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Number Toolkit

Number

Finding a reciprocal

  • Inverting a number gives its reciprocal: 1 is divided by the number, and the result is what the original must be multiplied by to reach 1
  • Every non-zero value and its reciprocal have a product of exactly 1
  • For a fraction, numerator and denominator swap places
    • Inverting 3/8 gives 8/3
  • The reciprocal of an integer n is 1/n
    • The reciprocal of 5 is 1/5
  • A decimal is easiest to invert by first writing it as a fraction
    • 0.4 = 2/5, so its reciprocal is 5/2 = 2.5
  • Zero has no reciprocal, because division by zero is undefined
  • In index form the reciprocal of a is a⁻¹
Worked example

Finding the reciprocal of a mixed number

Write down the reciprocal of 2 1/4.

Solution:

  • Convert the mixed number to a top-heavy fraction: 2 1/4 = 9/4
  • Swap numerator and denominator: the reciprocal is 4/9
  • Check: 9/4 × 4/9 = 36/36 = 1
Exam tip

This is marked as a final answer, so whatever stands last on the answer line is what counts. Either form scores — 1/4 and 0.25 both earn the reciprocal of 4 — but a fraction followed by a "simplified" version of it loses the mark.