True number sentences

In your book, Maths Mela (Chapter 9), we look at number sentences like 48 ÷ 3 = 4 × 4. A number sentence is true when both sides of the '=' sign have the same value. Work out each side on its own, then compare.

48 ÷ 3 = 16 and 4 × 4 = 16. Both sides are 16, so 48 ÷ 3 = 4 × 4 is true. 8 × 9 = 72 and 70 + 2 = 72, so that one is true too. But 20 − 6 = 14 and 7 × 3 = 21. 14 is not 21, so 20 − 6 = 7 × 3 is false. And 89 − 9 = 80 while 90 + 0 = 90, so that one is false.

We can fill a blank to make a sentence true. In 7 × 6 = ___ + 17, the left side is 42. So the blank plus 17 must make 42. 42 − 17 = 25, so the blank is 25: 7 × 6 = 25 + 17.

Some statements about numbers are always true, some are sometimes true, and some are never true. 'When two odd numbers are added, the sum is even' is always true: 3 + 5 = 8, 7 + 9 = 16, 11 + 1 = 12, and you will never find two odd numbers that add up to an odd number. 'Multiplication by an odd number gives an even number' is only sometimes true: multiplying 2 by the odd number 3 gives 6, which is even, but multiplying 5 by 3 gives 15, which is odd.

One example where a statement fails is enough to show it is not always true. 'Halving a number always leads to an even number' is not always true, because half of 10 is 5, which is odd.