Subtraction of Rational Numbers

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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
Addition rational numbers
Subtraction of rational numbers
Conversion of rational numbers to decimal
Irrational Numbers

Number system Page

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