**Algebra vs. Arithmetic**

What is the Difference between Algebra and Arithmetic? Arithmetic and Algebra are two different branches of mathematics, so it is important that we can distinguish what each one consists of.

**What is Difference between Algebra and Arithmetic**

**Arithmetic**

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

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

**Algebra**

On the other hand, Algebra is another branch of mathematics. The word derives from Arabic (it was the Arabs who contributed most to this branch) al-Jabr, which is an old 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 former, it works with unknown values that are combined with numbers.

Algebraic operations can easily be identified by symbols such as X, Y, A, B … These are usually the main variables for working in algebraic operations. Algebra has to do with the rules that are followed to manipulate or work with arithmetic operations.

In addition, it involves complex algorithms and numbers. It uses products and factorization, formal theorems and quadratic binomials; among others, to get to solve the equations.

For example:

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

x = 3 (it is an algebraic expression).

In short, we can say that Arithmetic is about the calculation of certain numbers, while Algebra is about 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. The key difference between arithmetic and algebra is:

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