Reciprocal In Algebra

Turn it upside down!

Reciprocal of a Number

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

Examples:

Number Reciprocal As a Decimal
2 1/2 = 0.5
8 1/8 = 0.125
1,000 1/1,000 = 0.001

Reciprocal of a Variable

If you are given a variable "x", its reciprocal is "1/x".

Likewise, if you are given something more complicated like "x/y" then the reciprocal is just "y/x". In other words turn it upside down.

Example: What is the Reciprocal of x/(x-1) ?

Answer: take x/(x-1) and flip it upside down: (x-1)/x

Flipping a Flip

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

Reciprocals

Example:

The reciprocal of ax/y is y/ax

The reciprocal of y/ax is ax/y (back again)

Example: What is:

  1
1/w

Answer: w

Notation

The reciprocal of "x" is shown as:

1/x

or x-1 (see exponents)