To name a fraction of a shape, first count how many equal parts make the whole. That is the bottom number (the denominator). Then count the parts you are asked about. That is the top number (the numerator). If the parts are not all the same size, measure them with equal units first, because fractions only work with equal parts.
Explore this idea with maths tools
Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- numerator
- the top number: how many parts are counted
- denominator
- the bottom number: how many equal parts make the whole
- equal parts
- parts that are exactly the same size
Worked examples
A strip has 5 equal parts and 2 are shaded. What fraction is shaded?
- 1.There are 5 equal parts, so each is 1/5.
- 2.2 parts are shaded: 2/5.
= 2/5
A grid has 8 equal squares and 3 are shaded. What fraction is not shaded?
- 1.8 − 3 = 5 squares are not shaded.
- 2.5 of 8 squares: 5/8.
= 5/8
A strip is cut into pieces 2, 1 and 1 units wide; the 2-unit piece is shaded. What fraction is shaded?
- 1.The whole strip is 4 equal units.
- 2.The shaded piece covers 2 of 4 units: 2/4 = 1/2.
= 1/2
For parents
Method: Count equal parts
What to say: How many equal parts make the whole? How many of them does the question ask about?
Common mistakes:
- Compares the part asked about with the rest of the shape (part to part) instead of with the whole.
- Names the unshaded part when asked for the shaded part, or the shaded part when asked for the unshaded part.
- Counts pieces as if they were equal parts, even when the pieces are different sizes.
- Counts the lines on a strip (including both ends) instead of the parts between them.
- Writes the fraction upside down, with the number of parts in the whole on top.