Roots and Powers of Algebraic Expressions

Subtracting Integers: Rules & Examples

In this lesson, we will cover definitions, rules, and examples for subtracting integers. We'll also cover some helpful tips when 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:

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.
o 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.
o Example: 14 - (-3) = 17

Helpful hint: What you can take away from these two rules: if you have a positive and a negative number you are subtracting, take the sign from the first number and then add the two numbers together.

Negative - Negative = Negative + Positive Why? Change that double negative into a positive. The answer is a bit trickier here. Subtract the two numbers. Your sign will be the sign of the greatest number. See the example for this one!

Example: -6 - (-10) = ? To solve, change the double negative so that -6 + 10 = ? Take the sign from greatest number (10) and subtract. The answer is 4.

Positive - Positive = Positive + Negative Why? Remember, add the opposite here. Then, just as before, you will take the sign of the greatest number and subtract the two numbers for your answer.

Example: 8 - 9 = ? To solve, add the opposite number so that you have 8 + (-9) = ? Then, take the sign from the greatest number (9) and subtract. The answer is -1.

Lesson Summary:

Integers are positive and negative numbers. In mathematical terms, subtracting means to add the opposite. Pay attention to your signs when subtracting integers, and when you get stuck, think of the numbers in terms of having or owing money! When subtracting double negatives, remember that double negatives cancel one another out, leaving a positive number.