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Reciprocal - GCSE Maths Definition

Reviewed by: Dan Finlay

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In mathematics, the product of a number and its reciprocal is 1. Loosely speaking, a reciprocal is a fraction with the numerator and denominator swapped. (In the case of whole numbers, the denominator would be considered as 1.)

Examples,

  • the reciprocal of 5, is 1 fifth, since 5 cross times 1 fifth equals 1
    (or, to always treat everything as a fraction, the reciprocal is symbol that fraction "flipped upside down", 5 over 1 cross times 1 fifth equals 1)

  • the reciprocal of 2 over 3 is 3 over 2, since 2 over 3 cross times 3 over 2 equals 1

When working in geometry - specifically straight-line graphs - you may come across the phrase negative reciprocal. This would be where the product of a number and its reciprocal is -1. This is the case for the gradients of any two perpendicular lines - the product of their gradients is -1; i.e. the gradient of one line is the negative reciprocal of the other.

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Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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