Maths topic

fractions

Fractions describe equal parts of a whole, equal parts of a group, or a position between whole numbers.

Practise fractions Explore fraction wall Back to topics

the big idea

A fraction names part of a whole or part of a group. The parts must be equal. The denominator tells how many equal parts make the whole. The numerator tells how many parts we are talking about.

whole one whole split fairly
denominator how many equal parts
numerator how many parts used

build a fraction

Change the whole into equal parts, then choose how many parts are shaded.

3/4

equal parts4 equal parts make 1 whole parts used3 parts are shaded meaning3/4 means 3 of 4 equal parts.
equal parts
shaded parts

fractions need equal parts

A fraction can only name parts when the whole has been split into equal parts.

  • Equal parts are the same size.
  • The whole is the complete shape, object, group or length.
  • If the parts are different sizes, the fraction name is not fair yet.
halves 2 equal parts
thirds 3 equal parts
quarters 4 equal parts

Same-size parts make fair fraction names.

numerator and denominator

In a fraction, the bottom number tells how many equal parts make the whole. The top number tells how many parts are used.

  • In 3/4, the denominator is 4 because the whole has 4 equal parts.
  • In 3/4, the numerator is 3 because 3 parts are shaded or chosen.
  • The fraction bar separates the numerator and denominator.
3 4
numerator: 3 parts used denominator: 4 equal parts make the whole

unit and non-unit fractions

A unit fraction has 1 as the numerator. A non-unit fraction has more than 1 as the numerator.

  • 1/4 is a unit fraction because it names 1 equal part.
  • 3/4 is a non-unit fraction because it names more than 1 equal part.
  • Both fractions still use equal parts of the same whole.
1/4 unit fraction
3/4 non-unit fraction

equivalent fractions

Equivalent fractions have the same value even when the numbers look different.

  • 1/2 and 2/4 cover the same amount of the same whole.
  • Equivalent means equal value.
  • Fraction walls help us see when different fraction names match.
1/2
=
2/4

Same amount, different names.

comparing fractions

To compare fractions, use the same whole and look at how much is shaded or chosen.

  • The whole must be the same size before comparing.
  • With the same denominator, more shaded parts means a larger fraction.
  • 3/4 is greater than 1/4 because 3 equal parts is more than 1 equal part.
1/4
<
3/4

Same whole. Same denominator. More shaded parts is larger.

fractions on a number line

Fractions can show positions between whole numbers on a number line.

  • The space from 0 to 1 can be split into equal jumps.
  • Four equal jumps make quarters.
  • 3/4 is three equal jumps from 0 toward 1.
0 1/4 2/4 3/4 1 3/4

3/4 is three equal jumps from 0.

fraction words

These words help us read, build and compare fractions.

1 whole all of it

the complete shape, group or length

2 equal part fair part

one part that is the same size as the other parts

3 numerator top number

how many equal parts are used

4 denominator bottom number

how many equal parts make the whole

5 fraction bar line

the line between the numerator and denominator

6 equivalent same value

different fraction names for the same amount

fraction facts

3/4 3 of 4 equal parts
1/4 a unit fraction
3/4 a non-unit fraction
1/2 2/4
fact 3/4 > 1/4
4/4 1 whole

real world examples

pizza sharing a pizza into equal slices
measuring cup using 1/2 cup or 1/4 cup in a recipe
ruler reading halfway or quarter-way marks
clock seeing quarter and half turns around a clock
sport playing 3/4 of a game
groups finding part of a collection

quick fractions quiz

Try a few fraction ideas. This quiz only asks about ideas shown on this page.

What must be true before a fraction can name parts of a whole?

In 3/4, what does the denominator 4 tell us?

In 3/4, what does the numerator 3 tell us?

Which fraction is equivalent to 1/2?

Which is larger when the whole is the same size?