What is a mixed number?
Year 5 converts between mixed numbers and improper fractions. Year 6 adds and subtracts them. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
A mixed number is a whole number and a fraction written together, like 2½.
What it means
2½ means 2 wholes and half of another one. It is the same amount as the improper fraction 5/2.
Mixed numbers are easy to picture, which is why recipes and measurements use them: 1½ cups, 2¼ hours.
A worked example
Write 3⅖ as an improper fraction
- Each whole is 5 fifths, so 3 wholes are 3 × 5 = 15 fifths.
- Add the 2 fifths: 15 + 2 = 17.
- 3⅖ = 17/5.
The common mistake
Multiplying the whole number by the numerator. 3⅖ is not 6/5. Multiply the whole number by the denominator, then add the numerator: 17/5.
How it comes up in the 11+
Which is bigger, 2¾ or 13/4? By how much?
Answer: 13/4 is bigger, by ½
- Change 13/4 to a mixed number: 13 ÷ 4 = 3 remainder 1, so 13/4 = 3¼.
- 3¼ is bigger than 2¾.
- 3¼ − 2¾ = ½.
Try it yourself
The wall opens on ⅖, the fraction part of 3⅖ in the worked example. Look straight down to find the fractions worth the same.
A fraction wall shows one whole split into halves, thirds, quarters and more, so equal fractions line up.
Related words and practice
More maths words
Questions parents ask
Is a mixed number the same as a mixed fraction?
Yes. Both names mean a whole number and a fraction together, like 1¾.
How do you turn a mixed number into a decimal?
Keep the whole number and change the fraction: 2¾ = 2 + 0.75 = 2.75.
Knowing the words is half of an 11+ maths question
11+ papers use maths vocabulary without explaining it. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.