Page 21 - Maths Skills - 8

Rational Numbers 19

Let’s Attempt

Example 1: What should be added to - 7 to get 13 ? Example 2: Subtract − from − 3 5 .
16 20 5 6
Solution: Let the required number be x. 5 3 5 3

Solution:
- 7 13 6 5 6 5
x
+=
16 20  LCM of 6 and 5 is 30.
13  − 7 13 7

or x = −   = + ( 55 ) ( 36 ) 25 18 7
20  16  20 16 30 30 30 .
(13× 4) +(7× 5)
= Example 3: Multiply 7 and 3 .
80 9 4

52 +35 87 7 7 3 71
= = =1 Solution: Required product = ×
80 80 80 9 3 4 34

7 7
Thus, 1 has to be added to - to = 7 .
80 16 12
get 13 .
20
-14 7 - 6 5
Example 4: Divide the sum of and by the product of and
15 11 12 .
9
-14 7 −14 7 − 42 + 35 − 7
Solution: The sum of and = + = = ...(i)
9
15 15 9 45 45
- 6 5 − 6 5 − 5
The product of and = × = ...(ii)
11 12 11 12 2 22

Dividing (i) by (ii), we get − 7 ÷ − 5 = − 7 × − 22 = 154
45 22 45 5 225
Example 5: Give the additive inverse of (i) 5 (ii) - 3
7
9
5 - 5 5 − 5
Solution: (i) The additive inverse of is , since + = 0
9 9 9
9
(ii) The additive inverse of - 3 is 3 , since − 3 + 3 = 0
7 7 7 7
2 -19 7 2
Example 6: Give the multiplicative inverse of (i) (ii) (iii) 5 (iv) ×
3 17 8 5
2 3 2 3
Solution: (i) The multiplicative inverse of is , since × =1
3 2 3 2
- -19 17 −19 −17
(ii) The multiplicative inverse of is , since × =1
17 19 17 19
1
(iii) The multiplicative inverse of 5 is .
5
(iv) Since 7 2 7 . The multiplicative inverse of 7 is 20 .
8 5 20 20 7
4