Fractions on a number line: count the intervals, not the marks

To place a fraction on a number line, divide each whole into the number of equal intervals shown by the denominator. Count the numerator's number of intervals from zero. For 3/4, divide one whole into four equal intervals and count three.

Before you start

A fraction is a number, so it has a position on the line. The denominator tells you the size of the equal parts. The numerator tells you how many of those parts to count. Keep the distance between consecutive whole numbers the same.

Start with halves and quarters between zero and one. This is a useful bridge from partitioning shapes to locating numbers. Extend the exercise beyond one whole or place equivalent fractions on the same line once equal intervals make sense.

Step by step

  1. Establish one whole

    Locate 0 and 1. Their distance represents one whole. If the line continues to 2, the interval from 1 to 2 must have the same length. Check the labels before assuming the end of the line is 1.

  2. Divide into equal intervals

    For quarters, split each whole into four equal spaces. There are five boundary marks between 0 and 1 when both endpoints are included. Count the spaces, not all the marks.

  3. Count from zero

    For 3/4, move three quarter-sized intervals to the right of 0. Label the landing point 3/4. The zero mark is the starting point, so do not count it as the first quarter.

  4. Check the size

    Three quarters must be between one half and one. Five quarters is greater than one and lands at 1 1/4. Use these size checks to catch a counting or partitioning mistake.

Worked example: locating three quarters

Original number line. Each space is one quarter of the distance from 0 to 1.

01/41/213/4
Three quarter-sized intervals from zero locate 3/4.

Use the denominator

The denominator is 4, so one whole has four equal intervals.
Explanation. Unequal spaces would represent different amounts and would not show quarters.

Use the numerator

Count 1/4, 2/4, 3/4. The third landing point is three quarters.
Explanation. You count intervals travelled from zero. The starting mark does not represent one interval.

Compare an equivalent fraction

If each quarter is split in half, the same point is six eighths: 3/4 = 6/8.
Explanation. The parts become smaller and you count more of them, but the distance from zero stays the same.

A larger denominator means smaller parts of the same whole

One eighth is smaller than one quarter when both use the same whole. Eight equal parts divide that whole more finely than four. Do not choose the larger fraction just because its denominator is larger.

To compare fractions on a line, use a shared scale. The number farther to the right is larger. Separate drawings with different whole lengths can make a visual comparison misleading.

Continue the pattern beyond one

A line does not stop counting fractions at 1. On a quarter scale, the marks continue 4/4, 5/4, 6/4. Four quarters equals one whole; five quarters equals one whole and one quarter.

Try it yourself

Draw a number line from 0 to 2. Divide each whole into four equal intervals.

  1. Mark 1/4, 3/4 and 5/4.
  2. Label 5/4 as a mixed number.
  3. Put 2/4 and 1/2 on the line and explain what you notice.

Check your answer

The points are one quarter, three quarters and five quarters of a whole from zero. 5/4 = 1 1/4, so it is just beyond 1. 2/4 and 1/2 share a position. Your line has eight intervals from 0 to 2 and nine boundary marks.

Common questions

Why are there five marks for four quarters?

Four intervals need a boundary at each end and three inside. That makes five marks including zero and one. The denominator counts equal intervals within a whole.

Can a fraction be larger than one?

Yes. Five quarters is one whole and one quarter. Continue the same quarter-sized intervals past the mark for one.

Why do 1/2 and 2/4 share a point?

Both represent half of the same whole. Dividing each half into two equal parts changes the labels to quarters without changing the amount or position.

Curriculum connection

Year 4 Australian Curriculum Mathematics includes locating fractions, including mixed numbers, on number lines and recognising equivalent fractions. Halves and quarters provide a starting task before the extension beyond one whole.

QCAA: Australian Curriculum v9.0 Year 4 Mathematics

Sources and further reading

These resources provide background on the skill. The examples and practice tasks above are original.

Use a number line in your next fraction question

Open numeracy practice in NAPLAN Expert. Sketch equal intervals for a fraction question, then use the fraction's size to check your answer.

Practise fraction positions

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Examples and activities are NAPLAN Expert teaching material. Sources checked in October 2026.