Addition of Rational Numbers

In this article, you will learn about the Addition Operation and how to perform the Addition of Rational Numbers. Usually, the Addition of Rational Numbers is much similar to the Addition of Fractions. The First and Foremost Step to keep in mind when it comes to the Rational Numbers Addition is the denominators should be positive. If the denominators aren’t positive simply rearrange them to make them positive.

The two subcategories that you encounter while dealing with the Addition Operation in Rational Numbers are listed below. You can check out the solved examples explained step by step for reference and get a grip on the concept.

Rational Numbers with the Same Denominator

Let suppose a/b, c/b be two rational numbers having the common denominator b then Addition of Rational Numbers is given by the summation of numerators leaving the common denominator unchanged i.e. (a+c)/b.

Solved Examples

(i) Add 4/7 and 13/7?

Solution:

Given Rational Numbers are 4/7 and 13/7

Adding them we get 4/7+13/7

= (4+13)/7

= 17/7

Therefore, the Sum of 4/7 and 13/7 is 17/7.

(ii) Add 5/12 and -3/12?

Solution:

Given Rational Numbers are 5/12, -3/12

Adding them we get 5/12+(-3)/12

= (5-3)/12

= -2/12

Rational Numbers with the Different Denominator

In the case of Rational Numbers with Different Denominators, we need to find the LCM of Denominators. After that, express the given rational numbers with a common denominator and then add the numerators of the obtained rational numbers while keeping the denominator unchanged.

Solved Examples 

(i) Add 4/5 and 7/9?

Solution:

Clearly, the denominators are different and we need to figure out the LCM of Denominators.

LCM(5,9) is 45

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

4/5 = 4*9/5*9 = 36/45

7/9 = 7*5/9*5 = 35/45

Add the Numerators of the Rational Numbers while keeping the Denominator unchanged to get the sum of Rational Numbers.

= 36/45+35/45

= 71/45

Therefore the sum of 4/5 and 7/9 is 71/45.

(ii) Find the Sum of -7/6 and 5/12?

Solution: 

Given Rational Numbers are -7/6 and 5/12

Since the denominators aren’t equal find the LCM of them

LCM of 6, 12 is 12

Express the given rational numbers with a common denominator using the LCM acquired.

-7/6 = -7*2/6*2 = -14/12

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

Adding the Rational Numbers we get

= (-14+5)/12

=-9/12

Therefore, the Sum of -7/6 and 5/12 is -9/12.