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After coming to the top of this column, start with the bottom of the next column, and travel in the same direction. The number is 8. So think of the next number after 21 that ends with 8, which is 28. Proceed in the same way until the last number, 3, corresponding to 63. Next, use the 0 at the bottom. It corresponds to 70. Then, start again ...
First step of solving 6785 × 8. In the first column, the number by which the biggest number is multiplied by is located. In this example, the number was 8. Only row 8 will be used for the remaining calculations, so the rest of the board has been cleared for clarity in explaining the remaining steps. Second step of solving 6785 × 8
In arbitrary-precision arithmetic, it is common to use long multiplication with the base set to 2 w, where w is the number of bits in a word, for multiplying relatively small numbers. To multiply two numbers with n digits using this method, one needs about n 2 operations.
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]
Subtraction was impossible, except by adding the complement of a number (for instance, subtract 2.50 by adding 9,997.50). Multiplication was a simple process of keying in the numbers one or more columns to the left and repeating the "addition" process. For example, to multiply 34.72 by 102, key in 3472, pull crank, repeat once more. Wheels show ...
Since 9 = 10 − 1, to multiply a number by nine, multiply it by 10 and then subtract the original number from the result. For example, 9 × 27 = 270 − 27 = 243. This method can be adjusted to multiply by eight instead of nine, by doubling the number being subtracted; 8 × 27 = 270 − (2×27) = 270 − 54 = 216.
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A large part of analytic number theory deals with multiplicative problems, and so most of its texts contain sections on multiplicative number theory. These are some well-known texts that deal specifically with multiplicative problems: Davenport, Harold (2000). Multiplicative Number Theory (3rd ed.). Berlin: Springer. ISBN 978-0-387-95097-6.
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