A fraction is a number representing a part of a single whole object or a group of objects. It is defined by two numbers, one on top and the other at the bottom of a fraction bar, known as numerator and denominator respectively. We can represent a fraction as a number of different fractions without changing the original fraction simply by altering the value of its numerator and denominator. This is one reason a fraction may not always be in its simplest form. In this article, we shall discuss how to simplify fractions.

#### 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. E.g., 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.

#### Methods to Simplify Fractions

The only rule to simplify fractions is that by whatever number you divide the numerator, you must divide the denominator using the same number.

There are two ways to simplify fractions:

- Keep dividing the numerator and denominator by 2, 3, 5, 7, etc. until you cannot go any further. E.g., 12/24 = (6×2)/(12×2) = 6/12 = (3×2)/(6×2) = 3/6 = (1×3)/(2×3) = 1/2

- A better and shorter way to simplify fractions is to find the highest common factor (HCF) of the numerator and denominator and divide both of them by it. Considering the same example 12/24. The HCF of 12 and 24 is 12. Dividing both of them by 12, we get: 12/24 = (1×12)/(2×12) = 1/2

We get 1/2 by both the methods, which is the simplest form of 12/24.

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