Reciprocal of Number

The reciprocal of a number is one divided by that number

Reciprocal of a Fraction

To get the reciprocal of a fraction, simply switch the top and bottom of the fraction (numerator and denominator).

Reciprocal of a Reciprocal

The reciprocal of a reciprocal takes you back to where we started:

Remember that “Reciprocal” comes from the Latin reciprocus meaning returning.

Examples

NumberReciprocalIn DecimalReciprocal of Reciprocal
21/20.52
41/40.254
101/100.110
1/22/12.01/2
1/44/14.01/4
1/1010/110.01/10
2/33/21.52/3
3/44/31.333/4
5/66/51.25/6

Not for Zero

Every number except 0 has a reciprocal, because 1/0 is undefined

Reciprocal is what to multiply a value by to get 1

Try to multiply a number by its reciprocal:
5 × (1/5) = 5 x 0.2 = 1
Another example:
10 × (1/10) = 10 x 0.1 = 1
We always get 1
So:

Multiply a Number by Its Reciprocal Gets Us 1

The reciprocal is also called the “Multiplicative Inverse

Learn More

Table of Factors and Multiples

Common Factor

Complex Numbers

Simplifying Square Roots

Numbers Index

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