Simplifying Fractions

Simplifying (or reducing) fractions means to make the fraction as simple as possible. A fraction is in its simplest form if its numerator and denominator are co-prime or have no common factors except 1.

simplifying fractions

An important step that we do while we solve fraction questions is to reduce them to the simplest form. Though we simplify them, the value of the fraction is going to remain unchanged. The simplest form of a fraction is equivalent to the given fraction.
For example, the fraction 35 is in the simplest form. Because 3 and 5 have no common factor except 1.

How to Simplify Fractions?

There are two ways to simplify a fraction:
Method 1

Example 1 : Simplify the fraction 836 :
Step 1: The factors of 8 and 36 are
Factors of 8: 1, 2, 4, and 8
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36

Step 2: The common factors of 8 and 36 are 1, 2 and 4.
Step 3: Divide the numerator and denominator by their highest common factor (HCF). The highest common factor of 8 and 36 is 4. Dividing the numerator 8 and the denominator 36 by 4 will directly give us the simplest form of the fraction. simplifying fractions example 8/36

So, the shortest way to break down a fraction into its simplest form is to divide the numerator and denominator by its highest common factor.

Method 2
Try to exactly divide (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 ,... etc, until we can't go any further.

Example 2 : Simplify the fraction 3648simplifying fractions 36/48 Thus, 34 is the simplest form of the fraction 3648.

Simplifying Mixed Fractions

In order to simplify a mixed fraction, you need to simplify the fractional part only. 

Example 3 : Simplify the mixed fraction 239simplifying mixed fractions Therefore, the mixed fraction 239 can be simplified as 213.

Simplifying Improper Fractions

To simplify improper fractions we need to convert them to mixed fractions. For that, we need to divide the numerator by the denominator. Then, we write it in the mixed number form by placing the quotient as the whole number, the remainder as the numerator, and the divisor as the denominator.

Example 4 : Simplify the improper fraction 143 :
When we divide 143, we get 4 as the quotient and 2 as the remainder. Therefore, the simplified form of the improper fraction 143 is 423.