Algebra vs. Arithmetic: How do they differ?

Algebra vs. Arithmetic
Algebra vs. Arithmetic

As a teacher, I discovered that the word “mathematics” alone is enough for many people to send shivers down their spine. But when it comes to mathematics, there are two main areas: algebra and arithmetic. While they may seem like interchangeable terms, they are very different from one another.

So, algebra vs. arithmetic, how do they differ? Arithmetic is the branch of mathematics that studies the computation of specific numbers and essential operations, including addition, division, subtraction, and multiplication. On the other hand, algebra is a branch of mathematics that studies mathematical symbols and the rules for manipulating these symbols, such as using variables.

Read on to explore the differences between the two and help you make an informed decision. If you also want to understand the differences and similarities between arithmetic and calculus.

What Is Algebra?

Algebra is all about finding the unknown. It involves equations and variables wherein we try to solve for the value of an unknown variable. Algebra is not only about numbers but also about symbols and letters. It allows us to solve problems more simply by using an equation instead of a word problem.

Algebra is perfect for individuals who enjoy playing with numbers and finding solutions to complex problems. It is essential for students who wish to pursue higher studies in mathematics, engineering, or physics.

If you are looking to build strong foundations I encourage you to check out Khan Academy. For more about algebra, watch the video below.

What Is Arithmetic?

Arithmetic is the study of numbers and their manipulation; it is the branch of mathematics that deals with basic mathematical operations like addition, subtraction, multiplication, and division. Arithmetic is essential to perform day-to-day tasks, such as calculating bills, managing finances, and calculating interest rates.

Arithmetic requires less background knowledge than algebra, and its simplicity makes it the perfect subject for young children who are just beginning to learn mathematics.

If you want to want to learn more about arithmetic, I encourage you to check out Khan Academy or watch the video below.

Differences Between Arithmetic and Algebra

Arithmetic is a field of mathematics that deals with numbers and how to combine them using math operations, including addition, subtraction, multiplication, and division. Advanced algebra differs from arithmetic because, in addition to specific numbers, it also involves variables with no particular value or an unknown value (Source: University of Utah)

Furthermore, an algebraic expression is a collection of letters and numbers connected by the four primary arithmetic operations. 

At first glance, algebra and arithmetic seem similar, but they are not the same. The two subjects differ in many ways, and here are their differences and similarities.

Arithmetic is the study of numbers and operations such as addition, subtraction, multiplication, and division. It is the foundation for more advanced mathematics concepts. On the other hand, algebra is the study of mathematical equations and their solutions. It involves the use of letters and symbols to represent values, making it more abstract than arithmetic.

Arithmetic and algebra are essential tools for any math student’s daily life and academic journeys.

One key difference between arithmetic and algebra is the type of problems they solve. Arithmetic deals with numerical problems that involve real numbers.

Algebra solves problems that may have unknown variables and abstract concepts, such as solving for x in an equation like 2x +5 = 13. Algebra helps students understand the relationship between unknown quantities and how they can be solved using a set of rules.

Another difference is the level of complexity in both subjects. Arithmetic is the more straightforward of the two, limited to basic operations such as addition, subtraction, multiplication, and division. Algebra requires a more advanced level of thinking, including logical reasoning and problem-solving skills.

Algebraic problems often require multiple steps and advanced manipulation of formulas and equations.

Moreover, algebra and arithmetic are also used differently in real-life situations. Arithmetic is used in everyday tasks such as calculating the bill amount, determining change, or figuring out the cost of an item on sale. Algebraic concepts are used in engineering, physics, computer science, and other fields that require abstract reasoning and problem-solving skills.

While Algebra and Arithmetic have unique uses, it ultimately depends on your goal. Algebra is perfect for individuals who wish to pursue higher studies in mathematics, engineering, or physics, as it provides the foundation for these study areas.

On the other hand, arithmetic is essential to perform day-to-day tasks and is a life skill that every person must know. Nevertheless, whatever field you decide to pursue, Arithmetic will always continue to be necessary.

Even though students tend to associate algebra with just number and letter concepts, it also helps students develop their critical thinking abilities. Algebra teaches students how to unravel complex problems and develop a structured solution supported by evidence.

Algebra also enhances spatial reasoning, problem-solving, and logical thinking. In turn, all these skill sets become essential to succeed in any field you choose to pursue.

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Closing Thoughts

I believe that both algebra and arithmetic are essential tools for math students. Arithmetic provides the groundwork for understanding numbers, while algebra builds on this foundation to address more complex problems.

Arithmetic is the study of the basic principles that govern numbers, and everybody must be competent in it to perform daily life activities. Algebra provides a foundation for learning complex mathematics, which is essential for engineering, physics, and mathematics careers.

While algebra provides a solid foundation for other mathematical concepts, arithmetic remains an essential life skill. Everyone must strive to gain skills and knowledge in both fields to become well-rounded individuals.


I am Altiné. I am the guy behind When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting

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