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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.
Decimal: Binary: 11 3 1011 11 5 6 101 110 2 12 10 1100 1 24 1 11000 —— —————— 33 100001 Describing the steps explicitly: 11 and 3 are written at the top; 11 is halved (5.5) and 3 is doubled (6). The fractional portion is discarded (5.5 becomes 5).
Cycles of the unit digit of multiples of integers ending in 1, 3, 7 and 9 (upper row), and 2, 4, 6 and 8 (lower row) on a telephone keypad. Figure 1 is used for multiples of 1, 3, 7, and 9. Figure 2 is used for the multiples of 2, 4, 6, and 8. These patterns can be used to memorize the multiples of any number from 0 to 10, except 5.
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
In algebra, it is a notation to resolve ambiguity (for instance, "b times 2" may be written as b⋅2, to avoid being confused with a value called b 2). This notation is used wherever multiplication should be written explicitly, such as in " ab = a ⋅2 for b = 2 "; this usage is also seen in English-language texts.
Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit.
However, until the late 1970s, most minicomputers did not have a multiply instruction, and so programmers used a "multiply routine" [1] [2] [3] which repeatedly shifts and accumulates partial results, often written using loop unwinding. Mainframe computers had multiply instructions, but they did the same sorts of shifts and adds as a "multiply ...
An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd. A square has even multiplicity for all prime factors (it is of the form a 2 for some a). The first: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (sequence A000290 in the OEIS).