Mathematics (Core)Exam code: 0580
Types of Numbers
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
Exam tip
Give the reciprocal as a value
Reciprocals were set in 9 of the 22 papers. When a question asks for the value of the reciprocal of a decimal, writing 1/0.625 or 1 ÷ 0.625 earns only one of the two marks: the second is for the value. Write the decimal as a fraction, turn it over and simplify, so 0.625 = 5/8 gives 8/5 = 1.6.
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