# Find the value of 4 muliplied by the reciprocal of 4?

Apr 14, 2018

Multiplying any number by its reciprocal gives us $1$. Hence $4$ muliplied by the reciprocal of $4$ too is $1$.

Apr 25, 2018

$1$

#### Explanation:

$1$ is known as the identity element for multiplication and division.

It is obtained by multiplying any number by its multiplicative inverse - also known as the reciprocal.

$x \times \frac{1}{x} = \frac{x}{x} = 1 \text{ } \leftarrow \left(x \ne 0\right)$

$\frac{4}{1} \times \frac{1}{4} = \frac{4}{4} = 1$

And so it is for any value except $0$

$\sqrt{2} \times \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{\sqrt{2}} = 1$

$\frac{3}{7} \times \frac{7}{3} = \frac{21}{21} = 1$