# Reciprocals (Mathematics Glossary)

# What Is a Reciprocal?

The reciprocal of a quantity is the result of dividing 1 by that quantity.

#### Dictionary Definition

The Oxford English Dictionary defines a reciprocal as "based on an inverse relationship."# Real Examples of Reciprocals

The reciprocal can't be found for numbers, letters and more complicated quantities, like terms and expressions.

Type of Quantity | Quantity | Reciprocal |
---|---|---|

Numbers | ||

Letters | ||

Terms | ||

Expressions | ||

# More Real Examples of Reciprocals

The slider below shows more real examples of reciprocals.

# Reciprocals of Fractions

To find the reciprocal of a fraction, 1 is divided by the fraction.

Dividing 1 by a fraction turns the fraction upside down.

Read more about how to find the reciprocal of a fraction

##### Interactive Test

**show**

Here's a second test on reciprocals.

Here's a third test on reciprocals.

##### Note

# Exponent Notation For a Reciprocals

To denote the reciprocal of a quantity, place ** ^{-1}** to the top-right of the quantity. This is an exponent of -1.

Read more about exponents of -1

# Multiplying a Quantity With Its Reciprocal Equals 1

Multiplying a quantity with its reciprocal equals 1.

# Be Careful With Notation

Sometimes brackets are needed to indicate which part of a term is a reciprocal.

For example,

is different from