Adding and subtracting negative numbers
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Adding/subtracting negative numbers
Adding and subtracting negative numbers
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 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 one, you have 2, you have 3, you have 4
 and you keep going.
 And if I were to say what's 2+2
 you'd start at 2, and then you'd add 2
 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+2=4
 And if I asked you what's 21
 or let's say what's 32
 If you start at 3 and you subtracted 2
 you would end up at 1
 That's 2+2=4, and 32=1
 And this is a joke for you.
 Now what if I were to say what is 13?
 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.
 1, 2, 3, and so on.
 So if I start at 1 right here, so 13
 so I go 1,2,3, I end up at 2
 So 13=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 one degree,
 but tomorrow it's going to be three degrees colder,
 you might already know intuitively,
 well then we're going to be
 at a temperature of negative two degrees.
 So that's all a negative number means.
 And just remember when a negative number is big,
 so like 50, that's actually colder than 20, right?
 So a 50 is actually even a smaller number than 20
 because it's even further to the left of 20
 That's just something you'll get an intuitive feel for.
 Sometimes when you start you feel like
 oh, 50 is a bigger number than 20
 but it's a 50 as opposed to a 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 512
 I think you already might have an intuition
 of what this equals.
 But let me draw a line, 512
 So let me start with 10, 9, 8
 I think I'm going to run out of space 7, 6, 5
 I should have this predrawn  4, 3, 2, 1
 0,1,2,3,4, and I'll put 5 right here.
 I'm gonna push this arrow out a little bit. Okay.
 512
 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...
 Negative 7
 That's pretty interesting.
 Because it also happens to be
 that 12  5 = +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.
 In this situation we're also saying
 that the difference between 5 and 12 is 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 512=7
 Let's do another one.
 What's 3+5?
 Well, let's use the same number line.
 Let's go to 3 plus 5
 So we're going to go to the right 5
 One, two, three, four, five.
 It's a two.
 It equals two.
 So 3 + 5 = 2
 That's interesting because 5  3 is also equal to 2
 Well, it turns out that 5  3 is the same thing,
 it's just another way of writing 5 plus 3
 or 3 plus 5
 A general, easy way to always do negative numbers
 is it's just like regular addition and subtraction,
 but now when we subtract
 we can go to the left below zero
 Let's do another one.
 So what happens when you get
 let's say, 2 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 +3
 and that just equals 5
 Another way you could say is let's do another one
 what is 7 minus 2?
 Well that's the same thing as 7 + 2
 And remember, so we're doing to start at 7
 and we're going to move 2 to the right.
 So if we move 1 to the right we go to 6
 and then we move 2 to the right we get 5
 That makes sense because 7 + 2
 that's the same thing as 2  7
 If it's two degrees and
 it gets seven degrees colder, it's 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 7  3
 Well, now we're going to go 3 to the left of 7
 We're going to get 3 less than 7
 so that's 10, right?
 That makes sense, because if we had 7 + 3
 we're at 7 to the right of 0
 and we're going to go 3 more to the right of 0
 and we get positive 10
 So for 7 to the left of 0 and go 3 more to the left,
 we're going to get 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 let's say 3 minus 3
 well, these negatives cancel out,
 so that just equals 6
 What's 33?
 Well, 33, that's easy.
 That's just 0
 What's 3 nimus 3?
 Well now we're going to get 3 less than 3
 well that's 6
 What's 3 minus 3
 Interesting.
 Well, the minuses cancel out, so you get 3 plus 3
 Well, if we start 3 to the left of 0 and we move 3 to the right,
 we end up at 0 again.
 So that makes sense, right?
 Let me do that again.
 3 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  13
 That's pretty easy.
 Well, 12  12 = 0, so12  13 = 1
 because we're going to go 1 the left of 0
 Let's do 8  5
 Well, this one is just a normal problem, that's 3
 What's 5  8?
 Well, we're going to go all the way to 0
 and then 3 more to the left of 0, so it's 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 at 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.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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This discussion area is not meant for answering homework questions.
what happens if you get 7+4???? does the minus still turn into a +?
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!
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
you work with whats in the ( ) first (:
so when u hav a problem like 23 then u wood just change the minus into plus and the negative into positive? im trying to make things more simple for my brain!!! :)
Yes, basically! Copy, Change, Change. It was the method I was taught!
why dont u get the same answer when u subtract 3  3 as to when u subtract 3  3
because when you subtract a negative it is really like adding a positive so really your equation is 3+3 which equals 0
illustrate using the number line why subtracting a negative number from another
negative number that it is necessary to change the sign of the subtracting number
to a positive to get the correct answer or is it the case of a rule that must be
learned with no reasoning behind it. sal passed over this in the video.
negative number that it is necessary to change the sign of the subtracting number
to a positive to get the correct answer or is it the case of a rule that must be
learned with no reasoning behind it. sal passed over this in the video.
Why do negative number's cancel out?
Because negative numbers are the opposite of positive numbers.
Why does Sal use a shorthand notation at 5:43?
what about an equation like 1+9???now what do I do???
The above answer is incorrect.
Grace, remember that 1 + 9 is the same as 9 + 1. Think of it this way. When using a positive number you move to the RIGHT on a number line. When using negative numbers, you move to the LEFT on the number line.
Put your finger on 9. To add 1, you will move 1 space to the RIGHT. Now where is your finger? On 8 correct? That is your answer.
Likewise you could put your finger on 1. Then move your finger to the left 9 spaces. Now where is your finger? 8? See you got the same answer.
Good Luck
Grace, remember that 1 + 9 is the same as 9 + 1. Think of it this way. When using a positive number you move to the RIGHT on a number line. When using negative numbers, you move to the LEFT on the number line.
Put your finger on 9. To add 1, you will move 1 space to the RIGHT. Now where is your finger? On 8 correct? That is your answer.
Likewise you could put your finger on 1. Then move your finger to the left 9 spaces. Now where is your finger? 8? See you got the same answer.
Good Luck
Thank you so much! Donna that really helps
Sal makes it easier to understand..
but when you add a two negatives isn't it the same as adding two positives?
but when you add a two negatives isn't it the same as adding two positives?
can you subtract a negative number the traditional way , and then just make the answer a negative number?
example: problem: 1215 (so i would turn that into: ) 1512= 3, and then I would turn 3, into 3
does that always work? (:
example: problem: 1215 (so i would turn that into: ) 1512= 3, and then I would turn 3, into 3
does that always work? (:
im confused!!!
you too.... rewatch the video until you get it! :)
wats a nother way instead of using the number line
switching the signs or using paper or some other material chips and laying them out, and then canceling. look on other websites too for further help if your arent finding your answers here.... :)
When he says "3 minus minus 3'' does he mean 3 minus negative 3?
Yes it does, it doesn't really matter which is it so:
3 3 = ?
This is what he means basically.
3 3 = ?
This is what he means basically.
33 turn to 3+3
Yes! Minus is the same as negative so it's basically 3 minus "negative 3"
yes that is what he means
it would be 0
woudnt it be 33 and if it was more into the negative numbers?sorry if i sound carazy,didnt see the whole video..........
yes. but a positive number (let's say 8) minus a negative number (let's say negative 5) = 8 5. I know that x (positive number) minus y (negative number) equals x PLUS y. I don't know why. But I just know it. THat's all.
how would you subtract 8 from 1?
1(8)=9 not 9. Normally, you move left on the number line when you subtract. But when you subtract a negative number, you have to move the opposite way. Minus a negative is the same as adding.
that would be 9
Do you get a negative number if you subtract a negative number from a negative number?
depending the number... for say 2+(3)=1 but 3+(2)=1
hope i helped :)
hope i helped :)
this is so much harder than multiplying/dividing integers to me. why could that be.
Maybe because multipliying and dividing fractions is more easy then adding and subtracting them.
A little confusing about the negative  negative and how it almost makes a positive.
make a number line in your brain.then you will see
do you always have to write/draw a number line?
no, you'll get better and won't have to use it
no only if it helps
i dont get that if 50 is a smaller amount then 20then how do u minus 20 from  50????
would it just be 30??? or is there somthing i am missing
would it just be 30??? or is there somthing i am missing
20  50 = 30 (remember that the double minus cancels itself out so it becomes a plus, like the video says).
However, 50  20 = 30 (again, the double minus cancels itself out and becomes a plus).
Make sense now?
However, 50  20 = 30 (again, the double minus cancels itself out and becomes a plus).
Make sense now?
thank you that explains everything
the minus's turn into +'s so u would add 20++50
What is 69
Oh now I know 3
I still don't get it.
im just confused about this
search further into the web....theres tons of info out there! :)
How whould I solve this 3 + 4 ( 2 ) or which video can I refer to ?
It might be easier to split the expression into smaller parts: 4  2 = 2 thus the expression becomes 3 + 2 Then we can replace those two numbers by their negations (their corresponding negative or positive numbers): 3  2 = 1 and then negate the whole expression: 1
Or you can just negate it from the very beginning:
3 + 4  2 = (3  4 + 2) = (3 + 2  4) = (5  4) = 1
Or you can just negate it from the very beginning:
3 + 4  2 = (3  4 + 2) = (3 + 2  4) = (5  4) = 1
Why do the signs in the problem 23 become addition or cancel such as in the video of adding/subtracting negative numbers at 5:27 on the timer?
Because the "" sign negates (or changes the sign of) the expression: 1 is the negation of +1 and +2 is the negation of 2. The author of the video should have read "two minus negative three" instead of "two minus minus three". It makes more sense. So, you are negating the number 3 (negative three).
I still don't understand it.HELP!!!
@mvu347: I think that this is fine. People do that all the time when they need help and there is nothing wrong with it.
If you have 1(4) its 1+4=5 ok if you have 1(4) 1+4=3 is 3 ok if you have 14 it 14=5
this isn't a question
so, what you mean is,subbtracting negativie numbers turn in to adding,and adding negative numbers turn in to subtracting,right??
ok what about if I have (4)(8) = ?
@Aziz Sobirov: It helps to break this down. The problem you just game is (negative of negative 4) minus (negative 8)
I put the parentheses there just for clarity. I was only trying to break it down. The first thing that I see is the whole negative of negative 4 thing. When you are taking the negative of a number, all that you are really doing is flipping the sign. So then, when you take the negative of a negative number, it will result in a positive number. That whole half of the expression can then be simplified to just a plain positive 4.
Next we are subtracting a negative number. Subtracting a negative number is the exact same thing as adding it as if it were a positive number. It works the same way. Just like last time, the negatives cancel out and result in positives. So that just turns into a simple + 8
Thus, we get:
4 + 8
And that's pretty easy. That's just 12.
With the original problem you gave in your original question (4  8), like I just said a moment ago, subtracting a negative number is the same thing as adding it as if it were a positive number. 4  8 is the same thing as 4 + 8, and that is also 12.
I hope this helps!
I put the parentheses there just for clarity. I was only trying to break it down. The first thing that I see is the whole negative of negative 4 thing. When you are taking the negative of a number, all that you are really doing is flipping the sign. So then, when you take the negative of a negative number, it will result in a positive number. That whole half of the expression can then be simplified to just a plain positive 4.
Next we are subtracting a negative number. Subtracting a negative number is the exact same thing as adding it as if it were a positive number. It works the same way. Just like last time, the negatives cancel out and result in positives. So that just turns into a simple + 8
Thus, we get:
4 + 8
And that's pretty easy. That's just 12.
With the original problem you gave in your original question (4  8), like I just said a moment ago, subtracting a negative number is the same thing as adding it as if it were a positive number. 4  8 is the same thing as 4 + 8, and that is also 12.
I hope this helps!
Negative and negative is positive. 4  8 == 4 + 8 = 12.
i don't understand why 3++3=0...please can anyone answer please
to make it simpler think it as 3+3 so if u start at the negative side of the numberline at 3, then u encounter the plus sign so u move to the right 3 times so u reach 0
3++ 3=0 is the same as 3+3=0 and is the same as 33=0. Instead of 3 + 3 = 0 I switched the numbers to get +33=0.
oh thank you........i do understand it now
what is 1003567
what is 1002567
well whats 3567100? tht will be your answer in negative form lol :)
a negative plus a positive equals a negative right and a negative plus a negative equals a bigger negative right? b cause if its true i am such a genius!!!!!!!!!!!!!!
No. 3+6=3. But your second theory is correct.
oh then what if u add negative plus a positive wat do u get oh and by the way who is this
I still dont get it so can someone please help me summarize this in detail the differences between getting a positive number and a negative number? Thank you.
well a positive number is above 0 & a negtive is below 0 (read slow)
I am still struggling, could anyone help me?
sorry this isnt an awnser but fear not i dont get it either!!!!!!! /:I
I just don't know all the rules!
E. 5+7=?
I don't get it
"I am a student here help me'!!!!!!!'!!!!!!!!!!!!!!!!!!!!!!''!!!!!!!!!!!!!!!!"
Your frustrated pupil,
Maria
E. 5+7=?
I don't get it
"I am a student here help me'!!!!!!!'!!!!!!!!!!!!!!!!!!!!!!''!!!!!!!!!!!!!!!!"
Your frustrated pupil,
Maria
5+7 is the same as 7+5. What happens if the problem was 5+7?
2 would be the correct answer, but the 7 is a negative. So what would 5+7 be?
2 would be the answer, because 5+7 is the same as 57. so what does it mean to add a negative number? Adding a negative is the same as subtracting a positive. 5+7 = 57. That means 5+7 is the same as 57 or 75. Now you tell me,
What is 5+7?
2 would be the correct answer, but the 7 is a negative. So what would 5+7 be?
2 would be the answer, because 5+7 is the same as 57. so what does it mean to add a negative number? Adding a negative is the same as subtracting a positive. 5+7 = 57. That means 5+7 is the same as 57 or 75. Now you tell me,
What is 5+7?
Hmmm....the following still bugs me....when you have somthing like:
8   7 = ?
I understand the procedure...2 minus signs become plus sign and you add the numbers to get 15. Messes me up, though. Can someone explain this? I read it as if we're suppose to subtract a neg 7 from 8. A real world example would help, too. thanks, cheers.
8   7 = ?
I understand the procedure...2 minus signs become plus sign and you add the numbers to get 15. Messes me up, though. Can someone explain this? I read it as if we're suppose to subtract a neg 7 from 8. A real world example would help, too. thanks, cheers.
When you see a minus and a minus, just change it into one plus. If you see a minus and a plus or a plus and a minus, change it into one minus. If you see a plus and a plus, change it into one plus. Thus 8 7 is 8+7 = 15, and 8+7 is 87 = 1, and 8+7 is 87=1, and lastly 8++7 is just 8+7=15
Oh, and as for your real life example, imagine the minus sign as meaning 'opposite of' the following sign, or the 'inverse of' the following sign, while the plus sign means 'the same as ' the following sign. Thus 2 will read 'the opposite of 2' or 'the inverse of 2', which is, of course +2. By the same token, +2 could be read as 'the opposite of +2' which is 2. Also, +2 can be interpreted as 'the same as 2' which is just 2, and ++2 can be interpreted as 'the same as +2" which is just +2. If you understand graphs, you could think of it as a graph. If you had to draw the line y=(2), you could visualize this as "the inverse of the line y=2, which would be the line y=+2...and so forth. Feel free to email me if you want to discuss this further, my email address is achieve.learn@gmail.com. Hope this helps you. :)
I can't visualize 3  3 on the number line. Can't that be shown too? Just to say the minuses cancel out is not a full answer. How do they cancel out?
yes it can when you draw the # line it will go back 3 from 3 so its 0 on the # line quite simple really
think about say the negative 3's  and the minus sign merge together to make a + sign. hope that can give you a visual of it...=D
None of this video helps me with this excersises, only the comments
videos help me a bit but comments help me a lot
if you listen carefully you will pick out all the info you need. you can also pause it to stop the video and take notes or something if you need them on something. :)
thanks, it helped
make a acount on khan acadamy sorry for my spelling
I would listen to it more carfully then...cuz I think it helped everyone else!!! But take it slower and turn the volume up more maybe!! Hope I helped!
i am still struggling boooooohoooooooohoooooohoooooohooo
i feel sorry for you
73=4
37=4
37=10
37=????
37=4
37=10
37=????
why does is have to be so confussing?!?
i dont think anything is confusing not trying to brag.... but like which ones are you confused on? like the ones where you have to have a positive number plus a negitive number?
all you have to do is make it all positive and the opisite operation such as 5+7
just make the operation its opisite which is subtraction and make that negitive seven positive all you have to do now is answer the question and your answer would be a negitive number but that's just how it works so your answer would be 2 btw(by the way) glad i could help :)
all you have to do is make it all positive and the opisite operation such as 5+7
just make the operation its opisite which is subtraction and make that negitive seven positive all you have to do now is answer the question and your answer would be a negitive number but that's just how it works so your answer would be 2 btw(by the way) glad i could help :)
its because sal is cunfussing you =D
whats the confussing thing for you??
how some of the problems are written the same but the answer isn't always a negative or a positive.
thx person i dont know that helps alot (: and i know what btw meens :p im shelby :D
i liked minute 4:56
oh no it was min 3:00
don't you think at 2 20 Sal gets vague
what does vague mean?
yeah,i noticed that.
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At 2:33, Sal said "single bonds" but meant "covalent bonds."
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