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How do you calculate how much is 93 x 97 in your head? Sounds that impossible?
There are many quick algorithms depending on the nature of the numbers you want to multiply. In some situations fits better one algorithm, in other situations maybe there are better algorithms.
Use the algorithm below only if the following conditions are simultaneous meet:
- the numbers are closed to 100 (ex: 97, 112, 51 or 149 are closer to 100, while 7, 45 or 151 are too far from 100)
- both numbers have the same number of digits
- the first digits are the same
- the sum of the last digit (of both numbers) equals to 10
We assume an upper base like 100. We subtract each number from the base and obtain the corresponding difference:
100 100
93 97
———–
7 3
To obtain the first digits of the product you should either subtract 7 from 97 or 3 from 93 (the result will be always the same):
93-3 = 97-7 = 90
So the first digits of our product is “90”.
To find the last digits of our product just multiply the 7 with 3, which is “21”.
So 93×97=9021.
The interesting thing here is that you ca use this technique to multiply such numbers “in your head”.
Well, if you will attempt to use the same technique when comes to multiply 43 x 96 I guess you will not impress anyone. Try yourself!
In that case I suggest you using the double-cross multiplication.
Let’s calculate this product: 43 x 96
– to obtain the last digit multiply 3 with 6, which is 18; we write 8 as the last digit and save in memory 1
– later we have to multiply the extremes and to add the result of each other; 4x6 + 3x9 = 24 + 27 = 51; we already have 1 saved into memory so the result will be 52; so the next digit (from right to left) is 2 and save 5 into memory
– to obtain the first digits you multiply 4 with 9, which is 36; we already have 5 into memory so 36+5=41; the product will then become 4128
The picture below shows you how to multiply each number to get the final product:
The thing about this is that you can do all these operations in your mind, you don’t need a pen to calculate this. Maybe (but this depends from one person to another) you need only to see these numbers on a piece of paper. That’s all!