Equivalent fractions

In your book, Maths Mela (Chapter 2), Sameer takes a square and cuts it into 3 equal upright strips. He shades the middle strip, so 1/3 of the square is shaded. Then he draws one horizontal line across the middle of the square. Now there are 6 equal parts, and the shaded strip has become 2 of them: 2/6. With two horizontal lines there are 9 equal parts and 3 are shaded: 3/9. With three lines there are 12 equal parts and 4 are shaded: 4/12.

The shaded part never changed! So 1/3, 2/6, 3/9 and 4/12 all show the same part of the whole. Fractions like these are called equivalent fractions: the same part of a whole, with different names. In the same way, 1/2 = 2/4, because two 1/4 pieces are as big as one 1/2 piece.

Do you see the pattern? When every part is cut into 2 equal parts, the number of parts doubles AND the number of shaded parts doubles. When each part is cut into 3, both are multiplied by 3. So to make an equivalent fraction, multiply the top number and the bottom number by the SAME number. 1/3 = 2/6 = 3/9 = 4/12, and going on, 1/3 = 8/24 = 12/36.

For 2/5: multiply both by 2 to get 4/10; both by 10 to get 20/50; both by 20 to get 40/100. To fill a box, find what the known number was multiplied by. In 3/4 = ?/16, the 4 became 16, which is 4 × 4, so the 3 becomes 3 × 4 = 12: 3/4 = 12/16.

To test whether two fractions are equivalent, check whether the same number turns one into the other, top and bottom. 3/5 and 6/10 are equivalent (both numbers × 2). 6/9 and 1/3 are not: 3/9 is 1/3, so 6/9 is twice as much, 2/3.