Rational Numbers – Addition

In this tutorial, we will learn the operation of addition of rational numbers.

In the process of addition of rational numbers there are two types of categories.

(1) Addition of Rational Numbers with Same Denominator

(2) Addition of Rational Numbers with Different Denominator

(1) Addition of Rational Numbers with Same Denominator

In this case we define (a/b + c/b) = (a + c)/b

Addition of Rational Numbers with same denominator is like addition of like fractions.

If two rational numbers are added we should first convert each of them into a rational number with positive denominator.

Example: Add two rational numbers 8/7 + 5/7

= 8/7 + 5/7

= (8 + 5)/7

= 13/7

Therefore the result after adding the rational numbers as 13/7.

(2) Addition of Rational Numbers with Different Denominator

Any two or more rational number with different denominators can be added by following steps.

(i) Find the LCM of the denominators.

(ii) Make the denominators same, that is taking out their LCM, to convert them into equivalent rational numbers with a common denominator.

(iii) Now add the numerators.

Example: Add 5/6 + 4/9

First, LCM of the denominators is to be carried out, so the LCM of 6 and 9 is 18.

We add 5/6 and 4/9 into forms in which both of them have same denominators.

5/6 + 4/9

= {(5 x 3)+(4 x 2)}/18

= (15 + 8)/18

= 23/18

Solved examples

(1) Solve: 6/8 + 5/8

= 6/8 + 5/8

= (6 + 5)/8

= 11/8

Therefore the result after adding the rational numbers as 11/8.

(2) Solve: 3/4 + 9/4

= 3/4 + 9/4

= (3 + 9)/4

= 12/4

= 3/1

Therefore the result after adding the rational numbers as 3/1.

(3) Solve: 9/5 + 12/5

= 9/5 + 12/5

= (9 + 12)/5

= 21/5

Therefore the result after adding the rational numbers as 21/5.

(4) Solve: 13/7 + 5/7

= 13/7 + 5/7

= (13 + 5)/7

= 18/7

Therefore the result after adding the rational numbers as 18/7.

(5) Solve: 5/3 + 7/4

First, LCM of the denominators is to be carried out, so the LCM of 3 and 4 is 12.

We add 5/3 and 7/4 into forms in which both of them have same denominators.

5/3 + 7/4

= {(5 x 4)+(7 x 3)}/12

= (20 + 21)/12

= 41/12

(6) Solve: 3/5 + 9/2

First LCM of the denominators is to be carried out, so the LCM of 5 and 2 is 10.

We add 3/5 and 9/2 into forms in which both of them have same denominators.

3/5 + 9/2

= {(3 x 2)+(9 x 5)}/10

= (6 + 45)/10

= 51/10