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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

After watching this video lesson, you will be able to add and subtract negative numbers with ease. Learn what you need to watch for and what will make your job easier.

Looking at our number line, we see that **negative numbers**, which are our numbers less than zero, make up half of it. That means they are just as important as our positive numbers. In fact, for every positive number, we have a matching negative number. What does this mean? It means that we will see negative numbers in math problems just as much as positive numbers. So, we need to know how to add and subtract negative numbers just as well as we do positive numbers. This is just what we will do in this video lesson.

Let's start with adding negative numbers. Adding negative numbers is very much like adding positive numbers. What happens when you add positive numbers? Your number gets bigger. It is the same with negative numbers. The number after the negative sign gets bigger. The only difference is that, in reality, your answer is even more negative, meaning that your number is actually getting smaller. For example, (-2) + (-3) gives you -5. Yes, the number after the negative sign got bigger, but your real answer is a bigger negative, meaning it is a smaller number.

If we look at negative numbers as opposites of positive numbers, we see how it works. If our positive numbers get bigger when added, then our negative numbers should get smaller when added. What we did to get our result of -5 was add the numbers, ignoring the negative sign, and then just make sure to write a negative sign in front of our answer. It's important not to forget the negative sign.

Look at this example: what is (-10) + (-8)?

Ignoring the negative signs and just adding the numbers, we get 10 + 8 = 18. Now, because we are working with negative numbers, we can't forget the negative sign in front of our answer. So, our answer then is -18. Does this make sense? Yes, it does. We got an even smaller number for our answer. This makes sense because we are working with negative numbers, and we expect it to give us an opposite kind of answer than if we were working with positive numbers.

So, what about subtracting negative numbers? Can we expect it to behave in an opposite way to positive numbers? Yes, we can. Working with positive numbers, we know that 3 - 2 = 1. But what if we have (-2) - (-3)? What do we do here? If we think of this as working in an opposite way as subtraction with positive numbers, we can simply flip the numbers around, and turn it into a subtraction problem with positive numbers. We get 3 - 2. We know what that equals. How did we do that? Well, we see a negative two at first followed by a minus minus three. This double negative actually turns that 3 into a positive, so we really have -2 + 3. We can switch places to rewrite the problem as 3 - 2, which is the same subtraction problem written the opposite way using positive numbers. This works with all subtraction problems involving negative numbers.

Look at this example: what is (-5) - (-10)?

We have two negatives in front of the 10, so this problem is actually -5 + 10. We can rewrite this with the 10 in front so we get 10 - 5. Do you see how this is the opposite problem, using just positive numbers? We've switched the numbers around and gotten rid of the negative numbers. We've made everything opposite. What is our answer? 5.

Let's review what we've learned. **Negative numbers** are our numbers less than zero. To add negative numbers, we simply add the numbers, ignoring the negative sign, and make sure to include the negative sign in the answer. To subtract negative numbers, we notice that the double negative turns the second number into a positive number. We can then flip the subtraction problem around and use only positive numbers. So, we will have the second number minus the first number.

You should have the ability to do the following after this lesson:

- Define negative numbers
- Explain how to add and subtract negative numbers

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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