# data[].attributes.body
its JASON

# data[].attributes.headline
Adding and Subtracting integers   -Allie Everhart

# data[].attributes.subject
Adding and Subtracting integers   -Allie Everhart

# data[].attributes.body
https://www.youtube.com/watch?v=PQTacxlfX5E

# data[].attributes.attachment_link.readable_text
Find the sum 15 plus negative 46 plus 29. Let's just think about this first part over here where we have 15 plus negative 46. And we'll worry about the plus 29 later on. So let's just do 15-- let me do that in a different color-- plus negative 46. I'll do it in that orange. Let me draw a number line here, just so we can properly visualize what is going on. That's my number line. And we're starting at 15. So let's draw a 0 over here. And so we're starting at 15. 15 could be right over here. So this is 15. Let me draw a big fat arrow to signify this is 15. 15 has an absolute value of 15, so the length of this arrow would be 15. Now we're adding negative 46 to that 15. This is equivalent to 15 minus 46, which means we are going to move 46 spots to the left of 15. A negative sign or a minus means we're moving to the left on the number line. So we're going to move 46 to the left. We're starting at 15, and we are going to move 46 to the left. So the length of this arrow right here is going to be 46, and we're moving to the left. This is the negative 46 that we're adding to the 15. We're going to end up at some point over here. That point is clearly 0. Because we were 15 to the right. Now we're going to move 46 to the left. So we're definitely going to be to the left of 0. It's definitely going to be a negative number. And we can even think about the absolute value of that negative number. We can just visualize it. This yellow arrow has a length of 15. This orange arrow has a length of 46. The blue arrow that I'm about to draw, which is the sum of these two, is going to have this length right over here. And just visually, how can we figure out the length of this blue part if we know the length of this orange part and we know the length of this yellow part? Well, it's just going to be the difference. It's just going to be the difference of these two. So the absolute value of the sum is going to be the difference between this length, 46, and 15. Let me just figure that out, 46 minus 15. 6 minus 5 is 1. 4 minus 1 is 3. So the length of this is going to be 31, and it's going to be 31 to the left of 0. So this is going to be negative 31 right over here. We know that this first part over here is negative 31, and then to that we are going to add 29. So we're going to add 29. Let me do that in another color. What does that mean? That means that we're going to start at negative 31, and we're going to move 29 to the right. We're adding 29, so we're going to move 29 to the right. So maybe that gets us right about there. I'm trying to draw an arrow of length 29. I can draw a cleaner looking arrow than that. I'll do it right over here, actually. So then we're going to move 29 over to the right. That's the 29 part. Now this is a positive 29, and so how do we figure out what this is? This is 29 right here that we're adding. This is going to land us right over here on the number line. So how do we figure out what number that is? Well, once again, we can just visualize it. And eventually you won't have to draw number lines and stuff, but I think it'll be useful here. We're starting at negative 31. We're adding 29 to it, so it's going to make it less negative. But we're still adding less than 31, so we're not going to get all the way back to 0. We're still going to have a negative number. But how could we figure out the absolute value of that negative number, its distance? Well, once again, that little white part right there, that white part plus this 29, is going to equal 31, if you just think of absolute value, if we don't think about the signs, if we just think about the length. Or another way to think about it, 31 minus 29 will give us the length of that white part. And of course, it's going to be negative, because the negative number here is larger than the positive number. And we're adding the 2. If we do 31 minus 29, you could borrow and all of that, but that's clearly just going to be equal to 2. You could say that's 11. This is a 2. You subtract, this is equal to 2. But since it's negative 31 plus 29, it's going to be a negative 2. We're still going to stay negative. We haven't moved far to the right enough to pass 0. So this right here is going to be negative 2. Or another way to think about it, the length of this white bar, the absolute value, is going to be 2. 2 plus 29 is 31. But we're operating to the left of 0, so it's negative 31. This is negative 2. Anyway, hopefully you found that useful. And let me make it clear. Our final answer is negative 2.

# data[].attributes.attachment_link.description
Find the sum 15 plus negative 46 plus 29. Let's just think about this first part over here where we have 15 plus negative 46. And we'll worry about the plus 29 later on. So let's just do 15-- let me do that in a different color-- plus negative 46.

# data[].attributes.attachment_link.readable_text
Learn About Integer Addition With Example Problems And Interactive Exercises.

Problem: George owes his friend Jeanne $3. If he borrows another $6, how much will he owe her altogether?

Solution: This problem is quite simple: just add $3 and $6 and the result is $9.

The problem above can be solved using addition of integers. Owing $3 can be represented by ⁻3 and owing $6 can be represented by ⁻6. The problem becomes:
⁻3 + ⁻6 = ⁻9

Look at the number line below. If we start at 0, and move 3 to the left, we land on ⁻3. If we then move another 6 to the left, we end up at ⁻9.

Rule: The sum of two negative integers is a negative integer.

Example 1: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.

Adding Negative Integers
Integers | Sum
⁻2 + ⁻9 = | ⁻11
⁻5 + ⁻8 = | ⁻13
⁻13 + ⁻7 = | ⁻20

Do not confuse the sign of the integer with the operation being performed. Remember that:⁻2 + ⁻9 = ⁻11 is read as Negative 2 plus negative 9 equals negative 11.

Rule: The sum of two positive integers is a positive integer.

Example 2: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.

Adding Positive Integers
Integers | Sum
⁺2 + ⁺9 = | ⁺11
⁺17 + ⁺5 = | ⁺22
⁺29 + ⁺16 = | ⁺45

Do not confuse the sign of the integer with the operation being performed. Remember that:

⁺29 + ⁺16 = ⁺45 is read as Positive 29 plus positive 16 equals positive 45.

So far we have added integers with like signs (either both negative or both positive). What happens when we add integers with unlike signs? How do we add a positive and a negative integer, or a negative and a positive integer?

Procedure: To add a positive and a negative integer (or a negative and a positive integer), follow these steps:

1. Find the absolute value of each integer.

2. Subtract the smaller number from the larger number you get in Step 1.

3. The result from Step 2 takes the sign of the integer with the greater absolute value.

We will use the above procedure to add integers with unlike signs in Examples 3 through 7. Refer to the number line to help you visualize the process in each example. We will use money as an alternative method for adding integers.

Example 3: Find the sum of ⁺7 and ⁻4.

Step 1: |⁺7| = 7 and |⁻4| = 4

Step 2: 7 - 4 = 3

Step 3: The number 3 will take a positive sign since ⁺7 is farther from zero than ⁻4.

Solution 1: ⁺7 + ⁻4 = ⁺3

Solution 2: If you start with $7 and you owe $4, then you end up with $3.

Example 4: Find the sum of ⁻9 and ⁺5.

Step 1: |⁻9| = 9 and |⁺5| = 5

Step 2: 9 - 5 = 4

Step 3: The number 4 will take a negative sign since ⁻9 is farther from 0 than ⁺5.

Solution 1: ⁻9 + ⁺5 = ⁻4

Solution 2: If you owe $9 and you are paid $5, then you are still short $4.

Example 5: Find the sum of ⁺6 and ⁻7.

Step 1: |⁺6| = 6 and |⁻7| = 7

Step 2: 7 - 6 = 1

Step 3: The number 1 will take a negative sign since ⁻7 is farther from 0 than ⁺6.

Solution 1: ⁺6 + ⁻7 = ⁻1

Solution 2: If you start with $6 and you owe $7, then you are still short $1.

Example 6: Find the sum of ⁻6 and ⁺7.

Step 1: |⁻6| = 6 and |⁺7| = 7

Step 2: 7 - 6 = 1

Step 3: The number 1 will take a positive sign since ⁺7 is farther from 0 than ⁻6.

Solution 1: ⁻6 + ⁺7 = ⁺1

Solution 2: If you owe $6 and you are paid $7, then you end up with $1.

Example 7: Find the sum of ⁺9 and ⁻9.

Step 1: |⁺9| = 9 and |⁻9| = 9

Step 2: 9 - 9 = 0

Step 3: The integer 0 has no sign.

Solution 1: ⁺9 + ⁻9 = 0

Solution 2: If you start with $9 and you owe $9, then you end up with $0.

In Example 7 you will notice that the integers ⁺9 and ⁻9 are opposites. Look at the problems below. Do you see a pattern?

⁻100 + ⁺100 = 0

⁺349 + ⁻349 = 0

⁻798 + ⁺798 = 0

Rule:   The sum of any integer and its opposite is equal to zero.

Summary: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.

Exercises

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. | ⁻6 + ⁻9 = ?

2. | ⁺7 + ⁺11 = ?

3. | ⁺5 + ⁻3 = ?

4. | ⁻2 + ⁺7 = ?

5. | ⁺9 + ⁻12 = ?

Sign Up For Our FREE Newsletter!

Sign Up For Our FREE Newsletter!

# data[].attributes.attachment_link.description
Learn About Integer Addition With Example Problems And Interactive Exercises.

# data[].attributes.body
https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-add-and-sub-integersss/v/adding-integers-with-different-signs

# data[].attributes.body
Falcata

# data[].attributes.attachment_link.title
Math Games: Fruit Shoot Integer Addition

# data[].attributes.attachment_link.description
Learn how to add integers the fun way with Fruit Shoot Integer Addition math game.

# data[].attributes.body
http://www.math.com/school/subject1/lessons/S1U1L11DP.html

# data[].attributes.attachment_link.readable_text
We can use the number line as a model to help us visualize adding and subtracting of signed integers. Just think of addition and subtraction as directions on the number line. There are also several rules and properties that define how to perform these basic operations.

To add integers having the same sign, keep the same sign and add the absolute value of each number.

To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest.

Subtract an integer by adding its opposite.

Watch out! The negative of a negative is the opposite positive number. That is, for real numbers,

Here's how to add two positive integers:

If you start at positive four on the number line and move seven units to the right, you end up at positive eleven. Also, these integers have the same sign, so you can just keep the sign and add their absolute values, to get the same answer, positive eleven.

Here's how to add two negative integers:

If you start at negative four on the number line and move eight units to the left, you end up at negative twelve. Also, these integers have the same sign, so you can just keep the negative sign and add their absolute values, to get the same answer, negative twelve.

Here's how to add a positive integer to a negative integer:

If you start at negative three on the real number line and move six units to the right, you end up at positive three. Also, these integers have different signs,

so keep the sign from the integer having the greatest absolute value and subtract the smallest absolute value from the largest.

Subtract three from six and keep the positive sign, again giving positive three.

Here's how to add a negative integer to a positive integer:

If you start at positive five on the real number line and move eight units to the left, you end up at negative three. Also, these integers have different signs, so keep the sign from the integer having the greatest absolute value and subtract the smallest absolute value from the largest, or subtract five from eight and keep the negative sign, again giving negative three.

To subtract a number, add its opposite:

Because they give the same result, you can see that subtracting eight from five is equivalent to adding negative eight to positive five. The answer is - 3.

To subtract a number, add its opposite:

Because they give the same result, you can see that subtracting negative six from negative three is equivalent to adding positive six to negative three. The answer is 3.

# data[].attributes.attachment_link.title
Numbers - Adding and Subtracting Integers - In Depth

# data[].attributes.attachment_link.description
We can use the number line as a model to help us visualize adding and subtracting of signed integers. Just think of addition and subtraction as directions on the number line. There are also several rules and properties that define how to perform these basic operations.

# data[].attributes.body
https://www.mathgoodies.com/lessons/vol5/addition

# data[].attributes.body
https://www.tes.com/lessons/EjgAXWVTFsY7jA/red-1-2-adding-integers

# data[].attributes.attachment_link.title
Red 1.2 Adding Integers - Lessons - Tes Teach

# data[].attributes.attachment_link.description
Our Topic .adding integers with chips.Put in Your Notes.Adding positive and negative integers on a number line.Put in Your Notes.Practice.BrainPOP | Math | Learn about Adding and Subtracting Integers.Adding Integers Blues Song by Mr. W..Integer Rule Song.Arcademic Skill Builders - Orbit Integers.Math Racing - Adding Integers Game - Math Play.Do to Check Out.

# data[].attributes.body
https://www.youtube.com/watch?v=ZxbXjORORSU

# data[].attributes.attachment_link.title
Adding Integers - MathHelp.com - Math Help

# data[].attributes.attachment_link.description
For a complete lesson on adding integers, go to http://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students review the addition and subtraction of positive and negative integers using a number line, where a positive integer represents a move to the right, and a negative integer represents a move to the left.

# data[].attributes.attachment_link.description
Cheezburger.com - Crafted from the finest Internets.

# data[].attributes.headline
Math comic for some fraction to decimal help.

# data[].attributes.subject
Math comic for some fraction to decimal help.