Reciprocal Value

The reciprocal value of $x$ is the number $y$ when multiplied by $x$ gives you $1$ . That is, $x \cdot y = 1$ . For example, the reciprocal of $2$ is the number $\frac{1}{2} = 0.5$ , because $2 \cdot \frac{1}{2} = 1$ . Every number except 0 has a reciprocal value.

RememberReciprocal value of a fraction

For a fraction $x = \frac{a}{b}$ , you get the reciprocal value by swapping the numerator and denominator, which gives you $y = \frac{b}{a}$ .

The fraction $\frac{b}{a}$ is also called reciprocal fraction of $\frac{a}{b}$ .

Examples

The reciprocal value of $x = - 250$ is $y = \frac{1}{- 250} = - 0.004$ .

The reciprocal value of $x = 0.000001$ is $y = \frac{1}{0.000001} = 1000000$ .

The reciprocal value of $x = \frac{3}{2}$ is $y = \frac{2}{3}$ .

Further notations

The reciprocal value of $x$ is denoted as $y = \frac{1}{x}$ or $y = x^{- 1}$ .

So $x \cdot \frac{1}{x} = x \cdot x^{- 1} = 1$ .

Properties

The reciprocal value of a negative number is also negative.
If $y$ is the reciprocal of $x$ (i.e., $x \cdot y = 1$ ), then $x$ is also the reciprocal of $y$ , since $y \cdot x = x \cdot y = 1$ . So taking the reciprocal of the reciprocal $y$ of $x$ gives you again the number $x$ .
If a number $x$ appraoaches zero, then its reciprocal $y$ runs away from zero, and vice versa.

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