How to Simplify Fractions? Methods and Solved Examples

What are Simplified Fractions?

Simplified fractions are fractions in which the numerator (top number) and denominator (bottom number) are both divisible by the same number. This number is called the “common denominator.” For example, the fractions 3/4 and 6/8 can be simplified because both the numerator and denominator are divisible by 2. The simplified fractions would be 3/8 and 6/12.

When simplifying fractions, it is important to remember that the fractions must have the same denominator in order to be simplified. If the fractions do not have the same denominator, they cannot be simplified. For example, the fractions 1/4 and 2/5 cannot be simplified because they have different denominators (4 and 5, respectively).

There are a few different methods that can be used to simplify fractions. One method is to use the greatest common factor (GCF) of the numerator and denominator. The GCF is the largest number that can be divided evenly into both the numerator and denominator. For example, the GCF of 12 and 30 is 6. This means that the fractions 6/12 and 1/30 can be simplified to 3/12 and 1/30, respectively.

Another method for simplifying fractions is to use the least common multiple (LCM) of the numerator and denominator. The LCM is the smallest number that can be multiplied together to produce both the numerator and denominator. For example, the LCM of 12 and 30 is 120. This means that the fractions 12/120 and 1/30 can be simplified to 1/10 and 1/120, respectively.

How to Simplify Fractions Step by Step

There are different ways to simplify fractions and all these methods are explained below.

Method 1:

Go through the step by step procedure given below to understand how to simplify fractions.

Step 1: Write the factors of the numbers which are there in numerator and denominator.

Step 2: Identify the common factors of both numerator and denominator.

Step 3: In this step, we have to divide the numerator and denominator by the common factors until they have no common factor other than 1.

Example: Write the simplified form of the fraction 12/24.

Solution:

Given fraction is 12/24.

Step 1: Let us write the factors of 12 and 24.

Factors of 12 are: 1, 2, 3, 4, 6, 12

Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Step 2: Let us identify the common factors of 12 and 24.

Common factors are: 1, 2, 3, 4, 6, 12

Step 3: Keep dividing the numerator and denominator by the common factors.

(12 ÷ 2)/(24 ÷ 2) = 6/12

And

(6 ÷ 2)/(12 ÷ 2) = 3/6

Now divide by 3,

(3 ÷ 3)/(6 ÷ 3) = 1/2

Thus, 1/2 is the simplified fraction of 12/24 is 1/2.

Method 2:

This method is the easiest one to simplify fractions. Let’s understand this method of simplifying fractions.

Step 1: Write the prime factors of numerator and denominator or express the numerator and denominator as their product of prime factors.

Step 2: Find the highest common factor (HCF) of numerator and denominator.

Step 3: Divide the numerator and denominator by the highest common factor obtained.

Thus, the fraction obtained is called the simplified fraction.

Example: What is the simplified fraction of 16/28?

Solution:

Given fraction is 16/28.

Step 1: Let us write the numerator, i.e., 16 and the denominator, i.e. 28 as the product of prime factors.

16 = 2 × 2 × 2 × 2

28 = 2 × 2 × 7

Step 2: Now, we have to find the HCF of 16 and 28.

HCF of 16 and 28 = 2 × 2 = 4

Step 3: Now, divide both numerator and denominator by 4.

(16 ÷ 4)/ (28 ÷ 4) = 4/7

Hence, the simplified fraction of 16/28 is 4/7.

How to Simplify Fractions with Variables?

Fractions with variables in their numerator and denominator are referred to as rational expressions Let us learn how to simplify the fractions with variables.

Suppose 2ab²/ ab is a fraction with variables in the numerator and denominator.

This type of fraction can be simplified by taking the numerator and denominator as the product of variables and then cancelling the common variables.

So,

2ab²/ab = (2 × a × b × b)/(a × b) = 2b

Thus, the simplified fraction of 2ab²/ab is 2b or 2b/1.

How to Simplify Fractions with Exponents and Powers?

In this section, you will learn how to simplify fractions with exponents and power with the help of an example.

Example: Consider the fraction 25/23. Write its simplified form.

Solution:

Given fraction is: 25/23

Now, we have to expand the powers in the numerator and denominator.

25/23 = (2 × 2 × 2 × 2 × 2)/(2 × 2 × 2)

Let us cancel the common numbers in the expanded form.

= (2 × 2)/1 = 4