Let us discuss in detail How to Add Rational Numbers with Different Denominators. To find the Sum of Rational Numbers you can have a look at the below examples provided. Check the detailed procedure to add rational numbers not having the common denominator.

## How to Add Rational Numbers with Different Denominators?

Go through the below-mentioned steps to add rational numbers having different denominators. They are along the lines

**Step 1:** Check the Rational Numbers and see whether the denominators are positive or not. If any of the denominators is negative rearrange them to become positive.

**Step 2:** List out the denominators of rational numbers in the earlier step.

**Step 3: **Determine the LCM of the denominators of the given Rational Numbers.

**Step 4:** Express the Rational Numbers in a way that they have the Common Denominator using the LCM obtained.

**Step 5:** Write down the numerator as the sum of numerators of rational numbers obtained in the earlier step and denominators is the LCM obtained in Step 3.

**Step 6:** Rational Number obtained in Step 5 is the required sum and simplify if required.

### Solved Examples on Adding Rational Numbers with Different Denominator

1. Add Rational Numbers -8/21 and 3/9?

**Solution:**

Given Rational Numbers are -8/21, 3/9

= -8/21+3/9

Firstly, find the Least Common Multiple of the Denominators i.e. 21, 9

LCM(21, 9) = 63

Express the Rational Numbers with Common Denominator using the LCM Obtained.

-8/21 = -8*3/21*3 = -24/63

3/9 = 3*7/9*7 = 21/63

Adding them we get

-24/63+21/63

= (-24+21)/63

= -3/63

Simplifying further we get -1/21

Therefore the Sum of -8/21 and 3/9 is -1/21.

2. Add 3/4 and 5?

**Solution:**

Given Rational Numbers are 3/4 and 5/1

= 3/4+5/1

Find the LCM of 4, 1

LCM(4, 1) = 4

Express the Given Rational Numbers in terms of Common Denominator using the LCM obtained.

3/4 = 3*1/4*1 = 3/4

5/1 = 5*4/1*4 = 20/4

Add the obtained rational numbers numerators with a common denominator

= (3+20)/4

= 23/4

Therefore, the Sum of 3/4 and 5 is 23/4.

3. Simplify 5/-12+7/-4?

**Solution:**

Given Rational Numbers are 5/-12 and 7/-4

Since the rational numbers are having a negative denominator rearrange them to have a positive denominator.

5/-12 = 5*(-1)/-12*(-1) = -5/12

7/-4 = 7*(-1)/-4*(-1) = -7/4

Find the LCM of Denominators of the Rational Numbers.

LCM(12, 4) = 12

Express the Rational Numbers with Common Denominator using the LCM obtained.

-5/12 = -5*1/12*1 = -5/12

-7/4= -7*3/4*3 = -21/12

Add the Obtained Rational Numbers Numerators and keep the denominator unchanged.

= (-5-21)/12

= -26/12

Thus, 5/-12+7/-4 is -26/12.