Reciprocal In Algebra

Turn it upside down!

Reciprocal of a Number

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

reciprocal of 8 is 1/8


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

Likewise, the reciprocal of a variable "x" is "1/x".

And the reciprocal of something more complicated like "x/y" is "y/x".

In other words turn it upside down.
dog upside down

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

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

More Examples:

Expression Reciprocal
2x 12x
3x x3
(2x−3)(x+5) (x+5)(2x−3)


Flipping a Flip

When we take the reciprocal of a reciprocal we end up back where we started!



The reciprocal of axy is yax

The reciprocal of yax is axy (back again)

Example: What is:


Answer: w

Why? because the reciprocal of 1/w is w/1 which is just w

Or with numbers: What is 1½ ? Divide 1 into halves, and the answer is 2


The reciprocal of "x" can be shown as:


or x−1 (see exponents)