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2. Karatsuba algorithm - Wikipedia

   en.wikipedia.org/wiki/Karatsuba_algorithm

   The standard procedure for multiplication of two n-digit numbers requires a number of elementary operations proportional to , or () in big-O notation. Andrey Kolmogorov conjectured that the traditional algorithm was asymptotically optimal, meaning that any algorithm for that task would require () elementary operations.

3. Multiplication algorithm - Wikipedia

   en.wikipedia.org/wiki/Multiplication_algorithm

   More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications). When implemented in software, long multiplication algorithms must deal with overflow during additions, which can be expensive.

4. Multiplication table - Wikipedia

   en.wikipedia.org/wiki/Multiplication_table

   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.

5. Multiplication - Wikipedia

   en.wikipedia.org/wiki/Multiplication

   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. Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 ⁠ 1 / 2 ⁠ × 2 ⁠ 1 / 2 ⁠ = 11 ⁠ 1 / 4 ⁠

6. Elementary arithmetic - Wikipedia

   en.wikipedia.org/wiki/Elementary_arithmetic

   The sum of two numbers is unique; there is only one correct answer for a sums. [8] When the sum of a pair of digits results in a two-digit number, the "tens" digit is referred to as the "carry digit". [9] In elementary arithmetic, students typically learn to add whole numbers and may also learn about topics such as negative numbers and fractions.

7. Promptuary - Wikipedia

   en.wikipedia.org/wiki/Promptuary

   The units digit of this addition, 1, is written down as the next digit of the multiplication result. The tens digit, which is 1, is carried into the next band. The third band from the right has five digits, 2, 4, 3, 1 and 6 plus the carried 1. These are all added to produce 17. The units digit of this, 7, is written as the next digit of the result.