Reciprocal In Algebra
Turn it upside down!
Reciprocal of a NumberTo 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!
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) |