Equal fractions

In your book, Maths Mela (Chapter 5), you fold a rectangle of paper into 3 equal parts, unfold it, and colour one part. The coloured part is 1/3. Now fold it back into 3 and then fold it in half. Unfold: the paper has 6 equal parts, and the coloured part covers 2 of them. It is 2/6. Fold in half once more and there are 12 equal parts, with 4 of them coloured: 4/12. The coloured part never changed size, so 1/3 = 2/6 = 4/12.

Try the same starting with halves. Colour 1/2. Fold in half: 2 of 4 parts are coloured, 2/4. Fold again: 4 of 8, 4/8. So 1/2 = 2/4 = 4/8. Fractions that cover the same amount of the whole are equal fractions.

The book shows a fraction chart: a strip for 1 whole, then strips cut into halves, thirds, quarters, and so on down to tenths, all the same length. From the chart: two 1/4 pieces are as long as 1/2. Two 1/8 pieces are as long as 1/4. Ten 1/10 pieces make the whole strip.

The chart also helps us compare. Is 2/3 more than 1/2? Yes: two thirds reach past the half-way mark. And the book asks: are three pieces of 1/6 equal to two pieces of 1/8? No! Three 1/6 pieces make 3/6, which is half the strip. Two 1/8 pieces make only 2/8, which is a quarter of the strip.