Adding and subtracting negative numbers
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 2-1
- or let's say what's 3-2
- If you start at 3 and you subtracted 2
- you would end up at 1
- That's 2+2=4, and 3-2=1
- And this is a joke for you.
- Now what if I were to say what is 1-3?
- 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.
- -1, -2, -3, and so on.
- So if I start at 1 right here, so 1-3
- so I go 1,2,3, I end up at -2
- So 1-3=-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 5-12
- I think you already might have an intuition
- of what this equals.
- But let me draw a line, 5-12
- 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 pre-drawn -- -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.
- 5-12
- 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...
- 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 5-12=-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 3-3?
- Well, 3-3, 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.
ok so when two negative numbers are beimg added or subtracted then they cancel eachother out? need a little clarity on that
Ajenkins1027
No! when you add a positive to a negative, something is cancelled. when you add a negative to a negative, the absolute amount is more. So (-3)+(-4)=-7. Nothing is cancelled there.
Michiel van der Blonk
Sprinkler2000
what happens if you get 7+-4???? does the minus still turn into a +?
You start from the positive end of the number line, because 7 is positive. Then because 4 has a negative sign in front of it, that means go BACK TO THE LEFT towards the ZERO ... going LESS.... four spaces. -4 means go back to the less than direction, back to or past zero, to the left. Now, the sentence reads, 7 going LESS 4.... 7-4... Where does the number stop? At 3, if you start at +7 and go left 4 spaces on the number line. The number stays positive because the sentence only asked you to go 4 spaces back towards zero, not past the zero into the negative (less than zero) numbers. If it had read, 7- -8, that would mean start at +7, go back (-)8 spaces. That is more than seven, which would have landed you at 0 (zero), but asked for -8... so going one more space past zero, landing you at -1. Just hop to the less direction (-)..when the number has a negative sign, go back left. Even if you start on the negative side of the number line, -7 and -3...start at -7, hop three spaces left (- sign), you land on -10. Hope this helps.
Adding and subtracting negative numbers are really hard ,i dont get it. Cn someone plz help me by explaining it a little better? *.*
@blakester95:
if its a positive number and a negative number
then why not just write it like this: -4+7 instead of -4++7???
it just makes it a little confusing for some people..
I'm just trying to help.. oh and another thing..
how come Sal never answers these questions for us???
blakester95 please help me to understand why he does this..
if its a positive number and a negative number
then why not just write it like this: -4+7 instead of -4++7???
it just makes it a little confusing for some people..
I'm just trying to help.. oh and another thing..
how come Sal never answers these questions for us???
blakester95 please help me to understand why he does this..
I haven't done math in a very long time, so I am a little rusty. I am finding it hard to visualize problems such as -3 - -3. How would you present that visually?
Okay, you need 12 plates for your dinner party (-12) [I used a negative because this is the number you NEED. You don't neccesarily have the plates. So you are down 12]. Now let's say you have 9 plates in your cubbord (+9). [I used a posetive sign because you DO have these. You are up 9]. So if you need 12, but have 9, then how many plates do you need to make this party happen? (3). But you don't have the three, so it's a negetive number (-3). It's a lot like saying 12-9=3, except that you are talking about a lack of plates instead of plates that you have available.
So that would be -12 plates +9 plates, equal -3 plates. (-12+9=-3)
Okay, so let's say your dog fido comes in and smashes two plates. You DID only need to buy 3 plates. (three plates you don't have is -3) Now you have to buy an additional 2 plates. (two plates you don't have is -2) Now that means you have to buy 5 plates. (five plates you don't have is -5) This would be written as -3+-2=-5 though many leave out the + as it's implied, and just write -3-2=-5. I hope this helped.
ps. I also haven't done math in for ever, but I'm pretty sure it's right. If anyone who reads this thinks I'm wrong, please feel free to correct me, and do let me know!
So that would be -12 plates +9 plates, equal -3 plates. (-12+9=-3)
Okay, so let's say your dog fido comes in and smashes two plates. You DID only need to buy 3 plates. (three plates you don't have is -3) Now you have to buy an additional 2 plates. (two plates you don't have is -2) Now that means you have to buy 5 plates. (five plates you don't have is -5) This would be written as -3+-2=-5 though many leave out the + as it's implied, and just write -3-2=-5. I hope this helped.
ps. I also haven't done math in for ever, but I'm pretty sure it's right. If anyone who reads this thinks I'm wrong, please feel free to correct me, and do let me know!
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 does Sal use a shorthand notation at 5:43?
I have no idea why he did that at 5:43
samuelmurugasu
what is 100--3567
well whats 3567-100? tht will be your answer in negative form lol :)
Bridoo05
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
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.... :)
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 :)
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)
Llohr4
frankie0693
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)
you work with whats in the ( ) first (:
Why do negative number's cancel out?
what do you mean with cancel out?
why does is have to be so confussing?!?
its because sal is cunfussing you =D
Springreign
I still don't understand it.HELP!!!
this isn't a question
Mvu347
Skywalker94
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.
i am still struggling boooooohoooooooohoooooohoooooohooo
i feel sorry for 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?
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
Gj10mnz
Can someone please tell me the difference between negative 1 and minus 1?
In my opinion, I think you use 'minus' as in 1 MINUS 2, and use 'negative' as in 1 minus 2 equals NEGATIVE 1. Am I correct or what? @.@
In my opinion, I think you use 'minus' as in 1 MINUS 2, and use 'negative' as in 1 minus 2 equals NEGATIVE 1. Am I correct or what? @.@
You are absolutely right about the use of Negative.
Minus is a bit trickier because people use it in different ways. The temperature could be "minus 1 outside", if people say that they mean the EXACT SAME THING as "it is negative 1 outside".
BUT they could also say "3 minus 1" which is the same as saying "3 subtract 1" or "3 take away 1".
Minus is a bit trickier because people use it in different ways. The temperature could be "minus 1 outside", if people say that they mean the EXACT SAME THING as "it is negative 1 outside".
BUT they could also say "3 minus 1" which is the same as saying "3 subtract 1" or "3 take away 1".
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
THANK YOU SAL. I HAVE LEARN ARTHEMATICS FROM VIDEOS AND I FIND VERY EASY. MAY GOD PERSERVE YOU
ok good for you and sal and this is not the comments section the comments are up there just under the video
so when u hav a problem like 2--3 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!
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
Missmaria123
-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 5-7. so what does it mean to add a negative number? Adding a negative is the same as subtracting a positive. 5+-7 = 5-7. That means -5+-7 is the same as -5-7 or -7-5. 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 5-7. so what does it mean to add a negative number? Adding a negative is the same as subtracting a positive. 5+-7 = 5-7. That means -5+-7 is the same as -5-7 or -7-5. Now you tell me,
What is -5+-7?
don't you think at 2 20 Sal gets vague
Alanzo
yeah,i noticed that.
None of this video helps me with this excersises, only the comments
videos help me a bit but comments help me a lot
does Einstein's method "A negative times a negative equal a positive" work as well for addition and subtraction of negative numbers? a negative plus a negative equals a positive? and a a negative plus a positive equals a negative? I'm confused!
As you say, that only works for the results of the multiplication, and works regardless of the size of the numbers, for instance, -100 * -1 = 100, and, -100 * 1 = -100 .
In the addition, it is a little different, since it works for the SIGN, understood as the direction in which addition takes place (left or right). The size of the numbers becomes relevant for the answer being positive or negative, for instance:
-100 + -1 = -101 , and if you change the sign, -100 + 1 = -99.
Note that in the example above we were moving towards 'minus' (left) when the signs were equal, and towards 'more' (right) when the signs were different.
The sign on the answer would change if you have a positive number greater than the negative number in the operation, for instance:
-100 + 101 = 1 (which is a positive number).
If you add a negative number to a negative one, you will go left (-- = <---)
If you add a positive number to a positive one, you will go right (++ = --->)
If you add a positive number to a negative one, you will go right (+- = --->)
If you add a negative number to a positive one, you will go left (-+ = <---)
Is this helpful?
In the addition, it is a little different, since it works for the SIGN, understood as the direction in which addition takes place (left or right). The size of the numbers becomes relevant for the answer being positive or negative, for instance:
-100 + -1 = -101 , and if you change the sign, -100 + 1 = -99.
Note that in the example above we were moving towards 'minus' (left) when the signs were equal, and towards 'more' (right) when the signs were different.
The sign on the answer would change if you have a positive number greater than the negative number in the operation, for instance:
-100 + 101 = 1 (which is a positive number).
If you add a negative number to a negative one, you will go left (-- = <---)
If you add a positive number to a positive one, you will go right (++ = --->)
If you add a positive number to a negative one, you will go right (+- = --->)
If you add a negative number to a positive one, you will go left (-+ = <---)
Is this helpful?
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.
what about an equation like 1+-9???now what do I do???
Drew.footballnut
Awww i feal sorry for everyone else...
they dont have alot of "answers" like elijah :/ srry!!
Oh and I'm just gunna go with..
this is a really old video..
horrible graphics..
they dont have alot of "answers" like elijah :/ srry!!
Oh and I'm just gunna go with..
this is a really old video..
horrible graphics..
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.
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. :)
do you always have to write/draw a number line?
no, you'll get better and won't have to use it
Why do the signs in the problem 2--3 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).
so, what you mean is,subbtracting negativie numbers turn in to adding,and adding negative numbers turn in to subtracting,right??
That's right. To add a negative number decreases the sum, and to subtract a negative number increases the sum.
ok what about if I have -(-4)-(-8) = ?
THANK YOU SOOOOOOOOOO MUCH !!!!
im only if fourth grade and i love this!!
wow i cant believe u undertand this
can you subtract a negative number the traditional way , and then just make the answer a negative number?
example: problem: 12-15 (so i would turn that into: ) 15-12= 3, and then I would turn 3, into -3
does that always work? (:
example: problem: 12-15 (so i would turn that into: ) 15-12= 3, and then I would turn 3, into -3
does that always work? (:
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
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
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.
im confused!!!
you too.... re-watch the video until you get it! :)
So if i were to Subtract 7 and -3 would it be the same as saying 3+7?
Bethany Asher
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?
Ugh when I do the exercise I keep messing up on one problem and having to start over! :(
this is not a question
What is 6-9
Rehan Mir
I am still struggling, could anyone help me?
sorry this isnt an awnser but fear not i dont get it either!!!!!!! /:I
i liked minute 4:56
oh no it was min 3:00
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.
i do under stand
what??? this is the questions section!!!!!
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
thank you that explains everything
How do i get a black hole or a sun badge? and how do i acquire points?
i asked a query and i get "this is not a place to ask!!!" and 'EXACTLY" remarks.
this does not make sense
this does not make sense
is sal a jerk i think he is
WHY DID YOU CALL HIM A JERK?!!!!!!!!!!!!!!!???????!!!!!!! HE'S AMAZING!!!!!!!!! oh... you were kidding! HA HA! LOL :)
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