Reciprocal In Algebra
Turn it upside down!
Reciprocal of a Number
To get the reciprocal of a number, we 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
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
../numbers/images/reciprocal.js?numer=x&denom=(x-1)
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!
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)
311, 1621,308, 1622, 2313, 3153, 2311, 2312, 3151, 3152