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Astronomers had to make thousands of such calculations, and because the best method of multiplication available was long multiplication, most of this time was spent taxingly multiplying out products. Mathematicians, particularly those who were also astronomers, were looking for an easier way, and trigonometry was one of the most advanced and ...
492 is close to 500, which is easy to multiply by. Add and subtract 8 (the difference between 500 and 492) to get 492 -> 484, 500. Multiply these numbers together to get 242,000 (This can be done efficiently by dividing 484 by 2 = 242 and multiplying by 1000). Finally, add the difference (8) squared (8 2 = 64) to the result: 492 2 = 242,064
The potential problems with immediate-execution calculators stem from the fact that they are imperative. This means that the user must provide details of how the calculation has to be performed. Thimbleby has identified the need for a calculator that is more automatic and therefore easier to use, and he states that such a calculator should be ...
The second example computes 6785 × 8. Like Example 1, the corresponding bones to the biggest number are placed in the board. For this example, bones 6, 7, 8, and 5 were placed in the proper order as shown below. First step of solving 6785 × 8. In the first column, the number by which the biggest number is multiplied by is located.
Similarly, the totient is equal to 4 when n is one of the four values 5, 8, 10, and 12, and it is equal to 6 when n is one of the four values 7, 9, 14, and 18. In each case, there is more than one value of n having the same value of φ(n).
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.
Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.
Since 8.8 in the top scale represents 88, the answer must additionally be multiplied by 10. The answer directly reads 1.76. Multiply by 100 and then by 10 to get the actual answer: 1,760. In general, the 1 on the top is moved to a factor on the bottom, and the answer is read off the bottom where the other factor is on the top.
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