How to Simplify Fractions with Steps and Examples

A fraction represents a part of a whole. It has two parts: numerator and denominator. In this post, we will learn how to simplify a fraction in its lowest forms.

A fraction is always of the form:

$\dfrac{p}{q}$

where p and q are integers with q≠0.

Steps to Simplify Fractions

Let us consider a fraction $\dfrac{p}{q}$. The below steps have to be followed in order to simplify the fraction p/q in the lowest terms.

• Step 1: Note that the numerator is p and the denominator is q. First, check whether p and q have common factors or not.
• Step 2: If they do not have a common factor other than 1, then the given fraction $\dfrac{p}{q}$ is already in the lowest terms.
• Step 3: If they have common factors other than 1, then note down the greatest common factor (GCF).
• Step 4: Put d:= GCF(p, q).
• Step 5: Divide both p and q by d, the resulting fraction will be the simplified form of the given fraction which is $\dfrac{p \div d}{q \div d}$.

Let us now understand the above procedure to get a simplified reduced fraction with an example.

Also Read: How to simplify 8/12.

Examples of Simplifying Fractions

Example 1:

Let us simplify the fraction 2/4.

Here the numerator is 2 and the denominator is 4.

Factors of 2 are 1, 2.

Factors of 4 are 1,2, 4.

So the greatest common factor (GCF) of 2 and 4 is 2, that is, GCF(2,4) = 2. So the simplified form of 2/4 is given as follows:

$\dfrac{2 \div 2}{4 \div 2}$ = $\dfrac{1}{2}$

Thus, 1/2 is the reduced lowest form of 2/4.

Example 2:

We will now simplify the fraction 1/3.

See that 1 and 3 do not have common factors other than 1.

So by the above method of simplifying fractions, we can conclude that 1/3 is already in its lowest form.

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