Basic Arithmetic Operations: The Four Fundamental Operators

Just like Julie Andrews told us in The Sound of Music, we should “start at the very beginning” because it’s “a very good place to start.” In math, we don’t start with Do-Re-Mi, but we do build on the fundamentals known as arithmetic operations!

Mastering arithmetic operations means setting a strong foundation for a lifetime of successful math learning, so we strongly encourage taking the time to really commit to these skills!

If you’re looking for more of a broad overview of the arithmetic branch of mathematics, let’s take a step back so we can go through arithmetic as a whole first.

Ready to get started with arithmetic operations?

First of all, what is “arithmetic operations”?

Arithmetic operations are the building blocks for all mathematical processes and methods. (Yeah, they’re kind of a big deal!) These types of operations are part of the “arithmetic” branch of math.

Arithmetic operations strip math down to the basics that we use every day, whether we realize it or not. Those basics are addition, subtraction, multiplication, and division.

Not so scary, right?

Basic arithmetic

You’ll sometimes hear arithmetic operations referred to as “basic arithmetic,” meaning the most fundamental mathematical operations.

Fundamental arithmetic operations

The fundamental arithmetic operations are typically thought to be addition, subtraction, multiplication, and division.

We’ll dive into each more thoroughly in a moment!

Some schools will also include comparing numbers and evaluating powers (or exponents) as part of arithmetic operations. If you’re not there yet, don’t worry! Everyone moves at their own pace — and we can always help you when you do get there.

The four basic operations of math

Whether you’re balancing your checkbook or ordering pizza for a party, chances are you’re using some of the four basic arithmetic operations daily.

But sometimes, when something is so second-nature, it can be hard to explain it well. Here’s a table of terms and examples that you can use when describing the four basic operations:

Operation Verb Example Result vocabulary
Addition Add $$1 + 1 = 2$$ The result of addition is the “sum”
Subtraction Subtract $$3 - 2 = 1$$ The result of subtraction is the “difference”
Multiplication Multiply $$displaylines{4 × 2 = 8 \\ 2 * 3 = 6 \\ 5 ⋅ 2 = 10}$$ The result of multiplication is the “product”
Division Divide $$\displaylines{12 ÷ 3 = 4 \\ 10/2=5}$$ The result of division is the “quotient”

Now that we know more about each operation, we can drill down even further and take a look at each operation’s operator.

What are arithmetic operators?

Arithmetic operators are the symbols we see in math problems that represent an action we should take. They’re like little math GPS instructions, telling us what needs to happen in order for us to reach our final destination.

In other words, the operator tells us which operation to perform! For example, the $$-$$ operator tells us that we should subtract.

Let’s look at each operator a little more closely:

Arithmetic operators: a guide

Learning arithmetic operators (and their related operations) is like learning to drive a car — you need know which pedal does what before you can hit the gas and start steering.

Here’s a handy chart explaining what each operator means and how it might look on the page:

Operator Operation
$$+$$ Addition
$$-$$ Subtraction
$$×, *, ⋅$$ Multiplication
$$÷ , /$$ Division

Sometimes, you’ll see more than one operator in the same problem. If those operators are different — for example, a “+” and a “÷” in the same problem — you’ll need to follow the PEMDAS structure.

As a reminder, PEMDAS stands for:

  1. Parentheses
  2. Exponents
  3. Multiplication (left to right)
  4. Division (left to right)
  5. Addition (left to right)
  6. Subtraction (left to right)

Arithmetic operations examples

Understanding the context behind arithmetic operations will help strengthen learning, but the thing that will really cement these skills is trying them out! Working through problems — and, honestly, getting a few wrong — ensures that the learner is fully involved.

So, when you’re ready, try solving these example problems:

  1. $$3 + 4$$
  2. $$6 ÷ 2$$
  3. $$2 \times1$$
  4. $$8 – 5 + 2$$
  5. $$3 \times4 – 1$$
  6. $$\frac{4}{2} + \frac{6}{3}$$
  7. $$5 – 1 + 3$$
  8. $$7 \times 3 \times 2$$
  9. $$12 ÷ 3 + 5$$
  10. $$2 \times 0$$

Having trouble? That’s okay! Whether we like it or not, feeling uncertain or stuck is actually part of the learning process. The good news is that you don’t have to stay stuck! Scan the tricky problem with your Photomath app and we’ll walk you through each step.

P.S.: You can also check your answers to the example problems by scanning them with the app!

Here’s what it looks like:

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One more thing: Which two basic arithmetic operations are commutative?

Addition and multiplication are known as “commutative” (in other words, they follow the Commutative Property). This means that you can switch the order of the numbers and still get the same result.

You might notice this when you work through the example problems, but the Commutative Property means that $$2 + 3$$ equals the same sum as $$3 + 2$$. Likewise, $$4 \times 5$$ gets us the same product as $$5 \times4$$ would.

However, this does not mean that we can switch between addition and multiplication. For example, $$2 + 3 4$$ is not the same as $$2\times34$$. That’s why PEMDAS is so important!

We hope that, by now, you’re feeling a little more at ease with arithmetic operations. The math itself isn’t too intimidating, so as long as you have a strong understanding of the terms and symbols, you’re ready to take on arithmetic operations!

When you’re ready to advance beyond the four basic operations, we can also teach you more about comparing numbers and evaluating powers!

No matter where you are in your math journey, if you find yourself stuck with a tricky problem in front of you, all you have to do is scan it with your Photomath app — from there, we can describe each step of the solving process in detail. That way, nothing gets missed or forgotten, and you have an expert roadmap for next time.

Remember: Math doesn’t have to be stressful, because we’re always on your team!

Got arithmetic homework?

Head over to the Photomath app for instant, step-by-step solutions to all of your arithmetic problems.