Why are compatible numbers useful?

Answer 1

Compatible numbers are numbers which are easy to add, subtract, multiply or divide mentally. It is sometimes possible to simplify an apparently complicated problem in arithmetic by using compatible numbers and the basic properties of numbers.

For example, to calculate 49*24 +34

Note that 49 = 50 - 1

So 49*24 = (50 - 1)*24 = 50*24 - 1*24

Now use 50*2 = 100. Therefore 50*24 = 50*(2*12) = (50*2)*12 = 100*12 = 1200.

so that 50*24 - 1*24 = 1200 - 24

Finally 1200 - 24 + 34 = 1200 + 34 - 24 = 1200 + (34 - 24) = 1200 + (30 - 20) + (4 - 4)

= 1200 + 10 + 0 = 1210.

It is simpler not to find the answer to 1200 - 24 but combine the -24 with +34.