Negative numbers and absolute value
Multiplying and dividing negative numbers
None
Multiplying positive and negative numbers
Here we explain some rules of thumb regarding the multiplication of positive and negative numbers.
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what happens if the equations is positive x positive x Negative
posted 11:20 ET USA
posted 11:20 ET USA
The product would be negative; Positive times negative is a negative, and another positive number won't change that:
5*4*2=40.
5*4*2=40.
The answer would be _negative_ because as illustrated in the video, pos. x neg. is equal to negative. When you do neg. x pos. again, then that would still be negative. For example, 2 x 2 x 2 = 4 x 2 = 8. Good question.
```
2 x 2 x 2 = 8
2 x 2 x 2 = 8
2 x 2 x 2 = 8
Because
2 x 2 = 4
4 x 2 = 8
Or
2 x 2 = 4
4 x 2 = 8
```
Even quantity of negative factors results in a positive product.
Odd quantity of negative factors results in a negative product.
```
Even
2 x 2 = 4
Odd
2 x 2 x 2 = 4
```
Try to see the pattern here.
```Even: 1 x 1 = 1
Odd: 1 x 1 x 1 = 1
Even: 1 x 1 x 1 x 1 = 1
Odd: 1 x 1 x 1 x 1 x 1 = 1
Even: 1 x 1 x 1 x 1 x 1 x 1 = 1
Odd: 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1```
I used the factors of 1 here because I didn't want the product to increase, so you don't focus on the wrong thing. The important thing here is the negative sign in front of the one.
These are even numbers: 2, 4, 6, 8, 10
These are odd numbers: 1, 3, 5, 7, 9
Negative one times a negative one is positive one. Negative and negative cancel out. I use two negative factors, and two is an even number of factors.
Negative one times a negative one is positive one, times another negative one makes it negative again. Here I use three negative factors, and three is an odd number of factors.
I hope this helps.
2 x 2 x 2 = 8
2 x 2 x 2 = 8
2 x 2 x 2 = 8
Because
2 x 2 = 4
4 x 2 = 8
Or
2 x 2 = 4
4 x 2 = 8
```
Even quantity of negative factors results in a positive product.
Odd quantity of negative factors results in a negative product.
```
Even
2 x 2 = 4
Odd
2 x 2 x 2 = 4
```
Try to see the pattern here.
```Even: 1 x 1 = 1
Odd: 1 x 1 x 1 = 1
Even: 1 x 1 x 1 x 1 = 1
Odd: 1 x 1 x 1 x 1 x 1 = 1
Even: 1 x 1 x 1 x 1 x 1 x 1 = 1
Odd: 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1```
I used the factors of 1 here because I didn't want the product to increase, so you don't focus on the wrong thing. The important thing here is the negative sign in front of the one.
These are even numbers: 2, 4, 6, 8, 10
These are odd numbers: 1, 3, 5, 7, 9
Negative one times a negative one is positive one. Negative and negative cancel out. I use two negative factors, and two is an even number of factors.
Negative one times a negative one is positive one, times another negative one makes it negative again. Here I use three negative factors, and three is an odd number of factors.
I hope this helps.
The answer is negative.
If there is a odd number of negative numbers then the answer will be negative. if there Is a even number of negative numbers then the answer will be positive. hope this helps!
thank u! this is very helpful :3
If it was for example 2 x 2 x 2 it would still come out negative and in this situation 8
really thanks i couldnt figure it out
how can I remember all of this? do you have a idea or any suggestions?
Two `like` signs become a positive, and two `unlike` signs become a negative.
If a positive thing happens to a positive person, then that is positive(good), like a good scientist winning the Nobel Prize.
If a negative thing happens to a positive person, like someone getting robbed that's negative (bad).
If a positive thing happens to a negative person, that's negative (bad) like a robber being decreed innocent.
If a negative thing happens to a negative person, that's positive(good) like a robber being caught.
Hope that this helps you. :D
If a negative thing happens to a positive person, like someone getting robbed that's negative (bad).
If a positive thing happens to a negative person, that's negative (bad) like a robber being decreed innocent.
If a negative thing happens to a negative person, that's positive(good) like a robber being caught.
Hope that this helps you. :D
Here are some good examples:
1. Two like signs become a positive, and two unlike signs become a negative.
2. My friends' friends are my friends
My enemies' friends are my enemies
My friends' enemies are my enemies
My enemies' enemies are my friends
3. Count the total number of "sticks" signs made of. If you got even, result will have an even too, same goes for odd.
1. Two like signs become a positive, and two unlike signs become a negative.
2. My friends' friends are my friends
My enemies' friends are my enemies
My friends' enemies are my enemies
My enemies' enemies are my friends
3. Count the total number of "sticks" signs made of. If you got even, result will have an even too, same goes for odd.
Multiplying or dividing numbers with identical signs result in a positive number, but with opposing signs result in a negative number.
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Nonono you mutilply this is not exponents and it is not right.
Multiplication/division rules
same sign positive
different sign negative
same sign positive
different sign negative
My friends' friends are my friends
My enemies' friends are my enemies
My friends' enemies are my enemies
My enemies' enemies are my friends
I hope you enjoy this version!
My enemies' friends are my enemies
My friends' enemies are my enemies
My enemies' enemies are my friends
I hope you enjoy this version!
Helle how can I subtracting negative numbers
Count the total number of "sticks" signs made of. If you got even, result will have an even too, same goes for odd.
why when we multiply or divide two negative number it is always positive?
The two negative signs cancel each other out to become positive. Or they cross to make a positive sign.
This may help. It explains why a negative times a negative is a positive. Hope it helps. https://www.khanacademy.org/math/arithmetic/absolutevalue/mult_div_negatives/v/whyanegativetimesanegativeisapositive
that answer would be positive
Yes, they the 2 negative signs cancel each other out, not the other way
yes because 2 negatives is equal to a positive and it cancels each other out
Think of it this way, suppose 2x4,this is saying minus x minus = plus and multiplication is just a simpler way of doing addition so you could say multiplication. That is why a neg. x neg.= pos. number
Because when you do a problem and it has two numbers that are both negative the negative minus out and you can do the problem the same as you normally would. For example 10*5= 50 although 5*10=50 because there is not another negative number in the the problem. And one last thing, a positive and a positive = positive because there is nothing to multiply but the numbers.
Hope it helps, Hermione
Hope it helps, Hermione
yes because the sign cancel each other out because they are the same.
Can somebody explain what 2 x 3 "means"? Like 2 x 3 means 2+2+2.
2 means that it is a number below 0, if you add to negatives then you will get a positive or a number above 0. The answer to this question would be 6 because you added two negatives, this makes a positives. If you have the equation 2 + +3 this would be 6 because if their is one negative number in a equation it automatically turns into a negative answer!
Please correct me if I am wrong, But adding a positive to a negative will not always give you a positive number. The positive number that you ad to the negative number MUST be larger.
ie; any number added to 3 MUST be larger than 3 to become a positive number, if you add 2 to 3 you will still have 1 and also you started talking about adding numbers when it was a multiplication question. It gets kind of confusing when someone wants to know why a neg x neg = pos. Just my thoughts when I was reading the answer and you said 2 + +3 would be 6 when it is actually +1 and because if there is one negative number in an equation it automatically turns into a negative answer is incorrect. Only in certain equations , it is not the standard for all equations.
ie; any number added to 3 MUST be larger than 3 to become a positive number, if you add 2 to 3 you will still have 1 and also you started talking about adding numbers when it was a multiplication question. It gets kind of confusing when someone wants to know why a neg x neg = pos. Just my thoughts when I was reading the answer and you said 2 + +3 would be 6 when it is actually +1 and because if there is one negative number in an equation it automatically turns into a negative answer is incorrect. Only in certain equations , it is not the standard for all equations.
So when you multiply 0 with any number, positive or negative, you get 0? Is that right?
yes zero multiply by any number is all ways zero  or +
Yes, you are right.
yes. use the identity property of multiplication or division
what would 5 x 1 be? 1 x any other number is that number but i do not know if that works for negatives.
Yes, it works for negatives, too. 1 is a pretty cool number.
5 times 1 is 5 because any nonzero number multiplied by 1, regardless of its sign, equals that number.
5 x 1 IS 5, not 1
are you really talkin to me
5x1 would be 1
thanks that really helped
When Sal said any number times 0=0, does any number include infinity? Is infinity even a number, just an expression, or something else?
The way I see it is that if we must have a number, we must be able to finish counting e.g. 10 apples, 7 cars, etc. Given infinity, we cannot finish countingagree? So, technically, infinity is not a number at all. It is just the idea of something so big that we cannot finish counting.
If I'm not mistaken some branches of math (calculus e.g.) treat infinity as a number but math with infinity is quite complicated I think.
If I'm not mistaken some branches of math (calculus e.g.) treat infinity as a number but math with infinity is quite complicated I think.
adamchessulrich  Infinity is not a number. To say that it is means that it is countable. Any infinite would be in an uncountable set. The result would be an indeterminate form if you tried. So, it's like dividing by 0, you just can't do it basically.
@karsang  Calculus doesn't treat infinity as a number. It still treats it as a concept. You would be talking about limit  as a number approaches infinity for example (e.g.: an exceptionally large number).
@karsang  Calculus doesn't treat infinity as a number. It still treats it as a concept. You would be talking about limit  as a number approaches infinity for example (e.g.: an exceptionally large number).
I thought u said they would be negative im confused
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what helped me is to make a triangle and put two negative sign at bottom and a positive sign at the top and when I got two negative signs I would cover up the bottom negative signs and the positive sign at the top would show and Id know that it was a positive example 3x(9)=negative cause Id cover up a positive cause positive 3 and cover up a negative cause negative 9 and it would be a negative 27
No. If you know how to multiply and put in negative # signs, it is only too easy.
same sign= positive.
different sign= negative
different sign= negative
why wouldnt 1 times 0 be 0?
what hlped me make tirangl and put two
I just thought that two lines like in 2 x3 and their are two lines in a positive sign like in +6 so that is my way of looking at it.
Yeah that's what the answer is just look at 1:14
epauls or equals
yes 2x3 epauls 6
How about neg + neg + pos?
Multiplying two negatives and a positive would give you a positive, but by adding them it depends on the size of the numbers.
whatever there is more of
If you did negative 1 or positive 1, how would you know what 1 it is? Because 1*1=1 . Would that 1 be a positive or negative 1?
That's why you have the () sign before a number and in your case if one of the ones is negative, you will see 1
i do not know
Let's look at the four possibilities:
1 * 1 = 1. OR positive 1 * positive 1 = positive 1.
1 * 1 = 1, OR negative 1 * positive 1 = negative 1.
1 * 1 = 1, OR positive 1 * negative 1 = negative 1.
1 * 1 = 1, or negative 1 * negative 1 = positive 1.
1 * 1 = 1. OR positive 1 * positive 1 = positive 1.
1 * 1 = 1, OR negative 1 * positive 1 = negative 1.
1 * 1 = 1, OR positive 1 * negative 1 = negative 1.
1 * 1 = 1, or negative 1 * negative 1 = positive 1.
why neg neg = to pos ?
Well, negative times negative and negative divided by negative both equal positive, as Anthony said, but your statement is actually incorrect. A negative number minus a lower negative number equals a positive number, since  negative= add positive, and the absolute value of the lower negative number is greater. However, a negative number minus a higher negative number equals a less negative number, but still negative, since the absolute value of the higher negative number is lesser.
This is a postulate that applies to all numbers:
Negative * Negative = Positive
Negative * Positive = Negative
Positive * Negative = Negative
Positive * Positive = Positive
Negative / Negative = Positive
Negative / Positive = Negative
Positive / Negative = Negative
Positive / Positive = Positive
Negative * Negative = Positive
Negative * Positive = Negative
Positive * Negative = Negative
Positive * Positive = Positive
Negative / Negative = Positive
Negative / Positive = Negative
Positive / Negative = Negative
Positive / Positive = Positive
Why is that if you mulitiply a negative number by 0, it doesnt equal 0. At 4:10 it explains it but it still doesnt make any sense!
Zero is neither positive, nor negative. But, anything times zero is zero because if you have nothing, then more of nothing is still nothing.
This actually helped a lot! Thank you! <3
Yay, glad this helped you! But next time, please post comments like these in the "Tips and Thanks" section, not the comments section. : )
What about 10 times 4 times 2 do all of them cancel out?
No, if you're multiplying an odd number of negative values then your final answer will be negative.
Nathan is right and another way of thinking about it is this: so let's say 10 x 4 x 2
10 x 4 would be +40. then you multiply +40 by 2 and you'll get 80
multiplying three (or any odd number of) negative numbers will always have a negative answer
10 x 4 would be +40. then you multiply +40 by 2 and you'll get 80
multiplying three (or any odd number of) negative numbers will always have a negative answer
neg times neg pos_ pos times pos pos_ neg times pos neg_ pos times neg neg?
Yup. You can think of it like this: when one is positive and the other one is negative (or viceversa), they are different, right? They "disagree", so the answer is immediately negative. When both of them are positive (or negative), they are identical, they "agree", therefore the answer is positive :) hope it helped ;)
165,729,862
Yeah. I find it easy to think, if both numbers are on the same side of the number line, they come out positive, and viceversa.
what number do you have to multiply with a negative to make it a postive! simplest form please!
You can multiply any negative with another negative to get a positive!
What does he mean by 1 x 0 =0
when you multiple in the zeros by any number your answer will always be zero
what indacates division?
Other than the divide symbol, the forward slash, the underline bar (between the numerator and denominator), and the colon (for ratios) can also indicate division.
When typing on your computer, it is acceptable to use a forward slash for division. In other instances a dash with a dot above and below is used.
What about fractions? How does that work? Dividing and multiplying fractions? I know with regular fractions that you would just want the denominators to be the same, would the math work the same way? just being either a negative or positive? Is it weird that I find multiplication of negatives and positives easier than adding and subtracting negatives from positives?
The same rule applies to fractions. If you multiply a negative fraction by a positive fraction, your result will be a negative fraction. If you multiply two negative fractions, your result will be a positive fraction. If you multiply two positive fractions, your result will be a positive fraction.
It doesn't really matter what kind of numbers you're dealing with (fractions, decimals, or integers). Just remember that a positive and a negative give a negative; a negative and a negative give a positive; and a positive and a positive give a positive.
Multiplying and dividing fractions are quite simple. To multiply fractions, you multiply the numerators and the denominators together, and then simplify your product. To divide fractions, you flip the second fraction over and multiply. For example:
1/2 divide by 1/4=1/2 times 4/1=4/2=2.
There are lots of videos on this topic on Khan Academy.
It doesn't really matter what kind of numbers you're dealing with (fractions, decimals, or integers). Just remember that a positive and a negative give a negative; a negative and a negative give a positive; and a positive and a positive give a positive.
Multiplying and dividing fractions are quite simple. To multiply fractions, you multiply the numerators and the denominators together, and then simplify your product. To divide fractions, you flip the second fraction over and multiply. For example:
1/2 divide by 1/4=1/2 times 4/1=4/2=2.
There are lots of videos on this topic on Khan Academy.
In your videos can u give at least one challenging problem because I want to see if I understand the concept. Thank u so much for what u did u really helped me in my academics.
how do you do this? its confusing me and Im not exactly a math person but im not bad at it. Can anyone help me on this? IT IS VERY CONFUSING!
I can help 2 k :>
It's not really confusing; you would multiply/divide the two numbers as you normally would and all you need to know is that (neg x pos = neg) (neg x neg = pos) (and of course pos x pos = pos)
example: 8 x 4 just get the answer which is 32 and then you can remember that (pos x neg = neg), so you get 32
hope this helps
example: 8 x 4 just get the answer which is 32 and then you can remember that (pos x neg = neg), so you get 32
hope this helps
@ 4:07 how does 0 times 1 = o and not o?
0 is a neutral number. If you put zero on a number line, it would be the middle of all the numbers.
So same signs positive, opposite sides negative. Am I getting the point?
Yes, you are correct!
1 * 1 = 1
1 * 1 = 1
1 * 1 = 1
1 * 1 = 1
1 * 1 = 1
1 * 1 = 1
Is there a counterexample for my assumption that 1 multiplied by any number equals that number?
No. Your statement is a rule, therefore thus far it has not been proven wrong. In other words, there is not counterexample.
Is there a 0?
Zero is neither negative nor positive. However, in a math problem you can have something like 2  0 = 2.
does commutative property work with negative numbers??
Yes. Commutative property works always, thats why it's so cool.
I need help trying to watch a video
I can help you.
what do you need help with
How does a negative times a negative equals a positive number, or a negative divided a negative equals a positive number?
Think of the sign of a number as a light bulb. When the number is positive the bulb is on, when it's negative the bulb is off.
When you multiply by a positive number you do not touch the light switch. When you multiply by a negative number you flip the light switch.
So if a number is positive (then it's light is on) and you multiply by a negative number, do the multiplication (for the numbers) and flip the switch once (for the sign)... flip the switch once, the light goes out, the answer is negative.
If you then multiply that number by another negative number, the multiply the values and flip the switch... you get a number and the light goes on, so the answer is positive.
So 2 x (3) bulb is initially on,, 2 x 3 = 6, hit switch once, bulb goes off, answer is 6
6 x 4, bulb is initially off, 6 x 4 = 24, hit switch once, bulb comes back on, answer is 24
It may not make a lot of sense at this point, but it is a rule you can always use. Understanding is always better, but having a rule you can use sometimes has suffice until understand develops.
When you multiply by a positive number you do not touch the light switch. When you multiply by a negative number you flip the light switch.
So if a number is positive (then it's light is on) and you multiply by a negative number, do the multiplication (for the numbers) and flip the switch once (for the sign)... flip the switch once, the light goes out, the answer is negative.
If you then multiply that number by another negative number, the multiply the values and flip the switch... you get a number and the light goes on, so the answer is positive.
So 2 x (3) bulb is initially on,, 2 x 3 = 6, hit switch once, bulb goes off, answer is 6
6 x 4, bulb is initially off, 6 x 4 = 24, hit switch once, bulb comes back on, answer is 24
It may not make a lot of sense at this point, but it is a rule you can always use. Understanding is always better, but having a rule you can use sometimes has suffice until understand develops.
So on the chart on the bottom it doesn't say what is a negative times a positive or is it the same as a positive times negative?
Yes. With multiplication, the order doesn't matter (the commutative property of multiplication), so a negative times a positive is the same thing as a positive times a negative.
A positive times a negative and a negative times a positive are both a negative.
So a negative times a negative is a positive?
Yes, a negative times a negative is a positive
At 0:32 he starts telling us about positives and negatives. Does my saying work; If a Bad thing happens to a bad person (x  x) its a good thing (answer would be a positive)?
Mathematically, we would get a neutral or positive. We wold probably represent it more as an addition problem in math, but the abstract concept of a negative negative will always give a positive still stands in your saying. :)
It's kind of saying like : I will not not do something...
Interesting Question. :)
Sylvia.
It's kind of saying like : I will not not do something...
Interesting Question. :)
Sylvia.
Thank you for helping me out! :)
would the product of 2 and 3 the same as 3 and 2?
Yes, in multiplying different symbols this would equal the same answer.
If there are an odd number of negatives, the product will be negative.
If there are an even number of negatives, the product will be positive.
I hope that helped!
If there are an odd number of negatives, the product will be negative.
If there are an even number of negatives, the product will be positive.
I hope that helped!
why is it so tricky?
Well, I guess because it has negative numbers involved. To make it easy, all you need to remember is that positive x positive = positive, negative x negative = positive and positive x negative = negative. After you memorise that, it will hopefully become easier :)
What if it was a positive times a positive times a negative? Or a negative times a negative times a positive? Like 6 x 23 x 17.
If you have an odd number of negative numbers being multiplied, then the product will be negative. If you have an even number of negative numbers being multiplied, then the product will be positive.
e.g. 1 x 1 x 1 x 1 x 1 (There are five 1 is this problem, five is odd) = 1
e.g. 1 x 1 x 1 x 1 (There are four 1 is this problem, four is even) = 1
e.g. 1 x 1 x 1 x 1 x 1 (There are five 1 is this problem, five is odd) = 1
e.g. 1 x 1 x 1 x 1 (There are four 1 is this problem, four is even) = 1
But there is no video about multiplying 3 different numbers that are negative, but if there is tell me about it please kinda confused.
You can multiply two of the numbers and get the answer. Multiply that answer by the third number.
Here's an example: Multiply (3)(4)(2)
First multiply 3 by 4 = 12
Then multiply the answer 12 by 2 = 24
So the answer is 24.
Hope this helps.
Here's an example: Multiply (3)(4)(2)
First multiply 3 by 4 = 12
Then multiply the answer 12 by 2 = 24
So the answer is 24.
Hope this helps.
so if I understand this correctly  0 x 1 = 0 instead of 0? is there ever a case where 0 will be negative as opposed to positive? I'm thinking I understand that 0 is always 0 and never negative  am I right?
0 is neither a positive or a negative number. This is because numbers are classified as whether or not they are larger or smaller than 0. It would be like saying 0>0 or 0<0, which is not correct because 0=0. Just remember 0 as a kind of placeholder on a number line.
0 is a neutral number.
Thank you very much!
Why is not working??
i am always getting confused with if you multiply a negative and a positive and a negative = what and a negative and negative or a positive and a positive = what ? same with division
a negative times a positive is a negative and the same the other way around, and a negative times a negative and a positive times a positive is a positive. so the negative times the positive will be a negative, and that times the other negative will be a positive.
This has always made it easier for me to remember 
positive = love
negative = hate
If you love love or hate hate, then you are positive.
If you love hate or hate love, then you are negative.
This also works for addition and subtraction for getting the signs correct.
Example: 6 + 4 =
The "plus negative" can be looked at as loving hate ("negative" or simply changing the sign to minus), so you are actually subtracting the 4 from the 6. The answer, of course, being 2.
I hope this helps.
positive = love
negative = hate
If you love love or hate hate, then you are positive.
If you love hate or hate love, then you are negative.
This also works for addition and subtraction for getting the signs correct.
Example: 6 + 4 =
The "plus negative" can be looked at as loving hate ("negative" or simply changing the sign to minus), so you are actually subtracting the 4 from the 6. The answer, of course, being 2.
I hope this helps.
hi everyone!! how can you add the neg times a pos
If you have a "neg times a pos" then it will be a negative. Calculate the number (which will be negative) then add as usual.
The way I remember it, is that among deer, one male deer has this whole group of female deer, and he's more powerful than them. And if another male deer tries to take over, they fight, and sometimes they both die. So the negative is like the male deer, and the positive is like a female deer. The female deer get along, so pos x pos = pos. If a male deer confronts a female deer, the female deer will back down, so neg x pos = neg. And if two male deer confront each other, they both die, so they cancel out: neg x neg = pos. I'm probably the only one who understands this, but I want to share it anyway.
do you have any practice on mutiplying positive and negative numbers ?
yes i am the top person on multiplication in my school with positive and negatives # (numbers) 9x5=45 or just do this 9+9+9+9+9=45 and for negatives is love and hate.
for example 9 x 5 =45 because u hate to love so it = hate
9 x 9 = 81 because u hate to hate so it = love
hate =  and love= +
for example 9 x 5 =45 because u hate to love so it = hate
9 x 9 = 81 because u hate to hate so it = love
hate =  and love= +
Shouldn't 1 divided by 0 equal 1??
No, anything divided by 0 is undefined.
Essentially you are asking how many groups of 0 do I need to get 1, and there is no valid answer to that question.
Essentially you are asking how many groups of 0 do I need to get 1, and there is no valid answer to that question.
heller my name id madea how wer durn
This is not a question. ;)
Do you have a question on the video or concept?
Do you have a question on the video or concept?
Please post that somewhere else
Hi.Can anybody tell me how to use a timestamp?please.
Hi Abhimanyu!
Say you are referring to 2:15 in a video then all you have to do is type 2 : 1 5.
(Without the spaces in between the numbers☺).
I hope that helped!
Say you are referring to 2:15 in a video then all you have to do is type 2 : 1 5.
(Without the spaces in between the numbers☺).
I hope that helped!
Why is math so mindblowing?
Why do I continue to ask so many questions.
Why is math so confusing?
Why do I continue to ask so many questions.
Why is math so confusing?
1) Because it's awesome.
2) Because you are naturally curious.
3) Because you are working hard and you care.
Keep up the good work! You can do it!
2) Because you are naturally curious.
3) Because you are working hard and you care.
Keep up the good work! You can do it!
What if you add negative with a negative?
Add the 2 numbers, keep the common sign. Example: 2 + (7) = 9
Here is topic that has videos on this subject: http://www.khanacademy.org/math/prealgebra/negativesabsolutevalueprealg/addsubtractnegativesprealg
Here is topic that has videos on this subject: http://www.khanacademy.org/math/prealgebra/negativesabsolutevalueprealg/addsubtractnegativesprealg
Salman Khan says in the video that 2 + 2 equals 4. Don't the negative signs cancel out and make it +4?
That being said, wouldn't the answer to 2 + 2 + 2 be +2?
I'm asking because when finding 10 to the 6th power, for example, you would break it down like:
10 x 6 x 6 x 6 x 6 x 6 x 6
10 x 6 = 60
60 x 6 x 6 x 6 x 6 x 6
The negative signs in 60 x 6 cancel out, making the answer positive.
60 x 6 = +120... and et cetera.
Is it just different while doing an exponent problem?
That being said, wouldn't the answer to 2 + 2 + 2 be +2?
I'm asking because when finding 10 to the 6th power, for example, you would break it down like:
10 x 6 x 6 x 6 x 6 x 6 x 6
10 x 6 = 60
60 x 6 x 6 x 6 x 6 x 6
The negative signs in 60 x 6 cancel out, making the answer positive.
60 x 6 = +120... and et cetera.
Is it just different while doing an exponent problem?
If you look at a number line for this problem, you are starting at 2. When you add 2 the negative signs do not actually cancel. You move 2 to the left of 2. Also 10 to the 6th power actually equals 1/(10 x 10 x 10 x 10 x 10 x 10). You can see a video on negative exponents here https://www.khanacademy.org/math/algebra/exponentequations/algintegerexponents/v/introductiontonegativeexponents
The difference is the operation addition vs. multiplication (exponentiation is a type of multiplication). When you multiply 2 negative numbers, the result is always a positive number. When you add 2 negative numbers, the result is always negative. For your example of 2 + 2 :: imagine you have a savings account and you are overdrawn by 2 dollars. Your balance is 2, that is, you OWE the bank 2 dollars. Now if you withdraw another two dollars, you have 2 dollars PLUS the 2 you just withdrew, for a total of 4; you now owe the bank 4 dollars. I hope that helps.
What if you have a negative*neg*pos*neg*pos what would be the symbol?
The product will be a negative number.
*An odd number of negative numbers multiplied together will always give a negative product*. Here 3 negative numbers are multiplied resulting in the product to be negative.
If there are *an even number of negative numbers being multiplied together then the product will be positive*.
*An odd number of negative numbers multiplied together will always give a negative product*. Here 3 negative numbers are multiplied resulting in the product to be negative.
If there are *an even number of negative numbers being multiplied together then the product will be positive*.
why isnt zero a defined number????
zero is defined number, but deviding by zero isn't.
What do you mean by defined number?
what if i have 2 negative numbers and 1 positive number?
You multiply it in order. Let's say we have this equation:
2 * 5 * 3 (negative 2 times 5 times negative 3)
You first do 2 times 5. Which equals 10. Then you multiply that by 3. So the answer to that problem is 30 :)
So just keep multiplying in the order given.
2 * 5 * 3 (negative 2 times 5 times negative 3)
You first do 2 times 5. Which equals 10. Then you multiply that by 3. So the answer to that problem is 30 :)
So just keep multiplying in the order given.
At 2:39, could someone demonstrate how this works on the number line? Negative numbers to the left of zero, positive numbers to the right.
I can't do a video to show you, but I can explain it and if you draw it on a number line, you can see for yourself how it works.
The expression was 2 * 3.
Let me first explain how you would represent 2 * 3 on the number line.
2 means go left 2 postions. Start at zero and go left two postions and then go left two more postions and then go left two more positons. You are now at 6.
Ok, now lets do 2 * 3. Two is positive so it means go right two postions. The minus on the second number means opposite, So, start at 0 and go the opposite of right two postions and go opposite of right right more postions and go opposite of right two more positions. And again you are at 6.
Now lets do 2 * 3. The negative on the two means go right. The negative on the three means go opposite.
So start at zero. Go the opposite of right two positons and go the opposite or right two more postons and go the opposite of right two more postions. You are now at 6.
So 2*3 = 6 and you have shown it on a number line.
I hope that helps.
The expression was 2 * 3.
Let me first explain how you would represent 2 * 3 on the number line.
2 means go left 2 postions. Start at zero and go left two postions and then go left two more postions and then go left two more positons. You are now at 6.
Ok, now lets do 2 * 3. Two is positive so it means go right two postions. The minus on the second number means opposite, So, start at 0 and go the opposite of right two postions and go opposite of right right more postions and go opposite of right two more positions. And again you are at 6.
Now lets do 2 * 3. The negative on the two means go right. The negative on the three means go opposite.
So start at zero. Go the opposite of right two positons and go the opposite or right two more postons and go the opposite of right two more postions. You are now at 6.
So 2*3 = 6 and you have shown it on a number line.
I hope that helps.
This vid was very helpful!
Thats great! But this sould be in tips&thanks! :D
At 3:17, how is it that a negative times a negative is a positive?
Just an example that might be helpful:
If I say "Eat!" I am encouraging you to eat (positive)
But if I say "Do not eat!" I am saying the opposite (negative).
Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).
If I say "Eat!" I am encouraging you to eat (positive)
But if I say "Do not eat!" I am saying the opposite (negative).
Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).
I'm having trouble remembering
+ x + = +
 x  = ?
I can never remembering what combinations equal what. Any story thingys that help you remember? I know the previous person said "Does my saying work; If a Bad thing happens to a bad person (x  x) its a good thing (answer would be a positive)?" But I need every other combination and the answers to it you know:
Negative times positive equals what?
Positive times negative equals what?
+ x + = +
 x  = ?
I can never remembering what combinations equal what. Any story thingys that help you remember? I know the previous person said "Does my saying work; If a Bad thing happens to a bad person (x  x) its a good thing (answer would be a positive)?" But I need every other combination and the answers to it you know:
Negative times positive equals what?
Positive times negative equals what?
Count up the number of negatives that are being multiplied or divided. If you have an even number of negatives, your answer will be positive. If you have an odd number of negatives, your answer will be negative.
The order in which they are multiplied does not matter.
The order in which they are multiplied does not matter.
How's this? Consider a picture format of the answers above 9 months ago.
If you have a group of positive people all standing around with their giant plus signs on their shirts because they're all so positive, they always remain positive. + times + = +
Let's say you have one of each: a happy positive person, wearing her plus size shirt, happy and bouncy and just having a great day...just bursting with joyous song and happy news to share, but in walks Mr. Negativity. They sit together on the bench (=) and BLAMMO! Mr. Negativity starts blathering about all his problems. His pet turtle is sick. It pottied on his new mohair carpet. He stepped in the pile. He was then late as he had no other shoes but couldn't bear to clean them (ew) so he had to buy new shoes. He received the wrong change. Our positive friend tries for a time to be consoling, but alas, that negativity just keeps seeping instraight to her marrow. And in the end: 
+ times  =  no matter whether they sit on the bench that way or this:  times + = 
But what if...
If you have two negative people, with their mouths drawn straight across in a big mad minus mouth, and you multiply them together, they're so hateful that they end up killing each other and leaving only happiness in the room by their absence:  times  = +
But any time you have an odd number of those negative Nellies, they pair off and kill each otherexcept for that one leftover meanie, and he's left standing in the room with this straightmouth meanness:  times  times  times  times  =  (odd # of negs)
But let's say you have a couple of positive people and a few negative people all in this same room, they're all jumbled up together. Those positive folks are all wearing their green shirts with their big ol' giant plus signs on them, and they're trying, but MAN! No matter where they stand, those negative fellas are tough. They all fight it out with those mean faces killing each other off (yay! say the positive people), but ONE negative jerk is left over and brings the whole crowd down. Bummer.
+ times  times  times + times  = negative. (see? an odd number of negatives)
If you have a group of positive people all standing around with their giant plus signs on their shirts because they're all so positive, they always remain positive. + times + = +
Let's say you have one of each: a happy positive person, wearing her plus size shirt, happy and bouncy and just having a great day...just bursting with joyous song and happy news to share, but in walks Mr. Negativity. They sit together on the bench (=) and BLAMMO! Mr. Negativity starts blathering about all his problems. His pet turtle is sick. It pottied on his new mohair carpet. He stepped in the pile. He was then late as he had no other shoes but couldn't bear to clean them (ew) so he had to buy new shoes. He received the wrong change. Our positive friend tries for a time to be consoling, but alas, that negativity just keeps seeping instraight to her marrow. And in the end: 
+ times  =  no matter whether they sit on the bench that way or this:  times + = 
But what if...
If you have two negative people, with their mouths drawn straight across in a big mad minus mouth, and you multiply them together, they're so hateful that they end up killing each other and leaving only happiness in the room by their absence:  times  = +
But any time you have an odd number of those negative Nellies, they pair off and kill each otherexcept for that one leftover meanie, and he's left standing in the room with this straightmouth meanness:  times  times  times  times  =  (odd # of negs)
But let's say you have a couple of positive people and a few negative people all in this same room, they're all jumbled up together. Those positive folks are all wearing their green shirts with their big ol' giant plus signs on them, and they're trying, but MAN! No matter where they stand, those negative fellas are tough. They all fight it out with those mean faces killing each other off (yay! say the positive people), but ONE negative jerk is left over and brings the whole crowd down. Bummer.
+ times  times  times + times  = negative. (see? an odd number of negatives)
why is it that a negative times a positive and a positive times a negative?
watch the 2nd video then you will know
How come if it's negative times positive, it's negative, and if it's positive times negative, it's still negative? Or is it the same with the normal multiplication?
If it's negative times positive yes, it's negative but when it's positive times negative times positive it's negative too.(Does not matter which way just like it is in normal multiplication.Your right.)
so I don't get why negative + negative = a positive
Actually, it's negative x negative.
I don't really get it either, but that's how it works.
I don't really get it either, but that's how it works.
Negative + negative equals a negative, but yes, negative X negative = positive. This is because of what multiplying by a negative number represents. We learned negative numbers as "taking away" or owing something, in the context of adding and number lines. If you have 3 dollars, then you owe someone that much, or if you start with 4 apples, and have to give away 5 apples, you are one apple "short" or you "have 1 apples."
In the context of multiplication, we talk about how many total we have if we have 3 groups of 5 apples  that is 3x5=15 apples. Well, that doesn't quite work for negatives, unless we start to talk about owing again: we owe 3 people $5 each, so 3x(5)=15 we owe 15 dollars. But now, what about two negatives? There are "3" people to whom we owe 5 dollars... maybe that means three people owe us? So (3)x(5)=15 so we actually GET $15. Not terribly sensical, but maybe someone else can elaborate further?
In the context of multiplication, we talk about how many total we have if we have 3 groups of 5 apples  that is 3x5=15 apples. Well, that doesn't quite work for negatives, unless we start to talk about owing again: we owe 3 people $5 each, so 3x(5)=15 we owe 15 dollars. But now, what about two negatives? There are "3" people to whom we owe 5 dollars... maybe that means three people owe us? So (3)x(5)=15 so we actually GET $15. Not terribly sensical, but maybe someone else can elaborate further?
Would brackets have any effect on these equations or no?
Thanks!
Thanks!
I don't think it would, most of the problems he does here are singlestep (just a * b), instead of multi steps where you use the order of operations(bedmas)(a+c*b/de), since brackets only real purpose are to tell you to do this first, before you do anything else, a pair of brackets wouldn't change anything.
Hope this helped
Hope this helped
Can someone demonstrate how this works on the number line?
how does Negative Times a Negative works on the number line?
a negative number times a negative number would equal a positive; so on the number line you would mark it as a positive number
When Sal talks about at 2:32, Why does two neg make a pos ?
try the video here
http://www.khanacademy.org/math/arithmetic/negativenumbers/v/whyanegativetimesanegativeisapositive
http://www.khanacademy.org/math/arithmetic/negativenumbers/v/whyanegativetimesanegativeisapositive
yea what Joyce Wang said.
how does this guy have the time to do all this?!
It's his job. This is his business and he changed the world for better and for always! And, its easy to do this when you already know the material and most importantly when you are driven by the idea of changing something for better :) I hope this link will answer more of your questions about Sal :)
https://www.youtube.com/watch?v=gM95HHI4gLk&list=PL20CEC80FE46830DE
https://www.youtube.com/watch?v=gM95HHI4gLk&list=PL20CEC80FE46830DE
i know, but, like, all this would take like..........100 years ti make! xP
How do you divide negative numbers!?
if you are talking about both the numerator and the denominator are negative then 8/4 then your answer will be 2/1 or 2.as you divided 8/4 then you will also cancel the numerator's negative sign with the denominator negative sign.thus,you reached at +2/1 or +1.
if your numerator is negative (8/4) then your answer will be _2/1 or _2.in this problem you don't have negative denominator but do have negative numerator that is why you wasn't able to cancel negative sign.
i hope it work.............
if your numerator is negative (8/4) then your answer will be _2/1 or _2.in this problem you don't have negative denominator but do have negative numerator that is why you wasn't able to cancel negative sign.
i hope it work.............
Ok. I'll try and make this as clear as possible. During the video Sal keeps saying two negatives always make a positive. But when you multiply a negative by a negative wouldn't you either get the number you are multiplying or 0?
Say I'm multiplying 6 by 7. I would go from 6 to zero. Then onward to positive 6. But then the current answer would be positive so wouldn't I subtract 6 the next time?
Say I'm multiplying 6 by 7. I would go from 6 to zero. Then onward to positive 6. But then the current answer would be positive so wouldn't I subtract 6 the next time?
But you aren't adding and subtracting here, you are multiplying.
Adding 2 negatives will always give you a negative answer
Multiplying 2 negatives will always give you a positive though.
Another way of saying negative is "the opposite of".
So every time you multiply by a negative the sign will flip.
If you have 1, 3, 5, . . . negative factors in a string of multiplications, the final answer is negative.
If you have 2, 4, 6, ... negative factors the final answer will be positive.
(2)(3) = +6 or just 6
(2)(3)(1) = 6
Using arrows on a number line helps when you are adding but not when you are multiplying.
I hope this helps.
Adding 2 negatives will always give you a negative answer
Multiplying 2 negatives will always give you a positive though.
Another way of saying negative is "the opposite of".
So every time you multiply by a negative the sign will flip.
If you have 1, 3, 5, . . . negative factors in a string of multiplications, the final answer is negative.
If you have 2, 4, 6, ... negative factors the final answer will be positive.
(2)(3) = +6 or just 6
(2)(3)(1) = 6
Using arrows on a number line helps when you are adding but not when you are multiplying.
I hope this helps.
I don't get what he meant at 0:04
How would you write out a *pos* times a *neg* number?
At 0:42, he explained how to write out *2 x 3*:
`2 x 3 = 2 + 2 + 2 = 6`
How would you write out the *3 x 2*?
Because if you were to write it out like above:
`3 x 2 = 3 ?`
Then what? Do you subtract the numbers, like:
`3 x 2 = 3  3 = 0`
You are _not_ supposed to get *0*.
At 0:42, he explained how to write out *2 x 3*:
`2 x 3 = 2 + 2 + 2 = 6`
How would you write out the *3 x 2*?
Because if you were to write it out like above:
`3 x 2 = 3 ?`
Then what? Do you subtract the numbers, like:
`3 x 2 = 3  3 = 0`
You are _not_ supposed to get *0*.
Are you having trouble with a calculator? If so, try enclosing the negative number in parentheses: 3 x (2) = (6). Otherwise, there may be a negative number button that you need to use.
School standards have dropped. I am already past this in 6th.
yeah. I remember learning this in 6th.
In each positive question make sure there must be 2 negative and one positive. XD
at 7 secins it stop`t at first
Hi, guys. I'm new on khan academy and could you tell me where can i find some exercises, please?
Here https://www.khanacademy.org/math . I hope you will find this link useful :)
You can go to to *LEARN* at the top of the page and click on the *Knowledge Map* link and it will take you to the map of exercises.
what about the laws of pemdas?
negative numbers are just like positive numbers when it comes to PEMDAS.
So a positive+positive is positive neg+neg is negative. I understand that a positive times pos is positive but how is it that a negative times negative is positive? Ex: 2 x 4=8 . How is that possible! Is it because 2 goes into 8 4 times meaning positive?
I'm confused
I'm confused
Same sign is always positive, different sign is always negative. That's mean
+ times + = +
 times  = +
(see same sign)
+ times  = 
 times + = 
(different sign)
+ times + = +
 times  = +
(see same sign)
+ times  = 
 times + = 
(different sign)
Does a positive and a negitive equal a negitive and why?
A positive times a negative DOES equal a negative. Why? Well, here:
Say we're multiplying 5 and 3. 5 is just 5, but we can write 3 as 1*3. So we have: 1*3*5 The 3*5 part is easy, it's just 15. Then we have to multiply by 1, and if we add 1 to itself 15 times, we get 15. Hope that helps!
Say we're multiplying 5 and 3. 5 is just 5, but we can write 3 as 1*3. So we have: 1*3*5 The 3*5 part is easy, it's just 15. Then we have to multiply by 1, and if we add 1 to itself 15 times, we get 15. Hope that helps!
i used to think that those were hard they kinda easy if u listien and ask ouestions
Thankkss again for this video :)
The only problem that I am having is I will watch some of the videos and they do not fill in green as watched. I do not understand this because some of the videos are pretty long and my Instructor checks the site to see if I watched so she might think I am not watching when I am in fact watching.
thanks :) I appreciate the feedback
The best thing to do is to tell her your problem. As long as you are watching them, you two should be able to figure out a solution.
i thought the when the neg is bigger its alway a neg
what is electromotive force
what is electric charge
How many multiplications of positive + negative integers are there with an answer of 6 ?
one negative and one positive example 3x(2)
Negitive 1 times a negitive 5 is negitive 5 right ?
Do you mean 1 X 5=?
1 X 5 = 5
1 X 5 = 5
no it's not a negative 5 because any negative number times any negative number is always positive
Does 2 x 3=2 x 3
Yes, I think its just an extension of the communitive property.
Why is it when they are both negative then you just regularly multiply but when one is negative and the other isn't you have to have a negative answer?
At 2:48 why does pos times neg have to be neg? is there a reason for that?
If you tell yourself that Multiplication is the same as repeated addition, then:
4x 9
is the same as saying "four times 9", or:
9 + 9 + 9 + 9 > 9999 = 36
4x 9
is the same as saying "four times 9", or:
9 + 9 + 9 + 9 > 9999 = 36
sal I really think your viedo really help me
Is timesing, a negative and a negative basically timesing a positive and a postive...? eg. 1 x 1 = 1, 3 x 3 = 9?
Yes, multiplying a negative and a negative will always give you a positive result.
its not realy that hard to me somtimes like neg. times a poz = neg. or poz times a poz =poz or a neg times a neg =poz examples 7x1=7 7x1=7 7x1=7 i think thhats how it gose
you should do cross multplication :)
i dont like demicals but i am getting used to it if aby of you can give me inves about it that would me good thanks
Decimals are really good to learn about
i hope u know about place value system in which "0" is the place value holder
similarly this just an extension of the place value system for fractions which as no greatest common divisor
for an example
5/2
there is no number which divides them
but using decimals u can do it and u will end up with 1/2 which is
equal to 0.5 and here according to place value system the place value system of 5 is 1/10 and many numbers of great importance like "golden number",pi
etc which are frequently used are based on this concept.
i hope this worked
i hope u know about place value system in which "0" is the place value holder
similarly this just an extension of the place value system for fractions which as no greatest common divisor
for an example
5/2
there is no number which divides them
but using decimals u can do it and u will end up with 1/2 which is
equal to 0.5 and here according to place value system the place value system of 5 is 1/10 and many numbers of great importance like "golden number",pi
etc which are frequently used are based on this concept.
i hope this worked
so if 2 x 3 = then if they were negative would it be 6 (the problem:3 x 2) and how would it equal a positive
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