Page 70 - Maths Skills - 7

68 Maths

3. Express each rational number with the LCM as the common denominator.

4. Add the rational numbers.

Let’s Attempt

5 − 5
Example 1: Add − 8 and 12 .

5
Solution: The denominator of − 8 is negative. Multiply the numerator and the denominator with (–1) to get

the positive denominator,
5 5×−( 1) − 5
= = The LCM of 8 and 12 is 24.
− 8 −× −( 1) 8
8

Now, − 5 = −×53 = −15 , and − 5 = −×52 = −10 .
×
8 83 24 12 12 × 2 24
−
∴ −15 + −10 = −15 + −10( ) = −15 10 = − 25
24 24 24 24 24
4 − 3
Example 2: Add and .
5 4
Solution: The denominators of the given rational numbers are positive.
4 44× 16 − 3 −× − 15
35
Now, = = , and = = . The LCM of 5 and 4 is 20.
5 54× 20 4 45× 20
4 ( − 3) 16 ( −15) 16 −15 1
∴ + = + = =
5 4 20 20 20 20
− − 5 7 11
Example 3: Find the sum of the three rational numbers: , and .
8 12 16
Solution: The denominators of the given rational numbers are all positive.
The LCM of 8, 12 and 16 is 48.

Now, − 5 = −×56 = − 30 , − 7 = −×7 4 = − 28 and 11 = 11 × 3 = 33
8 86 48 12 12 × 4 48 16 16 × 3 48
×
− 5 − 7 11 − 30 − 28 33 − 30 − 28 33 − 25
+
∴ + + = + + = =
8 12 16 48 48 48 48 48
Additive Inverse Property
For every rational number there exists a rational number such that their sum is equal to zero.
p r p r p
In general, if and are any two rational numbers such that + = 0, then is called the additive inverse of
q s q s q

r
s and vice versa.
3 − 3 5 5
For example; (i) Additive inverse of is . (ii) Additive inverse of − is .
7 7 9 9