Negative numbers and absolute value
Adding and subtracting negative numbers
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Adding/subtracting negative numbers
Adding and subtracting negative numbers
Discussion and questions for this video
 Welcome to the presentation on adding and subtracting
 negative numbers.
 So let's get started.
 So what is a negative number, first of all?
 Well, let me draw a number line.
 Well it's not much of a line but I think you'll
 get the picture.
 So we're used to the positive numbers, so if that's 0, you
 have 1, you have 2, you have 3, you have 4, and you keep going.
 And if I were to say what's 2 plus 2, you'd start at 2 and
 then you'd add 2 and you'd get to 4.
 I mean most of us it's second nature.
 But if you actually drew it on a number line
 you'd say 2 plus 2 is 4.
 And if I asked you what's 2 minus 1 or let's
 say what's 3 minus 2?
 If you start at 3 and you subtracted 2, you
 would end up at 1.
 That's 2 plus 2 is equal to 4 and 3 minus 2 is equal to 1.
 And this is a joke for you.
 Now what if I were to say what is 1 minus 3?
 Huh.
 Well, it's the same thing.
 You start at 1 and we're going to go 1  well, now we're
 going to go below 0  what happens below 0?
 Well then you start going to the negative numbers.
 Negative 1, negative 2, negative 3, and so on.
 So if I start at 1 right here, so 1 minus 3, so I go 1, 2,
 3, I end up at negative 2.
 So 1 minus 3 is equal to negative 2.
 This is something that you're probably already doing
 in your everyday life.
 If I were to tell you that boy, it's very cold today, it's 1
 degree, but tomorrow it's going to be 3 degrees colder, you
 might already know intuitively, well then we're going to be
 at a temperature of negative 2 degrees.
 So that's all a negative number means.
 And just remember when a negative number is big, so like
 negative 50, that's actually colder than negative 20, right?
 So a negative 50 is actually even a smaller number than
 negative 20 because it's even further to the left
 of negative 20.
 That's just something you'll get an intuitive feel for.
 Sometimes when you start you feel like oh, 50's a bigger
 number than 20, but it's a negative 50 as opposed
 to a positive 50.
 So let's do some problems, and I'm going to keep using the
 number line because I think it's useful.
 So let's do the problem 5 minus 12.
 I think you already might have an intuition of
 what this equals.
 But let me draw a line, 5 minus 12.
 So let me start with minus 10, minus 9, minus 8 I think I'm
 going to run out of space  minus 7, minus 6, minus 5  I
 should have this predrawn  minus 4, minus 3, minus 2,
 minus 1, 0, 1, 2, 3, 4, I'll put 5 right here.
 5 minus 12.
 So if we start at 5  let me use a different color  we
 start at 5 right here and we're going to go to the left 12
 because we're subtracting 12.
 So then we go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
 Negative 7.
 That's pretty interesting.
 Because it also happens to be that 12 minus 5
 is equal to positive 7.
 So, I want you to think a little bit about why that is.
 Why the difference between 12 and 5 is 7, and the difference
 between  well, I guess it's either way.
 Because in this situation we're also saying that the difference
 between 5 and 12 is negative 7, but the numbers are that far
 apart, but now we're starting with the lower number.
 I think that last sentence just completely confused you, but
 we'll keep moving forward.
 We just said 5 minus 12 is equal to minus 7.
 Let's do another one.
 What's negative 3 plus 5 equals what?
 Well, let's use the same number line.
 Let's go to negative 3 plus 5.
 So we're going to go to the right 5.
 1, 2, 3, 4, 5.
 It's a 2.
 It equals 2.
 So negative 3 plus 5 is equal to 2.
 That's interesting because 5 minus 3 is also equal to 2.
 Well, it turns out that 5 minus 3 is the same thing, it's just
 another way of writing 5 plus negative 3 or
 negative 3 plus 5.
 A general, easy way to always do negative numbers is it's
 just like regular subtraction and addition and subtraction,
 but now when we subtract we can go to the left below 0.
 Let's do another one.
 So what happens when you get let's say 2 minus minus 3?
 Well, if you think about how it should work out I think
 this will make sense.
 But it turns out that the negative number, the negative
 signs actually cancel out.
 So this is the same thing as 2 plus plus 3, and
 that just equals 5.
 Another way you could say is  let's do another one  what
 is negative 7 minus minus 2?
 Well that's the same thing as negative 7 plus 2.
 And remember, so we're doing to start at negative 7 and we're
 going to move two to the right.
 So if we move one to the right we go to negative 6, and then
 we move two to the right we get negative 5.
 That makes sense because negative 7 plus 2, that's the
 same thing as 2 minus 7.
 If it's 2 degrees and it gets 7 degrees colder, it's minus 5.
 Let's do a bunch of these.
 I think the more you do the more practice you have, and the
 modules explain it pretty well, probably better than I do.
 So let's just do a ton of problems.
 So if I said negative 7 minus 3.
 Well, now we're going to go three to the
 left of negative 7.
 We're going to get 3 less than negative 7 so that's
 negative 10, right?
 That makes sense, because if we had positive 7 plus 3 we're at
 7 to the right of 0 and we're going to go three more to the
 right of 0 and we get positive 10.
 So for 7 to the left of 0 and go three more to the left we're
 going to get negative 10.
 Let's do a bunch more.
 I know I'm probably confusing you, but practice is what's
 going to really help us.
 So say 3 minus minus 3, well, these negatives cancel out
 so that just equals 6.
 What's 3 minus 3?
 Well, that's easy that's just 0.
 What's minus 3 minus 3?
 Well now we're going to get three less than minus 3,
 well that's minus is 6.
 What's minus 3 minus minus 3?
 Interesting.
 Well, the minuses cancel out so you get minus 3 plus 3.
 Well, if we start three to the left of 0 and we move three to
 the right we end up at 0 again.
 So that makes sense, right?
 Let me do that again.
 Minus 3 minus minus 3.
 Anything minus itself should equal 0, right?
 That's why that equals 0.
 And that's why it makes sense that those two negatives
 cancel out and that's the same thing as this.
 Let's do a bunch more.
 Let's do 12 minus 13.
 That's pretty easy.
 Well, 12 minus 12 is 0, so 12 minus 13 is negative 1
 because we're going to go one the left of 0.
 Let's do 8 minus 5.
 Well, this one is just a normal problem, that's 3.
 What's 5 minus 8?
 Well, we're going to go all the way to 0 and then 3 more to the
 left of zero, so it's minus 3.
 I could draw a number line here.
 If this is 0 this is 5, and now we're going to go to left 8,
 then we end up and negative 3.
 You could do that for all of these.
 That actually might be a good exercise.
 I think this will give you good introduction and I recommend
 that you just do the modules because the modules actually,
 especially if you do the hints, it has a pretty nice graphic
 that's a lot nicer than anything I could draw
 on this chalkboard.
 So try that out and I'm going to try to record some more
 modules that hopefully won't confuse you as badly.
 You could also attend the seminar on adding and
 subtracting negative numbers.
 I hope you have fun.
 Bye.
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I am still trying to grasp the 3(3)=6 I know that you say it means you cancel the negatives and make it a positive but I just can't visualize why. It's not enough for me to just except that that is what you do. I need to really understand it. I cant figure out how to recreate it on the number line. Can anyone show 3(3) looks on a number line?
Someone explained it to me this way. This made more sense to me. Hope this might help others here.
"It goes back to what we understand of finding the difference between two numbers. You are finding the difference between 3 and 3. Draw a number line to see how many units these two numbers are apart. you will see that 6 units separate these two numbers. Thus, 3(3) has to be equal to 6 units of difference."
"It goes back to what we understand of finding the difference between two numbers. You are finding the difference between 3 and 3. Draw a number line to see how many units these two numbers are apart. you will see that 6 units separate these two numbers. Thus, 3(3) has to be equal to 6 units of difference."
I know this was a couple months ago when asked, but hopefully you might still find the explanation helpful. You're right that the idea of subtracting a negative is hard to grasp. It's not really intuitive and there's no easy way to explain it in a way that makes a lot of sense using a number line.
Think about what it means to be a negative number. If you have a number, let's say 5, what does 5 really represent? It represents another number that you can add to 5 to get zero. Now, what about the opposite? If you start with 5, what does 5 represent? Well, it's the same thing. Again, 5 is a number that you add to 5 to get zero. So these two numbers, 5 and 5, are what are called "inverses" of each other (specifically they are additive inverses, but don't worry about that for now). Imagine the number line. If you start at 0 and go five spaces to the right, you get to the number 5. If you want to get back to 0, you move five spaces back to the left (or 5). Now, you're back at 0 and you move five spaces to the left and end up at 5. What do you do to get back to 0 again? Move five spaces to the right (+5 or just 5).
5 + (5) = 0
5 + 5 = 0
Now, the way we can find the inverse of a number is by putting a negative sign in front of it. This is sometimes referred to as "negating" a number. You want to negate the number 9? It's 9. If you negate 182, you get 182. So how do you negate 11? Well, it would be (11). You just slap a negative sign in front of it. But remember from above, what is negating? It's finding the inverse, or the number that you can add to your original number to get back to 0. And we know that if we're at 11 then we need to move eleven places to the right to get back to zero, so the inverse is 11. And now you can see that (11) should be equal to 11. If you want to think about it in terms of the number line, the negative sign tells you to move the opposite direction on the number line.
8 means eight places to the RIGHT of zero on the line
8 means eight places to the LEFT of zero on the line
(8) means eight places back to the RIGHT of zero
((8)) means eight places back to the LEFT of zero
And on it goes. When you hear people talking about two negative signs "canceling each other out" this is what they're talking about, which you'll learn more about when you get to multiplication involving negative numbers. It's an easy rule to remember when you want to simplify a problem.
So back to the original problem: 3  (3) = 6
If we don't think about this as a subtraction problem, but instead think about it as an addition of negatives, then it might make a little more sense.
3  (3) = 3 + ((3)) = 6
So what's going on? We have 3 and we want to add the inverse of the inverse of 3. We know the inverse of 3 is 3 and then we take the inverse of that and we're back to 3. Or more simply, because you understand the rule now, you look at those two negative signs next to each other and simply cancel them out. Which leaves you with:
3  (3) = 3 + ((3)) = 3 + 3 = 6
I hope that wasn't too confusing.
Think about what it means to be a negative number. If you have a number, let's say 5, what does 5 really represent? It represents another number that you can add to 5 to get zero. Now, what about the opposite? If you start with 5, what does 5 represent? Well, it's the same thing. Again, 5 is a number that you add to 5 to get zero. So these two numbers, 5 and 5, are what are called "inverses" of each other (specifically they are additive inverses, but don't worry about that for now). Imagine the number line. If you start at 0 and go five spaces to the right, you get to the number 5. If you want to get back to 0, you move five spaces back to the left (or 5). Now, you're back at 0 and you move five spaces to the left and end up at 5. What do you do to get back to 0 again? Move five spaces to the right (+5 or just 5).
5 + (5) = 0
5 + 5 = 0
Now, the way we can find the inverse of a number is by putting a negative sign in front of it. This is sometimes referred to as "negating" a number. You want to negate the number 9? It's 9. If you negate 182, you get 182. So how do you negate 11? Well, it would be (11). You just slap a negative sign in front of it. But remember from above, what is negating? It's finding the inverse, or the number that you can add to your original number to get back to 0. And we know that if we're at 11 then we need to move eleven places to the right to get back to zero, so the inverse is 11. And now you can see that (11) should be equal to 11. If you want to think about it in terms of the number line, the negative sign tells you to move the opposite direction on the number line.
8 means eight places to the RIGHT of zero on the line
8 means eight places to the LEFT of zero on the line
(8) means eight places back to the RIGHT of zero
((8)) means eight places back to the LEFT of zero
And on it goes. When you hear people talking about two negative signs "canceling each other out" this is what they're talking about, which you'll learn more about when you get to multiplication involving negative numbers. It's an easy rule to remember when you want to simplify a problem.
So back to the original problem: 3  (3) = 6
If we don't think about this as a subtraction problem, but instead think about it as an addition of negatives, then it might make a little more sense.
3  (3) = 3 + ((3)) = 6
So what's going on? We have 3 and we want to add the inverse of the inverse of 3. We know the inverse of 3 is 3 and then we take the inverse of that and we're back to 3. Or more simply, because you understand the rule now, you look at those two negative signs next to each other and simply cancel them out. Which leaves you with:
3  (3) = 3 + ((3)) = 3 + 3 = 6
I hope that wasn't too confusing.
3(3) = 6. Lets look at 3  3 first.
This is pretty easy:
__________________________
3 2 1 0 1 2 3
<
You start at 3 and then subtract 3 so now you have 0.
So how does this relate to 3(3) = 6 ?
Think of it this way:
__________________________
3 2 1 0 1 2 3
<
You start with your 3  3 = 0 equation. But there is another negative sign.
So what do we do? You flip it. You still start at 4 but you flip your arrow on the number line. Think of it as heading the opposite way of using just one negative sign.
so you have:
__________________________
3 2 1 0 1 2 3
<
and you start at the same point but flip the direction of the line so you get:
_____________________________________
3 2 1 0 1 2 3 4 5 6 7
>
When it comes down to it you just need to learn as a rule that
()() = +
(+)(+) = +
()(+) = 
(+)() = 
Hopefully that helps.
This is pretty easy:
__________________________
3 2 1 0 1 2 3
<
You start at 3 and then subtract 3 so now you have 0.
So how does this relate to 3(3) = 6 ?
Think of it this way:
__________________________
3 2 1 0 1 2 3
<
You start with your 3  3 = 0 equation. But there is another negative sign.
So what do we do? You flip it. You still start at 4 but you flip your arrow on the number line. Think of it as heading the opposite way of using just one negative sign.
so you have:
__________________________
3 2 1 0 1 2 3
<
and you start at the same point but flip the direction of the line so you get:
_____________________________________
3 2 1 0 1 2 3 4 5 6 7
>
When it comes down to it you just need to learn as a rule that
()() = +
(+)(+) = +
()(+) = 
(+)() = 
Hopefully that helps.
Think about this in a nonmathematical way: If someone said to you, "I don't want you to not enjoy yourself." It is an awkward way of saying, "I want you to enjoy yourself." But the person used 2 negatives to express a positive: "I don't (negative 1) want you to not (negative 2)enjoy yourself." When you negate something that is already negative, you are converting it to a positive, whether that's in math or communication or logic.
So, 3(3) equals 3+3, just as "I don't want you not...." equals "I want you to..."
So, 3(3) equals 3+3, just as "I don't want you not...." equals "I want you to..."
YES you do need to understand  don't just do something because someone tells you to. That's how I learned  not how I teach!
Google: national library of virtual manipulatives and scroll down to colr chip subtraction. Do this interactive activity  it shoul help
Google: national library of virtual manipulatives and scroll down to colr chip subtraction. Do this interactive activity  it shoul help
Whenever you have 2 or more negative signs, just cross them both out because they cancel each other out. They turn into a + signs. Example: 3(3)=6 3+(3)=6
im still confused too
Instead of trying to use negative numbers you can use positive numbers but flip the addition/subtraction. Whenever you see that you are adding a negative number instead subtract it as a positive number. Conversely, if you see that you are subtracting a negative then you should think about it as if you were adding a positive number.
I think of it this way. The negative sign means do the opposite. So 5  2
reads as positive 5 minus positive 2. When you have a double negative, they cancel each other out like the sentence "I don't have no pencil" really means I do have a pencilthe double negatives turn into a positive.
reads as positive 5 minus positive 2. When you have a double negative, they cancel each other out like the sentence "I don't have no pencil" really means I do have a pencilthe double negatives turn into a positive.
i do not completely understand myself, but i like to think of 3   3 as more like an old saying, a negative plus a negative equals a positive, but a positive plus a positive is still a positive, in my mind, the negatives cancel each other out, leaving a positive
I am confused by that too.
3[3]=6 because when u are adding a negative number to a negative is a positive does why 33 =6
Thus, the answer is 6. <>
0 1 2 3 4 5 6 7
>
0 1 2 3 4 5 6 7
>
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Jackfox68, you said: "I too am a confused 43(almost 44) year old. I don't get the logic behind it. You would think that if you took 3(3) you would get 6. So you start on the number line at 3 and take another 3 away from it and you get 6. 3 means you go to the left three."
I'm 44 years old and had to learn this to help my daughter. Let me try to share with you what I know, one semigeezer to another ;) ....
3  (3) = 0, NOT 6! Here's why:
You start with negative three then you take away (the operation sign tells you to subtract) negative three. Well if you take away what was there, what do you have left? Nothing, zero, nada, zip!
Put another way, think of the negative sign as a traffic sign that tells you to travel in the opposite direction. The subtraction sign tells us to go DOWN the number line. After that, we encounter a negative sign that says, "No, go the opposite way! Go UP the number line."
So, if we start at zero and go down 3 (that's the FIRST 3 in the problem) then reverse and go in the opposite direction and go UP 3 (which is subtracting the SECOND 3) we end up right where we started: ZERO!
Yet another way to look at it is that SUBTRACTING a NEGATIVE is the SAME as ADDING a POSITIVE. So...
3  (3) = becomes
3 + 3 =
Whenever you ADD two opposite numbers the answer is ALWAYS zero!
See my answers to other questions below to get a more detailed explanation of how to work with negative numbers, especially subtracting them!
Hope this helps!!
I'm 44 years old and had to learn this to help my daughter. Let me try to share with you what I know, one semigeezer to another ;) ....
3  (3) = 0, NOT 6! Here's why:
You start with negative three then you take away (the operation sign tells you to subtract) negative three. Well if you take away what was there, what do you have left? Nothing, zero, nada, zip!
Put another way, think of the negative sign as a traffic sign that tells you to travel in the opposite direction. The subtraction sign tells us to go DOWN the number line. After that, we encounter a negative sign that says, "No, go the opposite way! Go UP the number line."
So, if we start at zero and go down 3 (that's the FIRST 3 in the problem) then reverse and go in the opposite direction and go UP 3 (which is subtracting the SECOND 3) we end up right where we started: ZERO!
Yet another way to look at it is that SUBTRACTING a NEGATIVE is the SAME as ADDING a POSITIVE. So...
3  (3) = becomes
3 + 3 =
Whenever you ADD two opposite numbers the answer is ALWAYS zero!
See my answers to other questions below to get a more detailed explanation of how to work with negative numbers, especially subtracting them!
Hope this helps!!
You need to think of 3(3) as saying "three minus one times negative three" or actually write it as 31(3). You know that 1 times 3 is positive 3, so 3(3) is the same as 3+3.
well... id answer but it looks like you have enough to figure it out
I think of the   cancellation as giving you 3 apples then taking them back. Hope that helps with visualizing.
When you have two  signs right next to each other, they pair uo and make a + sign. This might help with the problems that you are having trouble with, although it is not a number line.
Yeah at first it will seem confusing but you will get the hang of it.
take the negative sign and put it opposite way of the minus sign to make a postive sign.. ()+()
My teacher told me to add/subtract the opposite. for example, say you need to answer the problem 43(+39). you add/subtract the opposite. 43+(39). now it is the same as adding negative numbers with the same signs. you add the numbers and keep the sign. so 43+(39)=82 is the same as 43(+39)=82. Hope that helps.
great work i love it thanks
when you see 2 of the same signs, ( + ) you always add. opposites subtract.
If you have an IOU for $5 and I take away the IOU, then I don't owe you anything.
3(3) = 6. Lets look at 3  3 first.
This is pretty easy:
__________________________
3 2 1 0 1 2 3
<
You start at 3 and then subtract 3 so now you have 0.
So how does this relate to 3(3) = 6 ?
Think of it this way:
__________________________
3 2 1 0 1 2 3
<
You start with your 3  3 = 0 equation. But there is another negative sign.
So what do we do? You flip it. You still start at 4 but you flip your arrow on the number line. Think of it as heading the opposite way of using just one negative sign.
so you have:
__________________________
3 2 1 0 1 2 3
<
and you start at the same point but flip the direction of the line so you get:
_____________________________________
3 2 1 0 1 2 3 4 5 6 7
>
When it comes down to it you just need to learn as a rule that
()() = +
(+)(+) = +
()(+) = 
(+)() = 
Hopefully that helps.
copy: awesome
I know this was a couple months ago when asked, but hopefully you might still find the explanation helpful. You're right that the idea of subtracting a negative is hard to grasp. It's not really intuitive and there's no easy way to explain it in a way that makes a lot of sense using a number line.
Think about what it means to be a negative number. If you have a number, let's say 5, what does 5 really represent? It represents another number that you can add to 5 to get zero. Now, what about the opposite? If you start with 5, what does 5 represent? Well, it's the same thing. Again, 5 is a number that you add to 5 to get zero. So these two numbers, 5 and 5, are what are called "inverses" of each other (specifically they are additive inverses, but don't worry about that for now). Imagine the number line. If you start at 0 and go five spaces to the right, you get to the number 5. If you want to get back to 0, you move five spaces back to the left (or 5). Now, you're back at 0 and you move five spaces to the left and end up at 5. What do you do to get back to 0 again? Move five spaces to the right (+5 or just 5).
5 + (5) = 0
5 + 5 = 0
Now, the way we can find the inverse of a number is by putting a negative sign in front of it. This is sometimes referred to as "negating" a number. You want to negate the number 9? It's 9. If you negate 182, you get 182. So how do you negate 11? Well, it would be (11). You just slap a negative sign in front of it. But remember from above, what is negating? It's finding the inverse, or the number that you can add to your original number to get back to 0. And we know that if we're at 11 then we need to move eleven places to the right to get back to zero, so the inverse is 11. And now you can see that (11) should be equal to 11. If you want to think about it in terms of the number line, the negative sign tells you to move the opposite direction on the number line.
8 means eight places to the RIGHT of zero on the line
8 means eight places to the LEFT of zero on the line
(8) means eight places back to the RIGHT of zero
((8)) means eight places back to the LEFT of zero
And on it goes. When you hear people talking about two negative signs "canceling each other out" this is what they're talking about, which you'll learn more about when you get to multiplication involving negative numbers. It's an easy rule to remember when you want to simplify a problem.
So back to the original problem: 3  (3) = 6
If we don't think about this as a subtraction problem, but instead think about it as an addition of negatives, then it might make a little more sense.
3  (3) = 3 + ((3)) = 6
So what's going on? We have 3 and we want to add the inverse of the inverse of 3. We know the inverse of 3 is 3 and then we take the inverse of that and we're back to 3. Or more simply, because you understand the rule now, you look at those two negative signs next to each other and simply cancel them out. Which leaves you with:
3  (3) = 3 + ((3)) = 3 + 3 = 6
I hope that wasn't too confusing.
more copy!!!!!!!!!!!!!!
This is pretty easy:
__________________________
3 2 1 0 1 2 3
<
You start at 3 and then subtract 3 so now you have 0.
So how does this relate to 3(3) = 6 ?
Think of it this way:
__________________________
3 2 1 0 1 2 3
<
You start with your 3  3 = 0 equation. But there is another negative sign.
So what do we do? You flip it. You still start at 4 but you flip your arrow on the number line. Think of it as heading the opposite way of using just one negative sign.
so you have:
__________________________
3 2 1 0 1 2 3
<
and you start at the same point but flip the direction of the line so you get:
_____________________________________
3 2 1 0 1 2 3 4 5 6 7
>
When it comes down to it you just need to learn as a rule that
()() = +
(+)(+) = +
()(+) = 
(+)() = 
Hopefully that helps.
copy: awesome
I know this was a couple months ago when asked, but hopefully you might still find the explanation helpful. You're right that the idea of subtracting a negative is hard to grasp. It's not really intuitive and there's no easy way to explain it in a way that makes a lot of sense using a number line.
Think about what it means to be a negative number. If you have a number, let's say 5, what does 5 really represent? It represents another number that you can add to 5 to get zero. Now, what about the opposite? If you start with 5, what does 5 represent? Well, it's the same thing. Again, 5 is a number that you add to 5 to get zero. So these two numbers, 5 and 5, are what are called "inverses" of each other (specifically they are additive inverses, but don't worry about that for now). Imagine the number line. If you start at 0 and go five spaces to the right, you get to the number 5. If you want to get back to 0, you move five spaces back to the left (or 5). Now, you're back at 0 and you move five spaces to the left and end up at 5. What do you do to get back to 0 again? Move five spaces to the right (+5 or just 5).
5 + (5) = 0
5 + 5 = 0
Now, the way we can find the inverse of a number is by putting a negative sign in front of it. This is sometimes referred to as "negating" a number. You want to negate the number 9? It's 9. If you negate 182, you get 182. So how do you negate 11? Well, it would be (11). You just slap a negative sign in front of it. But remember from above, what is negating? It's finding the inverse, or the number that you can add to your original number to get back to 0. And we know that if we're at 11 then we need to move eleven places to the right to get back to zero, so the inverse is 11. And now you can see that (11) should be equal to 11. If you want to think about it in terms of the number line, the negative sign tells you to move the opposite direction on the number line.
8 means eight places to the RIGHT of zero on the line
8 means eight places to the LEFT of zero on the line
(8) means eight places back to the RIGHT of zero
((8)) means eight places back to the LEFT of zero
And on it goes. When you hear people talking about two negative signs "canceling each other out" this is what they're talking about, which you'll learn more about when you get to multiplication involving negative numbers. It's an easy rule to remember when you want to simplify a problem.
So back to the original problem: 3  (3) = 6
If we don't think about this as a subtraction problem, but instead think about it as an addition of negatives, then it might make a little more sense.
3  (3) = 3 + ((3)) = 6
So what's going on? We have 3 and we want to add the inverse of the inverse of 3. We know the inverse of 3 is 3 and then we take the inverse of that and we're back to 3. Or more simply, because you understand the rule now, you look at those two negative signs next to each other and simply cancel them out. Which leaves you with:
3  (3) = 3 + ((3)) = 3 + 3 = 6
I hope that wasn't too confusing.
more copy!!!!!!!!!!!!!!
I started with the idea that the negative sign means do the opposite, so 5  2 reads as positive 5 minus positive 2. When you have two negatives: 5 2, they are like a double negative which equals a positive like in the sentence I don't have no bananas today, which really means I do have bananas.
ing twice will move the other way.
this is crazy and confusing i agree with you sw84902
what happens if you get 7+4???? does the minus still turn into a +?
no, it doesn't, you still have (+7)+(4) = (+3), to 7 positive units you add 4 negative units, that substract themselves from this positive and you are left with 3 positive units...
cheers
cheers
Think of 4 as a loss of 4, so when 7 gets a loss of 4 it's basically just 7  4.
its basically 74=3
no. it's still a . You can always to ignore +
no it still is a minus
no it turns into 74 which equals 3 by the way
Yes it does. It still meets the rule.
In the problem 7 + (4), you can solve in two ways.
Method 1: The integer 4 means that, if you tried this on a number line, you would plot the 7 and move to the left for 4 units, since the negative numbers are on the left of 0. This would give you 3.
Method 2: You can use a process called LCO, which stands for Leave Change Opposite. Using 7 + (4), the step Leave comes first. You leave the 7 alone and do not change it. In the Change step, you change the "+" symbol into a "" symbol (since subtraction is the inverse of addition). Finally is the Opposite step. The opposite of 4 is 4, because they cancel each other out. So you now have 7  4, which has a difference of 3.
Method 1: The integer 4 means that, if you tried this on a number line, you would plot the 7 and move to the left for 4 units, since the negative numbers are on the left of 0. This would give you 3.
Method 2: You can use a process called LCO, which stands for Leave Change Opposite. Using 7 + (4), the step Leave comes first. You leave the 7 alone and do not change it. In the Change step, you change the "+" symbol into a "" symbol (since subtraction is the inverse of addition). Finally is the Opposite step. The opposite of 4 is 4, because they cancel each other out. So you now have 7  4, which has a difference of 3.
+ =  so 74= 3.
yup this is just so i can answer asdfghj asdfghj
No, I don't think so. If I'm wrong, sorry for that...
7+(4) is the same as 74, which equals 3.
Answer 3 because you would turn the + into a  because if a  and a + are together you get a .
it would be 3 because its 7 positive  4 negative so it turns into 3 positive
yes use integer hill so the 7 is bigger than 4 than just subtract and u get 3
When your doing 7+4 the minus 4 needs parentheses and it will make sense. So it's almost like 74.
do you mean 7+4 if you mean this then is is just negative 7 +4 which is 3
Here are some tips,Negative adding and subtracting is just like regular addition and subtraction. But,when you get a question with a regular number and a negative number (Example: 9+ 4)
You simply subtract 4 from 9 :)
You simply subtract 4 from 9 :)
no. think about it. there is a positive plus a negative. so you SUBTRACT 74. Hope this helps :)
Yes. 7+(4) becomes 7(+4) or 74. To spell it out plainly: Seven plus negative four is the same as seven minus four. Your answer is 3. Good question :)
No, the  stays a . Its like doing 74, with a positive 7 taking a loss of 4. Therefore, 7+4(74) is Positive 3.
well if u see a + and a  together it turns to a minus ex:5+3=2
no it will be 74 becos + equals subtraction and ur answer is 3
No, when you add a negative number it is the same as subtracting
Think of 4 as 04
Instead of 7+4 you have 7+04
7+0 = 7
so 74 = 3
Think of 4 as 04
Instead of 7+4 you have 7+04
7+0 = 7
so 74 = 3
7+(4) is the same thing as 74 (since adding a negative to a positive will result in subtraction) so the answer here should be 3.
Yes it does turn into a negative
3 because 7 is bigger than negative three so 74=3
No, I don't think so. I think you would get 3 because of the one minus. But that's my understanding. Hope that helps!
no, the + turns into a  and the equation is now 74 so the answer is 3.
No it turns into a negative number.
no it equals just 11
Actually these are the rules.
+=
+=
++=+
=+
So that would be a plus.
+=
+=
++=+
=+
So that would be a plus.
No. You subtract 4 from 7 instead
No because every time when theres a positive number and a negative number
The negative symbol stays wth the product.
The negative symbol stays wth the product.
There is no minus, it is the negative sign
No. The 4 is subtracted from the 7 and = 3
no if you add a negative to a positive or another negative it is like subtracting a positive.
no only two minus is +
when you have 7+4 it is like minus
when you have 7+4 it is like minus
Adding a negative is the same as subtracting a positive. So just do 74. It would be 3.
you get positive 3. in this problem, the negative number does not switch to positive.
no the anwser is 3 cuz your stupid
7+(4)= 3 because a + and a  turn into a  , so that makes +(4) a 4 .
No the minus does not turn into a plus
No you would have to turn the negative number to stay a negative because a positive and negative is a negative.
1+1=11
1+1=11
Yes u keep the problem
Well, first of all you have to put parenthisis around the four like this 7+(4). Then since the positive 7 is bigger than the 4 so the answer is going to be a positive
7+4... I make it seem like I have $7.00 and spend $4.00 = 3
no, it doesn't the + gets removed so the problem then is 74=3
7 + 4 is the same as 7  4, but it just looks weird. You could write +7 + 4, also. All are the same.
It's really confusing until it finally clicks!
yes, as long as the + number is bigger than the  number adding them always equals a + number
No your answer will be a 
Nope. In this case, adding a negative number is the same thing as subtracting by that number. In the example you provided 7+4 is the same thing as 74 which the answer is 3.
no, it does not because 7+4 is the same as 4+7 only two negitives by each other make a plus.
ex:7+4=7 4=3 your answer is negative 3
yes and then it equals 3
When a question has the signs + simultaneosly like the above the question, then we do is subtraction since + is . Therefore the answer of your question becomes 74=3
no. the minus remains a minus
Yes it does... use the highest absolute value and use that number's value. In this case the Absolute Value is 7 so the problem would just be 7+4=11.
you if that answer has a minus you change it to plus and get the answer!
no because there is already a +
Of course not!
No cause a positive + a negative = negative
7 + 4 is the same as drawing this on the number line:
```
4 3 2 1
*<<<*
>
          
0 1 2 3 4 5 6 7 8 9 10
````
```
4 3 2 1
*<<<*
>
          
0 1 2 3 4 5 6 7 8 9 10
````
7+4 is the same thing as 74, so it's 3 . If you had subtracted 8 from 7 or added negative 8 to seven, you would be in the negatives. I hope this helps! :)
7+4 = 3 and no minus does not turn into a +
I believe it would be 2 but I'm not positive
when you see a + and  you automatically change it into a minus. so 7 + (4) would equal 74 which is 3
The answer would be positive 3 and yes the minus does turn into a positive because your subtracting the 4 from 7and since the positive number is bigger you don't reach to the negative numbers yet
No. Think of it this way: An odd number of negatives ahead of a number will always give a negative number. An even number always gives a positive answer.
Examples (You wouldn't see them written like this, but just to illustrate the idea):
+  4 = 4
    4 = +4
+  +  4 = + 4
   4 = 4
etc. Hope I helped!
Examples (You wouldn't see them written like this, but just to illustrate the idea):
+  4 = 4
    4 = +4
+  +  4 = + 4
   4 = 4
etc. Hope I helped!
you help me out a little bit but how do you subtract (13)(7)?
no its basically 74
:)
:)
When adding or subtracting, the negative sign "flips" the operator in front of it.
So "3 + ˉ2" is the same as "3  2", and "3  ˉ2" is the same as "3 + 2".
So "3 + ˉ2" is the same as "3  2", and "3  ˉ2" is the same as "3 + 2".
No the minus stay minus
No, 7 + 4 is 3 because + a negative is equal to just subtracting.
answer is 3
and your question should be 7+(4)
i hope this helps
and your question should be 7+(4)
i hope this helps
It doesn't. It's as if you put 0 in between: 7+04=74=3.
I use K.C.C Keep Change Change, So Id Do 7 Stays +> and 4>+4 So 74= The answer
yes he turned into a +
The answer is a positive number since the absolute value of 7 is greater than 4. BUT, the"+" do NOT turn to a +！！！ It is still 74. Only two minus sign together like 7(4) makes a + (or a plus sign), So the 7(4) becomes 7+4.
no + = 
 = +
++ = +
+ = 
basicly if there are two the same it's a + and if the two are different it's a 
 = +
++ = +
+ = 
basicly if there are two the same it's a + and if the two are different it's a 
That would be 3. Because you're going 7 to the right of 4.
try making it 4+7 see if that helps
yes by kcc(keep change change)
no, because the calculation is 'adding 4" , which is the same as subtracting 4.
So, the minus remains a minus.
So, the minus remains a minus.
7 + (4) = 3.
If you have a plus sign and a negative number, simply cut out the plus sign and replace with the negative sign.
7  4
Hope that helped.
If you have a plus sign and a negative number, simply cut out the plus sign and replace with the negative sign.
7  4
Hope that helped.
When you add a negative number. It's similar to subtracting a positive, since the negative number goes backwards. So you have to subtract 4 from 7, and get 3. Positive 3!
The easiest way to visualize this would be with the number line. If it were a positive four, you would move to the right on the number line as normal (7+4=11). Since it's a negative four, you would move in the opposite direction on the number line. (74=3).
The minus cancels out, so you are left with 7 + 4. Does that help a little bit?
If not I am sorry. I thought that would help. I might be wrong.
If not I am sorry. I thought that would help. I might be wrong.
it will be 11
As 7 + 4=5 6 7 8 9 10 11
= 11
As 7 + 4=5 6 7 8 9 10 11
= 11
If you have 7 and you add a 4 to it, it's the same as "74" to witch the answer is 3
if you add a number that is being subtracted it would be the same as just subtracting it.
I would say that if you were to start with a bank account with $7 in it and then you added debt of $4 then this would be the same as 7+ 4=? You start in the positive with 7 on the number line. Then you must add a negative number. A negative number means you must travel left from 7 on the number line. So,
3...4...5...6...7
3...4...5...6...7
The negative four does not become a positive. In this case, your answer would be three because it is technically saying that the problem is 74 because you have a positive number and you are adding a negative number to it.
You subtract like it would be a problem with positive numbers or like any regular problem you could also just make a number line
If you have a even number of negitive signs, then it becomes a positive. If you don't, it becomes a negitive.
Ex.
1(9)=10
1+(9)=(8)
Sometimes you can even find this...
1(9)=?
Then you just count the signs and figure it out.
1(9)
=1+9
=10
Hope this helps.
Ex.
1(9)=10
1+(9)=(8)
Sometimes you can even find this...
1(9)=?
Then you just count the signs and figure it out.
1(9)
=1+9
=10
Hope this helps.
no it does not, when you have two different signs you subtract and keep the sign of the larger number 7 minus 4 is 3 more positives than negatives so the three stays positive.
Yes. But the + turns into a minus too.
7+4=7+4
7+4=7+4
so go 74 break it apart 7 take out the first  sign then its74=3 then add the sign to the answer so its 3
Actually, the best way to explain it, it's just to say, that the minus is always the main. If you have + at the same time, you should use subtraction.
no the minus don't conberts into a plus the minus and the plus converts in a minus because + plus  is  and the answer is 3
then do math son !!
I believe there is a video on what you are talking about.
yeah dude i think you are correct
Yes it does.7+4 is 3. Try and figure it out in the video{secretly, though}
So a second Minus means that its a plus?
Think of it as removing a subtraction. To remove a subtraction, you have to add. For example, if I start with 5 and subtract 3 from it, I end up with 2.
5  3 = 2
Now, if I want to get back to 5, I have to remove the subtraction I did earlier.
2  3 = 5
The double negative sign in this example could then be interpreted as "Start at 2, and remove a subtraction of 3".
2 "Start at 2,"
 "and remove"
3 "a subtraction of 3"
Once again, to remove a subtraction, you have to add. So "remove a subtraction" becomes "add"
2 "Start at 2,"
+ "and add"
3 "3"
2 + 3 = 5
5  3 = 2
Now, if I want to get back to 5, I have to remove the subtraction I did earlier.
2  3 = 5
The double negative sign in this example could then be interpreted as "Start at 2, and remove a subtraction of 3".
2 "Start at 2,"
 "and remove"
3 "a subtraction of 3"
Once again, to remove a subtraction, you have to add. So "remove a subtraction" becomes "add"
2 "Start at 2,"
+ "and add"
3 "3"
2 + 3 = 5
Yes,apparently
yes that means u add the oppisite meaning : 2 2=4 2 plus a negitive 2 equal a postive 4
I GUESS HE SAID THAT AN HE IS SOO SMART
Yes just like two odds make an even and vice versa and one odd and one even make an odd and vice versa. So =+ and ++=+ and += and ++
ya if there is too  it = +
yes it does, I always thought of it as the two negatives make+ +=+
Yes. The minuses cancel each other out. Example: 77, automatically change it to 7+7.
Yeah, pretty much. Subtracting a negative number causes the negatives to cancel out, so basically it is just the same thing as adding it as if it were a positive number. 15  15 = 15 + 15.
I hope this helps. :)
I hope this helps. :)
+ + means it stays positive (I don't know where that would come up though)
+  means it is negative
  means it is positive
+  means it is negative
  means it is positive
Yes if there is ever a minus with a negative number next to it they will cancel each other out which will make a positive.
it depends on which number is bigger you use the sign of the bigger number
cowgirl3425
You have answered a question here. See the big "A." next to your comment. If this confuses you and you want help, you should ask a question. When you do ask a question, be more specific about what confuses you. I went to 5:28 in the video and all Sal said was, "...our final answer is negative 2." (2) As a result I can't help you, except to say watch the video again and ask a question in the correct place.
You have answered a question here. See the big "A." next to your comment. If this confuses you and you want help, you should ask a question. When you do ask a question, be more specific about what confuses you. I went to 5:28 in the video and all Sal said was, "...our final answer is negative 2." (2) As a result I can't help you, except to say watch the video again and ask a question in the correct place.
But i don't get 5:28 it still confuses me.
yes or in Spanish si.
Alternatively, two minuses is the SAME as two pluses, which is why they can be interchanged.
Another way to put it, if you subtract a negative, you move to the right just like you would by adding a positive on the number line. Since they move the same way, they work the same.
Another way to put it, if you subtract a negative, you move to the right just like you would by adding a positive on the number line. Since they move the same way, they work the same.
Yes, the minuses do cancel each other out.
I still don't understand adding and subtracting negative numbers. I need some help could someone explain this to me or refer me to a site or book that will explain adding and subtracting negative numbers, please!
Adding and subtracting negative numbers is TRICKY, so I've spent the last couple of days reviewing the subject. Cbelle2000, your first example problem (i.e., 3+(4)=7) is solved correctly. (You wondered about how NEG + NEG is "supposed" to result in a positive. Not really. ANY TIME you ADD integers/numbers that share the SAME sign [+/] their sum/answer will ALWAYS have the same sign as the original numbers [addends]. So, 3+4 [both positive] =7; 3+(4) [both negative] =7.)
SUBTRACTING two negatives, though, is a different matter, and this is where you went wrong. The answer to your second example problem (i.e., 3  (5)=8) should be 2. Here is why (get out your scratch paper and follow along – doing is learning!):
We start with 3 and subtract 5 from it. The first number is called the minuend; the second number is the subtrahend. (Not necessarily important to remember, just interesting to know....) So, we have:
3  (5) =
Think of negative signs as traffic signs that tell you to hit the brakes and then go in the OPPOSITE direction. So, because subtracting says "go DOWN the number line", when you see it followed by a number with a negative sign, that negative sign is saying, "Nope! Hit the brakes!! Go the other way! Go UP the number line!" In other words, ADD. Subtracting a negative number is the SAME as adding a positive number, so the problem NOW reads like this:
3 + 5 =
Simple enough, right? We aren't done, though. What's next?
ADDING opposite signed integers together is very easy if you remember the following:
1) Ignore the negative sign. That's right, drop it! (For now....)
2) SUBTRACT the smaller number from the larger number.
3) The answer (called the DIFFERENCE) is now given a positive or negative sign, depending on which absolute number (in this case, 3 and 5) is bigger. So....
3 + 5 becomes 5  3 and the answer is 2. The answer is also POSITIVE because before we converted to a final subtraction problem the number with the larger absolute value (see the video on absolute values) was positive 5, not negative 3.
So, here is our completed problem:
3  (5) = 2!
Let's do that again, without the commentary, as you would on your homework sheet:
3  (5) becomes
3 + 5 becomes
5  3 = 2 *
*Remember, looking at the middle step where it is an addition problem, 5 has greater absolute value than 3, so the final answer, 2, is positive, like the 5!
What if the original minuend and subtrahend were reversed, though? The answer would be 2! Here's why:
5  (3) becomes
5 + 3 becomes
5  3 = 2 BUT
In the middle step, negative 5 has a greater absolute value than positive 3, so....
The answer is 2!
You can also think through NEG  NEG problems this way:
3  (5) =
Say to yourself: "Self, the bigger absolute number, 5, minus 3 equals 2. Hold that thought!"
Now say to yourself: "Self, the second number in this problem, the subtrahend, is a negative 5, and if I went through all the trouble to do it on paper it would become a positive 5. Now, hold that thought!"
Finally, say to yourself: "SELF! The absolute value of positive 5 is greater than the absolute value of negative 3, so the answer is positive 2!"
Now,let's do it with the numbers reversed:
5  (3) =
Say to yourself: "Self, the bigger absolute number, 5, minus 3 equals 2. Hold that thought!"
Now say to yourself: "Self, the second number in this problem, the subtrahend, is a negative 3, and if I went through all the trouble to do it on paper it would become a positive 3. Now, hold that thought!"
Finally, say to yourself: "SELF! The absolute value of negative 5 is greater than the absolute value of positive 3, so the answer is negative 2!"
...and there you go!! It becomes very simple when you understand the steps. Subtracting negative numbers is the trickiest, but the most fun, too, when you know what to do.
You can try this with any two negative numbers. Check your answers with a calculator until you are comfortable enough to do it without having to check. Just plug in your negative numbers:
NEG  NEG = becomes
NEG + POS = becomes
Larger absolute number  smaller absolute number =
The answer is signed either positive or negative depending on the larger absolute addend in the second step.
I hope this helps! (Sorry it was so LENGTHY!) Have fun!!!
SUBTRACTING two negatives, though, is a different matter, and this is where you went wrong. The answer to your second example problem (i.e., 3  (5)=8) should be 2. Here is why (get out your scratch paper and follow along – doing is learning!):
We start with 3 and subtract 5 from it. The first number is called the minuend; the second number is the subtrahend. (Not necessarily important to remember, just interesting to know....) So, we have:
3  (5) =
Think of negative signs as traffic signs that tell you to hit the brakes and then go in the OPPOSITE direction. So, because subtracting says "go DOWN the number line", when you see it followed by a number with a negative sign, that negative sign is saying, "Nope! Hit the brakes!! Go the other way! Go UP the number line!" In other words, ADD. Subtracting a negative number is the SAME as adding a positive number, so the problem NOW reads like this:
3 + 5 =
Simple enough, right? We aren't done, though. What's next?
ADDING opposite signed integers together is very easy if you remember the following:
1) Ignore the negative sign. That's right, drop it! (For now....)
2) SUBTRACT the smaller number from the larger number.
3) The answer (called the DIFFERENCE) is now given a positive or negative sign, depending on which absolute number (in this case, 3 and 5) is bigger. So....
3 + 5 becomes 5  3 and the answer is 2. The answer is also POSITIVE because before we converted to a final subtraction problem the number with the larger absolute value (see the video on absolute values) was positive 5, not negative 3.
So, here is our completed problem:
3  (5) = 2!
Let's do that again, without the commentary, as you would on your homework sheet:
3  (5) becomes
3 + 5 becomes
5  3 = 2 *
*Remember, looking at the middle step where it is an addition problem, 5 has greater absolute value than 3, so the final answer, 2, is positive, like the 5!
What if the original minuend and subtrahend were reversed, though? The answer would be 2! Here's why:
5  (3) becomes
5 + 3 becomes
5  3 = 2 BUT
In the middle step, negative 5 has a greater absolute value than positive 3, so....
The answer is 2!
You can also think through NEG  NEG problems this way:
3  (5) =
Say to yourself: "Self, the bigger absolute number, 5, minus 3 equals 2. Hold that thought!"
Now say to yourself: "Self, the second number in this problem, the subtrahend, is a negative 5, and if I went through all the trouble to do it on paper it would become a positive 5. Now, hold that thought!"
Finally, say to yourself: "SELF! The absolute value of positive 5 is greater than the absolute value of negative 3, so the answer is positive 2!"
Now,let's do it with the numbers reversed:
5  (3) =
Say to yourself: "Self, the bigger absolute number, 5, minus 3 equals 2. Hold that thought!"
Now say to yourself: "Self, the second number in this problem, the subtrahend, is a negative 3, and if I went through all the trouble to do it on paper it would become a positive 3. Now, hold that thought!"
Finally, say to yourself: "SELF! The absolute value of negative 5 is greater than the absolute value of positive 3, so the answer is negative 2!"
...and there you go!! It becomes very simple when you understand the steps. Subtracting negative numbers is the trickiest, but the most fun, too, when you know what to do.
You can try this with any two negative numbers. Check your answers with a calculator until you are comfortable enough to do it without having to check. Just plug in your negative numbers:
NEG  NEG = becomes
NEG + POS = becomes
Larger absolute number  smaller absolute number =
The answer is signed either positive or negative depending on the larger absolute addend in the second step.
I hope this helps! (Sorry it was so LENGTHY!) Have fun!!!
It occurs to me that in my previous post I was only dealing with subtracting TWO negative numbers. What if you are only subtracting with ONE negative number? That is even easier (when you know what to do)!
Here is how:
9  4 =
The single negative sign (9) tells me NOT to subtract, but to ADD, so, the problem now looks like this:
9 + 4 =
The answer, of course, is 13. Wait! Is it positive 13 or negative 13? This is easy to know.
Look at the original problem: 9  4. The first number (called the MINUEND) is a negative number. That tells you the answer will ALSO be a negative number:
9  4 = 13!
So, whenever you are subtracting with ONE negative number, it becomes an addition problem with the answer receiving the same sign (+/) as the original minuend! It is as simple as that!!
Let's do a few (get out your scratch paper again and check with your calculator until you have it down):
9  4 = 13 (9 + 4)
9  (4) = 13 (9 + 4)
4  9 = 13 (4 + 9)
4  (9) = 13 (4 + 9)
For fun, here are some more:
1,234  (419) = 1,653 (1,234 + 419)
1,234  419 = 1,653 (1,234 + 419)
419  (1,234) = 1,653 (419 + 1,234)
419  1,234 = 1,653 (419 + 1,234)
As you can see from all these examples, the difference always carries the same sign as the minuend. It could not be any easier!
To sum it up:
When subtracting with ONE negative number, simply ADD the two absolute values (see the video on absolute values) and then assign the answer the same sign as the original minuend. Voila! You're done!
Have fun!!
Here is how:
9  4 =
The single negative sign (9) tells me NOT to subtract, but to ADD, so, the problem now looks like this:
9 + 4 =
The answer, of course, is 13. Wait! Is it positive 13 or negative 13? This is easy to know.
Look at the original problem: 9  4. The first number (called the MINUEND) is a negative number. That tells you the answer will ALSO be a negative number:
9  4 = 13!
So, whenever you are subtracting with ONE negative number, it becomes an addition problem with the answer receiving the same sign (+/) as the original minuend! It is as simple as that!!
Let's do a few (get out your scratch paper again and check with your calculator until you have it down):
9  4 = 13 (9 + 4)
9  (4) = 13 (9 + 4)
4  9 = 13 (4 + 9)
4  (9) = 13 (4 + 9)
For fun, here are some more:
1,234  (419) = 1,653 (1,234 + 419)
1,234  419 = 1,653 (1,234 + 419)
419  (1,234) = 1,653 (419 + 1,234)
419  1,234 = 1,653 (419 + 1,234)
As you can see from all these examples, the difference always carries the same sign as the minuend. It could not be any easier!
To sum it up:
When subtracting with ONE negative number, simply ADD the two absolute values (see the video on absolute values) and then assign the answer the same sign as the original minuend. Voila! You're done!
Have fun!!
my teacher showed me this when i was confused in adding and sudtracting neegitave numbers it is like a cheat sheet
+ (+)  = 
 (+) + = 
+ (+) + = +
 ()  = 
hope it works for you :D :):):):):):):):):):
+ (+)  = 
 (+) + = 
+ (+) + = +
 ()  = 
hope it works for you :D :):):):):):):):):):
Hi, I would love to help but beware it may be confusing but most likely not.
Okay so I do this with a couple of tricks.
It seems easier when you do this, so I will break it down.
If you want to add negative numbers together, this following trick will help you...
All I do (Sorry, I keep repeating myself, bad habit) is... This part will be confusing if I dont give you an example, so here you go,
3+4=___
This is simple, what is 3+4, 7 right. So once you add the numbers then all you do is put the negative sign infront of it.
Which would equal 7.
Which frankly I have NO idea if this is right because isnt a negative plus a negative SUPPOSED to equal a possitive, huh. Well that's what i do anyway so let's move onto subtracting.
3(5)=
This was tricky and it took alot of doing for me to understand subtracting negatives, but finally yet slowly I passed this portion. So my trick for this is... what is 3+5? 8. So then i put a negative sign infront of the number... which would equal 8! But the number line deal also works... hope I helped.
Okay so I do this with a couple of tricks.
It seems easier when you do this, so I will break it down.
If you want to add negative numbers together, this following trick will help you...
All I do (Sorry, I keep repeating myself, bad habit) is... This part will be confusing if I dont give you an example, so here you go,
3+4=___
This is simple, what is 3+4, 7 right. So once you add the numbers then all you do is put the negative sign infront of it.
Which would equal 7.
Which frankly I have NO idea if this is right because isnt a negative plus a negative SUPPOSED to equal a possitive, huh. Well that's what i do anyway so let's move onto subtracting.
3(5)=
This was tricky and it took alot of doing for me to understand subtracting negatives, but finally yet slowly I passed this portion. So my trick for this is... what is 3+5? 8. So then i put a negative sign infront of the number... which would equal 8! But the number line deal also works... hope I helped.
Here's the lesson summarized in an easier way to understand, you don't have to think about the direction of arrows in your head (I learned this in class):
 + (negative with positive) → subtract the numbers and keep the sign of the biggest number. Example: 7 + 8 = ? Subtract 8  7 and add the sign of the biggest number to the result. The biggest number is 8 (positive), so you keep the positive sign. So 7 + 8 = 1 (or +1)
  (negative with negative) → add the numbers and keep the sign of the biggest number. 24 = 2+4 = 6. Then add the negative sign from 4 (biggest number) and it becomes 6.
+ + (positive with positive) → add the numbers and keep the sign of the biggest number. 6+6 = 12.
Easy and simple to remember!
 + (negative with positive) → subtract the numbers and keep the sign of the biggest number. Example: 7 + 8 = ? Subtract 8  7 and add the sign of the biggest number to the result. The biggest number is 8 (positive), so you keep the positive sign. So 7 + 8 = 1 (or +1)
  (negative with negative) → add the numbers and keep the sign of the biggest number. 24 = 2+4 = 6. Then add the negative sign from 4 (biggest number) and it becomes 6.
+ + (positive with positive) → add the numbers and keep the sign of the biggest number. 6+6 = 12.
Easy and simple to remember!
If i have 10 pennies and take away 1 I have 9 pennies. 10 1 = 9
Now I have 9 pennies and and decide to give back that minus 1.
9  1 = 10. I guess it just shows as a minus because it was taken away in the past. If you never gave it away in the first place and you got a penny it would just be 9 + 1 but since it was giving back something that happened before we are subtracting that negative transaction which means we are adding it back to our balance. I had trouble with this one too. Hope that helps.
Now I have 9 pennies and and decide to give back that minus 1.
9  1 = 10. I guess it just shows as a minus because it was taken away in the past. If you never gave it away in the first place and you got a penny it would just be 9 + 1 but since it was giving back something that happened before we are subtracting that negative transaction which means we are adding it back to our balance. I had trouble with this one too. Hope that helps.
for subtracting you imagine the problem without the postitive and negative signs, then you find the difference of the numbers (if there are two) and take the sign (positive or negative) of the larger number
Think of it as riding on an elevator. If I am on the 10th floor and I need to go down to floor 5, the problem would be written like this: 10  5. Simple addition there. But what if I am on the 5th floor and now I need to get to the below ground parking garage on level 3. The problem would be written like this 5  (3). The answer would be 8. You could visualize a building with a parking garage beneath. Count in your head how many floors you are going down (subtractions) or up (addition). Don't forget that ground level is not the first floor. That is zero. Basically we are taking the number line and flipping it vertical. http://thetutorhouse.com
KHAN ACADEMY
just when you see the first # smaller than the second # that means you will get a Negative #. If you need more help keep on asking until some one can actually help you.
isnt 3  (3) equal to 6? hows it = +6 i didnt get it?
two negative numbers added becomes a positive.
3 + 3 is zero they cancel each other out. Just need to practice. I m on here to practice too.
You can also think that () If you connect some lines you get... +!!!
the answer is six because your taking away the number that holds back the other number from growing bigger
you can add the oppisite if there is a minus sign. so 3(3. so you turn the minus sign into a plus. then turn the negetive into a positive. so it turns into 3+3=6
Even though I read the questions and answers I still don't get it. Please reply.
Imagine you have 6 Tables, 3 Tables are Clean (Positive) But the other 3 are Stained (Negative), After you Clean the stains off (Subtract) you now have 6 Clean Tables.
when you put parenthesis on a negative number, it turns into a positive number.if a negative number turns into a positive number then the minus sign will turn into a addition sign.3+3=6.i hope you got this!
I'll give you example O=+ and o= OOOooo=OOOOOO because when negatives are together it equals positive(o=negative and=negative ,so OOO minus with ooo wich is negative + negative so it is positive)For example; 1(1)=2think... Oo=?Pic. OOO you have three But then somebody came to you and stole ooo negative three,think if the robber gets three you will have none BUT the robber took negative three so you get three instead
well i guess your saying 33=0
Because Negative+Negative=positive and the operations switch when there is two numbers so 3+3=+6.
look at my answer right under your question.
its 0 because of absolute value for 3 so change it to subtraction 33=0
Well, 3 (3) is like saying 3+(3). The negative of 3 is positive 3. Therefore, 3+3=6
pretend you have 3 dollars and you owe your mom 3 dollars because she did your chores 3 dollars is the money of yours you owe it to your mom which is negative 3 dollars so you subtract 3 by 3 because you give money away
when you subtract a positive from a negative you are really just adding, who knew kindergarten math would help with adding and subtracting negative numbers!
Should I pretend or should I confirm?
pretend ( in the problem is an addition sign. so it would be 3+3=6
Quinn, I had d same doubt dat is y i asked d question
a a = a? if a=3 den?? 33=+3 how can dat hapen?
andrew2002sac i din get u/!
andrew2002sac i din get u/!
A minus plus a minus equals a plus.
negative times a negative is a positive
It cancels out the negative sign and you add instead of subtract no clue why.
Hope this helped!!
Hope this helped!!
it took me forever to figure it out
Yeah, it took me a second to get it too lol.
THANK WHORLEDPEAS!
YEP it helps thank u all guys and gals
thank u all of whom answered my query
At 5:28 I too was confused as to the warrant for the minus symbol canceling out. I don't understand this. If it cancels itself out, isn't it redundant? And if so, why is it that way?
That's a great question, actually. To answer your question, I'll be blunt and simple: It is redundant. If you are going on a day trip to a park, and need $15 for admissions and want $15 for food, you probably won't say that you'll need 15  15 dollars, and this would be a good case of where you don't need to write it out like this. That doesn't mean that this stuff isn't useful, however.
You are probably wondering why this stuff is even important, if it's so redundant like that anyway. Well, it is more useful in algebra, when dealing with variables, and for many, many other purposes. I think you will probably see that with time. For example, what if you are subtracting a variable, and what if you don't know if the variable is positive or negative? Let's look at this:
y = 8  x
I'm assuming you have a knowledge of basic algebra (I understand that this is a prealgebra playlist). Basically, this says that the variable Y, will equal 8 minus whatever X equals. If X is 5, than Y will be 8  5, which equals 3, so Y is 3 when X is 5.
But anyway, you don't actually know what X will equal. If you put positive numbers in for X, you are just doing basic subtraction, but what will Y equal when X is, say, 2?
Here, we have Y = 8  2... Redundant, huh? But if we didn't know how to do this kind of subtraction, our equation y = 8  x would only work with positive numbers for X. But, since we know how to subtract negative numbers, we know that Y = 10 when X = 2. But we would be scratching our heads wondering what to do with this if we didn't know how to do this kind of subtraction.
Or what if you are adding or subtracting different equations? (See the "systems of equations" in the algebra playlist). Here, you'll also run into such "redundant" math operations.
It is for reasons like this when you are dealing with variables that you need to worry about this stuff. It's because you don't know if the variables contain positive or negative numbers. It's an extremely foundational concept in algebra, and it is my belief that you would not be able to pass an algebra course without learning this, because there is so much going on with variables where you don't know if the variables contain positive or negative numbers. It will probably become more clear to you as you go on towards algebra. I think that you'll see that there are a huge number of applications to this stuff, even though it seems redundant at first.
I hope this helps!
You are probably wondering why this stuff is even important, if it's so redundant like that anyway. Well, it is more useful in algebra, when dealing with variables, and for many, many other purposes. I think you will probably see that with time. For example, what if you are subtracting a variable, and what if you don't know if the variable is positive or negative? Let's look at this:
y = 8  x
I'm assuming you have a knowledge of basic algebra (I understand that this is a prealgebra playlist). Basically, this says that the variable Y, will equal 8 minus whatever X equals. If X is 5, than Y will be 8  5, which equals 3, so Y is 3 when X is 5.
But anyway, you don't actually know what X will equal. If you put positive numbers in for X, you are just doing basic subtraction, but what will Y equal when X is, say, 2?
Here, we have Y = 8  2... Redundant, huh? But if we didn't know how to do this kind of subtraction, our equation y = 8  x would only work with positive numbers for X. But, since we know how to subtract negative numbers, we know that Y = 10 when X = 2. But we would be scratching our heads wondering what to do with this if we didn't know how to do this kind of subtraction.
Or what if you are adding or subtracting different equations? (See the "systems of equations" in the algebra playlist). Here, you'll also run into such "redundant" math operations.
It is for reasons like this when you are dealing with variables that you need to worry about this stuff. It's because you don't know if the variables contain positive or negative numbers. It's an extremely foundational concept in algebra, and it is my belief that you would not be able to pass an algebra course without learning this, because there is so much going on with variables where you don't know if the variables contain positive or negative numbers. It will probably become more clear to you as you go on towards algebra. I think that you'll see that there are a huge number of applications to this stuff, even though it seems redundant at first.
I hope this helps!
For a concrete example, consider the situation of a bank account. Adding a negative would be like getting another bill in the mail you would need to subtract that from your account. Subtracting a negative would be like someone snatching a bill from your hand and saying "I'll pay that for you.". So "taking away a negative" is equivalent mathematically to "adding a positive". It's just the situation that is different. It really does come up in REAL life!
It might be easier to understand the problem, 2  (3) = ? , if you draw a number line and work it out graphically. Remember, subtraction means moving to the left on the number line. For example, 2  2 = 0. This is the same equation as
(+2)  (+2) = 0. You move +2 units in the direction of subtraction, i.e., to the left.
For the equation, 2  (3) = ? , again, subtraction indicates moving to the left on the number line. However, in this case, you're subtracting in a *negative* direction (3), so you move in the opposite direction, or to the right. So starting at 2 and subtracting 3, you end up at +5.
Saying that the minus symbols "cancel out" really means that subtracting in a negative direction is the same thing as adding: 2  (3) = 2 + 3 = 5.
(+2)  (+2) = 0. You move +2 units in the direction of subtraction, i.e., to the left.
For the equation, 2  (3) = ? , again, subtraction indicates moving to the left on the number line. However, in this case, you're subtracting in a *negative* direction (3), so you move in the opposite direction, or to the right. So starting at 2 and subtracting 3, you end up at +5.
Saying that the minus symbols "cancel out" really means that subtracting in a negative direction is the same thing as adding: 2  (3) = 2 + 3 = 5.
Instead of trying to use negative numbers you can use positive numbers but flip the addition/subtraction. Whenever you see that you are adding a negative number instead subtract it as a positive number. Conversely, if you see that you are subtracting a negative then you should think about it as if you were adding a positive number.
There are some great answers, but I think a video answer is what we want: http://www.youtube.com/watch?v=uhrqCL7aLTo
An intuitive way of thinking about negative numbers is opposites. Negative 3 is the opposite of 3. Also, 3 is the opposite of 3.
So if you have (3); that really means the opposite of 3, which is 3. You are basically taking the opposite of an opposite. If you play Uno, it's the same idea as playing a reverse, and then playing another reverse... they cancel out.
So if you have (3); that really means the opposite of 3, which is 3. You are basically taking the opposite of an opposite. If you play Uno, it's the same idea as playing a reverse, and then playing another reverse... they cancel out.
but when the is in the inside wat dose that mean
does the minus is the plus and the plus is the minus i am confused. please help
Think of subtraction on a number line. A subtraction sign means to travel left. But a negative sign AFTER a minus sign tells you to reverse directions. In other words, go to the right, and going to the right on a number line is what we do when we add. So a minus sign and negative sign together have the same effect on the problem as a single + sign. It also works when you add a negative number. The + sign means travel to the right on the number line, but if it is followed by a negative sign, it again means to reverse directions, and in this case you would travel to the left on the number line, just like when doing subtraction. So a + sign and  sign is the same as having a single  sign.
Here's an answer: POSNEG=POS, for the minuses cancel out and it turns out to be adding positive numbers. POS+NEG=Neg or POS, like 7+2=5. I don't have time. I'll show the rest another day, OK?
Instead of trying to use negative numbers you can use positive numbers but flip the addition/subtraction. Whenever you see that you are adding a negative number instead subtract it as a positive number. Conversely, if you see that you are subtracting a negative then you should think about it as if you were adding a positive number.
think of this problem as owing money (7+2=5) so if you owe $7 you have 7 but then you pay $2 of it you only owe 5 there for you only have 5. because its a negative number when you add positive number the negative gets smaller.
you can just think of it like positive numbers like 7+5=2 because it is like 75. still confused okay think of it like 6+4=2 it is like 6 minus 2 but keep it negative unless it is like 5+9=4 just think 95 i really hope this helps
Yes it is backwards (I think. Sorry it is not reassuring) and I myself get confused to. I am still working on this section because i am ahead in school.
I am tooooo
If you have 3(3)=? Then why don't you just say that you change the minus sign to a plus and then the sign of the second number??? 3(3)=? is equal to 3+(+3)=6. Right??? Maybe I'm over thinking this....
Changing the double negative to a positive is the mechanism, however the understanding is in that when adding or subtracting negative values you are being asked to add or subtract the lack of something. If you lack 30 (30) and I tell you to subtract the lack of 15: 30(15) you must add 15 to account for subtracting the lack (absolute value) of 15. Your lack decreases to 15. If i tell you to add a lack of 15: 30+(15), your lack increases to 45.
You didn't have to ask this question, he tells us the answer in 7:04.
33=6. that's correct. since negatives cancel, 33 is the same as 3++3, which would be written as 3 minus 3. (33) 3 minus 3 = positive 6. Watch the movie again if you're having problems. Listen carefully and good luck!
You are measuring the difference from one point on the number line to the next. If I were skydiving up in the air over an ocean and then I let my parachute go, now I am plummeting towards the water. After I hit the water, I go below sea level. If I was to measure the distance from where I started in the sky (above sea level) to when I stopped beneath the water (below sea level). 1200 feet  (30 feet) = 1230 feet. If I just subtracted 30 from 1200, it would leave me hanging in the sky just above the ocean, subtracting that way didn't include the distance below sea level. http://thetutorhouse.com
yes! that is how my teacher taught us.
i had d same prblm
lol
lol
u got it correct. a negative minus a negative is the same as plus a positive 33=3+3=6
Now I understand how to add and subtract and it has helped me in school. But, how do you subtract when you have three numbers? ex: 18(17)(11)
18(17)(11) = 18+17+11 = (18+17)+11 = 35+11 = 46
if you have 181711 then the answer will be like this:
181711 = (1817)11 = 111 = 10
if you have 181711 then the answer will be like this:
181711 = (1817)11 = 111 = 10
First switch your double negative signs to positives. 18(17)(11) = 18+17+11 = 46. So if you had something like this: 18+1711 = (18+17)11 = 111 = 12. Hope that helps.
You don't really need to worry about the (). So just take them out and you get 181711. That looks confusing. Exactly. The parentheses help space things out.