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The remainder is multiplied by 3 to get feet and carried up to the feet column. Long division of the feet gives 1 remainder 29 which is then multiplied by twelve to get 348 inches. Long division continues with the final remainder of 15 inches being shown on the result line.
Another method is to perform the division only partially and retain the remainder. For example, 7 divided by 2 is 3 with a remainder of 1. These difficulties are avoided by rational number arithmetic, which allows for the exact representation of fractions. [75] A simple method to calculate exponentiation is by repeated multiplication.
The Electronic Delay Storage Automatic Calculator (EDSAC) was an early British computer. [1] Inspired by John von Neumann 's seminal First Draft of a Report on the EDVAC , the machine was constructed by Maurice Wilkes and his team at the University of Cambridge Mathematical Laboratory in England.
The process of substituting remainders by formulae involving their predecessors can be continued until the original numbers a and b are reached: r 2 = r 0 − q 2 r 1 r 1 = b − q 1 r 0 r 0 = a − q 0 b. After all the remainders r 0, r 1, etc. have been substituted, the final equation expresses g as a linear sum of a and b, so that g = sa + tb.
The county council was elected by and provided services to the remainder of the county outside those two boroughs, which area was termed the administrative county. [4] Shirehall, Market Avenue, Norwich: Council's meeting place 1889–1968. The first elections were held in January 1889, and the council formally came into being on 1 April 1889.
The last rule can be used to move modular arithmetic into division. If b divides a, then (a/b) mod m = (a mod b m) / b. The modular multiplicative inverse is defined by the following rules: Existence: There exists an integer denoted a −1 such that aa −1 ≡ 1 (mod m) if and only if a is coprime with m.
Derek J. de Solla Price (1922–1983) with a model of the Antikythera mechanism. Captain Dimitrios Kontos (Δημήτριος Κοντός) and a crew of sponge divers from Symi island discovered the Antikythera wreck in early 1900, and recovered artefacts during the first expedition with the Hellenic Royal Navy, in 1900–01. [32]