What are improper fractions and mixed numbers?

We explain what improper fractions and mixed numbers are and how the relationship between them can be taught to primary-school children.
What are improper fractions and mixed numbers?
A mixed number is made up of a whole number and a fraction. For example:
An improper fraction is one that is 'top-heavy' so the numerator is bigger than the denominator. For example:
Working with mixed numbers and improper fractions in KS2
In Years 5 and 6 children need to start to be able to see equivalence between mixed numbers and improper fractions.
In the diagram above 8/3 is equivalent to 2 2/3.
In the diagram above 10/3 is equivalent to 3 1/3.
Converting improper fractions into mixed numbers
What is 16/5 as a mixed number?
- Divide the numerator by the denominator (16 ÷ 5 = 3 R 1).
- Your answer is the whole number and your remainder becomes the numerator of the fraction next to the whole number, so your answer is 3 1/5.
Converting mixed numbers into improper fractions
What is 2 7/8 as an improper fraction?
- Multiply the whole number by the denominator (2 x 8 = 16) and then add the numerator (16 + 7 = 23).
- This answer becomes the numerator; the denominator stays the same: 23/8.