What is an improper fraction?
Year 5 recognises mixed numbers and improper fractions and converts from one form to the other. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
An improper fraction has a numerator that is bigger than, or equal to, its denominator, like 7/4.
What it means
An improper fraction is worth 1 whole or more. 7/4 is seven quarters, which is one whole (4 quarters) and 3 quarters more: 1¾.
Writing a number as a whole number and a fraction, like 1¾, is called a mixed number.
A worked example
Write 11/4 as a mixed number
- Divide the numerator by the denominator: 11 ÷ 4 = 2 remainder 3.
- The 2 is the whole number, and the remainder 3 is still quarters.
- 11/4 = 2¾.
The common mistake
Thinking an improper fraction is a wrong answer that must always be changed. It is a proper way to write a number, and often easier to calculate with. 11+ questions say when they want a mixed number.
How it comes up in the 11+
Write 23/5 as a mixed number.
Answer: 4⅗
- 23 ÷ 5 = 4 remainder 3.
- That is 4 wholes and 3 fifths left over, so 23/5 = 4⅗.
Try it yourself
The wall opens on ¾, the fraction part of 2¾ in the worked example. Tap a piece to explore other parts of a whole.
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 5/5 an improper fraction?
Yes. Its numerator equals its denominator, which counts as improper. It is worth exactly 1.
What is the opposite of an improper fraction?
A proper fraction, where the numerator is smaller than the denominator, like ¾. It is always worth less than 1.
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.