert the improper fraction into mixed number.]

Correct answer : (2)

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