Reciprocals

# Reciprocals

GCSE(F),

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

## Examples

1. What is the reciprocal of 10?

Answer: frac(1)(10)

Turn the number into a fraction: frac(10)(1). Then swap the numerator and the denominator for the reciprocal frac(1)(10)

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