Page 69 - Maths Skills - 7

Rational Numbers 67

3. In each of the following pairs of rational numbers, find the smaller one.

− 6 4 − 8 13 5 − 7 − 9 7
(i) , (ii) , (iii) , (iv) ,
15 − 9 − 21 14 − 6 21 14 −16
4. Fill in the with the correct symbol out of >, = or < .

− 3 6 − 4 − 3 − 2 5 − 3 4
(i) − 16 (ii) (iii) − 7 (iv) − 7
8 7 14 5 7
5. Arrange in ascending order.

3 4 − 3 7 − − 4 3 8 13
(i) ,, , (ii) , , ,
− 5 7 14 10 9 7 15 − 21

6. Arrange in descending order. 7. Write three rational numbers between.
5 13 − 15 1 1 − 3 17 13 −2 −3
(i) , , , (ii) , , , (i) –3 and –4 (ii) and
8 − 16 12 6 − 5 10 15 20 3 11

8. Write five rational numbers between.
1 6 −1 3
(i) and (ii) and
2 7 5 7

OPERATIONS ON RATIONAL NUMBERS

Addition of Rational Numbers
The addition of rational numbers is carried out in the same way as that of addition of fractions. If two rational
numbers are to be added, we should first convert each of them into rational numbers with a positive denominator.

(i) Rational Numbers with Same Denominator
To add two rational numbers with same denominators, we simply add their numerators and divide the sum by the
common denominator.
p r p r p + r
In general, if and are any two rational numbers, then + = .
q q q q q

Let’s Attempt

5 8 6 13
Example 1: Add 9 and − 9 . Example 2: Add 11 and 11 .

8 8×−( 1) − 8 6 13 613+ 19
Solution: Since, = = . Solution: We have, + = = .
− 9 − ( 9 × −) ( 1) 9 11 11 11 11

So, 5 + − ( 8) = 58− = − 3 = − 1 .
9 9 9 9 3

(ii) Rational Numbers with Different Denominators

To add rational numbers with different denominators, we follow the steps given below:
1. In case the denominators of the given rational numbers are negative, change them into positive denominators.

2. Find the LCM of the denominators.