Question

The two rational numbers which are their own multiplicative inverses are ______ .

Answer 1

Multiplicative Inverse:

Rational numbers are of the form ${\displaystyle \frac{p}{q}}$ , where $p$and $q$ are integers and $q\ne 0$.

From ,the multiplicative inverse property

If $\frac{p}{q}\times \frac{q}{p}=1$, then $\frac{q}{p}$ is said to be the multiplicative inverse of $\frac{p}{q}$.

where , $\frac{q}{p}$ is simply the reciprocal of $\frac{p}{q}$

In rational number$\left(\frac{p}{q}\right)$ form , $1$ can be written as $\frac{1}{1}$ , using multiplicative property we can write

$\frac{1}{1}\times \frac{1}{1}=1$

Thus , $1$ is the multiplicative inverse of $1$ itself.

similarly ,

In rational number$\left(\frac{p}{q}\right)$ form , $-1$ can be written as $\frac{-1}{1}$ , using multiplicative property we can write

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

Thus , $-1$ is the multiplicative inverse of $-1$ itself.

Therefore, the two rational numbers which are their own multiplicative inverses are $1and-1$.