Plotting a fraction on a scale bar

Why use a number line?

A number line allows you to visualise a fraction as a position between two whole numbers. This helps you to understand its value and to compare it easily with other numbers.

Step-by-step method

To plot a fraction a/b on a number line:

1. Draw a line segment between 0 and 1 (or longer if necessary).
2. Divide this segment into b equal parts (b = denominator).
3. Count a units from 0 (a = numerator): this is the position of the fraction.

Example

To plot 3/5 on a graduated line between 0 and 1:

• Divide the line segment [0; 1] into 5 equal parts.
• Move forward 3 parts from 0.
• This gives the position of 3/5, which lies slightly past the midpoint of the line segment.

Fractions greater than 1

For a fraction such as 7/4, divide each unit segment into 4 parts, then move forward a total of 7 parts. We therefore go past 1 and end up between 1 and 2, exactly at 1 + 3/4.

Summary table

Fraction	Approximate position
1/4	close to 0
1/2	halfway between 0 and 1
3/4	close to 1
5/4	slightly past 1

A common pitfall to avoid

Make sure you divide the line segment into equal parts: a common mistake is to mark out the divisions roughly by eye, which distorts the position of the fraction. Use a ruler and count the divisions precisely.