Skip to content
Get started
Mathematics 05801.2

Fractions, decimals and percentages

Converting between them and calculating with fractions.

Learning objectives

What you need to be able to do

Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.

  • 1.2.1Convert between fractions, decimals and percentages and order them.
  • 1.2.2Calculate with fractions, including mixed numbers.

5 minute read

Fractions, decimals and percentages

Converting

  • Fraction → decimal: divide top by bottom. 3/8 = 0.375
  • Decimal → percentage: multiply by 100. 0.375 = 37.5%
  • Percentage → fraction: put over 100 and simplify. 37.5% = 375/1000 = 3/8

To order a mixed list, convert everything to decimals first — comparing decimals is far safer than comparing fractions by eye.

Calculating with fractions

  • Adding and subtracting — you need a common denominator. 2/3 + 1/4 = 8/12 + 3/12 = 11/12
  • Multiplying — multiply tops and bottoms; no common denominator needed. 2/3 × 4/5 = 8/15
  • Dividing — multiply by the reciprocal (flip the second fraction). 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Mixed numbers

Convert to improper fractions before calculating, then convert back at the end. 2¼ = 9/4. Trying to add or multiply mixed numbers directly is where most errors appear.

Recurring decimals

A fraction whose denominator has prime factors other than 2 and 5 gives a recurring decimal: 1/3 = 0.333… = 0.3̇. A denominator of only 2s and 5s terminates.

Think of it like this

Adding fractions without a common denominator is like adding lengths in metres and feet — the numbers are meaningless until both are in the same unit. The denominator *is* the unit.

Worked examples

Method, step by step

Calculate 2¼ ÷ 1½, giving your answer as a mixed number.

  1. 1Convert to improper fractions: 2¼ = 9/4 and 1½ = 3/2.
  2. 2Dividing means multiplying by the reciprocal: 9/4 × 2/3.
  3. 3= 18/12, which simplifies to 3/2.
  4. 4Convert back: 3/2 = 1½.

1½

Common misconceptions

  • Adding denominators: `1/2 + 1/3` is not `2/5`. Only the numerators add, once denominators match.
  • Finding a common denominator before multiplying — unnecessary, and it makes the arithmetic harder.
  • Multiplying mixed numbers directly, e.g. treating `2½ × 2` as `4½`. Convert to `5/2` first.

In the exam

  • For ordering questions, convert everything to decimals to 3 decimal places — it is quicker and far less error-prone.
  • Show the improper-fraction conversion as a separate line; method marks are available even if the final arithmetic slips.