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Reciprocals
(KS3, Year 8)

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

Reciprocal of 5 is 1 over 5

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 2 1 over 2
3 1 over 3
8 1 over 8
Letters a 1 over a
x 1 over x
Terms 2x 1 over 2 x
t squared 1 over t squared
Expressions x + 1 1 over x plus 1
a plus b 1 over a

Lesson Slides

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.

reciprocal fraction example
how to find the reciprocal of a fraction

Note

Exponent Notation For a Reciprocals

to show the reciprocal of a quantity, place −1 to the top-right of the quantity. This is an exponent of −1.

5 to the minus 1 equals 1 over 5 exponents of −1

Multiplying a Quantity With Its Reciprocal Equals 1

Multiplying a quantity with its reciprocal equals 1.

2 times 1 over 2 equals 1. x times 1 over x equals 1

Beware

Be Careful With Notation

Sometimes brackets are needed to indicate which part of a term is a reciprocal. For example, reciprocal_notation_example_1 is different from reciprocal_notation_example_2
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This page was written by Stephen Clarke.

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