Before we begin the discussion on how to calculate the product, we will first define what we mean by complementary numbers.
Complementary numbers are two numbers that add up to a power of 10. For example, 2 and 8 are complementary, because they add up to 10. Also 22 and 78 are complementary, because they add up to 100, and so on.
Almost everyone would be expected to calculate 2*8 (or 2x8) through the memorisation of the multiplication table. A less well known fact is that 2x8 equals the difference of the square of 5 (average of two and eight) and the square of 3 (=8-5=5-2), i.e.
2*8=5*5-3*3=16.
To calculate the product of 42*58, we make use of the relationship described in the previous paragraph:
42*58=(50-8)*(50+8)=50*50-8*8=2500-64=2436
In other words, to multiply two numbers N1 and N2, we just have to square the average number N, (=5, 50, 500...) and subtract from it the square of the difference (N-N1).
N1*N2=N*N-(N2-N)*(N-N1).
Examples:
45*55 = 50*50 - 5*5 = 2500 - 25 = 2475
4899*5101 = 5000*5000 - 101*101 = 25,000,000-10201 = 24,989,799
This is a calculation that can be done without a calculator, and with a little practice, without pen and paper!