Reciprocal

It is simply: 1/number

Very simple! To get the reciprocal of a number, just divide 1 by the number.

Example: the reciprocal of 2 is ½ (a half)

More Examples:

Number Reciprocal As a Decimal
5 1/5 = 0.2
8 1/8 = 0.125
1,000 1/1,000 = 0.001

Like Turning the Number Upside Down

 

In fact, if you think that a whole number could be written as "number/1", then the reciprocal is just like "flipping it over":

Number   Reciprocal
5 = 5/1   1/5
8 = 8/1   1/8
1,000 = 1,000/1   1/1,000

For Fractions, Flip the Whole Fraction Over

Example: the reciprocal of 3/4 is 4/3

Read more at Reciprocal of a Fraction.

Flipping a Flip

If you take the reciprocal of a reciprocal you end up back where you started!

Reciprocals

Example:

The reciprocal of 4 is 1/4

The reciprocal of 1/4 is 4 (back to 4 again)

It may help you to remember that "Reciprocal" comes from the Latin reciprocus meaning returning. Like going to the shops and then returning home again.

But Not Zero

Every number has a reciprocal except 0 (1/0 is undefined)

Multiply a Number by Its Reciprocal and You Get 1

Let us try multiplying a number by its reciprocal:

2 × (1/2) = 2 x 0.5 = 1

And let us try another:

10 × (1/10) = 10 x 0.1 = 1

Yes! You always get 1

In fact that is a way to define Reciprocal:

Reciprocal: what to multiply a value by to get 1

In terms of multiplying it is the Inverse, so it is also called the "Multiplicative Inverse".