GCSEMathsEdexcelFoundationRevision NotesNumberTypes of Number, Prime Factors, HCF & LCMReciprocals

Reciprocals (Edexcel GCSE Maths: Foundation): Revision Note

Exam code: 1MA1

Written by: Jamie Wood

Reviewed by: Dan Finlay

Updated on 19 January 2026

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 $\frac{1}{3}$
- The reciprocal of $\frac{1}{3}$ is 3
- $3 \times \frac{1}{3} = \frac{1}{3} \times 3 = 1$
The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$
- The reciprocal of $\frac{3}{2}$ is $\frac{2}{3}$
- $\frac{2}{3} \times \frac{3}{2} = \frac{3}{2} \times \frac{2}{3} = 1$
Algebraically the reciprocal of $a$ is $\frac{1}{a}$
- The reciprocal of $\frac{1}{a}$ is $a$
- This can also be written using a power of -1
  - $\frac{1}{a} = a^{- 1}$

Worked Example

Write down a fraction that completes this calculation: $\frac{3}{7} \times \frac{. . .}{. . .} = 1$

Answer:

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

$\frac{3}{7} \times \frac{7}{3} = 1$

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