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By mental calculation, it is easier to multiply 16 by 3 ⁄ 16 than to do the same calculation using the fraction's decimal equivalent (0.1875). And it is more precise (exact, in fact) to multiply 15 by 1 ⁄ 3 , for example, than it is to multiply 15 by any decimal approximation of one third.
Division is also not, in general, associative, meaning that when dividing multiple times, the order of division can change the result. [7] For example, (24 / 6) / 2 = 2 , but 24 / (6 / 2) = 8 (where the use of parentheses indicates that the operations inside parentheses are performed before the operations outside parentheses).
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Engineer using a slide rule, with mechanical calculator in background, mid 20th century A more modern form of slide rule was created in 1859 by French artillery lieutenant Amédée Mannheim , who was fortunate both in having his rule made by a firm of national reputation, and its adoption by the French Artillery.
The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions. The least common multiple of more than two integers a , b , c , . . . , usually denoted by lcm( a , b , c , . . .) , is defined as the smallest positive integer that is ...
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
Among them, "division" is subtraction, "benefit" is addition, and "no entry" means that there is no counter-party, but multiplication and division are not recorded. [9] The Nine Chapters on the Mathematical Art gives a certain discussion on natural numbers, fractions, positive and negative numbers, and some special irrationality. Generally ...
Negative numbers and fractions were also incorporated into solutions of the great mathematical texts of the period. The mathematical texts of the time, the Book on Numbers and Computation and Jiuzhang suanshu solved basic arithmetic problems such as addition, subtraction, multiplication and division. [4]
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