The times chart

In your book, Maths Mela (Chapter 9), you fill a 10 × 10 chart. Each square holds the row number times the column number. Row 3, column 8 holds 3 × 8 = 24. Row 8, column 3 holds 8 × 3 = 24 too! Because 3 × 8 = 8 × 3, every row holds the same numbers as the matching column: row 7 is the same as column 7.

Look at the even and odd numbers. Rows 2, 4, 6, 8 and 10 have only even products: any number times an even number is even. The odd rows (1, 3, 5, 7, 9) mix even and odd products. Row 5, for example, goes 5, 10, 15, 20 … odd, even, odd, even.

Now look at the ones digits. Row 8 is 8, 16, 24, 32, 40, 48, 56, 64, 72, 80. Its ones digits are 8, 6, 4, 2, 0, and then 8, 6, 4, 2, 0 again. The pattern repeats, so we can guess beyond the chart: 11 × 8 ends in 8 (it is 88), 12 × 8 ends in 6 (96) and 13 × 8 ends in 4 (104).

Row 3 is 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Its ones digits are 3, 6, 9, 2, 5, 8, 1, 4, 7, 0: every digit from 0 to 9 appears once! Rows 1, 3, 7 and 9 all do this, and in those rows 0 appears only once, at the end. In row 8, 0 appears twice (40 and 80), and some digits, like 1, never appear.