On a number line a fraction is a distance from 0. Count the equal spaces between 0 and 1: that is the denominator. Then count the spaces from 0 to the point: that is the numerator. Count spaces (jumps), not marks. Past 1 the counting keeps going, giving improper fractions like 5/4. If 1 is not labelled, use a labelled mark to work out what one space is worth.
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
- number line
- a line with numbers placed at equal distances
- improper fraction
- a fraction with a numerator bigger than its denominator, like 5/4
- interval
- the space between two marks
Worked examples
0 to 1 is split into 4 equal spaces. The arrow is 3 spaces after 0. What fraction is it?
- 1.Each space is 1/4.
- 2.3 spaces from 0 is 3/4.
= 3/4
A line from 0 to 2 is split into quarters. The arrow is 5 spaces after 0. What fraction is it?
- 1.Each whole has 4 spaces, so each space is 1/4.
- 2.5 spaces is 5/4, which is 1 1/4.
= 5/4
The mark 2 spaces after 0 is labelled 1/3. The arrow is 5 spaces after 0. What fraction is it?
- 1.2 spaces make 1/3, so one space is 1/6.
- 2.5 spaces is 5/6.
= 5/6
For parents
Method: Count equal spaces from 0
What to say: How many jumps from 0 to 1? How many jumps from 0 to the arrow?
Common mistakes:
- Counts the marks instead of the spaces, both up to the arrow and along the whole line.
- Counts spaces to the arrow but marks for the whole, so the denominator is one too big.
- Counts back from 1 to the arrow instead of counting from 0.
- Writes the fraction upside down, with the number of spaces in a whole on top.
- Treats the whole drawn line as one whole, whatever its end label, so the denominator is the total number of spaces.
- Reads only the part after the last whole number, dropping the wholes (5/4 read as 1/4).
- Assumes each space is worth one part of the labelled fraction's denominator, without checking how many spaces reach the label.
- Counts on from the labelled fraction adding one to the numerator for each space.