Area models

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 and we use the numerator (the top number of the fraction) to select the number of pieces.

Example 1:

To represent four out of five equal parts, or $\frac{4}{5}$45​, we would divide the shape into five equal parts to make fifths and then select four of them.

Like this:

Each part of the shape represents $\frac{1}{5}$15​, so the remaining white part is one of out five equal pieces, or $\frac{1}{5}$15​.

Try this question for yourself:

question 1

Example 2:

This shape is representing a fraction:

There are four equal parts and three of them are shaded, so the fraction is $\frac{3}{4}$34​.

Try this question for yourself:

Question 2

The shape you 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 3: