How to Simplify Fractions?

Simplify Fractions

If a whole thing is divided into equal parts then each part is said to be a fraction. In other words, a fraction is a part of the whole. A fraction is formed up of two parts one on top as numerator and one at the bottom as denominator separated by a horizontal bar.

Expressed as -  numerator/denominator.

And simplifying a fraction means to convert it into its smallest form.

You can simplify fractions if the numerator and denominator can both be divided by the same number.

If we simplify fractions it becomes easier to deal with. We can easily

  • Add and Subtract Fractions

  • Compare Fractions

  • Convert fractions into Decimals and Percentages

In this article let us study how do you simplify fractions?

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Simplified Fractions

A fraction is said to be in its simplest form  when the numerator and denominator are not divisible by the same number. To simplify a fraction we divide both the numerator and denominator by the same number.

A common factor is a number that divides  both the numerator and denominator without leaving any remainders. We divide the fractions till we get 1 as the common factor for both the numerator and denominator.

If a fraction contains prime numbers in both the numerator and denominator then it is already in its simplest form,as we know that prime numbers are the special numbers which cannot be divided further.

We divide the fraction only by whole numbers. Decimals are not used to simplify the fractions as it will become difficult to see the proportions and it will no longer resin in simpler form.

Basically there are two methods to simplify the fraction. So let us study how to simplify fractions.

How to Simplify Fractions

There are two methods to simplify fractions.

Method 1

Try to divide both the numerator and denominator of the fraction by 2, 3, 5, 7, …...etc, until we cannot go any further.

For example, simplify the fraction 28 / 128.

Solution: 

28/ 70 ÷ 2 = 14 /35  

14 / 35  ÷ 7 = 2 /  5

Now you cannot further divide this fraction with the common number.

Thus, the fraction  2 / 5 is in the simplest form.


In another example, simplify 20 / 35.

Solution: in this situation, we cannot divide the number by 2 because 20 and 35 are not completely divisible by 2. Moreover, it can’t be divided by 3 because neither 20 nor 35 is completely divisible by it. So, let us use 5 as both 20 and 35 is completely divisible by 5.

Thus, 20 / 35 ÷5 = 4 / 7

And 4/7 is further not divisible by a common number.

So, the simplified fraction will be 4/7..

Method 2

Multiplying by a single will be a lengthy process in case of large numbers. A better and shorter way to simplify fractions is to find out  the highest common factor (HCF) of the numerator and denominator and divide both of them by it. 

For Example: Simplify fraction to its simplest form 8 / 20.

Solution: The highest common factor of numerator and denominator i.e of 8 and 20 is 4.

Now, divide both the numerator and denominator by 4 and you get

8 / 20 ÷ 4 = 2 / 5

So, the simplest form is 2 / 5.

Let us understand this by simplifying fractions problems

Solved Examples

Simplifying Fractions Problems

1. Simplify the given fraction 112 / 144 into simplest form.

Solution: find the highest common factor of both the numerator and denominator.

The HCF for 112 and 144 is 16

Divide both the numerator and denominator by 16

112/144 16 = 7/9

So the simplest form will be 7/9

2. Simplify the fraction 36/80

Solution :  let us start dividing numerator and denominator by 2 

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So the simplest form will be 3 / 7 as it is not further divided by any number.

Quiz Time

Simplifying fractions problems

  1. Simplify the fraction 36/60.

  2. Simplify the fraction 75/90.

FAQ (Frequently Asked Questions)

1. What is Like Fraction? 

Answer : In two or more fractions or a group of fractions when the denominator is exactly the same then they are said to be like fractions. Or you can say that fractions have the same number at the bottom.

Like fraction example -  2/4, 6/4, 8/4, 10/4. 

Here we can see that the denominator of all the fractions is 4, so these fractions are called fractions. 

  • Fractions like 2/8, 25/20, 9/12, 8/32 are also like fractions though they have different denominators because when they are written in the simplest form such as ¼, 5/4, ¾, ¼, we get the same denominator here 4.

  • Fractions like 5/2, 5/6, 5/10, 5/13 are not like fractions. Here you have the same  numerators, but the denominators are different.

  • Natural numbers like 2, 5, 6, 8  are called fractions because they have the same denominator 1. They are written as 2/1, 5/1, 6/1, 8/1.

Like fraction example

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2. What is the Cross Multiplication Method?

Answer: To perform addition or subtraction of two unlike fractions, first, we have to simplify the fraction into simplest form and make the denominators as coprime or relatively prime, then we have to follow the steps explained below in cross multiplication method. 

Step 1: Multiply the (top number)numerator of the first fraction by the (down number)denominator of the second fraction.

Step 2: Multiply the numerator of the second fraction by the denominator of the first fraction. 

Step 3: Multiply the denominators of both fractions and take it as a common denominator for the results of step 1 and step 2.

Step 4: After simplification, we will get the fractions with the same denominators and now we can carry out the given operation.

Example: Add 2/5 and 4/3

Solution: 

2/5 + 4/3

Applying cross multiplication method, we get;

= [(2 x 3) + (4 x 5)]/5 x 3

= (6 + 20)/15

= 26/15