# What Is Arithmetic?

Arithmetic is the study of mathematics that focuses on the numerical manipulation of numbers using primarily five kinds of operations such as addition, subtraction, multiplication, division and the extraction of roots. The axiom or rule of arithmetic is derived from two fundamental operations – addition and multiplication. When we add two or more numbers, we get the value called sum. In a similar fashion, we two or more numbers are multiplied, the result is called product. The axiom of arithmetic involves the rule for basic operations that are applicable to whole numbers, integers, rational and irrational numbers, in a single word, to all the real numbers. Whole numbers are also known as natural numbers. Whole numbers include positive numbers and zero. Integers include negative numbers as well as positive numbers where zero is in the middle of the number continuum. Rational numbers are defined as the ratio of two integers, whereas, irrational numbers cannot be expressed as the ratio of two integers, for example, square roots of numbers which are not perfect squares.

Historically, the researchers have found that the initial significance of arithmetic had been realized during the third century B.C.
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Arithmetic mean is a type of an average. The arithmetic mean of a set of a data is calculated by adding all the observations of a data and divided it by total numbers of observations.

Arithmetic mean = sum of all observations/ number of observations

If an arithmetic mean is calculated for a population, it is known as population mean. If arithmetic mean is calculated for a sample, then it is called sample mean. A sample mean shows the common results of a target population. The population mean is represented by a Greek letter 'Meu'. The sample mean is represented by 'x bar'. According to the properties of distribution of sample mean, the arithmetic mean of a sample mean is equal to the population mean.
thanked the writer. 