6.1.2 Folding Paper
Take a piece of blank notebook paper and fold it in half, creasing along the fold. Open it up and shade the left-hand side.
Since the 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.”
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 (or fourths), and the fraction of the paper shaded is .
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 the paper up, 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 .
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 which represent the shaded part are all equivalent to each other.