Fractions on a number line

A line between 0 and 1

Draw a straight line. Put 0 at the left end and 1 at the right end. The space between them is one whole. Now chop that space into equal steps. If you make two equal steps, you have a halves number line. If you make four, you have a fourths line. The denominator of your fraction is the number of equal steps between 0 and 1.

A number line is useful because it shows fractions as numbers, not just as pieces of a shape. Thinking of 3/4 as a point on a line helps you compare fractions, add them and see which ones are bigger.

Count the jumps

To find a fraction on the line, start at 0 and make jumps of the right size. Each jump is 1 over the denominator, so on a fourths line every jump is 1/4. The numerator tells you how many jumps to take.

• 1 jump of 1/4 lands on 1/4.
• 2 jumps land on 2/4, the same place as 1/2.
• 3 jumps land on 3/4.
• 4 jumps land on 4/4, which is 1, the right end of the line.

The left end is 0, and you can write it as 0/4. Zero jumps means zero parts. So the line runs from 0/4 to 4/4, and every tick in between has a fraction name.

Equal spaces, not equal tick marks

When you split a line, count the spaces, not the marks. A fourths line from 0 to 1 has five tick marks: 0, 1/4, 2/4, 3/4 and 4/4. But it has only four spaces between the marks, because the line is cut into four equal pieces. The denominator is the number of spaces.

Lines for larger denominators work the same way, but the ticks get close together. On an eighths line there are eight spaces and nine ticks. You can label only the ticks you need, and that is exactly what the diagram below does: it splits the line into eighths, then marks one point, 5/8.

Fractions beyond 1

Number lines do not have to stop at 1. Keep the same step size and carry on past the 1 mark. On a fourths line the next ticks are 5/4, 6/4, 7/4 and 8/4, which is 2. A number such as 5/4 sits between 1 and 2. It is an improper fraction, and you will meet those again in a later lesson.

Worked example

Show 5/8 on a number line. Step 1: the denominator is 8, so split the space from 0 to 1 into 8 equal parts. Step 2: the numerator is 5, so count 5 jumps from 0. Step 3: mark the point you land on and label it 5/8. Check your work: the point should sit past the middle of the line, because 5/8 is bigger than 4/8, which is a half.

Watch out for this

A line split into 6 equal parts gives sixth as the step size, not 1/5 or 1/7. Count the spaces carefully. Also remember that the tick at the far right is the whole, written as 6/6 or 6/6 = 1. The numerator and the denominator match when you have taken every jump.

Remember

• The denominator is the number of equal spaces between 0 and 1.
• The numerator is the number of jumps you take from 0.
• Count spaces to get the denominator, ticks to get the numerator.
• The point at the far right of a 0-to-1 line is 1, however it is written.