If you’re good at memorizing some
squares and use the tricks for some kinds of numbers, you’ll be able to quickly
multiply together many pairs of numbers that differ by 2, or 4, or 6.
Let’s say you want to calculate 12×14.
When two numbers differ by 2 their
product is always the square of the number in between them minus 1.
12×14 = (13×13)-1 = 169-1 = 168.
16×18 = (17×17)-1 = 289-1 = 288.
99×101 = (100×100)-1 = 10000-1 = 9999
If two numbers differ by 4 then their
product is the square of the number in the middle (the average of the two
numbers) minus 4.
11×15 = (13×13)-4 = 169-4 = 165.
13×17 = (15×15)-4 = 225-4 = 221.
If the two numbers differ by 6 then
their product is the square of their average minus 9.
12×18 = (15×15)-9 = 225-9 = 216.
17×23 = (20×20)-9 = 400-9 = 391.
This trick works effectively, if you’ve
memorized or can quickly calculate the squares of numbers.
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