Reciprocals (Edexcel GCSE Maths): Revision Note

Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Updated on

Reciprocals

What is a reciprocal?

  • The reciprocal of a number is the result of dividing 1 by that number

    • Any number multiplied by its reciprocal will be equal to 1

  • The reciprocal of 3 is 1 third

    • The reciprocal of 1 third is 3

    • 3 cross times 1 third equals 1 third cross times 3 equals 1

  • The reciprocal of 2 over 3 is 3 over 2

    • The reciprocal of 3 over 2 is 2 over 3

    • 2 over 3 cross times 3 over 2 equals 3 over 2 cross times 2 over 3 equals 1

  • Algebraically the reciprocal of a is 1 over a

    • The reciprocal of 1 over a  is a

    • This can also be written using a power of -1

      • 1 over a equals a to the power of negative 1 end exponent

Worked Example

Write down a fraction that completes this calculation:   3 over 7 cross times fraction numerator... over denominator... end fraction equals 1

Recall that a number multiplied by its reciprocal is equal to 1

3 over 7 cross times bold 7 over bold 3 equals 1

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Jamie Wood

Author: Jamie Wood

Expertise: Maths

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Author: Dan Finlay

Expertise: Maths 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.