Page 74 - Maths Skills - 7

72 Maths

p  p  −1 Fact-o-meter
Note: The reciprocal of is written as   .
q  q  � The product of rational number and its
multiplicative inverse is always 1.
− 
For example,  7  −1 =  13   1 = 13 � 1 and –1 are the only rational numbers


 13   7 −7 which are their own reciprocals.
− 
� 0 has no reciprocal value.
Let’s Attempt

− 21 5 27
Example 1: Simplify. (i) ×− 4( ) (ii) ×
6 9 − 25

− 21 − 21 − 4 − 21 × − 4 84 5 27 527× 3 − 3
Solution: (i) ×− 4( ) = × = = =14. (ii) × = = = .
×
6 6 1 61 6 9 − 25 9 ×− 25 − 5 5
− 6 29 8
Example 2: Multiply. (i) by (ii) by − 2
13 4 17
− 6 29 −×6 29 −174 −87 8 − 2 8×−( 2) − 16
Solution: (i) × = = = . (ii) × = = .
13 4 13 × 4 52 26 17 1 17 1× 17

Example 3: Find the reciprocal or the multiplicative inverse of
− 27 − 8 × 27
(i) 15 (ii) – 7 (iii) (iv) 9 − 24
19
1
Solution: (i) The reciprocal or the multiplicative inverse of 15 is .
15
1 − 1
(ii) The reciprocal or the multiplicative inverse of – 7 is or .
7− 7

−27 19 −19
(iii) The reciprocal or the multiplicative inverse of is or .
19 − 27 27
− 8 27 3
(iv) We have × = =1.
9 − 24 3
The reciprocal of 1 is 1.

Exercise 4.5

1. True or False.

(i) The product of two rational numbers is always not a rational number.

(ii) The product of two negative rational numbers is always a negative rational number.

−9 8
(iii) The multiplicative inverse of is . (iv) The reciprocal of – 8 is 8.
8 9

(v) 0 has no reciprocal.

(vi) The product of two positive rational numbers is always a positive rational number.