Page 11 - Start Up Mathematics_8 (Non CCE)

2 4
For example, =
7 14 Extension
Since 2 × 14 = 7 × 4 = 28 The square roots of prime
2 4 numbers are irrational.
So, and are equal rational numbers.
7 14

Addition of Rational Numbers

Rational numbers with same denominators
In order to add two rational numbers with the same denominator, add the numerators and keep the common
denominator as it is.
p r p + r
So, + =
q q q
−4 9 7 5
Example 2: Add and . Example 3: Add and .
13 13 16 16
(−4 ) 9 − ( 4 ) + 9 5 7 5 7 + 5 12 3
Solution: + = = Solution: + = = =
13 13 13 13 16 16 16 16 4

Rational numbers with different denominators
To add two rational numbers with different denominators, follow these steps:
Step 1: Make the denominator positive, in case it is negative.
Step 2: Find the LCM of the two denominators.
Step 3: Write their equivalent rational numbers with the LCM as common denominator.
Step 4: Then add them as rational numbers with the same denominator.
− −3 11
Example 4: Add and .
20 25 5 20, 25
Solution: LCM of 20 and 25 = 5 × 2 × 2 × 5 = 100 2 4, 5

−3 −×35 −15 −11 −11 4 −44 2 2, 5
×
= = = =
20 20 × 5 100 25 25 × 4 100 5 1, 5
(−3 ) (−11 ) (−15 ) (−44 ) (−15 ) + (−44 ) −59 1, 1
So, + = + = =
20 25 100 100 100 100

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

3