Subtracting Integers: Rules & Examples

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  • 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
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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

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