Comparing unit fractions

In your book, Maths Mela (Chapter 5), Sumedha notices something as each guest arrives: her share of the dhokla keeps getting smaller. With 2 children she had 1/2. With 3 she had 1/3, then 1/4, then 1/5. The more people share the same dhokla, the smaller each share.

So which is bigger, 1/4 or 1/5? Be careful: 5 is a bigger number than 4, but 1/5 means the whole is cut into 5 equal pieces, and 1/4 means it is cut into only 4. Fewer pieces means bigger pieces. So 1/4 is greater than 1/5. We write 1/4 > 1/5.

The same idea works every time, as long as the fractions are parts of the SAME whole. 1/6 > 1/9, because a dhokla cut into 6 pieces has bigger pieces than one cut into 9. 1/6 > 1/8 too. If a dhokla is shared among 6 people or among 8 people, the 6 people get the bigger pieces.

The book asks: will Sumedha eat more dhokla when it is shared among 9 people or among 11 people? Among 9, because then it is cut into fewer pieces, so each piece is bigger.