Difference Between Algebra and Arithmetic

It is known that the word mathematics comes from the Greek -mathema-, which means science, knowledge or learning. According to this statement, it can be said that mathematics is a science that studies the properties of abstract entities such as: numbers, geometric figures, shapes, among others, as well as the relationships established between them.

Mathematics is a science of great use for human life, because, through them, decision-making, logical thinking, exchange with other people and societies, among others, have been developed. This science has different branches that are responsible for the study of more specific elements, among them, we can mention arithmetic, algebra, function analysis, geometry, statistics and probability, among others.

Each of these branches has specific and differentiated fields of action. The object that concerns us is to establish the differences between two of those branches that are algebra and arithmetic , branches that tend to be confused because both work with numbers but in reality they are in charge of different processes which we will see next. .


Algebra is a branch of mathematics that deals with the study of operational properties of known numbers and unknown values. In this branch, operations are performed through the use of numbers, letters and symbols which can represent another number or another mathematical operation.

For example : the equation Y = 5 is an algebraic expression.


Arithmetic is the branch of mathematics that deals with the exclusive study of numbers and the operations performed with them. It can be said that it is the most elementary of all the branches of mathematics since its main operations are addition, subtraction, multiplication and division.

For example : the equation 3 + 2 = 5 is an arithmetic operation.

As has been seen in the previous definitions and examples, both algebra and arithmetic are two branches that are of great importance within mathematics but differ from each other.

Below is a table that highlights the most important differences between algebra and arithmetic:

Algebra Arithmetic
It deals with operations with numbers, letters and symbols. It handles operations with numbers.
Study various types of equations with quantities and operations expressed in numbers, letters or symbols. Study the composition and decomposition of quantities expressed in numbers.
It can be said that it belongs to the second level of branches of mathematics, since it is a science that includes complex operations. It can be said that it belongs to the first level of branches of mathematics since it is a science that includes basic operations.
Algebra is expressed in numbers, symbols, or letters. These symbols or letters represent values, equations or other operations. Arithmetic is expressed in numbers. These numbers represent certain values.
Algebra deals with variable values. For example: -Y- can be 7, 5 or 12, depending on the equation you want to represent. Arithmetic deals with specific numbers. For example: 7 , is always seven.

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