What are improper fractions and mixed numbers?

What are 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: 

The relationship between mixed numbers and improper fractions can be best explained through the diagram above. These two shapes have been cut into four pieces. We can either express the amount of the shape we have as a mixed number: (1 3/4) or as an improper fraction (7/4).

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.