Page 2 - LN3

 Addition of two Rational Numbers with different denominator

If we have to add two rational numbers with different denominators then we have to take the LCM of
denominators and find their equivalent rational numbers with the LCM as the denominator, and then
add them.

2 3
Example : Add and .
5 7
Solution: To add the two rational numbers, first, we need to take the LCM of denominators the find
the equivalent rational numbers.
LCM of 5 and 7 is 35.

 Additive Inverse

The additive inverse of rational numbers is the opposite of the given rational number
Example :i) Additive inverse of a rational number a is (–a). So that a + (–a) = 0.
3 3 3 3
ii) Additive inverse of a rational number is (− ) . So that + (− ) = 0
4 4 4 4
2. Subtraction:
If we have to subtract two rational numbers then we have to add the additive inverse of the rational
number that is being subtracted from the other rational number.
a - b = a + (-b)
4 8
Example: Subtract from .
21 21
 In the first method, we will simply subtract the numerators and the denominator remains
the same.

 In the second method, we will add the additive inverse of the second number to the first
number.