Find the multiplicative inverse of the following.
(i) $ -13 $
(ii) $ \frac{-13}{19} $
(iii) $ \frac{1}{5} $
(iv) $ \frac{-5}{8} \times \frac{-3}{7} $
(v) $ -1 \times \frac{-2}{5} $
(vi) $ -1 $.

To do:

We have to find the multiplicative inverse of the given rational numbers.

Solution:

The multiplicative inverse is that number which makes the existing number equal to unity on multiplication.

Multiplicative inverse of $a$ is $\frac{1}{a}$.

Therefore,

(i) The multiplicative inverse of $-13=\frac{1}{-13}$ 

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

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

(ii)The multiplicative inverse of $\frac{-13}{19}=\frac{1}{\frac{-13}{19}}$ 

$=\frac{-19}{13}$ 

The multiplicative inverse of $\frac{-13}{19}$ is $\frac{-19}{13}$.  

(iii) The multiplicative inverse of $\frac{1}{5}=\frac{1}{\frac{1}{5}}$ 

$=\frac{5}{1}$

$=5$ 

The multiplicative inverse of $\frac{1}{5}$ is $5$.   

(iv) $\frac{-5}{8} \times \frac{-3}{7}=\frac{-5\times(-3)}{8\times7}$

$=\frac{15}{56}$

Therefore,

The multiplicative inverse of $\frac{15}{56}=\frac{1}{\frac{15}{56}}$ 

$=\frac{56}{15}$ 

The multiplicative inverse of $\frac{-5}{8}\times\frac{-3}{7}$ is $\frac{56}{15}$.    

(v) $-1\times\frac{-2}{5}=\frac{-1\times(-2)}{5}$

$=\frac{2}{5}$

Therefore,

The multiplicative inverse of $\frac{2}{5}=\frac{1}{\frac{2}{5}}$ 

$=\frac{5}{2}$ 

The multiplicative inverse of $-1\times\frac{-2}{5}$ is $\frac{5}{2}$.

(vi) The multiplicative inverse of $-1=\frac{1}{-1}$ 

$=-1$ 

The multiplicative inverse of $-1$ is $-1$.      

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

25 Views

Kickstart Your Career

Get certified by completing the course

Get Started