Reciprocal In Algebra
Turn it upside down!
Reciprocal of a Number
To get the reciprocal of a number, we divide 1 by the number:
|Number||Reciprocal||As a Decimal|
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.
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
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:
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)|