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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 solve problems that ask you to add three or more integers together. Learn how you can break down the problem into steps that allow you to easily find the answer.

We deal with **integers**, positive and negative whole numbers, every day. We can't go a day without using numbers. For example, just look at the clock. What do you see on the clock's face? Integers!

Because integers are so important, knowing how to add them together is also important. For example, say you and your friends want to go to this arcade. Everybody is looking forward to having fun so you and your friends decide to combine everybody's money together so that all can share in the fun. The different amounts being combined are $5, $10, $8, and $12. At the arcade, you and your friends bring the combined amount to the token counter to purchase tokens for everyone. What is this total amount?

To find this total amount, you will need to add those four amounts together, like this:

5 + 10 + 8 + 12

Right now you are used to adding two numbers together. Here we are adding three or more integers together, specifically four integers together. How do we go about doing this? We can perform our addition in stages.

We begin by adding the first two numbers together:

5 + 10 = 15

We can replace the 5 + 10 with the 15 in our problem. Our problem is now:

15 + 8 + 12

We continue by repeating the process of adding the first two integers together. We get:

15 + 8 = 23

We can now replace the 15 + 8 with the 23 in our problem. What are we left with now? We are left with:

23 + 12

Hey look at that! We only have two integers left to add. When we are at this stage, this last addition will give us our answer. We get:

23 + 12 = 35

This means you and your friends have a total of $35 to spend at the token counter at the arcade.

Another method you can use to add all these numbers is to write the numbers stacked on top of each other. You write the numbers so that all the digits in the ones place are to the right. Then the digits for the tens place is to the left of that. The hundreds place digits will be to the left of the tens place, and so on and so forth.

So for our addition problem of 5 + 10 + 8 + 12, the digits 5, 0, 8, and 2 are lined up in the same column, the column to the far right. The digits 1 and 1 from the numbers 10 and 12 are then written in the column to the left of the column with the four digits.

5 | |

1 | 0 |

8 | |

1 | 2 |

You then write a plus sign to the left of the last number to let you know that you are adding. Then you draw a line underneath all the numbers. Your answer will go underneath this line. To add, you work for the rightmost column and you work your way to the left.

We first add 5 + 0 + 8 + 2. This equals 15. We write the 5 underneath the line in the ones place. Because this number is 10 or greater, we need to carry the tens place. We carry the tens place by writing the digit for our tens place above the tens place column.

1 | ||

5 | ||

1 | 0 | |

8 | ||

+ | 1 | 2 |

- | - | - |

5 |

We then add all the digits in the tens place column. We have 1 + 1 + 1. This equals 3. This is the last column, so we write the 3 underneath our line in the tens place column. Our answer is 35.

Let's look at a couple of examples so you get an even better grasp of this process.

You and your friends are now combining each person's money to figure out how much the group can spend on dinner. The different amounts are $5, $7, $3, and $2. How much can you and your friends spend for dinner?

Our addition problem here is:

5 + 7 + 3 + 2

We begin by adding the first two integers together. We get:

5 + 7 = 12

Our problem is now:

12 + 3 + 2

Now, repeating the process, we get:

12 + 3 = 15

Our problem now becomes:

15 + 2

Our answer then is:

15 + 2 = 17

Your group has $17 to spend on dinner.

After that the arcade and dinner is taken care, what can the group do? You and your friends start to plan for the next big activity. In two weeks time, you and your friends will each have made more money. The amounts that each will have made are $31, $12, $20, and $18. How much do you all have together? That will determine what kind of fun you guys can have.

Our addition problem is:

31 + 12 + 20 + 18

Tackling this problem two integers at a time, we get:

(31 + 12) + 20 + 18 = (43 + 20) + 18 = 63 + 18 = 81

I've added the parentheses to show which two integers we are taking care of at each step. You and your friends will have a total of $81 to spend on the next big activity? What can you guys do? Someone suggests the water park. That sounds like fun.

Let's look at using the other method. We write all our numbers stacked on top of each other. We then add the digits in the ones place. We get:

1 + 2 + 0 + 8 = 11

We write 1 on our answer line to the far right, and then we carry the 1 and write it over the tens place column. Then we add all the digits in that column. We get:

1 + 3 + 1 + 2 + 1 = 8

This is our last column, so we finish by writing the 8 in the tens place on the answer line. Our answer is 81.

What have we learned? **Integers** are positive and negative whole numbers. To add three or more integers together, we add two integers at a time. When we are done adding two integers, we replace those two integers with what they equal. We then proceed and repeat the process until we are left with our answer.

Another method that you can use involves stacking the numbers on top of each other so that the ones place is aligned and the tens place is aligned. You then proceed to add up all your digits in the ones place. If the answer here is 10 or greater, you write the ones digit in your answer line and you carry the tens place digit by writing that digit above the tens column. You then proceed to add up all the tens place digits. And you repeat the steps until you have reached the last column. Your answer line will then contain your answer.

Once you are finished with the lesson, you should be able to:

- Recall what integers are
- Solve an addition problem that includes three or more integers

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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 One-Digit Integers 4:17
- Addition Equations with Two-Digit Integers 3:55
- Adding Three or More Integers 7:14
- 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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