Quotient and remainder

In your book, Maths Mela (Chapter 9), Susie and Sunitha have 535 coconuts left to pack in bags of 25. They take away 20 bags of 25 (that is 500), leaving 35. Then 1 more bag of 25, leaving 10. 10 is less than 25, so no more full bags can be made. So 535 ÷ 25 gives quotient 20 + 1 = 21 and remainder 10.

Sometimes the divisor does not divide the dividend exactly, and something is left over. What is left over is called the remainder (R). The remainder must always be less than the divisor. If it is not, you can take away at least one more group.

We can check any division with this rule: dividend = divisor × quotient + remainder, or N = D × Q + R. For 535 ÷ 25: 25 × 21 = 525, and 525 + 10 = 535. It works!

Try 726 ÷ 4. Take away 100 × 4 = 400, leaving 326. Take away 80 × 4 = 320, leaving 6. Take away 1 × 4 = 4, leaving 2. So the quotient is 100 + 80 + 1 = 181 and the remainder is 2. Is 726 = 4 × 181? No: 4 × 181 = 724. So 726 = 4 × 181 + 2.

Now 902 ÷ 16. Take away 50 × 16 = 800, leaving 102. Take away 6 × 16 = 96, leaving 6. So the quotient is 56 and the remainder is 6: 902 = 16 × 56 + 6. When a number divides exactly, like 745 ÷ 5 = 149, the remainder is 0.