Page 15 - ICSE Math 8

p p p ÷ n
II. If is a rational number and ‘n’ is an integer, where n ≠ 0, then = .
q q q ÷ n

p 6 6 63÷ 2
For example, if = , n = 3 then = = .
q 18 18 18 3÷ 6
p p ÷ n
So, and are equivalent rational numbers.
q q ÷ n
r
←→ r
III. Two rational numbers p and are equal if, p × s = q × r, i.e., p ←→
q s q s
2 4
For example, =
7 14
2 4
Since 2 × 14 = 7 × 4 = 28. So, and are equal rational numbers.
7 14
Addition of Rational Numbers

You are familiar with addition of rational numbers. Let us revise what we have learnt in the previous class.

Rational numbers with same denominator
To add two rational numbers with the same denominator, add the numerators and keep the common denominator
p r p + r
as it is. So, + = .
q q q

−4 9 7 5
Example 2: Add: (a) and (b) and .
13 13 16 16
(−4 ) 9 − ( 4 ) + 9 5 7 5 7 + 5 12 3
Solution: (a) + = = (b) + = = =
13 13 13 13 16 16 16 16 4

Rational numbers with different denominators
To add two rational numbers with different denominators:

Step 1: Make the denominator positive, in case it is negative.
Step 2: Find the LCM of the two denominators.
Step 3: Write each rational numbers with the LCM as common denominator.

Step 4: Add them as rational numbers with the same denominator.
4 9
Example 3: Add and .
− 12 42
4
Solution: The rational number has a negative denominator, first make it
positive. − 12
1
4 4 ×−() − 4
= =
1
− 12 − ( 12 × −) () 12
LCM of 12 and 42 = 2 × 3 × 2 × 7 = 84
2 12, 42
4 − ( 4 ×) 7 − 28 9 92× 18 3 6, 21
= = and = =
− 12 12 7× 84 42 42 2× 84 2 2, 7
(−4 ) 9 (−28 ) 18 (−28 ) +18 −10 −5 7 1, 7
So, + = + = = =
12 42 84 84 84 84 42 1, 1

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