Arithmetic operations
The basic arithmetic operations are addition, subtraction, multiplication and division, although this subject also includes more advanced operations, such as manipulations of percentages, square roots, exponentiation, and logarithmic functions.
Arithmetic is performed according to an order of operations. The standard order of operations, or precedence, is expressed in the following chart:
- terms inside brackets
- exponents and roots
- multiplication and division
- addition and subtraction
This means that if a number or other symbol, or an expression grouped by one or more symbols of grouping, is preceded by one operator and followed by another, the operator higher on the list should be applied first.
Any set of objects upon which all four arithmetic operations (except division by zero) can be performed, and where these four operations obey the usual laws, is called a field. In abstract algebra, a field is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms. The most commonly used fields are the field of real numbers, the field of complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, various algebraic number fields, p-adic fields, and so forth.
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