Math Fractions Multiplicative inverse (reciprocal)

# Multiplicative inverse

In order to obtain the multiplicative inverse (or reciprocal) of a fraction, you have to interchange numerators and denominators.

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### Remember

A multiplicative inverse for a number x which is different from 0, is a number which when multiplied by x results in the multiplicative identity, 1.
Making a reciprocal of 0 is not possible.
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### Hint

The multiplicative inverse of a number (except 0) is formed by imagining a 1 in the denominator.
Example: $3=\frac31$. The multiplicative inverse of $\frac31$ is $\frac13$

In general, you can say: The multiplicative inverse of an integer $x$ is $\frac1x$.

### Examples:

• The multiplicative inverse of $\frac58$ is $\frac85$

• The multiplicative inverse of $10$ is $\frac{1}{10}$

• The multiplicative inverse of $\frac{25x}{13a}$ is $\frac{13a}{25x}$