Concept

Reciprocal

The reciprocal of a rational number is found by switching the numerator and denominator of the number.

Number	Reciprocal
$2$	$\frac{1}{2}$
$\frac{5}{7}$	$\frac{7}{5}$
$\frac{a}{b}$	$\frac{b}{a}$

The reciprocal of a number is also known as its multiplicative inverse, since the product of any rational number and its reciprocal is equal to $1 .$ $\frac{a}{b} \cdot \frac{b}{a} = 1$ A similar identity to this one is the additive inverse.

Concept

Negative Reciprocal

The negative reciprocal of a number is the reciprocal with changed sign.

Number	Negative Reciprocal
$2$	$- \frac{1}{2}$
$\frac{5}{7}$	$- \frac{7}{5}$
$\frac{a}{b}$	$- \frac{b}{a}$

An example of this is perpendicular lines where their slopes are negative reciprocals of each other.