Question #a306e

Nov 30, 2016

The reciprocal or multiplicative inverse of $\frac{a}{b}$ is $\frac{b}{a}$

Explanation:

You seem to have mixed two names together.

Every number has a reciprocal, which can also be called its multiplicative inverse.

'Inverse' implies 'opposite'

A number multiplied by its multiplicative inverse will give $0$
To find the multiplicative inverse, simply invert the number.

($0$ is the identity element for multiplication and division)

$\frac{\cancel{2}}{\cancel{3}} \times \frac{\cancel{3}}{\cancel{2}} = 1$

The multiplicative inverse of 6 is $\frac{1}{6}$

The multiplicative inverse of $- \frac{12}{17}$ is $- \frac{17}{12}$

The multiplicative inverse of $\pi$ is $\frac{1}{\pi}$

The reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$

The reciprocal of $\frac{13}{4}$ is $\frac{4}{13}$