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Arithmetic or arithmetics in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though in usage by professional mathematicians, it often is treated as synonym for number theory.

The traditional arithmetic operations are addition, subtraction, multiplication and division, although more advanced operations (such as manipulations of percentages, square root, exponentiation, and logarithmic functions) are also sometimes included in this subject. Arithmetic is performed according to an order of operations.

The arithmetic of natural numbers, integers, rational numberIn mathematics, a rational number (or informally fraction is a ratio of two integers, usually written as the vulgar fraction a ''b where b is not zero. The set of all rational numbers is denoted by Q or in blackboard bold. Using the set-builder notation is (in the form of fractionIn common usage a fraction is any part of a unit. In mathematics: A vulgar fraction is a rational number written as one integer (the numerator divided by a non-zero integer (the denominator . The line that separates the numerator and the denominator is cas), and real numberIn mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to " imaginary number". Real numbers mays (using the decimalDecimal also called denary is the base 10 numeral system, which uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 (called digits) together with the decimal point and the sign symbols + (plus) and − (minus) to represent numbers. Decimal is the princip place-value system known as algorismAbu Abdullah Muhammad bin Musa al-Khwarizmi Algorism is the name for the Indo-Arabic decimal system of writing and working with numbers, in which symbols (the ten digits 0 through 9) are used to describe values using a place-value system ( positional nota) is typically studied by schoolchildren, who learn manual algorithmFlowcharts were often used to represent algorithms. An algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will result in a corresponding recognisable end-state (contrast with heuristic). Algors for arithmetic. However, in adult life, many people prefer to use tools such as calculatorA calculator is a device for performing numerical calculations. It should not be confused with a calculating machine. Nowadays many people have a calculator with them as part of their mobile phone and/or personal digital assistant. Engineers and accountans, computertower of a personal computer. A computer is a device for making calculations or controlling operations that are expressible in numerical or logical terms. While factually accurate, this definition and those found in other dictionaries are so broad that ths, or the abacus to perform arithmetical computations.

The term arithmetic is also used to refer to number theory. This includes the properties of integers related to primality, divisibility, and the solution of equations by integers, as well as modern research which is an outgrowth of this study. It is in this context that one runs across the fundamental theorem of arithmetic and arithmetic functions. A Course in Arithmetic by Serre reflects this usage, as do such phrases as first order arithmetic or arithmetical algebraic geometry.