Methods for fast multiplication
In everyday life, we do not rarely have to multiply the numbers. Sometimes it needs to be done quickly, like calculators-virtuosos. The methods of fast multiplication are used for cross multiplication, which is very useful when operating with two-digit numbers. This way used in the olden times by the Greeks and Hindus and was called by the way of rapid multiplication by a cross.
For example, let it be necessary to multiply 24x32. Mentally we have numbers according to the following scheme, one under the other:
After that, you need to do the following:
- 4x2 = 8 is the last digit of the result;
- 2x2 = 4; 4x3 = 12; 4 + 12 = 16; 6 - penultimate figure of the result; unit is memorized;
- 2x3 = 6 and still retained in the mind unit, we have 7 - this is the first digit of the result.
We get all the numbers of the work: 7, 6, 8 - 768.
This method of rapid multiplication is absorbed very easily after a short exercise.
When the numbers to be multiplied are close to 100, it is convenient to apply another method of fast multiplication. It consists in the use of so-called "additions".
For example, you need to multiply 92x96. "Addition" for 92 to 100 will be 8, for 96 - 4. The action is performed according to the following scheme: multipliers: 92 and 96, "additions": 8 and 4.
The first two digits of the multiplication result are obtained by simply subtracting the multiplier of the "complement" of the multiplicand or vice versa. We subtract 4 out of 92 or from 96 to 8. In either case we have 88; to this number is attributed the product of "additions": 8x4 = 32. We get the result of 8832.
Another example is to multiply 78x77:
multipliers: 78 and 77, "additions": 22 and 23.
78 - 23 = 55,
22x23 = 506 (we use the method of fast multiplication by a cross),
5500 + 506 = 6006.
