Question

Find the multiplicative inverse of each of the following numbers:
$2,\frac{6}{11},\frac{-8}{15},\frac{19}{18},\frac{1}{1000}$

Answer 1

We know that the multiplicative inverse or reciprocal for a number $x$, denoted by $\frac{1}{x}$ or $x^{-1}$, is a number which when multiplied by $x$ yields the multiplicative identity $1$.

The multiplicative inverse of a fraction $\frac{a}{b}$ is $\frac{b}{a}$ $(\because \frac{a}{b}\times \frac{b}{a}=1)$

Similarly,

The multiplicative inverse of a number $2$ is $\frac{1}{2}$ $(\because 2\times \frac{1}{2}=1)$

The multiplicative inverse of a fraction $\frac{6}{11}$ is $\frac{11}{6}$ $(\because \frac{6}{11}\times \frac{11}{6}=1)$

The multiplicative inverse of a fraction $\frac{-8}{15}$ is $\frac{-15}{8}$ $(\because \frac{-8}{15}\times \frac{-15}{8}=1)$

The multiplicative inverse of a fraction $\frac{19}{8}$ is $\frac{8}{19}$ $(\because \frac{19}{8}\times \frac{8}{19}=1)$

The multiplicative inverse of a fraction $\frac{1}{1000}$ is $1000$ $(\because \frac{1}{1000}\times 1000=1)$