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If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
[1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most single-digit multiplications.
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.
The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. . This is achieved by noting that the final digit is completely determined by multiplying the last digit of the multiplic
If the sum contains more than one digit, the value of the tens place is carried into the next diagonal (see Step 2). Step 2. Numbers are filled to the left and to the bottom of the grid, and the answer is the numbers read off down (on the left) and across (on the bottom). In the example shown, the result of the multiplication of 58 with 213 is ...
Many common methods for multiplying numbers using pencil and paper require a multiplication table of memorized or consulted products of small numbers (typically any two numbers from 0 to 9). However, one method, the peasant multiplication algorithm, does not. The example below illustrates "long multiplication" (the "standard algorithm", "grade ...
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