Operations with Integers: Add, Subtract, Multiply & Divide

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: What are Variables in Math? - Definition & Examples

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:03 Basic Mathematical Operations
  • 0:35 Addition
  • 2:30 Subtraction
  • 4:00 Multiplication
  • 5:15 Division
  • 5:45 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Read this lesson to learn about the four basic arithmetic operations you can perform with integers. You'll also learn how you can visualize these operations in your head.

Basic Mathematical Operations

Add, subtract, divide and multiply...oh my! While thinking about working out math problems using these four basic mathematical operations might seem scary, math is actually not as complicated as it may seem. While there are many different types of numbers such as decimals, fractions and percentages, in this lesson we are going to look at using the four basic operations with integers, which are our whole numbers - both positive and negative.

Let's get started with the easiest of all operations - addition.


Adding integers is pretty straightforward. If it helps, you can think of your integers as dollar bills. Or, if you are comfortable with your number line, you can use that instead. So, a 3 would be $3 or 3 spaces to the right of 0 on the number line. Remember, positive integers go to the right and negative integers go to the left.

integer operations

For example, if you add a 2 to your 3, you will be going 2 spaces further to the right. You'll be at the number 5. If you think in money terms, you are adding $2 more to your current $3. So, you'll now have $5.

Since your integers can be both positive and negative, it is possible that you'll be asked to add a negative integer such as this:

  • 3 + ( - 2 )

When you are adding a negative number you are actually subtracting and, therefore, you'll need to go to the left on the number line. So you go 2 spaces to the left and you end up at 1. Take a look at the image below to see the sign rules for integers.

Integer Sign Rules for Addition and Subtraction

It is a great idea to memorize these rules and here is an easy way to do it:

  • Like signs = addition
  • Unlike signs = subtraction


You can actually write the above as a subtraction problem too. By using our sign rules for addition and subtraction, you can see that when you have an addition sign and a negative sign, they combine for a subtraction problem (remember, unlike signs equal subtraction). So, in the above problem, 3 + ( -2 ), the addition sign and negative sign combine for a subtraction problem and can be rewritten as 3 - 2.

  • 3 + ( -2 ) = 3 - 2 = 1

You can also expand a subtraction problem and rewrite it as an addition problem:

  • 4 - 5 = 4 + ( - 5 )

Now you can go ahead and evaluate like you do for addition. You start at the number 4 and you are subtracting a 5, or adding a negative 5, so you need to go 5 spaces left on the number line. This takes you to -1.

  • 4 - 5 = -1

Now let's look at subtracting a negative number:

  • 4 - ( - 5 )

Using our sign rules for addition and subtraction, we see that when we have two like signs, they combine to make an addition problem (remember, like signs equal addition). So, our problem can be rewritten to:

  • 4 - ( - 5 ) = 4 + 5

And you'll solve it like any addition problem.

  • 4 + 5 = 9


When it comes to multiplication, think of it as adding up equal groups of the same amount. So, think of 2 * 3 as adding up two groups of 3 each. This gives you 6.

integer operations

If you figure out your multiplication for all your numbers 1 through 9, you can create a multiplication table that you can use for reference.

integer operations

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account