Mixed numbers and improper fractions

A mixed number has a whole number and a fraction, like 2 ¾. An improper fraction has a top bigger than its bottom, like 11/4. They can be the same amount written in two ways.

Key facts

  • Mixed to improper: whole × bottom + top, over the same bottom.
  • Improper to mixed: divide; the remainder goes on top.
  • Use improper fractions when multiplying or dividing.

Worked examples

Example 1

Write 2 ¾ as an improper fraction.

  1. 2 wholes make 8 quarters. 2 × 4 = 8
  2. Add the 3 quarters. 8 + 3 = 11
  3. So it’s 11/4.

Answer: 11/4

Example 2

Write 17/5 as a mixed number.

  1. 17 ÷ 5 = 3 remainder 2
  2. 3 wholes and 2 fifths: 3 2/5

Answer: 3 ⅖