Difference Between Algebra and Arithmetic

Arithmetic and Algebra are two different branches of mathematics , for this reason it is important that we can distinguish what each one consists of. Difference Between Algebra and Arithmetic

ARITHMETIC  Difference Between Algebra and Arithmetic

The very term “Arithmetic” derives from a Greek word that means  number . It is the most basic branch of Mathematics and covers everything that has to do with numbers, therefore, it is used by people in their day to day life. Traditional Arithmetic works around the four main operations, which are: addition, subtraction, multiplication and division. It simply takes care of various types of calculations using numbers.

Higher Arithmetic is also known as number theory. This has to do with the characteristics of whole numbers, rational numbers, irrational numbers, and real numbers.


On the other hand, Algebra is another branch of Mathematics. The word derives from Arabic (it was the Arabs who contributed the most to this branch)  al-Jabr,  which is an ancient medical term whose meaning could be said to be “reunion of broken pieces.” Algebra can be considered as the second level in Mathematics, after Arithmetic. Unlike the first one, this one works with unknown values ​​that are combined with the numbers.

An algebraic operation can be easily identified by symbols like X, Y, A, B. These are usually the main variables to work with in algebraic operations. Algebra has to do with the rules that are followed to manipulate or work with arithmetic operations.

Also, it involves algorithms and complex numbers. Uses products and factoring, formal theorems, and quadratic binomials; among others, to get to solve the equations.

For instance:

3 + 3 = 6 (it is an arithmetic expression).

x = 3 (it is an algebraic expression).

In short, it can be said that Arithmetic deals with the calculation of certain numbers, while Algebra deals with the generalization of some conditions that are true for all integers. Unlike elementary arithmetic, elementary algebra uses letters as variables to solve problems; however, higher arithmetic makes use of letters in the same way as it does in the rest of the branches of mathematics.

Key difference between Algebra and Arithmetic

  • Arithmetic, being the most basic of the branches of mathematics, deals with the basic analysis of numbers; by using operations such as addition, subtraction, multiplication, and division. While Algebra, becomes the second level among the branches of mathematics and uses both numbers and variables to solve problems. It is based on widespread application for troubleshooting.

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