# Subtraction of Rational Numbers

In this section we will discuss about subtraction of rational numbers.

Subtraction of Rational-numbers :

In subtraction of rational-numbers apply the same method as that of addition of rational numbers.

Some solved examples :

1) Subtract 3 /4 from 5 / 6

Solution :

Subtract 3 /4 from 5 / 6 ⇒ 5 / 6 – 3 / 4

As the denominators are different.

LCM of 6 and 4 is 12.

5 / 6 = ( 5 x 2) / ( 6 x 2) = 10 / 12

3 / 4 = ( 3 x 3 ) / ( 4 x 3) = 9 / 12

10 / 12 – 9 / 12 = ( 10 – 9 ) / 12 = 1 / 12.
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2) Subtract -3 / 8 from – 5 / 7

Solution :

Subtract - 3 / 8 from - 5 / 7 ⇒ - 5 / 7 – ( - 3 / 8)
As the denominators are different.

LCM of 8 and 7 is 56.

- 5 / 7 = (- 5 x 8) / ( 7 x 8) = - 40 / 56

- 3 / 8 = ( - 3 x 7 ) / ( 8 x 7) = - 21 / 56

- 40 / 56 – ( -21 / 56 ) = ( -40 + 21 ) / 56 = -19 / 56 ( since – ( - 21 / 56) = + 21 / 56.
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3) The sum of two rational numbers is -3 / 5. If one of the number is – 9/ 20. Find the other.

Solution :

Sum of two numbers = - 3 / 5 , one number = - 9 / 20.

∴ The other number = sum – one number

= - 3 / 5 – ( - 9 / 20 )

= - 3 / 5 + 9 / 20 ( since [ – ( - 9 / 20 ) = + ( 9 / 20 ) ]
 (- 3) x 4 + 9 x 1 = ----------------         20    - 12 + 9 = -------------          20    - 3 = -----      20

Rational number

Representation of rational number on number line
Comparison of rational number