Adding Fractions (Addition of Fractions), deals with various concepts which are as under:-

- Adding Fractions with same Denominators ( Like Fractions )
- Adding Fractions with different Denominators ( Unlike Fractions )

To add Fractions with same denominators **( Like Fractions )**, we add the numerators and write the sum over the same denominator.

To add Fractions with different denominators **( Unlike Fractions )**, first we have to change the Unlike Fractions, into equivalent Like Fractions, and then add the two equivalent Like Fractions

### Adding Fractions with same Denominators ( Like Fractions )

**Example 1**

Find the sum of 5/12 and 1/12 and reduce to its lowest term.

**Solution**

Sum of Like Fraction = (5+1)/12

Sum of Like Fraction = 6/12

Hence, the sum of 5/12 and 1/12 is 6/12.

Simplifying further,

HCF of 6 and 12 is 6

Dividing both Numerator and Denominator by their HCF i.e,

Hence, the sum of 5/12 and 1/12 = 1/2

**Example 2**

Find the sum of 3/6 and 5/6 and reduce to its lowest term.

**Solution**

Sum of Like Fraction = (3+5)/6

Sum of Like Fraction = 8/6

Hence, the sum of 3/6 and 5/6 is 8/6

Simplifying further,

HCF of 8 and 6 is 2

Dividing both Numerator and Denominator by their HCF i.e,

Hence, the sum of 3/6 and 5/6 = 4/3

### Adding Fractions with different Denominators ( Unlike Fractions )

**Example 1**

Find the sum of 5/12 and 2/6 and reduce to its lowest term.

**Solution**

In order to add Unlike Fraction

Firstly, we have to change the Unlike Fraction, into equivalent Like Fractions, and then add the two equivalent Like Fractions

Take LCM of 12 and 6 is 12

Converting the Unlike Fraction into Equivalent Like Fraction

Simplifying further,

HCF of 9 and 12 is 3

Dividing both Numerator and Denominator by their HCF i.e,

**Example 2**

Find the sum of 1/3 and 2/4 and reduce to its lowest term.

**Solution**

In order to add Unlike Fraction

Firstly, we have to change the Unlike Fraction, into equivalent Like Fractions, and then add the two equivalent Like Fractions

Take LCM of 3 and 4 is 12

Converting the Unlike Fraction into Equivalent Like Fraction

Simplifying further,

HCF of 10 and 12 is 2

Dividing both Numerator and Denominator by their HCF i.e,