Rational Numbers – Subtraction

In this tutorial, we will learn the operation of subtraction of rational numbers. If we add the additive inverse of a rational number and other rational number then this is called subtraction of two rational numbers. Subtraction is inverse process of addition.

If a/b and c/d are two rational numbers, then subtracting c/d from a/b means adding additive inverse(negative) of c/d to a/b.

The subtracting of c/d from a/b is written as

a/b – c/d

a/b – c/d = a/b + (-c/d).

Additive inverse of c/d is -c/d

Additive inverse of 3/5 is -3/5

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

(1) Subtraction of Rational Numbers with Same Denominator

If two rational numbers with same denominators are subtracted, we just have to subtract the numerators since denominator is common.

Example1: Subtract 5/7 from 8/7

= 8/7 – 5/7

= (8 – 5)/7

= 3/7

Therefore the result after subtracting the rational numbers as 3/7.

Therefore the result after subtracting the rational numbers as 3/7.

(2) Subtraction of Rational Numbers with Different Denominator

Any two rational number with different denominators can be subtracted by making the denominator same, that is taking out their LCM, to convert them into equivalent rational numbers with a common denominator.

Example2: Solve 5/4 – 2/3

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

= {(5 x 3)-(2 x 4)}/12

= (15 – 8)/12

Next subtract the rational numbers.

= 7/12

Example3: Subtract the rational numbers 7/2 – 5/2

7/2 – 5/2

= (7 – 5)/2

= 2/2

= 1

Therefore the result after subtracting the rational numbers as 1/1.

Example4: Solve 8/3 – 5/2

First, LCM of the denominators is to be carried out, so the LCM of 3 and 2 is 6.

= {(8 x 2)-(5 x 3)}/6

= (16 – 15)/6

Next subtract the rational numbers.

= 1/6

Example5: Solve: 12/5 – 9/5

= 12/5 – 9/5

= (12 – 9)/5

= 3/5

Example6: Subtract 5/6 from 4/9

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

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

4/9 – 5/6

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

= (8 – 15)/18

= -7/18