Multiplying positive and negative numbers

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

Multiplying positive and negative numbers

Discussion and questions for this video
what happens if the equations is positive x positive x Negative

posted 11:20 ET USA
The product would be negative; Positive times negative is a negative, and another positive number won't change that:
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.
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.
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!
what would -5 x 1 be? 1 x any other number is that number but i do not know if that works for negatives.
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 counting-agree? 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.
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
Multiplying two negatives and a positive would give you a positive, but by adding them it depends on the size of the numbers.
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
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.
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.
Yay, glad this helped you! But next time, please post comments like these in the "Tips and Thanks" section, not the comments section. : )
No, if you're multiplying an odd number of negative values then your final answer will be negative.
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 vice-versa), 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 ;)
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!
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.
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.
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.
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!
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!
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?
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.
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.
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.
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.
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. :)
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!
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
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.
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.
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.
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.
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= +
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.
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!
Why is math so mind-blowing?
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!
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?
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
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*.
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.
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.
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).
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?
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.
why is it that a negative times a positive and a positive times a negative?
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.