Arithmetic

From Wikinfo

Arithmetic is the foundation of mathematics. It dates historically back through the Romans and Greeks to earlier times, when not everyone was educated. In those days it was thought to be an art but has become more recognized as a skill. The Romans, of course, worked with Roman numerals, and it was a profession to count up the number of troops and make a mark to represent that. To multiply the number of soldiers in one garrison times three garrisons took a professional. Arithmetic wasn't intuitive for the Romans. Today we use ten symbols including a zero, thanks to the arabs who got it from the Hindus. This is a more intuitive number system than Roman numerals and is much, much easier when using arithmetic.

But before arithmetic

To understand arithmetic a person must first understand symbolization; which is the idea that a symbol can represent or stand for, an object. The symbols arithmetic uses are numbers that represent quantity. Further, a person must then understand the idea of enumeration; the idea that a quantity of objects can be counted up and that quantity be represented by a symbol.

Arithmetic is the manipulation of symbols that stand in place of objects. Rather than manipulate objects, we manipulate numbers that stand for them. It is a manipulation of numbers according to rules in such a way that real, physical objects would be accurately represented if we did the same with real objects. For example, if giving every student a cupcake in a class of thirty students, arithmetic says that thirty cupcakes would be necessary. If every student received two pairs of socks, then 120 socks. If half of a cookie, 15 cookies.

Arithmetic Operations

The manipulations are called operations. They are addition, subtraction, multiplication and division. The idea of division brings along the idea of dividing a whole unit, such as a cake, into portions and introduces fractions. Operations are done with fractions of a whole object very much like operations are done with whole objects. Arithmetic includes exponentiation (a number times itself, some number of times). A square roots is a number which, if multiplied times itself, is the number we begin with, the number we are taking the root of. Square roots are a specific operation of the larger class of operations called roots, there exit cube roots and forth roots, and so on. Some applications of arithmetic require that several different operations be performed, such as multiplying quantities and then adding some bit to that product. Arithmetic is performed according to an order of operations.

Advanced arithmetic

The arithmetic of natural numbers, integers, rational numbers and real numbers is typically studied by school children in the elementary grades. Representations of numbers in terms of percentages are generally studied then as well. Calculators have increased the ease by which we perform arithmetical computations.

The term "arithmetic" is also used to refer to elementary number theory; it's in this context that one runs across the fundamental theorem of arithmetic and arithmetical functions.

See also: