Reciprocals

## Reciprocals

A reciprocal is the inverse of a number: it is the number turned upside down.

A reciprocal of an integer turns the number into a fraction, where the numerator is 1 and the denominator is the original number:

• the reciprocal of 12 is frac(1)(12)

For a fraction, the numerator and denominator change places:

• the reciprocal of frac(3)(4) is frac(4)(3)

Multiplying a number and its reciprocal always gives an answer of 1:

12 xx frac(1)(12)=frac(12)(12) = 1

frac(3)(4) xxfrac(4)(3)=frac(12)(12) = 1

Zero does not have a reciprocal.

The reciprocal is also known as the Multiplicative Inverse. A number multiplied by its inverse gives the Multiplicative Identity, which is 1.

## Example 1

What is the reciprocal of 10?

Turn the number into a fraction: frac(10)(1).

Then swap the numerator and the denominator for the reciprocal frac(1)(10)

Answer: frac(1)(10)

## Example 2

What is the reciprocal of -frac(1)(4)?

Note that the answer remains negative. Reverse the numerator and denominator for the receiprocal.