NZ Level 2
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Area models (2,3,4,5)


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 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

Here is a shape divided into parts, use it to answer the following questions.

  1. This shape has $\editable{}$ equal parts.

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

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

Which of the following shows $\frac{3}{4}$34 of the area of the shape shaded?

  1. A








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:

We are going to represent the fraction $\frac{1}{2}$12 on the shape below.

  1. How many parts do we divide the shape up into?

  2. Here is the shape, divided into $2$2 parts.

    Which of the following represents $\frac{1}{2}$12 on the shape?








  3. How big is this part?

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


The number of equal parts the shape is divided into is the denominator (bottom number).

The number of parts shaded to represent the fraction is the numerator (top number).



Know simple fractions in everyday use

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