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Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations In mathematics , a multiplication table (sometimes, less formally, a times table ) is a mathematical table used to define a multiplication operation for an algebraic system.
The number 12565, for instance, has digit sum 1+2+5+6+5 = 19, which, in turn, has digit sum 1+9=10, which, in its turn has digit sum 1+0=1, a single-digit number. The digital root of 12565 is therefore 1, and its computation has the effect of casting out (12565 - 1)/9 = 1396 lots of 9 from 12565.
The black numbers are the addends, the green number is the carry, and the blue number is the sum. In the rightmost digit, the addition of 9 and 7 is 16, carrying 1 into the next pair of the digit to the left, making its addition 1 + 5 + 2 = 8. Therefore, 59 + 27 = 86.
For 8-bit integers the table of quarter squares will have 2 9 −1=511 entries (one entry for the full range 0..510 of possible sums, the differences using only the first 256 entries in range 0..255) or 2 9 −1=511 entries (using for negative differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of ...
If the tables are held on single-sided rods, 40 rods are needed in order to multiply 4-digit numbers – since numbers may have repeated digits, four copies of the multiplication table for each of the digits 0 to 9 are needed. If square rods are used, the 40 multiplication tables can be inscribed on 10 rods.
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Multiplication is an arithmetic operation in which two numbers, called the multiplier and the multiplicand, are combined into a single number called the product. [ 50 ] [ d ] The symbols of multiplication are × {\displaystyle \times } , ⋅ {\displaystyle \cdot } , and *.
A large digit, known as the simple, is marked in the space at the top of the strip. A multiplication table is placed in each of the five squares. Each of these multiplication tables is identical—it lists the multiples of the simple and is laid out in a particular way: The square is divided into nine smaller squares in a three-by-three ...
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