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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 all kinds of integers together. This is a skill that will benefit you when playing games and when doing math tests. After watching the video, try some example problem on your own with our quiz.

You and your friends are playing this game where you each have ten playing pieces to play with. The goal of this game is to get the most points. The way to get points is to match the playing pieces to the ones that have already been played. See, each playing piece has two numbers on it, one on each end. You play by matching one end to a free end that has already been played. You then add up all the end numbers, and add it to your current score. Do you see one of the essential math skills that is used in this game? That's right, it's addition! You have to know how to add to make this game fun.

Well, in this video lesson, not only will you learn how to add two positive **integers**, or numbers, together, but you will also learn how to add two negative integers together, as well as a positive and negative integer together. Are you ready to begin? Let's go.

It's your friend's turn in the game. Your friend currently has 20 points. After playing his piece, he now needs to add 15 more points. How can he do this? He can write out the problem using math symbols on a piece of paper like this: 20 + 15. Now, he can either add them up by counting 15 more than 20, or he can look at the number line, find the number 20, and then count 15 spaces to the right. He can also break up the problem into pieces. First, he has 20, then he needs to add 15, which is 5 and 10 together. Well, adding a 10 to 20 is easy. That makes 30. What is 5 more than 30? 35! So, 20 + 15 = 35.

Let's try another problem.

*354 + 11*

We are adding 354 and 11 together. 11 breaks up into a 1 and a 10. Adding the 10 to 354 gives us 364. Adding the 1 gives us 365, so 354 + 11 = 365.

Now, what if both of our integers are negative? Well, you and your friends are now done playing the game. However, some of the players still have playing pieces left. This is because they weren't able to match these playing pieces to the ones that have already been played. What this means is that these players now need to deduct these numbers from their current score. Instead of being positive points now, these playing pieces have now become negative points.

But first, we must add together the pieces left. For instance, if your friend has two pieces that will be deducted, -3 and -5, how many points will he eventually deduct?

*(-3) + (-5)*

What do we do here? When we add two negative numbers together, what you do is you add your numbers while ignoring the negative signs, and then you just include the negative sign in your answer. So, for the problem (-3) + (-5), you would first add 3 + 5. This equals 8. Now your answer will just need a negative sign. So, (-3) + (-5) = -8, and you are done.

Let's try one more.

*(-10) + (-21)*

We are adding two negative integers together, so this means that we add 10 + 21. This equals 31. But this isn't our answer. We need a negative sign. So, our answer is -31.

Now that we know your friend has the 8 points left in front of him, he has to add the -8 to his current score of 120. Those 8 points he has left are negative points now since the game has ended. So, your friend needs to add 120 + (-8). What can he do?

To add a positive and negative integer together, we will actually turn the problem into a subtraction problem. This is because when we have a (+) next to a (-), it turns it into a (-). We will subtract whichever number is our negative number. So, your friend actually needs to figure out 120 - 8. Your friend can count down 8 spaces from 120, or he can use the number line, find the number 120, and count 8 spaces to the left. The answer is 112.

Let's try another.

*(-6) + 4*

The rule for adding a positive and a negative integer together is to turn it into a subtraction problem where the negative integer is subtracted from the positive. So, we have 4 - 6. Hmm. If we use the number line and count 6 spaces to the left from 4, we end up at -2. So, our answer is -2. Don't worry that this answer is negative. It is perfectly okay to get a negative answer. It doesn't mean you did anything wrong. This happens when you're subtracting a larger number from a smaller number. See, 6 is larger than 4.

Let's review what we've learned.

The word '**integer**' is another word for numbers. It includes all the numbers we see on the number line, both positive and negative. To add two positive integers, we go ahead and add them up by using whatever adding skills we know. To add two negative integers, we add them up while ignoring the negative signs. We, then, include the negative sign in our answer. To add a negative and a positive integer together, we turn the problem into a subtraction problem, where we have the positive integer minus the negative integer. Once we have turned it into a subtraction problem, though, we don't need to write the negative sign anymore. Then we go ahead with the subtraction.

Following this lesson, you should have the ability to:

- Define integer
- Explain how to add two positive or two negative integers and also how to add a negative and a positive integer

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

- Finding the Absolute Value of a Real Number 3:11
- Absolute Value & Opposite Integers 4:23
- Integer Inequalities with Absolute Values 7:51
- How to Compare Integers 4:03
- Adding Positive & Negative Integers 6:30
- Addition Equations with Two-Digit Integers 3:55
- Adding Three or More Integers 7:14
- Subtraction Equations with One-Digit Integers 6:21
- Subtraction Equations with Two-Digit Integers 5:35
- How to Simplify Expressions with Integers 5:12
- Dividing Integers: Rules & Terminology 6:03
- Multiplying Integers: Rules & Examples 10:53
- Go to 6th-8th Grade Math: Integers

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