Reciprocal

The reciprocal is simply: 1/number

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

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

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)

Multiplying a Number by Its Reciprocal

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

Try some more yourself! You should always get 1

And 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".