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### Course: Arithmetic > Unit 18

Lesson 9: Adding & subtracting integers# Adding integers: find the missing value

Use number lines to find missing addends in addition equations with integers. When we add a positive value, we move to the right on the number line. When we add a negative value, we move to the left. Created by Sal Khan.

## Want to join the conversation?

- so what if the problem looks like this (-29)-29 how would I find out the sum also my teacher said that when it looks something like 18-41 u make the 41 into a negative and change the whole problem into a addition problem but I don't under stand it also for reference im in 9th grad algebra 1 so just to make sure im getting the right answer ok bye(7 votes)
- So say you have a number line, -29 is 29 to the left of 0, then you move it another 29 spaces to the left and you have ur answer. Another way to think of it so if i for example have -2-2 i would just do 2+2=4 then slap a negative on and voila! The answer is -4(10 votes)

- or you can do two step equation

let x be the missing number

4 + x = -6

4 + x = -6

4 - = -4

-4 + -6 = -10

x = -10

4 + -10 = -6(10 votes) - what is the hardest math problem(7 votes)
- Question 6 of the 1988 math Olympaid.

It is famous.

Let a and b be positive integers such that ab + 1 divides a2 + b2. Show that a2 + b2 / ab + 1 is the square of an integer.(5 votes)

- Also I have more trouble with the equasions like -2-(-2)(3 votes)
- Guys it is really simple you basically are doing a negative and positive number fill in the blank if you get what I am saying.

ANYWAY... It's also easier when you memorize the positives and negatives and what it would equal if you added or subtracted those two.(2 votes) - - & + = -

+ & - = -

- & - = +

+ & + = +

Anybody tell me how the last 2 works? Thats like 2 bad luck= a good luck. And how does 2+ dont cancel out?(0 votes) - I like to remember that when there is like a -(- you take the minuses and cross them and make a plus!(2 votes)

## Video transcript

- [Instructor] We are asked
to find the missing value, and they give us a hint. Use the number line to
find the missing value. And let's see, they say, 4
plus something is equal to -6. So why don't you pause this video and see if you can work through this before we do it ourselves. All right, so let's just start at 4. So there's a couple of
ways to think about it. We could just say where
is 4 on the number line. 4 is here. One, two, three, four. We're going to start there, and we're going to add something to that 4 to get us to -6. To get us right there. So what are we going to add? Well, we're going to
be moving to the left. So we're going to be adding a negative number right over here. And we can see what that
negative number is going to be. How many units do we
have to move to the left? We have to move one,
two, three, four, five, six, seven, eight, nine, 10 to the left. So what do we add if we
want to move 10 to the left? We have to add a -10. So this is -10 right over here. Another way to think about it, if you're four to the right of zero, well, it's going take you
four just to get back to zero. That's four there. And it's going to take you another six to get you to -6. And then of course you're
moving to the left, so that's going to be a -10. Let's do another a example. So let me scroll down a bit so we can see that second example. So once again, find the missing value. And pause this video again
and try to work that out. All right, so there's a couple of ways we could think about it. We're saying -3 is equal
to something plus 5. So let's just see where
-3 is on this number line. - 3 is right over there. And something plus 5 is
going to be equal to -3. So plus 5, you could view it as you're going to start someplace, and you're going to move
five units to the right, something like that to
get to where you end up. So where could we start to
get five units to the right and be at -3? Well, if we just go
five units to the left, so one, two, three, four, five. If you start from this point, and you were to add 5, you were get to -3. And so what is this point right over here? Well, this right over here, let's see, this is -5, -6, -7, -8. So we have -8 plus 5 is equal to -3. Another way to think about it is, you could have used a
commutative property to say, "Hey, instead of blank plus 5, you could say this is -3
is equal to 5 plus blank. And so you could say, let's start at 5, let me do this in another color. Let's start at 5, and then what would I have
to add to it to get to -3? And so, well, I would have
to move to the left five and then three in order to get to -3. So you would essentially have to add -8. So that's another way that
you could think about that.