What the remainder means

In your book, Maths Mela (Chapter 9), Susie and Sunitha pack coconuts in bags, and each bag holds 25. How many bags do they need for 97 coconuts? 3 bags hold 75 coconuts, and 97 − 75 = 22 coconuts are left over. Those 22 coconuts cannot be left lying on the floor! They need another bag. So they need 4 bags.

The same thing happens with 535 coconuts. 535 ÷ 25 = 21, remainder 10. That is 21 full bags, with 10 coconuts still to pack. They need 21 full bags and 1 more bag for the 10 remaining coconuts: 22 bags.

So after dividing, always ask: what does the remainder mean in this story? If EVERYTHING must be packed or EVERYONE must get a seat, the leftover needs one more bag, bus or show, so we add 1 to the quotient. But if the question asks how many bags are FULL, the answer is just the quotient: 21 full bags.

A school takes 342 students to the Science Park, and each bus carries at most 41 students. 41 × 8 = 328, so 8 buses carry 328 students and 342 − 328 = 14 students are left. Nobody can be left behind, so the school needs 9 buses.

A theatre seats 45 people in one show, and 475 people have bought tickets for a puppet show. 45 × 10 = 450, so 10 shows seat 450 people, and 25 people are still waiting. One more show is needed: 11 shows. If there are 2 shows a day, 5 days give only 10 shows, so 6 days are needed.