Page 16 - Maths Skills - 8

14 Maths

Addition of Rational Numbers
Case I: When denominators are same.
To add the two or more rational numbers with same denominator, add the numerators and write the sum with
a c
the same denominator, i.e., If b and b are the two rational numbers with the same denominator ‘b’, then
a + c = a + c . 3 6 36 9
b b b For example, the sum of 5 and 5 is 5 5

Case II: When denominators are different.
To add the two or more rational numbers with different denominators, we follow the following steps.
Step 1: Find the LCM of the denominators.

Step 2: Express each of the rational numbers so that their denominators are equal to the LCM obtained in Step 1.
Step 3: As the denominators are equal, now add the numerators and sum them upto write a single rational
number.
×
34
For example, 3 3 So, −× = −12 and 35 = 15 .
×
×
5 4 54 20 45 20
LCM of 5 and 4 is 20. −12 15 −12 15 3
+
Thus, + = =
20 20 20 20
Subtraction of Rational Numbers
p r
We know that subtraction is inverse of addition. Therefore, if and are two rational numbers, then subtracting
q s
p
r
r from p means adding additive inverse of to .
s q s q
p r p r
ie..,
q s q s
Also the two cases with same denominator and different denominators can be solved in the same manner.

Multiplication of Rational Numbers
p r
If and are two rational numbers, then the product of these two rational numbers is given by
q s
p r pr Productofthe numerators
q s qs ie.., Productofthe denominators

Division of Rational Numbers
r
Division of rational numbers is the inverse of multiplication. This implies that if p and s are two rational numbers,
q
p r p s  r s 
then, ÷ = ×  Multiplicativeinverse of = 
q s q r  s r  Fact-o-meter

For any rational number
1
2
2
For example; 6 3 6 2 . p q
,
10 2 5 10 3 1 5 q p is called its reciprocal
Division is the reciprocal operation of multiplication. Dividing by a number or multiplicative inverse..
is the same as multiplying by its reciprocal.