What are fractions?

Part ofMathsFractionsYear 3

What is a fraction?

A fraction is part of a whole that has been divided into equal parts.

Fractions represent more than 0 but less than 1.

Fractions are written with two numbers, one on top of the other, separated by a division line.

The fraction one quarter. Written as 1 with a horizontal bar under it and then under that bar the number 4. The word 'numerator' is next to the 1. The word 'denominator' is next to the 4.

The top number is called the numerator. It shows how many parts you have.

The bottom number is called the denominator. It shows the total number of equal parts the whole is divided into.

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Activity: What is a fraction?

Complete this interactive activity to understand what fractions are. Then put your knowledge to the test.

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Unit fractions

When working with fractions it is important to know how many equal parts the whole has been divided into.

These shapes all have one part shaded.

Various depictions of fractions. A circle split into three equal parts with one part shaded, the fraction one third is below. There is a square made of four equal parts with one part shaded, the fraction one quarter is below. A triangle split into two equal parts with one part shaded, the fraction one half is beside it. A rectangle with eight equal parts with one part shaded, the fraction one eighth is beside it.

They are unit fractions. Unit fractions all have a numerator of 1.

The shapes have all been divided into different equal parts, so have different denominators.

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Non-unit fractions

Non-unit fractions have a numerator that is more than 1, but less than the denominator.

Below is a set of 9 hair beads. The set is the whole, so the denominator is 9.

9 beads in a row.

There are 2 yellow beads in the set, so \(\frac {2} {9}\) of the beads are yellow.

There are 3 red beads in the set, so\(\frac {3} {9}\) of the beads are red.

There are 4 pink beads in the set, \(\frac {4} {9}\) of the beads are pink.

2 yellow beads out of 9, 3 red beads out of 9 and 4 purple beads out of 9.

These are all examples of non-unit fractions.

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Example 1

There are two rows of 6 apples shaded dark grey.

Eva has 12 apples.

If \(\frac {1} {3}\) of the apples are red. How many red apples does she have?

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Example 2

Four bar models. Model A is split into four equal parts with three parts shaded. Model B is split into three equal parts with two parts shaded. Model C is split into ten equal parts with 9 parts shaded. Model D is split into five equal parts with two parts shaded.

What fractions do these bar models represent?

To find the denominator, count how many parts the whole has been divided into.

To find the numerator, count how many parts are shaded.

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Example 3

A number line between 0 and 1. The line is split into 6 parts.

Which fractions would you put on this number line?

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Play our fun maths game Guardians: Defenders of Mathematica
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More on Fractions

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