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What is the difference between Arithmetic and Algebra?

  • Last Updated : 17 Aug, 2021

Arithmetic is a mathematics operation concerned with numeral systems and their operations. It has been traditionally applied to get a definite single value. The term got its origin from the Greek word “arithmos” which means numbers. The traditional operations associated with arithmetic include addition, subtraction, multiplication, and division. These operations are being carried out in the field of trading, marketing, and monetization for centuries.

Arithmetic is the elementary branch of mathematics that specifically deals with the study of numbers and properties of traditional operations like addition, subtraction, multiplication, and division.

Besides the traditional operations of addition, subtraction, multiplication, and division arithmetic also include advanced computing of percentage, logarithm, exponentiation and square roots, etc. The article is focused on the study and explanation of these basic types of arithmetic operations.

History  of Arithmetic

  • The 17th-century Indian mathematician Brahmagupta is the “father of arithmetic”.
  • Carl Friedrich Gauss in 1801, provided the Fundamental principle of number theory.

Types of basic Operations in Arithmetic

The four basic operations of arithmetic that is addition, subtraction, multiplication, and division are discussed below:

Addition (+)

The simple definition for addition will be that it is an operation to combine two or more values or numbers into a single value. The process of adding n number of values is called summation.

0 is said to be the identity element of addition as while adding 0 to any value it gives the same result. For example, if we add 0 to 5 the result would be the same that is 5.

0 + 5 = 5

And, the inverse element includes the addition of the opposite value. The result of adding inverse elements will be an identity element that is 0. For example, if we add 3 with its opposite value -3, then the result would be

3 + (-3) = 0

Subtraction (-)

Subtraction is the arithmetic operation that computes the difference between two values (i.e. minuend minus the subtrahend). In the condition where the minuend is greater than the subtrahend, the difference is positive. It is the inverse of addition.

4 – 1 = 3

While, if the subtrahend is greater than minuend the difference between them will be negative.

1 – 4 = -3

Multiplication (×)

The two values involved in the operation of multiplication are known as multiplicand and multiplier. It combines two values that is multiplicand and multiplier to give a single product.

The product of two values supposedly a and b is expressed in a.b or a × b form.

2 × 3 = 6

Division (÷)

The division is the operation that computes the quotient of two numbers. It is the inverse of multiplication. The two values involved in it are known as dividends by the divisor and if the quotient is more than 1 if the dividend is greater than the divisor the result would be a positive number.

6/3 = 2


Algebra is generally connected to high school education. We do not use it in our daily life calculations like arithmetic more often. But the algebraic application can be seen all around. Imagine measuring the height of a building, if we know the distance how far it is from any other object nearby of any height. The height of the building can be easily determined with the help of algebraic expression.

Algebra is a branch of elementary mathematics which is concerned with relation of  variables and constants.

Algebraic expressions consist of variables, constants, and fundamental signs of addition, subtraction, multiplication, and division. Each expression connected by these signs is referred as terms of the expression.

History of Algebra

  • The origin of algebra was traced by Babylonians in 1900BC.
  • The Persian mathematician Al-Khwarizmi is referred as the ‘father of algebra’.

Types of Algebraic Expressions


The algebraic expressions having only one term are known as monomials. For example: 5x,10xy, etc.


The algebraic expressions having two unlikely terms are known as binomials. For example: 5xy + 3, 2x + y, etc


The algebraic expressions with more than two terms are known as polynomials. For example: ab+bc+ca,etc

Difference between Arithmetic and Algebra

S No.



1It is the branch of mathematics that deals with numbers, their writing systems, and their properties.It is the branch of mathematics that deals with variables and constants.
2The operations are carried out with the help of the information provided.The operations are carried out with the help of standard formulae and expressions.
3It is generally applicable in real life and associated with elementary education.Its direct application is not often observed in daily life and is associated with high school education.
4It has four basic methods of operation (addition, subtraction, multiplication, and division).It uses numbers, variables, and general rules or formulae to solve problems.
5It is related to the numbers and number systems.It is related to equations and formulae.

Sample Problems

Question 1: Who is known as the father of algebra?


The Persian mathematician Khwarizmi is known as the father of algebra.

Question 2: What are the application of arithmetics in real life?


The arithmetics is used for the purpose of computing, 

  • data analysing
  • basic calculations
  • monetization
  • sales, trade
  • measurement, etc

Question 3: List the branches of mathematics?


The major branches of mathematics are:

  • Algebra
  • Geometry
  • Trigonometry
  • Calculus
  • Arithmetic

Question 4: What are the types of algebraic equations?


The types of algebraic equations are listed below:

  • Polynomial equation
  • Quadratic equation
  • Cubic equation
  • Rational equation
  • Trigonometric equation

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