Contents 1 History
2
2.1
3
4.1 Basic arithmetic operations 4.2 Principles of compound unit arithmetic 4.3 Operations in practice 5
7.1 Related topics 8 Notes 9 References 10 External links History[edit]
The prehistory of arithmetic is limited to a small number of artifacts
which may indicate the conception of addition and subtraction, the
best-known being the
Leibniz's
Although the
If we have two sticks of lengths 2 and 5, then if we place the sticks one after the other, the length of the stick thus formed is 2 + 5 = 7.
Reduction where a compound quantity is reduced to a single quantity, for example conversion of a distance expressed in yards, feet and inches to one expressed in inches.[14] Expansion, the inverse function to reduction, is the conversion of a quantity that is expressed as a single unit of measure to a compound unit, such as expanding 24 oz to 1 lb, 8 oz. Normalization is the conversion of a set of compound units to a standard form – for example rewriting "1 ft 13 in" as "2 ft 1 in". Knowledge of the relationship between the various units of measure, their multiples and their submultiples forms an essential part of compound unit arithmetic. Principles of compound unit arithmetic[edit] There are two basic approaches to compound unit arithmetic: Reduction–expansion method where all the compound unit variables are
reduced to single unit variables, the calculation performed and the
result expanded back to compound units. This approach is suited for
automated calculations. A typical example is the handling of time by
UK pre-decimal currency 4 farthings (f) = 1 penny 12 pennies (d) = 1 shilling 20 shillings (s) = 1 pound (£) The addition operation is carried out from right to left; in this case, pence are processed first, then shillings followed by pounds. The numbers below the "answer line" are intermediate results. The total in the pence column is 25. Since there are 12 pennies in a shilling, 25 is divided by 12 to give 2 with a remainder of 1. The value "1" is then written to the answer row and the value "2" carried forward to the shillings column. This operation is repeated using the values in the shillings column, with the additional step of adding the value that was carried forward from the pennies column. The intermediate total is divided by 20 as there are 20 shillings in a pound. The pound column is then processed, but as pounds are the largest unit that is being considered, no values are carried forward from the pounds column. For the sake of simplicity, the example chosen did not have farthings. Operations in practice[edit] A scale calibrated in imperial units with an associated cost display. During the 19th and 20th centuries various aids were developed to aid
the manipulation of compound units, particularly in commercial
applications. The most common aids were mechanical tills which were
adapted in countries such as the United Kingdom to accommodate pounds,
shillings, pennies and farthings and "Ready Reckoners" – books
aimed at traders that catalogued the results of various routine
calculations such as the percentages or multiples of various sums of
money.
Lists of mathematics topics Mathematics Outline of arithmetic Slide rule Related topics[edit]
Notes[edit] ^ Davenport, Harold, The Higher Arithmetic: An Introduction to the
Theory of Numbers (7th ed.), Cambridge University Press, Cambridge,
1999, ISBN 0-521-63446-6.
^ Rudman, Peter Strom (2007). How
References[edit] Cunnington, Susan, The Story of Arithmetic: A Short History of Its
Origin and Development, Swan Sonnenschein, London, 1904
Dickson, Leonard Eugene,
External links[edit] Look up arithmetic in Wiktionary, the free dictionary. Wikibooks has more on the topic of: Arithmetic Wikimedia Commons has media related to Arithmetic. Wikiquote has quotations related to: Arithmetic MathWorld article about arithmetic
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