Reciprocal
The reciprocal of a number is one divided by that number. Formally
So, for example the reciprocal of 4 is one quarter:
Reciprocal of a fraction
To find the reciprocal of a fraction,
simply exchange the top and bottom of the fraction
(numerator and
denominator).
For example:
(Recall that any number divided by one leaves it unchanged.)
Reciprocal of a number
The reciprocal of a number is one over that number. So for example the reciprocal of 6 is one over 6:
This is really the same as the previous case since a number can be written as a fraction with a
denominator)
of one.
For example
and so
Reciprocal of a decimal
This is treated the same as a number. It is one over that number. For example:
If you use a calculator to divide one by 1.38 you will get 0.725, so:
If you do it twice
If you take the reciprocal twice, you get what you started with. For example:
and if you take the reciprocal again:
which is what we started with.
Other notation
The reciprocal of a number is sometimes expressed as the number raised to the power of negative one:
Raising any quantity the power of 1 is the same as taking its reciprocal.
The reciprocal of a number is also sometimes called its 'multiplicative inverse'.
Other fractions, percents, ratios topics
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