Arithmetic vs Mathematics  Math vs Arithmetic
Many people think that the words ‘arithmetic’ and ‘mathematics’ mean the same. What is mathematics? Mathematics is a difficult term to define as it covers many areas. Mathematics can be defined as the study of measurements and properties of quantities using numbers and symbols. Mathematics also includes proofs of theorems, other than the numbers and symbols. Arithmetic is a branch of mathematics that deals with properties of numbers.
Arithmetic
Arithmetic is the oldest, most basic and fundamental category in mathematics, that involves basic calculations with numbers. The four elementary operations in arithmetic are addition, subtraction, multiplication and division. Therefore, arithmetic can also be defined as the mathematics of numbers (real numbers, integers, fractions, decimals and complex numbers) under the operation of addition, subtraction, multiplication and division. The order of operation is given by BODMAS rule (or PEMDAS rule).
For many years, arithmetic has been a part of human life. For example, they use it in their day today life activities such as counting, purchasing and preparing their accounts and budgets. It is often used in some higher level scientific or mathematical calculation as well.
Mathematics
Mathematics is a very broad field, which is used as an essential tool in many fields. It is not specific. There are two main branches of mathematics; applied mathematics and pure mathematics. Also, it can be categorized as arithmetic, algebra, calculus, geometry and trigonometry.
What is the difference between Arithmetic and Mathematics? Arithmetic: • use numbers for calculation. • deals with four basic operations; addition, subtraction, multiplication and division. Whereas, Mathematics: • is the study of measurements and properties of quantities. • use numbers, symbols and proofs for explanations

David Goloff, PhD says
There are many areas of mathematics that fall outside your definition: Logic, Set Theory, Abstract Algebra, Geometric Ideas transcend measurement. I agree that – for the person familiar with arithmetic – your definition of mathematics would be comprehensible and move their mind in the right direction. Perhaps that was your intention. So what definition would I propose? In my mind it is a focus on the structure apart from the thing having the structure. But I am not sure that is correct or all inclusive. I would be very interested in what others have to say in general or propose as a definition of “mathematics” as distinct from any particular mathematical subject. I will check back.
Dairn says
It was my impression that this commenter was an expert on the subject who I felt enhanced the depth of this article. It’s one of the reasons why I like to read the comments sections on the interweb. But my favorite part is found in the meta lesson. The article was useful in calling attention to a distinction between two things which I hadn’t really put much thought into, and then comfortable in resolving the issue with an efficient explanation. The comment then added weight to the question, along with the framework to support it. This shed more light on the subject for a better view of an expanded landscape. The irony is that in taking things to the next level, it did not secure my understanding with the reinforcement of knowledge. Rather, the altitude made my head spin. Sure, I could see further standing on top of a ladder, but I also had my hands full with the weight of all that information! And not to put myself down (too much), but even the expert admitted, “But I am not sure that is correct or all inclusive.” Still, when all is said and done, I still prefer the angst of examination over the bliss of ignorance. Pretty stupid, huh? ;+D
Frank Q says
I love the previous comments. This will be my first mathematics discussion, which I’m excited about.
Mathematics and arithmetic used to be a big challenge for me. I bought into the idea that “I’m just not good at math”, even though I was still extremely fascinated by it. I believe the stigmatization of mathematics is something that is perpetuated by our culture. That changed a few years ago, when I read how the approach to math in this country is all wrong. So I began to believe and hope that I could truly improve not only my perspective and understanding on mathematics, but that I could also improve and understand more complex math.
I’ve finally started that journey. This was kickstarted by homeschooling my children, which brought math back into my life, and the current book I’m reading Mathematics For Human Flourishing by Dr. Francis Su.
Just a few minutes ago, I decided to find out the difference between mathematics and arithmetic.
From my understanding, arithmetic is a subset of mathematics that uses “simple” calculations such as addition, subtraction, multiplication, and division, to arrive at an answer. Arithmetic is used in our daily lives. In other words, it’s very practical.
Mathematics, however, includes these operations, but it also transcends them. Mathematics goes much broader and deeper than the aforementioned calculations, by using symbols and methods along with logic and reasoning to arrive at an answer. It can go beyond the practical, into the theoretical.