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While the first interpretation may be expected by some users due to the nature of implied multiplication, [38] the latter is more in line with the rule that multiplication and division are of equal precedence. [3] When the user is unsure how a calculator will interpret an expression, parentheses can be used to remove the ambiguity. [3]
492 is close to 500, which is easy to multiply by. Add and subtract 8 (the difference between 500 and 492) to get 492 -> 484, 500. Multiply these numbers together to get 242,000 (This can be done efficiently by dividing 484 by 2 = 242 and multiplying by 1000). Finally, add the difference (8) squared (8 2 = 64) to the result: 492 2 = 242,064
Dividing 272 and 8, starting with the hundreds digit, 2 is not divisible by 8. Add 20 and 7 to get 27. The largest number that the divisor of 8 can be multiplied by without exceeding 27 is 3, so it is written under the tens column. Subtracting 24 (the product of 3 and 8) from 27 gives 3 as the remainder.
The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school , this algorithm is sometimes called the grammar school method.
Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
Multiplication symbols are usually omitted, and implied, when there is no operator between two variables or terms, or when a coefficient is used. For example, 3 × x 2 is written as 3x 2, and 2 × x × y is written as 2xy. [5] Sometimes, multiplication symbols are replaced with either a dot or center-dot, so that x × y is written as either x ...
divide a 16-digit number by an 8-digit divisor. Addition or subtraction is performed in a single step, with a turn of the crank. Multiplication and division are performed digit by digit on the multiplier or divisor digits, in a procedure equivalent to the familiar long multiplication and long division procedures taught in
(omitted) Dividing 5884 by 594 yields 9 which is written as the new digit of the quotient. 58 − 5×9 = 13 so cross out the 5 and 8 and above them write 1 and 3. Cross out the 5 of the divisor. The resulting dividend is now 1384. 138 − 9×9 = 57. Cross out 1,3, and 8 of the dividend and write 5 and 7 above. Cross out the 9 of the divisor.