Succeed with maths – Part 1

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# 1.1 Folding paper

Take your 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.

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 and read as ‘one-half’.

The top number is called the numerator – it tells us how many parts there are in the fraction.

The bottom number is called the denominator – it tells us how many parts in the whole one there are altogether.

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

Figure 2 Defining a fraction

Now fold the 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 .

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:

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 of the paper is shaded. This fraction also represents the same amount as .

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 .

You might have heard that it doesn’t matter what size a piece of paper is, it can only be folded seven times. If you’re interested watch this video [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] to see if this is true. It is less than a minute long so won’t eat into your study time.

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