### Theory:

The reciprocal of a number is one divided by that number. Formally the reciprocal of \(x =\) $\frac{1}{x}$.

So, for example, the reciprocal of \(5\) is one quarter: The reciprocal of \(5\) is $\frac{1}{5}$.

If $\frac{1}{8}$ is number then, the reciprocal of $\frac{1}{8}$ is \(8\).

Important!

**Rational Number:**A number can be made by dividing two integers.

- An integer is a number with
**no fractional part**.

Example:

0.5 is a rational number because 0.5 \(=\) $\frac{3}{2}$ (3 and 2 are both integers.)

When $\frac{15}{8}$ is a rational number then, the reciprocal of $\frac{15}{8}$ is $\frac{8}{15}$, to get the product as \(1\)?

Thus, $\frac{15}{8}$ \(×\) $\frac{8}{15}$ \(=\) \(1\).

Similarly, $-\frac{4}{9}$ must be multiplied by $-\frac{9}{4}$ so as to get the product as \(1\).

We state that $\frac{15}{8}$ is the reciprocal of $\frac{8}{15}$ and $-\frac{4}{9}$ is the reciprocal of $-\frac{9}{4}$.

Can you guess what is the reciprocal of \(0\)?

Important!

Is there a rational number which when multiplied by \(0\) give \(1\)? Thus, zero has no reciprocal.