You may have already looked at representing fractions as fractions bars or points on the number line. Now watch this video to learn about fractions as areas of shapes.

Representing fractions

We can represent fractions using:

area

segments of lines

collections; and

as points on the number line.

Fractions as areas of shapes

With any model we use the:

denominator (the bottom number of the fraction) to decide how many pieces to divide it into. This shows the size of the fraction pieces.

numerator (the top number of the fraction) to select the number of pieces. This shows the value of the fraction.

Example 1

To represent five out of twelve equal parts, or $\frac{5}{12}$512, we divide the shape into twelve equal parts to make twelfths. Each part shows a value of $\frac{1}{12}$112 so we then select five of them to show $\frac{5}{12}$512.

Like this:

Each part has a value of $\frac{1}{12}$112, so the remaining white part is seven out of twelve equal parts, $\frac{7}{12}$712.

Try this question for yourself:

Question

Which of the following shows $\frac{2}{5}$25 of the area of the shape shaded?

A

B

C

D

Example 2

This shape is representing a fraction:

There are ten equal parts and seven of them are shaded, so the fraction is $\frac{7}{10}$710. The white part is showing $\frac{3}{10}$310.

Try this question for yourself:

Question

Which of the following shows $\frac{1}{10}$110 of the area of the shape shaded?

A

B

C

D

The shape we use to represent the fraction isn't important, it is the number of equal parts it is divided into and then how many parts are selected that shows the value of the fraction. The remaining part is also showing a fraction of the whole.

Try one more question for yourself:

Question

We are going to represent the fraction $\frac{1}{6}$16 on the shape below.

How many parts do we divide the shape up into?

Here is the shape, divided into $6$6 parts.

Which of the following represents $\frac{1}{6}$16 on the shape?

A

B

C

D

How big is this part?

This part is $\frac{\editable{}}{\editable{}}$ of the whole.

Remember!

The denominator shows the number of equal parts to make the whole (the size of the fraction pieces)

The numerator shows the number of parts in the fraction (the value of the fraction)