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Are you scared when comes to multiply a product like 123 x 321 in your head?
Well, that’s not so hard as it seems to be!
For this we can use a technique which reduce the number of operation to about half:
- first step is to multiply the units digits, 3×5=15; the last digit of our product will be 5, save 1 into memory
- next step is to do a double-cross multiplication and also addition between those products, I mean: 2×5 + 3×4 = 10 + 12 = 22; we recall the 1 from memory so we get 23; the next digit of product will be 3, save 2 into memory
- next step is to do cross-multiplication on diagonals and add the results, I mean: 1×5 + 3×3 + 2×4 = 5 + 9 + 8=22; we recall the 2 saved to memory so we get 24; the next digit of product will be 4, save 2 into memory
- next step is to do also the double-cross multiplication on the right, I mean: 1×4 + 2×3 = 4 + 6 =10; recall 2 from memory so we get 12; the next digit of product will be 2, save 1 into memory
- the last step is to multiply the first digits, I mean: 1 x 3 = 3; recall 1 from memory so we should have the fist digit of our product as 4
The product will be 42435. Well, you will say that you can do the math, but can you do that on your head? This method involves just 5 steps and simple to do math, so you will be able to calculate such products directly in your head (no pen need it, maybe just to visualize the 2 numbers on a piece o paper).