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In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144."
If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
But since the 7 is above the second set of numbers that number must be multiplied by 10. Thus, even though the answer directly reads 1.4 , the correct answer is 1.4×10 = 14 . For an example with even larger numbers, to multiply 88×20 , the top scale is again positioned to start at the 2 on the bottom scale.
The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian engineer Jakow Trachtenberg in order to keep his mind occupied while being held prisoner in a Nazi concentration camp. This article presents some methods devised by Trachtenberg.
Dividing 272 and 8, starting with the hundreds digit, 2 is not divisible by 8. Add 20 and 7 to get 27. The largest number that the divisor of 8 can be multiplied by without exceeding 27 is 3, so it is written under the tens column. Subtracting 24 (the product of 3 and 8) from 27 gives 3 as the remainder.
The grid method can be introduced by thinking about how to add up the number of points in a regular array, for example the number of squares of chocolate in a chocolate bar. As the size of the calculation becomes larger, it becomes easier to start counting in tens; and to represent the calculation as a box which can be sub-divided, rather than ...
For real and complex numbers, which includes, for example, natural numbers, integers, and fractions, multiplication has certain properties: Commutative property The order in which two numbers are multiplied does not matter: [27] [28] =. Associative property
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 x ⋅ ( 2 + x ) {\displaystyle x\cdot (2+x)} is the product of x {\displaystyle x} and ( 2 + x ) {\displaystyle ...