QUESTION

Find the multiplicative inverse of the following.  (i) -13  (ii) $\dfrac{1}{5}$  (iii) $\dfrac{{ - 5}}{8} \times \dfrac{{ - 3}}{7}$  (iv) $- 1 \times \dfrac{{ - 2}}{5}$  (v) -1

Hint- We know that the multiplicative inverse of a number is reciprocal of it, for example. 7 and 1/7 are multiplicative inverses of each other, here the sign of the number will never be changed.

Complete step-by-step solution -
(i) -13
So, we will take reciprocal if it.
The multiplicative inverse of -13 is $- \dfrac{1}{{13}}$.

(ii) $\dfrac{1}{5}$
so, we take the reciprocal of $\dfrac{1}{5}$
The multiplicative inverse of $\dfrac{1}{5}$is 5.

(iii) $\dfrac{{ - 5}}{8} \times \dfrac{{ - 3}}{7}$
$\Rightarrow \dfrac{{15}}{{56}}$
On taking reciprocal the multiplicative inverse of $\dfrac{{15}}{{56}}$ is $\dfrac{{56}}{{15}}$.

(iv) $- 1 \times \dfrac{{ - 2}}{5}$
$\Rightarrow \dfrac{2}{5}$
The multiplicative inverse of $\dfrac{2}{5}$is$\dfrac{5}{2}$.

(v) -1
The multiplicative inverse of -1 is -1.

Note:-
If you multiply by its multiplicative inverse of the product will be 1 because that’s the definition of a multiplicative inverse. Also, Sign doesn’t have any impact on multiplicative inverse. We should make sure that in hurry generally we commit mistakes by neglecting the sign and get confused by it.