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.
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?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
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.
Basically, two negatives make a positive.
it mean, that if you really focus on it you would get the answer right
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.
hi
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.
Think of it this way. when you see two subtraction symbols next to each other, they cancel each other out. so (8) is 8
...
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
huh
I need to know how to subtract negative fractions with a positive whole number.
Help!
Help!
If you are subtracting a negative number from a whole number, the the negative and the minus signs cancel each other out. For example: 12(11)=1 It's like you're subtracting 2 whole numbers
i am as lost as you are!
why dose a negative and a negative make a postive
Sal explains in this video: http://www.khanacademy.org/math/arithmetic/negativenumbers/v/whyanegativetimesanegativeisapositive
if you are talking about multiplication, lets say its 9 x 9 the two negatives cancel out so it would be positive 81 please vote up
Think of it this way:
If you have 3 and you TAKE AWAY 3, then you have 0.
If negative numbers confuse you, try to think of it like owing money. If I owe you $3, I have $3. If you take away the debt, I have $0. It's just as if you gave me $3. Having two negatives is like taking away debt. It's minusing the minus. 3  3 = 0.
If we ADD a negative number, that's like increasing the debt.
So if I owe you $3, then I borrow another $3, I owe you $6. 3 3 = 6.
If you have 3 and you TAKE AWAY 3, then you have 0.
If negative numbers confuse you, try to think of it like owing money. If I owe you $3, I have $3. If you take away the debt, I have $0. It's just as if you gave me $3. Having two negatives is like taking away debt. It's minusing the minus. 3  3 = 0.
If we ADD a negative number, that's like increasing the debt.
So if I owe you $3, then I borrow another $3, I owe you $6. 3 3 = 6.
why are the numbers in parentheses?
nancy,
sometimes it means you have to do them first. Like in the ex. 9( 3+4) you have to do 3+4 first instead of doing 9 times 3. i hope this was helpful please vote up
sometimes it means you have to do them first. Like in the ex. 9( 3+4) you have to do 3+4 first instead of doing 9 times 3. i hope this was helpful please vote up
The numbers shown in parentheses are used as a marker, that you need to do the section in the parentheses spot on the order of operations. They are also used to separate numbers so it is more clear that it is two separate numbers.
they just are
I don't understand
IT means that number goes first
It can also be used to multiply. (if still confused please reply)
if u mean like 3+(4)
its to seperate the signs
its to seperate the signs
why do they have negetive numbers
We have negative numbers because there is no smallest number. Think about it in money. You have $10. Then, you buy ten $1 candy bars, so you have no money ($0). Then, you need to buy lunch, so you borrow $5 from me. You now owe me money, or, in other words, you have negative money ($5). You could keep borrowing money from me, and you would owe me more and more money ($10, $15, etc.).
We have negative numbers because there is no end to numbers. You need negatives to be in debt. the negatives mean you can owe people money. They also make number lines work, so that the numbers can decrease and increase for infinity.
I don't understand what a redundant is can someone explain so I can understand what is being talked about
at 5:34 ,sal said that 2  3 becomes 2+ +3. How?
when you are trying to subtract a negative number from a positive number its kind of like a rule to change the negatives into positeves my math teacher told me to thing of it like this 2 3 is incomplete so you just make those two negative and replace them with one positive sign 2+3. does that help?
It makes sense when you look at it on a number line. You can also think of it as 2 minus signs combining to make 1 plus.
When your adding negative numbers will the answer always be negative ?
Yep, because when you add negative numbers, you are essentially subtracting. :)
Yes, because if you are adding negatives you are subtracting from the space to the nearest positive number. If you look at a number line, and take 2 + another 2, you get 4
That is correct.
2+8=110?
10 doesn't=11
they are not equal
We are learning how to add and subtract intergers. The question I have it the way the teacher has the students doing it is use the alphabet and find your numbers than the problem is like this:
Duncan = 2, 11, 7, 2, 1, 7
I am not sure how they want the work shown. Would it be
2 + 11=9 (7)=2 +2=4 + 1=5  (7) = 2 so the answer would be 2?
Duncan = 2, 11, 7, 2, 1, 7
I am not sure how they want the work shown. Would it be
2 + 11=9 (7)=2 +2=4 + 1=5  (7) = 2 so the answer would be 2?
I don't understand your question, what do you mean?
Please explain in ENGLISH!!!!!!!!
I don't quite understand your question, but you did the work wrong. 2+11= 13, not 9. 9 (7)+ 16, not 2. Subtracting a negative is like adding. 2+11+2+114=2.
I AM NOT SURE
But once you get it it is easy.
But once you get it it is easy.
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.
good question. you would probably do 18[17] which equals 1 than [11]1
u multi ply11
This video answers your question. https://www.khanacademy.org/math/arithmetic/absolutevalue/adding_subtracting_negatives/v/addingnegativenumbers I hope it helps.
u do what is in the ( ) first
Great logical thinking
you work with whats in the ( ) first (:
1711=6
How do you subtract negative numbers
does anyone have suggestions or tips?
does anyone have suggestions or tips?
Taking away a negative number works out the same thing as adding a positive number. In effect, the two minussigns together turn into a plus. So for example, 12  (9) is the same as 12 + 9, which is 21.
(7)(8)= so here is how you do this. KFC. K keep the 7. F Flip the sign so it is now a + sign. C Change the last number so it is positive 8. so now you have the problem 7+8=?. I think you know how to do this. If you don't you do 87+1 The bigger number is positive so the answer is positive. The answer is 1.
You add the negatives, and keep the same sign. The number will get smaller, even though it looks like it is getting bigger.
So, 125 and 5 12 will be equal in absolute value . I did not get the logic of this.
look at this as the distance on the xaxis from some number to 0; for example, you have 125=7, and 5  12 = 7, but in both cases youo have 7 units away from 0, doesn't matter, neg or pos, do you get now?
how does this guy write so good with a mouse
what happens if you have a 7 + 8 would the 8 turn in to a negative or would the 7 turn positive?
well, how do you think? if we think about these 2 numbers in terms of units, you will have 7 negative (7) units and 8 positive (8) units; the positive units outnumber the negative ones, so at the end you will be left with one (1) positive unit: 7 + 8 = 1
My math teacher showed me a way when there are 2 s are together they can be turned into +
example: 5  (6) =5 + (+6)
Right??
example: 5  (6) =5 + (+6)
Right??
Yes. If you change both signs, it's equal.
Help me! i love math but i do NOt get this, please help
What are you confused about?
i need help on multiplying and dividing negative numbers;]
When you multiply negative 2 negative numbers together, you do it as you would normally but the answer is going to be positive. Same with dividing, but if you have one positive and one negative, then the answer will be negative. I you have 2 positives, then it is exactly how you would multiply normally.
What age is PreAlgebra for?
The problems you face in the PreAlgebra course are ones that get you ready for Algebra. It is the foundation that you will build on, and if you can master the techniques in the Pre class then you will be better placed when you start learning Algebra.
You are a life saver Sal! I'm going to be a freshman this upcoming school year and I have summer homework for algebra (because I sadly didn't take it in middle school)and during the summer I forget EVERYTHING my teacher teaches me and I got confused on the first page, but watching your video has made me remember all of it and now I know this will be a breeze~ So thank you for being so awsome at explaining!
can you show (3)+(3)+97 on number line?
Yes, of course you can. You could do it in two ways. The first way to do it is too first solve the problem mathematically and then plot it on the number line. (3) =3 , so the question will simply be 3 + 3 +97 which is equal to 103 and now you could just plot it. The other way is dong the entire process on the number line, so you just start at 97 and add 3 twice.
I finished all of this but what do I do after?
next you move on to Multiplication and division.
Thank you for the help😃😃😃😃😃
your welcome <3
fractions are the most confusing i just don't get it
well i can tell you what is a fraction...
frac·tion
ˈfrakSH(ə)n/
noun
plural noun: fractions
1.
a numerical quantity that is not a whole number (e.g., 1/2, 0.5).
a small or tiny part, amount, or proportion of something.
"he hesitated for a fraction of a second"
synonyms: tiny part, fragment, snippet, snatch, smattering, selection More
a dissenting group within a larger one.
each of the portions into which a mixture may be separated by a process in which the individual components behave differently according to their physical properties.
2.
(in the Christian Church) the breaking of the Eucharistic bread.
frac·tion
ˈfrakSH(ə)n/
noun
plural noun: fractions
1.
a numerical quantity that is not a whole number (e.g., 1/2, 0.5).
a small or tiny part, amount, or proportion of something.
"he hesitated for a fraction of a second"
synonyms: tiny part, fragment, snippet, snatch, smattering, selection More
a dissenting group within a larger one.
each of the portions into which a mixture may be separated by a process in which the individual components behave differently according to their physical properties.
2.
(in the Christian Church) the breaking of the Eucharistic bread.
hahaha nice u actually looked it up. ;)
I don't understand why a when a negative subtracting a negative makes the a sum positive. For instance why isn't 10(15) = 5 ??
Hi Danny,
The answer lies in how we think about the way we move on the number line but also in how we handle the operators in the equation:
(15) is the same as 1(15) or spoken, "negative 1 times negative 15". A negative times a negative is a positive, so that it becomes + 15. On the number line subtraction means we move left and addition means we move right. So, we start at 10 and because (15) means + 15, we move 15 places right which makes the answer 25.
Hope that helps!
The answer lies in how we think about the way we move on the number line but also in how we handle the operators in the equation:
(15) is the same as 1(15) or spoken, "negative 1 times negative 15". A negative times a negative is a positive, so that it becomes + 15. On the number line subtraction means we move left and addition means we move right. So, we start at 10 and because (15) means + 15, we move 15 places right which makes the answer 25.
Hope that helps!
Ahhhh... that was easy to understand when explained in that manner. Illustrating the  outside the parentheses as 1, was the light bulb moment.
Now if you could only help me understand functions better...
Thank you so much.
Now if you could only help me understand functions better...
Thank you so much.
At about 7:50, when he started explaining how two negatives cancel each other out in 33, I kind of understood. But why don't you make the pluses in +3++3 minuses?
Look at it this way...negative numbers are a different breed of numbers written as x where x is a real number such that x + x = 0. Something like matter and antimatter, when we combine equal quantities of them we get NOTHING i.e. Zero.
The symbol "" also means take away or subtractagree?
Now look at the problem 3  3. Read it in English or whatever is your language. It says take away 3 from 3. Is the answer more obvious? Zero.
Similarly 3 + 3 = 6...in English, Add 3 to 3 (the  in front of the 3's only denotes a different 'type' of number)
You can also view 3  3 in a different way...subtracting is same as adding the opposite. Look below:
3  3 = 0 easy...
Now 3 + 3 = 0...we know that from definition of negative number
So 3  3 = 3 + 3 = 0
So, 3  3 = 3 + 3 = 0
The symbol "" also means take away or subtractagree?
Now look at the problem 3  3. Read it in English or whatever is your language. It says take away 3 from 3. Is the answer more obvious? Zero.
Similarly 3 + 3 = 6...in English, Add 3 to 3 (the  in front of the 3's only denotes a different 'type' of number)
You can also view 3  3 in a different way...subtracting is same as adding the opposite. Look below:
3  3 = 0 easy...
Now 3 + 3 = 0...we know that from definition of negative number
So 3  3 = 3 + 3 = 0
So, 3  3 = 3 + 3 = 0
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?
Subtracting three numbers is very similar to subtracting three or more numbers.
For example, if you have 6(9)14, then the first thing you do would be 6(9). This would equal 15 because it is the same as doing 6+9. Next you subtract 15 by 14. This equals 1.
For example, if you have 6(9)14, then the first thing you do would be 6(9). This would equal 15 because it is the same as doing 6+9. Next you subtract 15 by 14. This equals 1.
thank u guys for helping
Who did this video, they are awesome at explaing this stuff in math.
Sal Khan made this video and many other videos on Khan academy, except some on programming which are made by a woman. Does anyone know who she is? Anyways, Sal was on 60 minutes talking about his website (Khan Academy).
Sal made this video
so when you have 4+5=? what do you do????
You can express it as 5  4, and so you get 1.
Thank you kind sir. sencerly DJ LOGAN :)
When multiplying negative numbers, which direction do you move? Further negative, or positive?
negative times negative=positive
example 3 x 4 = 12
negative times positive=negative and positive times negative=negative since multiplication is commutative :)
example 3 x 4 = 12 and 3 x 4 = 12
When multiplying, if the signs match the answer is positive; when they don't match the answer is negative.
example 3 x 4 = 12
negative times positive=negative and positive times negative=negative since multiplication is commutative :)
example 3 x 4 = 12 and 3 x 4 = 12
When multiplying, if the signs match the answer is positive; when they don't match the answer is negative.
Well I can imagine multiplying as moving some number to times that distance along the number line. So I'll define a couple of ideas, Moving one full step in a direction moves me 2 unit distances in that direction. So if I have a road that runs westeast, and I let this be an example of a number line.
Well the point I start on the road can be said to be 0.
Facing west is the negative direction. (moving negative units)
Facing East Is the positive direction. (moving positive units)
Moving in the direction I'm facing is moving positive. (moving positive steps)
Moving in the direction I'm not facing (walking backwords) is moving negative. (moving negative steps)
So if I'm facing east and move forwards 5 steps that means I move 5 x 2 units in the positive direction.
If I'm facing west and moving backwards, I'm moving 5 x 2 units or 10 units in the positive direction.
Well the point I start on the road can be said to be 0.
Facing west is the negative direction. (moving negative units)
Facing East Is the positive direction. (moving positive units)
Moving in the direction I'm facing is moving positive. (moving positive steps)
Moving in the direction I'm not facing (walking backwords) is moving negative. (moving negative steps)
So if I'm facing east and move forwards 5 steps that means I move 5 x 2 units in the positive direction.
If I'm facing west and moving backwards, I'm moving 5 x 2 units or 10 units in the positive direction.
Well... this really help me out! I promise myself I would get proficient in my next math test ;)
Good ikr it's easier to ace i like got it in 3 min.
what if you get 6+4+2?
6+4 = 2 & 2+2 = 0 that is easy :)
the videos really help i am getting good grades
It was too blurry!
its an Old video !
i have watched this video so many times and it is not helping. In class i understand but not here
Adding a negative is the same as subtracting its opposite. Subtracting a negative is the same as adding its opposite.
5+5=10
55=0
5+5=0
55=10
5(5)=5+5=10
5+(5)=55=0
5+5=10
55=0
5+5=0
55=10
5(5)=5+5=10
5+(5)=55=0
what if there was 2 postive numbers would you just leave it postive?
yes because our adding to the right.
yes you would
So, What about multiplying negative numbers?, And Dividing negative numbers?
At 0:36 Somethinghappens
Thank you for the link.
Richard,
Here is the link to first video in the section on Multiplying and dividing negative numbers.
http://www.khanacademy.org/math/arithmetic/absolutevalue/mult_div_negatives/v/multiplyingpositiveandnegativenumbers
Here is the link to first video in the section on Multiplying and dividing negative numbers.
http://www.khanacademy.org/math/arithmetic/absolutevalue/mult_div_negatives/v/multiplyingpositiveandnegativenumbers
If the 56  92 = what is equal to?
Example : 92  52= 40 if the 52  92 = what is the different? The answer is  40.
This comment is by M3SONIC
Example : 92  52= 40 if the 52  92 = what is the different? The answer is  40.
This comment is by M3SONIC
What you would do is add a negative sign to 92 so it would be 56  (96) and then as you may know you subtract 56 from 96 and so you would get 40. So yes your answer is correct.
5:28. i still don't get when you are supposed to make the negative sign an addition sign, and when your not. HELP!
negative and negative = positive
positive and positive = positive
negative and positive = negative
positive and negative = negative
positive and positive = positive
negative and positive = negative
positive and negative = negative
At 5:23 I don't get it.
Same sign find the sum
Different sign find the difference (:
Different sign find the difference (:
I just imagine the positive sign (+) as two negative signs (). You make a positive with two negatives.
I think this can be really hard sometimes! I have gotten most of my answers worng!! Can you guys help me with this??? :)
A negative will turn positive addition sign when u have two negatives in a row...nothing inbetween. all the other times when u have two signs in a row they would b negative minus signs. Except add and add sys add. So ++=+ = += +=
oh ok thanks everybody for the help!
math is so complicated.
what is a positve plus a negitive number
Let us take the numbers 9+6 you subtract 6 from 9 and add the sign of the bigger number that is (+) then the answer will be 3.
I got a big number 118+314
Then you should subtract the smaller one from the bigger one and add the sign of the bigger one. When you do as I said the Answer will be 196.
why is this video so blurry?
This is an old video ! That is why :)
I think that this method is easier for me . Because the number line is not confuseing.
What if you add 2+2=what.is negative +negative=positive or negative still. Can you give me a .tip
With addition, if BOTH numbers are negative, just add them and keep the sign. So, 2 + 2 = 4
If one number is negative and the other positive, then you subtract them and keep the sign of the larger magnitude number.
So,  4 + 2 = 2 but 4 + 2 = 2
If one number is negative and the other positive, then you subtract them and keep the sign of the larger magnitude number.
So,  4 + 2 = 2 but 4 + 2 = 2
Just Keith did a good job of answering your question.
I think you asked a second question as to whether or not a negative plus a negative will be a positive or negative. It will ALWAYS be a negative. To be a positive number, it'd have to be greater than 0. You couldn't ever have a number greater than 0 if you're going to be subtracting from a number that is less than 0 to begin with. You could only ever be more negative.
I think you asked a second question as to whether or not a negative plus a negative will be a positive or negative. It will ALWAYS be a negative. To be a positive number, it'd have to be greater than 0. You couldn't ever have a number greater than 0 if you're going to be subtracting from a number that is less than 0 to begin with. You could only ever be more negative.
so ++ equals plus and  equals plus and + equals minus and + equals minus
Totallly get it
Totallly get it
Yep, good work. So if you have 4+(+5) That's the same as 4+5
If you have 4(5) that's the same as 4+5
4+(5) equals 45
And 5+(4) is the same thing :)
If you have 4(5) that's the same as 4+5
4+(5) equals 45
And 5+(4) is the same thing :)
yes that is right
How does the cancelling out of the minus sign work?
I still have trouble and adding and subrtracting them. Subtracting being the most difficult.
I still have trouble and adding and subrtracting them. Subtracting being the most difficult.
Think of it this way, do the problem, like 4(4)=?
So lets put this into a word picture: bob owes someone $4 (or he has $4). Then someone takes away his dept of $4 (or 4(4)). So he now has 0 dollars, and that is more than he had before.
Hope this helps!!
So lets put this into a word picture: bob owes someone $4 (or he has $4). Then someone takes away his dept of $4 (or 4(4)). So he now has 0 dollars, and that is more than he had before.
Hope this helps!!
What if the question is 7+7 would that mean it would be a subtraction problem or an addition problem
Technically all subtraction can be seen as a kind of addition since X minus Y is the same thing as X plus negative Y.
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
so,if I was to make an number line i should place an the number line
I haven't specifically looked for a video about this yet, but how do you add, subtract, multiply, or divide positives and negatives with variables?
explain why a minus sign & a neg. number, becomes a plus sign & a positive number ? i tried to use the number line to illustrate this but wasn't able to see the logic
What is 1+12
I don't understand, what if you are subtracting two negative numbers
3(9)
3(9)
it would actually be 6, if you have 3(9), a cool trick is that you make the ( into a + so it becomes 3+9, thus making it 6.
in order for me to solve any of the adding and subtracting negative #'s i just draw a number line it helps more then doing it in your head
so the answer to that would be 12
so the answer to that would be 12
if you are doing a negitive plus a negitive problem then it would be positve.
if you are doing a positive plus a positve it will be posiive.
if you are doing a positive plus a positve it will be posiive.
it would be six cuz u change it to 3+9=6
YW
YW
How do u do negative number problems like 9  6
think of a double negative as a positive
thanks
the two negatives between the 9 and 6 equal a positive then 9+6=3
also the number with the greater absolute value is the sign you will end up with in your answer.
also the number with the greater absolute value is the sign you will end up with in your answer.
a positive plus a negative will alaways equal a positive depending on the situation
When is the difference between a negative number and a positive number not positive?
How did Brahmagupta arrive at the following conclusion:
"A debt subtracted from zero is a fortune"
I am not doubting that the above statement is true, but I don't understand it. If I had a net worth of $500, and this $500 debt was subtracted I would now have a net worth of $0. I don't see how I would have a net worth of (positive) $500. Can anybody please explain this to me?
"A debt subtracted from zero is a fortune"
I am not doubting that the above statement is true, but I don't understand it. If I had a net worth of $500, and this $500 debt was subtracted I would now have a net worth of $0. I don't see how I would have a net worth of (positive) $500. Can anybody please explain this to me?
Think of it this way:
A debt is a negative value, so if I owed you $500, then, in this sense, I would have $500.
Ok, next step:
Zero minus negative 500
which can also be written as:
0500
Since subtracting a negative is equivalent to adding a positive, we can change the expression to:
0+500
Which is equal to $500.
A debt is a negative value, so if I owed you $500, then, in this sense, I would have $500.
Ok, next step:
Zero minus negative 500
which can also be written as:
0500
Since subtracting a negative is equivalent to adding a positive, we can change the expression to:
0+500
Which is equal to $500.
Would 8+(10) be 2?
yes you would be correct
Please help. I don't understand like, 08 even with this video!
it is so easy it equals 8eight.LOL :)(and DON'T WORRY I had a hard time to)
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