# Find the multiplicative inverse (reciprocal) of each of the following rational numbers:(i) 9(ii) $-7$(iii) $\frac{12}{5}$(iv) $\frac{-7}{9}$(v) $\frac{-3}{-5}$(vi) $\frac{2}{3} \times \frac{9}{4}$(vii) $\frac{-5}{8} \times \frac{16}{15}$(viii) $-2 \times \frac{-3}{5}$(ix)-1 $(x) \frac{0}{3}$(xi) 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 $9=\frac{1}{9}$

$=\frac{1}{9}$

The multiplicative inverse of $9$ is $\frac{1}{9}$.

(ii) The multiplicative inverse of $-7=\frac{1}{-7}$

$=\frac{-1}{7}$

The multiplicative inverse of $-7$ is $\frac{-1}{7}$.

(iii)The multiplicative inverse of $\frac{12}{5}=\frac{1}{\frac{12}{5}}$

$=\frac{5}{12}$

The multiplicative inverse of $\frac{12}{5}$ is $\frac{5}{12}$.

(iv) The multiplicative inverse of $\frac{-7}{9}=\frac{1}{\frac{-7}{9}}$

$=\frac{-9}{7}$

The multiplicative inverse of $\frac{-7}{9}$ is $\frac{-9}{7}$.

(v) The multiplicative inverse of $\frac{-3}{-5}=\frac{1}{\frac{-3}{-5}}$

$=\frac{-5}{-3}$

$=\frac{5}{3}$

The multiplicative inverse of $\frac{-3}{-5}$ is $\frac{5}{3}$.

(vi) $\frac{2}{3} \times \frac{9}{4}=\frac{2\times9}{3\times4}$

$=\frac{3}{2}$

Therefore,

The multiplicative inverse of $\frac{3}{2}=\frac{1}{\frac{3}{2}}$

$=\frac{2}{3}$

The multiplicative inverse of $\frac{2}{3}\times\frac{9}{4}$ is $\frac{2}{3}$.

(vii) $\frac{-5}{8} \times \frac{16}{15}=\frac{-5\times16}{8\times15}$

$=\frac{-2}{3}$

Therefore,

The multiplicative inverse of $\frac{-2}{3}=\frac{1}{\frac{-2}{3}}$

$=\frac{-3}{2}$

The multiplicative inverse of $\frac{-5}{8}\times\frac{16}{15}$ is $\frac{-3}{2}$.

(viii) $-2 \times \frac{-3}{5}=\frac{-2\times(-3)}{5}$

$=\frac{6}{5}$

Therefore,

The multiplicative inverse of $\frac{6}{5}=\frac{1}{\frac{6}{5}}$

$=\frac{5}{6}$

The multiplicative inverse of $-2\times\frac{-3}{5}$ is $\frac{5}{6}$.

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

$=-1$

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

(x)$\frac{0}{3}=0$

$=0$

Therefore,

The multiplicative inverse of $0$ is not defined as any number divided by 0 is not defined.

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

$=1$

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

Updated on: 10-Oct-2022

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