Find the multiplicative inverse of the following.

(i) -13

(ii) $ \frac{-13}{19} $

(iii) $ \frac{1}{5} $

Given:  (i) -13

(ii) $-\frac{13}{19}$

(iii) $\frac{1}{5}$

To find: We have to find the multiplicative inverse of the given numbers.

Solution: 

Multiplying a number by its multiplicative inverse results in 1.

Now,

i) - 13

Let the multiplicative inverse be = a

So,

- 13 x a = 1

$a\ =\ -\frac{1}{13}$

Therefore, multiplicative inverse of -13 is  $-\frac{1}{13}$.

ii) $-\frac{13}{19}$ 

Let the multiplicative inverse be = a

So,

$-\frac{13}{19} \ \times \ a\ =\ 1$

$\Longrightarrow \ a\ =\ -\frac{19}{13}$

Therefore, the multiplicative inverse of  $-\frac{13}{19}$  is  $-\frac{19}{13}$.

iii) $\frac{1}{5}$

Let the multiplicative inverse be = a

So,

$\frac{1}{5} \ \times \ a\ =\ 1$

$\Longrightarrow \ a\ =\ 5$

Therefore, the multiplicative inverse of  $\frac{1}{5}$ is 5.