# Equivalent Fractions Worksheet - Page 15

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.

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.

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.

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.

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.

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.

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.

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.]