Mental calculation

Mental calculation consists of arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator. People may use mental calculation when computing tools are not available, when it is faster than other means of calculation (such as conventional educational institution methods), or even in a competitive context. Mental calculation often involves the use of specific techniques devised for specific types of problems. People with unusually high ability to perform mental calculations are called mental calculators or lightning calculators. Many of these techniques take advantage of or rely on the decimal numeral system. Usually, the choice of radix is what determines which method or methods to use. Casting out nines 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: Sum the digits of the first operand; any 9s (or sets of digits that add to 9) can be counted as 0. 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. Repeat steps one and two with the second operand. At this point there are two single-digit numbers, the first derived from the first operand and the second derived from the second operand. Apply the originally specified operation to the two condensed operands, and then apply the summing-of-digits procedure to the result of the operation. Sum the digits of the result that were originally obtained for the original calculation. If the result of step 4 does not equal the result of step 5, then the original answer is wrong. If the two results match, then the original answer may be right, though it is not guaranteed to be.