Reciprocal

The reciprocal is simply: 1/number

reciprocal

To get the reciprocal of a number, we divide 1 by the number.

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

More Examples:

Number Reciprocal As a Decimal
5 15 = 0.2
8 18 = 0.125
1000 11000 = 0.001

Like Turning the Number Upside Down

dog  upside down  

We can think of a whole number as being "number/1", so the reciprocal is just like "flipping it over":

Number   Reciprocal
5 = 51   1 5
8 = 81   1 8
1000 = 10001   1 1000

For Fractions, Flip the Whole Fraction Over

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

Read more at Reciprocal of a Fraction.

dog  flipping frisbee

Flipping a Flip

The reciprocal of a reciprocal takes us back to where we started:

Reciprocals

Example:

The reciprocal of 4 is 1/4

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

It may help 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 Gets Us 1

Let us try multiplying a number by its reciprocal:

2 × (1/2) = 2 x 0.5 = 1

How about another:

10 × (1/10) = 10 x 0.1 = 1

Yes! We always get 1

In fact that is a way to define Reciprocal:

Reciprocal: what to multiply a value by to get 1

 

The reciprocal is also called the "Multiplicative Inverse".