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

Examples:

NumberReciprocalAs a Decimal
21/2= 0.5
81/8= 0.125
1,0001/1,000= 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:

ExpressionReciprocal
2x12x
3xx3
(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!

Reciprocals

Example:

The reciprocal of axy is yax

The reciprocal of yax is axy (back again)

Example: What is:

11/w

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

Notation

The reciprocal of "x" can be shown as:

1x

or x−1 (see exponents)