A fraction is said to be in its lowest terms when the **numerator and the denominator do not have any common factor except 1.**

By dividing the numerator and the denominator of a fraction by the same number, the value of the fraction does not change. We get an equivalent fraction.

In order to reduce a fraction to its lowest terms, **divide the numerator and the denominator of the fraction by their highest common factor (HCF)**.

For example consider the fraction \(\frac{14}{26}\).

HCF of 14 and 26 is 2.

So, dividing 14 and 26 of the fraction \(\frac{14}{26}\) by 2, we get \(\frac{14 \div 2}{26 \div 2} = \frac{7}{13}\)

Now 7 and 13 do not have any other common factor expect 1.

Thus, the fraction \(\frac{14}{26}\) is reduced to its lowest terms as \(\frac{7}{13}\).

Thus, \(\frac{14}{26}\) = \(\frac{14 \div 2}{26 \div 2} = \frac{7}{13}\).

## Rules to follow while simplifying a fraction:

Rule 1) Numerator and the denominator can be divided by any number, as long as we use the same number for both of them.

For example, you can’t divide the numerator by 6 and the denominator by 4.

Rule 2) Reduce the numerator and denominator as small as possible by applying proper division.

### Fractions: Reducing (Simplifying) Fractions Example1:

Reduce \(\frac{72}{90}\) to its lowest terms.

**Solution :**

First, we find the HCF of 72 and 90 by factorization method.

The factors of 72 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

The factors of 90 are:

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.

The common factors of 72 and 90 are:

1, 2, 3, 6, 9, 18

Therefore, HCF of 72 and 90 is 18.

Now, \(\frac{72}{90}\) = \(\frac{72 \div 18}{90 \div 18}\) { Dividing numerator and denominator by the HCF of 72 and 90 }

= \(\frac{4}{5}\).