Using a nearby number

In your book, Maths Mela (Chapter 6, The Dairy Farm), we find products using a nearby easy number. Take 4 × 19. 19 is just 1 less than 20, and 4 × 20 = 80 is easy. But 4 × 20 is 4 groups of 20, and we only wanted 4 groups of 19, so each group has 1 extra. That is 4 extra in all. So 4 × 19 = 4 × 20 − 4 = 80 − 4 = 76.

Now 14 × 21. 21 is 1 more than 20. 14 × 20 = 280, and we need one more group of 14: 14 × 21 = 14 × 20 + 14 = 280 + 14 = 294. In the same way, 99 × 15 is one 15 less than 100 × 15: 1,500 − 15 = 1,485.

Think of the product as rows and columns. If 17 × 23 = 391, then 17 × 24 has one more column of 17, so it is 391 + 17 = 408. And 18 × 23 has one more row of 23, so it is 391 + 23 = 414. Always ask: which number grew by 1? Then add one group of the OTHER number.

The same idea helps us see which expressions have the same answer without calculating. 101 × 42 is 100 × 42 and 42 more. 1999 × 2 is 2,000 × 2 − 2, which is 4,000 − 2 = 3,998. And if 99 × 100 = 9,900, then 99 × 99 is one 99 less: 9,900 − 99 = 9,801.