Adding Fractions, deals with various concepts which are as under:-

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

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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 and and reduce to its lowest term.

**Solution**

Sum of Like Fraction =

Sum of Like Fraction =

Sum of Like Fraction =

Hence, the sum of

Simplifying further,

HCF of 6 and 12 is 6

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

=

Hence, the sum of and =

**Example 2**

Find the sum of and and reduce to its lowest term.

**Solution**

Sum of Like Fraction =

Sum of Like Fraction =

Sum of Like Fraction =

Hence, the sum of and is

Simplifying further,

HCF of 8 and 6 is 2

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

=

Hence, the sum of and =

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

**Example 1**

Find the sum of and 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

We have to multiply , both the numerator and denominator of by 1

=

We have to multiply , both the numerator and denominator of by 2

=

Now + =

Simplifying further,

HCF of 9 and 12 is 3

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

=

Hence, the sum of and =

**Example 2**

Find the sum of and 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

We have to multiply , both the numerator and denominator of by 4

=

We have to multiply , both the numerator and denominator of by 3

=

Now + =

Simplifying further,

HCF of 10 and 12 is 2

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

=

Hence, the sum of and =

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