Simplification Fractions -Rule

A fraction is said to be in its simplest Form, if 1 is the only common factor of its numerator and denominator.

or

If a fraction have no common factor except 1, in their numerator and denominator is said to be it’s “Simplest Form”.

Example: Fraction 3/7 is in the simplest form because 1 is the only common factor of 3 and 7.

How to Simplify Fractions

There are 2 methods to simplify fractions.

Method 1:

Simplify Fractions Step by Step

Step 1: Write the factors of numerator and denominator.

Step2: Identify common the factors of the numbers which are in numerator and denominator.

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

So, the obtained fraction is in simplest form.

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

Write the fraction 8/16 in its simplest form.

Solution: Given fraction is 8/16.

Step1: Let us write factors of 8 and 16.

The factors of 8 and 16 are

Factors of 8: 1, 2, 4, and 8

Factors of 16: 1, 2, 4, 8 and 16

Step2 : Dividing the numerator and denominator by the common factors.

(8 ÷ 2 )/(16 ÷ 2) = 4/8

(4 ÷ 2 )/(8 ÷ 2) = 2/4

(2 ÷ 2 )/(4 ÷ 2) = 1/2

Thus, 1/2 is the simplified fraction of 8/16.

Method 2:

Step 1: Write the factors of numerator and denominator.

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

Step 3: Divide the numerator and denominator by highest common factor(HCF).

Obtain fraction is in the simplest form.

Let us simplify the fraction 8/16.

The highest common factor of 8 and 16 is 8.

Dividing both numerator 8 and denominator 16 by 8.

(8 ÷ 8)/(16 ÷ 8) = 1/2

We get simplest form of the fraction 8/16, that is 1/2.

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

Note: The simplest form of a fraction is equivalent to the given fraction.

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