Fractions on a number line

Where is one quarter without a slice picture?

Divide the distance from 0 to 1 into four equal intervals. One interval is 1/4; its endpoint from zero locates 1/4.

Imagine a straight path marked 0 at the start and 1 one chosen unit away. This is a number line: numbers appear as positions. The distance from 0 to 1 is one unit.

Divide that unit into four equal intervals. There are five boundary points, but four intervals to travel. The denominator 4 counts intervals in one unit, not boundary points.

From 0, one interval reaches 1/4, two reach 2/4, and three reach 3/4. Four intervals reach 4/4=1. The numerator counts intervals travelled from zero.

Continue with the same spacing after 1. One further interval reaches 5/4. Fractions are not restricted to the interval between 0 and 1: amounts larger than a whole also have positions.

Enlarging the drawing still leaves the first of four equal intervals at 1/4. What matters is the chosen unit, not its size in centimetres on a screen.

Listen one paragraph at a time

1 / 5

2 / 5

3 / 5

4 / 5

5 / 5

If you started by counting a point

At 0 you have not moved yet. Count one only after crossing the first interval.

Now change it yourself

Choose a denominator and move one interval at a time. Match the shaded quantity to the point, including beyond 1.

Equal parts per whole · denominatorParts taken · numerator

1/4 · One outlined strip = one equal-size whole

Every unit in one diagram has equal length. The denominator counts intervals per unit, not divisions of the entire displayed line.

Try with paper and objects

Draw a unit from 0 to 1, divide it equally and point to the intervals rather than counting the boundary points.

Check your idea with another example

Check your idea 1

Split 0 to 1 into five equal intervals. How many intervals?

Check your idea 2

Each interval is 1/6. Which position is four intervals from 0?

Try a different setting

You travel five intervals of one third of a metre. Is that beyond one metre?

Write an answer yourself

Return to the explanation

Compare with an explanation

5/8 · Each interval is 1/8; five intervals reach 5/8.

Does your explanation include these ideas?

Speak, point or draw on paper. Explain the reason, not just the numerical answer.

I identified the unit from 0 to 1.I counted equal intervals, not boundary points.I located the point after the numerator’s number of steps.

Continue, or pause here

Express an improper fraction as whole units and remaining parts, and connect it to a mixed number.