Skip to content
Skip to main content

About this free course

Download this course

Share this free course

Succeed with maths: part 1
Succeed with maths: part 1

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

1.1 Folding paper

It is possible to use a simple piece of paper to help understand fractions. Here you’ll see how.

Take a piece of paper and fold it in half, creasing along the fold. Open it up and shade the left-hand side. You don’t have to fill this completely, just make sure that one half is clearly different from the other.

A piece of paper is shown being folded in half, and then opened up with the left-hand half shaded.
Figure 1 Folding a piece of paper in half

Since your paper has been divided into two equal parts, each piece is half of the original. This fraction is written as one divided by two and read as ‘one-half’.

The ‘bottom number’ is called the denominator. It tells you how many parts of the whole one has been divided into. For example, if it’s a four, then the whole thing (piece of paper, cake, etc.) has been divided into four parts.

The ‘top number’ or numerator tells you how many of those parts you have. So for three divided by four, it means the whole thing is divided into four parts, and you have three of them.

The numerator and denominator are separated by a line known as the fraction bar.

Example fraction showing the numerator and denominator. Full description in Long description link.
Figure 2 Defining a fraction

Now fold your piece of paper back along the original crease and then in half again along the long side. If you open up the paper, you should see four pieces of the same size, with two of them shaded.

The paper is now divided into quarters, and the fraction of the paper shaded is two divided by four.

Piece of paper folded in half, then in quarters and opened up with the two left-hand quarters shaded.
Figure 3 Folding a piece of paper into quarters

Since you haven’t altered the shading in any way, this demonstration shows that one half is equal to two quarters: equation left hand side one divided by two equals right hand side two divided by four

Now fold the paper back into quarters along the crease lines, and then fold into three equal pieces or thirds along the long side. If you now open up the paper you can see that there are 12 equal pieces. These pieces are ‘twelfths’, of which six are shaded, so six divided by 12 of the paper is shaded. This fraction also represents the same amount as one divided by two.

Piece of paper folded in quarters, then in twelfths and opened up with the six left-hand twelfths shaded.
Figure 4 Folding a piece of paper into twelfths

You can continue to fold the paper into smaller and smaller pieces. Each time you open up the paper it will be divided into smaller fractions but half of it will still be shaded. The fractions that represent the shaded part are all equivalent to each other.

So equation sequence one divided by two equals two divided by four equals six divided by 12.

Now it’s time to look at equivalent fractions in more detail.