Copyright

Subtracting Integers: Rules & Examples

Subtracting Integers: Rules & Examples
Coming up next: What are Rational Numbers? - Definition & Examples

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

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:05 What are Integers?
  • 0:36 The Opposite of Addition
  • 1:22 Subtracting Double Negatives
  • 2:14 Subtraction Rules and Examples
  • 4:03 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

Timeline
Autoplay
Autoplay
Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

In this lesson, we will cover definitions, rules, and examples for subtracting integers. We'll also provide some helpful tips for dealing with tricky math problems.

What Are Integers?

Integers are whole numbers (numbers that aren't a fraction or a decimal). They include both positive and negative numbers. Positive numbers either have no sign or a plus (+) sign in front of the number. Negative numbers always have a negative (-) sign in front of the number. You can see negative numbers and positive numbers represented on a number line like this:

Positive and Negative Numbers Represented on a Number Line
Positive and Negative Numbers Represented on a Number Line

Many students find subtracting integers confusing, and why not? There are too many signs, right? Why can't everything be simple? It can be! When subtracting integers, you have to keep a few basic things in mind.

The Opposite of Addition

Subtraction is the opposite of addition. Wait, what? Yes! It's true! Subtraction is really just the opposite of addition. So when looking at any subtraction problem, think to yourself: add the opposite. For example, say you have the problem 5 - 2 = 3. You can get the same answer by adding (instead of subtracting) if you write the problem as 5 + (-2) = 3

Still a little confused? Try to think of integers in terms of money. Take the above problem, for example. You have $5 in your pocket. You owe your friend $2. Now ask yourself: are you going to have any money left over? Yes, because $5 - $2 = $3. The answer is a positive number.

Subtracting Double Negatives

Try this problem 5 - (-3)=?

Many people do a double take at problems like this. There are two negatives. What to do now? In math, double negatives cancel one another out - just like in English. For example, a double negative statement in English such as 'I cannot not go to this class' really means the same thing as this positive statement 'I have to go to this class.' It works the same way with mathematics. A double negative cancels out, and you are left with a positive number.

Remember, subtracting integers is like adding the opposite. So, we would start with the problem like this: 5+

What do we do with (-3)? What's the opposite? Right, positive three is the opposite of a negative three. So now my problem looks like this: 5 + 3 = 8.

Subtraction Rules and Examples

If you're still having some issues with subtracting integers, here are some basic rules to follow:

  • Negative - Positive = Negative Why? Remember, if you are adding the opposite, that positive number will change to a negative number.
    • Example: -5 - 10 = -15
  • Positive - Negative = Positive Why? Same as earlier, except this time your negative number will be the opposite, making it into a positive number.
    • Example: 14 - (-3) = 17

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
Support