![]() Multiplying any two numbers by attaching, subtracting, and routing ĭiscovered by Artem Cheprasov, there is a method of multiplication that allows the user to utilize 3 steps to quickly multiply numbers of any size to one another via three unique ways. Many of these methods work because of the distributive property. Thousands: 4 − 1 = 3, look to right, 075 44 so no need to borrow, One place at a time is handled, left to right. This method can be used to subtract numbers left to right, and if all that is required is to read the result aloud, it requires little of the user's memory even to subtract numbers of arbitrary size. ![]() When the above situation does not apply, there is another method known as indirect calculation. For example, evaluate 872 − 41 simply by subtracting 1 from 2 in the units place, and 4 from 7 in the tens place: 831. When the digits of b are all smaller than the corresponding digits of a, the calculation can be done digit by digit. It is a multiple of 10, 7 (the other prime factor of 14) and 3 (the other prime factor of 15).Ĭalculating differences: a − b Direct calculation Furthermore, any number which is a multiple of both 5 and 2 is necessarily a multiple of 10, and in the decimal system would end with a 0. Likewise, 14 is a multiple of 2, so the product should be even. Since 15 is a multiple of 5, the product should be as well. For example, to say that 14 × 15 was 201 would be unreasonable. When multiplying, a useful thing to remember is that the factors of the operands still remain. The same procedure can be used with multiple operations, repeating steps 1 and 2 for each operation. 5 = 5, so there is a good chance that the prediction that 6338 × 79 equals 500702 is right.Perform the original operation on the condensed operands, and sum digits: 2 × 7 = 14 1 + 4 = 5.Sum the digits of 79: 7 + (9 counted as 0) = 7.Sum the digits of 6338: (6 + 3 = 9, so count that as 0) + 3 + 8 = 11.Say that calculation results that 6338 × 79 equals 500702.If the two results match, then the original answer may be right, though it is not guaranteed to be. ![]() If the result of step 4 does not equal the result of step 5, then the original answer is wrong.Sum the digits of the result that were originally obtained for the original calculation.Apply the originally specified operation to the two condensed operands, and then apply the summing-of-digits procedure to the result of the operation.(These single-digit numbers are also the remainders one would end up with if one divided the original operands by 9 mathematically speaking, they are the original operands modulo 9.) There are two single-digit numbers, one condensed from the first operand and the other condensed from the second operand. Repeat steps one and two with the second operand.If the resulting sum has two or more digits, sum those digits as in step one repeat this step until the resulting sum has only one digit.Sum the digits of the first operand any 9s (or sets of digits that add to 9) can be counted as 0.After applying an arithmetic operation to two operands and getting a result, the following procedure can be used to improve confidence in the correctness of the result:
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