Negative numbers and absolute value

# Adding and subtracting negative numbers

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Discussion and questions for this video
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 pre-algebra 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!
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.
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.
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I need to know how to subtract negative fractions with a positive whole number.
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
why dose a negative and a negative make a postive
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
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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.). 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? When your adding negative numbers will the answer always be negative ? Yep, because when you add negative numbers, you are essentially subtracting. :) -2+-8=-1-10? -10 doesn't=-11 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? I don't understand your question, what do you mean? 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) 2 Votes 1 Comment 18-(-17)-(-11) = 18+17+11 = (18+17)+11 = 35+11 = 46 if you have 18-17-11 then the answer will be like this: 18-17-11 = (18-17)-11 = 1-11 = -10 How do you subtract negative numbers 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 minus-signs together turn into a plus. So for example, 12 - (-9) is the same as 12 + 9, which is 21. So, 12-5 and 5 -12 will be equal in absolute value . I did not get the logic of this. 3 Votes 3 Comments look at this as the distance on the x-axis from some number to 0; for example, you have 12-5=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 3 Votes 1 Comment 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 out-number 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?? 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? 3 Votes 1 Comment 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 Pre-Algebra for? The problems you face in the Pre-Algebra 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. 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! At about 7:50, when he started explaining how two negatives cancel each other out in -3--3, 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 anti-matter, when we combine equal quantities of them we get NOTHING i.e. Zero. The symbol "-" also means take away or subtract-agree? 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. 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). so when you have -4+5=? what do you do???? You can express it as 5 - 4, and so you get 1. 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. 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 5-5=0 -5+5=0 -5-5=10 5-(-5)=5+5=10 5+(-5)=5-5=0 what if there was 2 postive numbers would you just leave it postive? 2 Votes 2 Comments yes because our adding to the right. So, What about multiplying negative numbers?, And Dividing negative numbers? At 0:36 Somethinghappens 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 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 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 so ++ equals plus and -- equals plus and -+ equals minus and +- equals minus Totallly get it 2 Votes 1 Comment 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 4-5 And -5+(4) is the same thing :) How does the cancelling out of the minus sign work? 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!!
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,"
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)
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.
How do u do negative number problems like -9 - -6
think of a double negative as a positive
a positive plus a negative will alaways equal a positive depending on the situation
1 Comment
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?
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:
0--500
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