Always, sometimes, never

In your book, Maths Mela (Chapter 9), some statements about numbers are always true, some are never true, and some are sometimes true. To decide, try some examples. One example that does not work is enough to show a statement is not always true.

'Multiplying by 10 gives 0 in the ones place.' 4 × 10 = 40, 23 × 10 = 230, 7 × 10 = 70. It always happens: Always true. 'Multiplying a number by 2 gives an odd number.' 3 × 2 = 6, 5 × 2 = 10, 8 × 2 = 16. A double is always even, so this never happens: Never true.

'Multiplying a number by 5 gives 5 in the ones place.' 3 × 5 = 15 ends in 5, but 4 × 5 = 20 ends in 0. It happens for some numbers and not others: Sometimes true. 'The number just after an odd number is even.' After 7 comes 8, after 15 comes 16, after 99 comes 100: Always true.

'Halving any number gives an even number.' Half of 8 is 4, which is even. But half of 6 is 3, which is odd. So it is sometimes true. 'Adding 0 to a number increases it by 1.' 5 + 0 = 5: adding 0 does not change a number at all. Never true.