Making 100, 1,000, 10,000

In your book, Maths Mela (Chapter 4, We the Travellers — II), Sukanta likes the numbers 10, 100, 1,000 and 10,000. He wants to know what to add to a number to reach 100. For 32 + ___ = 100, his friend Piku shows him a clever way.

Piku first makes 99. Each digit needs a partner that makes 9: 3 + 6 = 9 and 2 + 7 = 9, so 32 + 67 = 99. Then 1 more makes 100: 32 + 68 = 100. For 59: 5 + 4 = 9 and 9 + 0 = 9, so 59 + 40 = 99 and 59 + 41 = 100.

The same idea reaches 1,000 and 10,000. Make 999, then add 1: 877 + 122 = 999, so 877 + 123 = 1,000. And 666 + 334 = 1,000. For 10,000, make 9,999 first: 4,103 + 5,896 = 9,999, so 4,103 + 5,897 = 10,000. And 5,555 + 4,445 = 10,000.

Namita likes the number 9. She finds a quick way to subtract 9: take away 10, then add 1 back, because 9 is 1 less than 10. 67 − 9 = 67 − 10 + 1 = 58. To subtract 99, take away 100 and add 1 back: 763 − 99 = 663 + 1 = 664.

She also asks what to take away to be left with 9. 32 − 23 = 9, and 56 − 47 = 9. To be left with 99: 877 − 778 = 99.