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Fractions on a number line — Mathematics, 7–10 years

A fraction is also a number with a place on the number line. Its position lets you compare it with whole numbers and with other fractions.

Fractions have places

To place a fraction, split the distance from 0 to 1 into as many equal steps as its denominator says. Count the numerator's steps from 0. The point 3/4 is three of four equal steps along, so it lies between 0 and 1, closer to 1.

Why use a number line?

Pictures of divided objects can help, but they do not show every fraction clearly or show how fractions fit among whole numbers. A number line gives every value a position. That makes size and order visible: a point farther right represents a greater number.

Placing 5/4

To place 5/4, mark 0, 1 and 2. Split each whole interval into 4 equal parts, because the denominator is 4. Count five quarter-steps from 0: 1/4, 2/4, 3/4, 4/4 and 5/4. The point is one quarter past 1, so 5/4 is greater than 1.

The denominator sets the steps

A common mistake is to count the denominator's number of marks instead of the spaces between them. That feels natural because we usually count objects, not gaps. But 1/4 means one of four equal spaces from 0 to 1, so there are three internal marks and four intervals.

Fractions as measurements

Fractions on number lines appear when measuring distance, time, temperature or progress. A runner who has completed 3/4 of a kilometre is three quarters of the way from 0 to 1 kilometre. The line helps compare that amount with a target without needing a picture of a cake or object.

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