Same whole, fair compare

In your book, Maths Mela (Chapter 2, Fractions), Tamanna is a student of Grade 5. She has two chocolates of different sizes. The small one has 4 pieces, in 2 rows of 2. The big one has 9 pieces, in 3 rows of 3. All the pieces are the same size.

Tamanna says that 1/3 of one of her chocolates is bigger than 1/2 of the other. Is that possible? We usually think 1/2 is more than 1/3. Let us check. Half of the small chocolate is 2 of its 4 pieces. One-third of the big chocolate is 3 of its 9 pieces. 3 pieces are more than 2 pieces! So Tamanna is right: 1/3 of the BIG chocolate is more than 1/2 of the SMALL chocolate.

So when is 1/2 of something more than 1/3 of something? Only when it is the same something! Half of a chocolate is more than one-third of that same chocolate. But half of a small chocolate can be less than one-third of a big one.

Your book gives the rule: to compare two fractions of two wholes, the wholes must be the same. Before you say which fraction is more, always ask: fractions of WHAT? The same whole, or different wholes?