﻿ Fraction in Simplest Form Worksheet | Problems & Solutions

# Fraction in Simplest Form Worksheet

Fraction in Simplest Form Worksheet
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1.
Express the fraction $\frac{12}{16}$ in its simplest form.
 a. $\frac{6}{8}$ b. $\frac{1}{7}$ c. $\frac{3}{4}$ d. $\frac{3}{8}$

#### Solution:

12 / 16 = 12÷2 / 16÷2 = 6 / 8
[Simplify the fraction by dividing both the numerator and the denominator by 2.]

As 6 / 8 is not the simplest form of the fraction, simplify the fraction further.

6 / 8 = 6÷2 / 8÷2 = 3 / 4
[Simplify the fraction by dividing both the numerator and the denominator by 2.]

So, the simplest form of the fraction 12 / 16 is 3 / 4.

2.
Simplify the fraction $\frac{2}{6}$ .
 a. $\frac{1}{4}$ b. $\frac{1}{3}$ c. $\frac{1}{2}$ d. $\frac{3}{4}$

#### Solution:

As 2 and 6 have common factors other than 1, simplify the fraction by dividing both the numerator and the denominator by a common factor.

2 / 6= 2÷26÷2 = 1 / 3
[Simplify the fraction by dividing 2 and 6 by the common factor 2.]

So, the simplified form of the fraction 2 / 6 is 1 / 3 .

3.
Is the fraction $\frac{2}{10}$ in its simplest form or not?
 a. No b. Yes

#### Solution:

A fraction is in simplified form, if the numerator and the denominator have no common factors other than 1.

As 2 and 10 have common factors other than 1, the fraction 2 / 10 is not in simplified form.

4.
Is the fraction $\frac{2}{5}$ in its simplest form or not?
 a. Yes b. No

#### Solution:

A fraction is in simplified form, if the numerator and the denominator have no common factors other than 1.

As 2 and 5 have no common factors other than 1, the fraction 2 / 5 is in simplified form.

5.
Is the fraction $\frac{3}{6}$ in its simplest form? If not, write it in its simplest form.
 a. Yes b. No, $\frac{1}{2}$ c. No, $\frac{1}{3}$ d. No, $\frac{2}{4}$

#### Solution:

A fraction is in simplified form, if the numerator and the denominator have no common factors other than 1.

As 3 and 6 have common factors other than 1, the fraction 3 / 6 is not in simplified form.

3 / 6 = 3÷3 / 6÷3 = 1 / 2
[Simplify the fraction by dividing both the numerator and the denominator by 3.]

So, the simplified form of the fraction 3 / 6 is 1 / 2.

6.
What is the simplest form of the fraction $\frac{27}{36}$?
 a. 1 b. $\frac{3}{5}$ c. $\frac{3}{4}$ d. none of these

#### Solution:

27 / 36 = 27÷3 / 36÷3 = 9 / 12
[Simplify the fraction by dividing both the numerator and the denominator by a common factor 3.]

As 9 / 12 is not the simplest form of the fraction, simplify the fraction further.

9 / 12 = 9÷3 / 12÷3 = 3 / 4
[Simplify the fraction by dividing both the numerator and the denominator by a common factor 3.]

So, the simplest form of the fraction 27 / 36 is 3 / 4.

7.
Write the simplified form of the fraction $\frac{2}{4}$.
 a. $\frac{1}{3}$ b. $\frac{2}{4}$ c. $\frac{1}{5}$ d. $\frac{1}{2}$

#### Solution:

As 2 and 4 have common factors other than 1, simplify the fraction by dividing both the numerator and the denominator by a common factor.

2 / 4 = 2÷2 / 4÷2 = 1 / 2
[Simplify the fraction by dividing 2 and 4 by 2.]

So, the simplified form of the fraction 2 / 4 is 1 / 2.

8.
Is the fraction $\frac{4}{6}$ in its simplest form or not?
 a. Yes b. No

#### Solution:

A fraction is in simplified form, if the numerator and the denominator have no common factors other than 1.

As 4 and 6 have common factors other than 1, the fraction 4 / 6 is not in simplified form.

9.
Is the fraction $\frac{3}{5}$ in its simplest form or not?
 a. No b. Yes

#### Solution:

A fraction is in simplified form, if the numerator and the denominator have no common factors other than 1.

As 3 and 5 have no other common factors other than 1, the fraction 3 / 5 is in simplified form.

10.
A pizza was cut and distributed among 4 persons. Each person got $\frac{3}{12}$ fraction of pieces. Write the fraction in its simplest form.
 a. $\frac{3}{4}$ b. $\frac{1}{4}$ c. $\frac{3}{5}$ d. $\frac{1}{3}$

#### Solution:

As 3 and 12 have common factors other than 1, simplify the fraction by dividing both the numerator and the denominator by a common factor.

3 / 12 = 3÷3 / 12÷3= 1 / 4
[Simplify the fraction by dividing 3 and 12 by 3.]

So, the simplified form of the fraction 3 / 12 is 1 / 4 .