# 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) $-1$.

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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 $-1$.

Updated on 10-Oct-2022 13:47:38