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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 $1$.
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