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The products of small numbers may be calculated by using the squares of integers; for example, to calculate 13 × 17, one can remark 15 is the mean of the two factors, and think of it as (15 − 2) × (15 + 2), i.e. 15 2 − 2 2.
Mental calculation is said to improve mental capability, increases speed of response, memory power, and concentration power. Many veteran and prolific abacus users in China, Japan, South Korea, and others who use the abacus daily, naturally tend to not use the abacus any more, but perform calculations by visualizing the abacus.
Take half of the neighbor, then, if the current digit is odd, add 5. Example: 42×5=210 Half of 2's neighbor, the trailing zero, is 0. Half of 4's neighbor is 1. Half of the leading zero's neighbor is 2. 43×5 = 215 Half of 3's neighbor is 0, plus 5 because 3 is odd, is 5. Half of 4's neighbor is 1. Half of the leading zero's neighbor is 2. 93 ...
The Mental Calculation World Cup is considered the most challenging and respected international competition that attempts to find the world's best mental calculator, and also the best at specific types of mental calculation, such as addition, multiplication, square root or calendar reckoning. The Mental Calculation World Cup is arranged every ...
Zerah was reported to have been able to solve fairly complex problems. For example, the sixth Fermat number is 2 2 5 +1 (or 2 32 +1). The question is whether this number, 4,294,967,297, is prime or not. Zerah calculated in his head that it was not and had a divisor of 641. (Its other proper divisor is 6,700,417).
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