Arithmetic

From ArticleWorld

The word arithmetic is derived from the Greek word "arithmētikē" which means "counting". In common usage, arithmetic refers to the branch of mathematics that deals with the basic operations of addition, subtraction, multiplication and division. Professional usage of the term refers to the branch of pure mathematics known as number theory, which deals with the properties of numbers and the relationships between them.

History

Basic arithmetic has been in use since the time of ancient civilisations. The Babylonians circa 1850 BCE are known to have had a thorough knowledge of elementary arithmetic. Also, the people of Ancient Egypt (before 1600 BCE) developed an algorithm for multiplication and knew how to use fractions for computation. In the 6th century BCE, arithmetic was considered to be one of the four mathematical sciences by the Pythagorean School in Greece.

Ancient mathematicians found it tough to deal with the number systems used prior to the invention of the decimal system. The Greek mathematician Archimedes (d. 212 BCE) wrote the work "The Sand Reckoner" in an attempt to count extremely large integers. Euclid (d. 265 BCE), another Greek mathematician, did not rely on analytic geometry (which deals with geometry using numerical principles) but on synthetic or non-numerical constructions because Greek arithmetic was inefficient in operating on real numbers. As opposed to this, mathematics developed rapidly in the Islamic world and in Europe after the 5th century CE due to the use of the decimal system. Modern algorithms for both manual and electronic computation were facilitated through the use of this number system, also known Arabic numerals. These numbers are taken for granted now, in spite of being the result of tremendous efforts by mathematicians through a long course in history.

Arithmetic operations

There are four basic operations in arithmetic: addition, subtraction, multiplication and division. More advanced operations include logarithms, square roots, powers and so on.

1. Addition: This is the process of combining two or more numbers (known as the addends) into a single number (the sum). It is denoted by +.
2. Subtraction: This is the process of deducting one number (known as the subtrahend) from another (known as the minuend). It is the opposite of addition. This operation is denoted by −.
3. Multiplication: This operation is basically repeated addition; it finds the product of two numbers known as the multiplier and the multiplicand. It is denoted by × or *.
4. Division: The opposite of multiplication, division finds the number of times (the quotient) one number (the divisor) is contained in another (the dividend). It is denoted by ÷ or /.