Negative numbers and absolute value

# Multiplying and dividing negative numbers

## Multiplying positive and negative numbers

Learn some rules of thumb for multiplying positive and negative numbers.
Back

## Multiplying positive and negative numbers

Discussion and questions for this video
So when you multiply 0 with any number, positive or negative, you get 0? Is that right?
Yes anything multiplying 0 is always going to be 0
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.
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.
Can somebody explain what -2 x -3 "means"? Like 2 x 3 means 2+2+2.
1 Comment
With apologies for the late answer, but since the other answers are just telling you how to solve the equation, here's a way you can think about the topic of multiplying with negative numbers:

Basically, if you're multiplying -2 x +3 you could read it as (for example) "I have zero dollars, and from this balance, I'm removing three dollars twice".

Going further, -2 x -3 could be "I'm removing a negative three dollars twice". You can see how there's a double negative in that: You're removing (one negative) something negative (second negative).

Say you owe two people three dollars each, and you keep a record of that. Your notes tell you that you've got a 6 dollar debt, or you've got -6 dollars. Then when you pay both of them back, you're removing this debt from your notes! So you're removing -3 dollars from your notes twice, or -2 x -3 dollars. -2 x -3 works out to 6, which is the amount of dollars you paid back. In your notes, you'd put down that you paid 6 dollars, and your new balance is 0 (= you don't owe anyone anything).

Generally speaking, a way to think about negative x ______ multiplication is to think of it as a reduction. From that, one way to think about negative x negative multiplication is to think of it as debt (<-- one negative) reduction (<-- the second negative).
Can 0 be positive or negative?
1 Comment
Zero is neither positive or negative, although you could say it's positive or negative. However zero is not used as a negative very often. (How often do you see -0 in a math problem?)
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
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.
Why negative times negative gives positive ?
-2 * 3 means add -2 to itself 3 times which equals -6
but what does -1 X -1 means ?
Think of it as taking away a debt of $1, one time. If you take that debt away,$1 more than you did before. So -1*-1=1
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
how would we multiply fractions
you do the recipricol of the problem
What if you have parenthesis? like 3 x (-4) = 3 x ?
There are parentheses around negative numbers to help separate them from the rest of the numbers and signs. A negative sign looks identical to a subtraction sign, so they want to separate them so people wouldn't get confused. Just work it like normal.
is there such thing as negative 0? like -0
No, Zero can't be a negative because it isn't a true value.
When you multiply a negative number and a negative number, does the number becomes more negative? I mean, LOL, does it go more to the left of the number line?
here is what i learned:
negative and negative is positive
positive and positive is positive
negative and positive is negative
positive and negative is negative
i hope this helps!
Why is it that two negitives equal a positive?
Because on a number line, each negative added together goes up the number line instead of down.
1 Comment
When Sal said any number times 0=0, does any number include infinity? Is infinity even a number, just an expression, or something else?
1 Vote
1 Comment
Infinity is an expression. No matter how many times you add, subtract, divide, or multiply, you will get either 0 or infinity. You cannot count to is, no matter if you are counting by fives, or counting by 1000s. However, you can express different occasions where you get infinity. e.g. 5/0. This makes many people believe that it is a number. However, wether it is used as an addend, or a divedend, you either get 0 or infinty. It is simply not a number.
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.
Why is negative times a negative a positive while positive times a positive is not negative?
1 Comment
Something times something else with the same sign always equals a positive number. Just remember that! :)
Happy holidays!!
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.
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.
Which video shows why a negative times a negative is a positive?
Why is 0 a neutral number?
Zero is the balance of a number line. It lies on neither side of negative or positive.
I know that anything times 0 = 0, but isn't it just times nothing? Like 400 x 0 = 0 right? But zero is like nothing so shouldn't it be 400?
It would still be 0, because it would be multiplying 400 by nothing, therefore you would have 400 nothings, which would be 0 because it's nothing.
I am a senior citizen and I am trying to understand neg and pos math problems and I need to see examples. what is -20 minus 12? 12 minus -20? 31 x -2? -10 divided by 5? -30 plus 7 , thank you for your help.
-20 minus 12 can be seen as
-20 - 12 = -32
The answer is -32 because the absolute value of -20 is 20, and the absolute value of minus 12 is 12. All you have to do is add 20 and 12, and add the negative sign.

31 x -2 = -2 x 31
If one neg number and one pos number are being multiplied together, I usually put the neg number first, but you can most certainly have your own way of setting up a problem.
-2 x 31 = -62
The answer is -62 because you are first multiplying pos 31 and pos 2 (ignore the neg sign for now). The product of 31 and 2 is 62. Now, you need to stop ignoring the neg sign on the 2 and put the neg sign beside the 62, which is -62.

-10 divided by 5 is the same thing as
-10 ÷ 5 = -2
If you divide pos 10 by pos 5 and ignore the neg sign beside the 10 for a moment, the answer is 2. Now you forget about ignoring the neg sign and put it beside the 2, so the answer is -2.

-30 + 5 is the same as
5 - 30 = -25
I look at this original problem, -30 +5, as 30 - 5, which is 25. Then, I add the neg sign to the 25, of which is -25. I set the problem up as 30 - 5 first because I know that |-30| = |30| and that |5| = |-5|. I also know that the neg sign can wait on the sidelines for a moment.

I hope that I helped you understand neg and pos math problems more.
what is that number
help me with negative numbers
What do you need help with?
Guys, if you want to be good at this, memorize all the combinations. Like this:

positive x negative = negative
positive x positive = positive
positive + negative = {[(no matter what the circumstance, if your adding or subtracting, subtract the bigger number by the smaller number not considering negative signs]
Example: -10 + 20
20-10 = 10
(the sign is determined by which number in the equation is bigger)
so... -10+20= 10
}
(if you didn't get this, it's ok, you'll get it eventually!!)
54÷(−6)=? how to do this ?
First, figure out what sign the answer would have. Because the six is a negative and 54 is a positive, the answer would be negative, as that is the rule. Now, you just use your multiplication skills to figure out the answer.
how does a negative times a negative a positve wouldn't it be negative?
Because a 'negative' symbol doesn't actually mean negative, it's more or less telling you to 'switch directions' on a number line. So a negative number multiplied by a negative number is basically canceling itself out.
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 :>
A tip:
1.) a*b = a + a + ... 'b' times
2.) -a*b = (-a) + (-a) + ... 'b' times = -a - a... 'b' times
3.) -a*-b = -a - a... '-b' times = [-(-a)] + [-(-a)] + ... 'b' times = a + a + ... 'b' times
This is kinda hard
once you learn a bit more you will soon understand it a whole lot better!
so that means that if you have -2 x 3 x -5 x 6 = +180
yes, you did the math right. Good Job! :)
How come when you multiply a negative times a negative u also get a positive?
Wouldn't that be a negative as well?.
no just multiplication and division has those rules it is what is is and much easier than adding or subtracting integers :) if you don't get it watch the videos it helped me :)
why do you get a positive number when you multiply two negative numbers?
Because the negative ALWAYS overtakes a positive think of Star wars, like Luke overcomes Darth or something like that. Just remember that " Positives are no match for the powerful negatives" :)
why must 2 negative numbers always cancel each other out?
if (x < 0) {Multiplying two negative numbers results in a positive number because the product of two negative numbers can be described as the additive inverse of a positive number.} 😁 😁 😁
don't get multiplying positive and negative numbers
if you multiply a negative number with a positive number you get a negative number, if you multiply a negative number with a negative number you get a positive number hope this helps :)
What is the math behind this?
well, think of it this way. -2 * 2. what is the answer? well, you have negative two on the number line. you multiply that, going in the same direction. (negative direction) by two. so you get four.
now, if you multiplied by -2 (so now the new problem is -2 * -2), you would change directions, again. first you were going in the positive direction. you changed to the negative direction(because of the start number being negative 2), and then, when you multiplied it by -2, you changed directions again. you can think of it as multiplying a number by negative one, means change directions.
So anyway, you now multiply by -2, change directions, and get 4. so the answer to -2 * -2 = 4. thanks! hope this helps!
I don't get this video? It doesn't make since to me i don't know why but I don't get it
The way I remember how to multiply negatives and positives is this:
Think of positive numbers as good guys and negative numbers as bad guys.

A good thing happening to a good guy is a good thing
Positive x Positive = Positive
A good thing happening to a bad guy is a bad thing.
Positive x Negative = Negative
Negative x Positive = Negative
Negative x Negative = Negative

I hope this helps. :-)
what if the question is pos+pos+neg
if you are adding, it depends on the numbers. for multiplying, the answer would be a negative.
How will this help me
do you have avidei of a mi x o negitive and positive numbers their called comlacaited number (i read it in a book)?
I have a question about subtracting negative numbers... how do you know how to subtract a problem like this: (-2) - 10 I will do it the way I know how...
(-2 - 10 = -8,
but this ends up being wrong and it's actually the answer you would get if you were to add. I am a little confused. Could someone help me answer this question? Thanks! ^_^
could a negative cancel out a positive
only if it's the same or higher number
If you multiply a positive times a positive times a negative...is is positive or negative?
you would use associotive property so multiply 4 and 2 first then by negative
the videos should include more difficult problems and not use things like -6+(3), just a suggestion
Multiplying and dividing negative numbers have always confused me. I'm sure that the answer is really obvious but how do you know if the answer is a positive or a negative?
Well, here are the four general rules to know:
Positive x Positive = Positive
Positive x Negative = Negative
Negative x Positive = Negative
Negative x Negative = Positive

Why is that when a negative plus a negative would be a positive I do not get that concept and when a positive pluse a positive is a negative
😳😕😧😦😜😝😎
decimals are like fraictons so its bellow 1.
exzample: 40.86 86 is on the right and the decilmals are pernosed tenths or hundredths so you need a - in your fraiction
@ 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 if a positive times a positive, it is still positive right?
Right. Its Positive x Positive is just like basic multiplication. :) positive answer every time
If I'm calculating -(-2)2 meaning negative 2 squared, is my answer to the problem of -1 x -4 a negative 4 or positive 4?
The answer is negative four because you first distribute the negative sign in front of the (-2) into (-2). A negative times a negative equals a positive, so the question is now (2)2.
2 • 2 = 4.
What would happen if you multiplied negative times negative times positive?
The commutative property of addition states order does not matter in multiplication so you can say:
1.negative times negative is a positive. positive times positive is positive.
2. negative times positive is negative. Negative times negative is positive.
So you would get a positive.
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
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.
its kinda confusing when we do a negative times a negative and get a positive how is that
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??
1 Vote
1 Comment
Yes. Commutative property works always, thats why it's so cool.
1 Comment
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.
I just thought that two lines like in -2 x-3 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