How to Simplify Fractions?

Before learning how to simplify fractions, first understand the meaning of fractions and the different types of fractions. A fraction is a number representing a part of a single whole object or a group of objects. Two numbers define it, one on top and the other at the bottom of a fraction bar, and they are called the numerator and denominator, respectively. We can represent a fraction as some different fractions without changing the original fraction simply by altering the value of its numerator and denominator. From this, we can say that a fraction may not always be in its simplest form. Thus, we can follow different methods to simplify the given fractions, including improper and proper fractions as explained in this article.

What are Simplified Fractions?

Simplified fractions are the fractions in their lowest, reduced and simplest form. The numerator and denominator of the fraction are reduced to the extent that the only common factor between them is 1. For example, 2/3 is the simplified fraction for 4/6, 8/12, 16/24 and so on. Here, ‘1’ is the only common factor between 2 and 3.

It is to be noted that the original value remains the same even after you simplify fractions. So, in other words, simplified fractions are equivalent fractions in which the numerator and denominator have no common factor except 1.

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.

Learn: Whole numbers

Let’s understand this method with the help of an example.

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.

Click here to learn how to find the HCF of given numbers.

Go through the example given below to understand this method in a better way.

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 powers 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

Practice Problems

1. Write the simplified form of the fraction 124/136.
2. What is the simplest form of the fraction 92/166?
3. Simplify the fraction (2x²y + 3xy)/xy.

Video Lesson on Fractions

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