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# Multiplying and dividing negative numbers

## Video transcript

welcome to the presentation on multiplying and dividing negative numbers let's get started so I think you're going to find that multiplying and dividing negative numbers are a lot easier than it might look initially you just have to remember a couple rules and I'm going to teach probably in the future elector I'm actually going to give you more intuition on on why these rules work but first let me just to teach you the basic rules so the basic rules are when you multiply two negative numbers so let's say I had negative 2 times negative 2 first you just look at each of the numbers as if there was no negative sign well you say well 2 times 2 that equals 4 and it turns out that if you have a negative times a negative that that equals a positive so let's write that first rule down a negative times a negative equals a positive what if it was negative 2 times positive 2 well in this case let's first of all look at the two numbers without signs we know that 2 times 2 is 4 but here we have a negative times a positive 2 and it turns out that when you multiply a negative times a positive you get a negative so that's another rule negative times positive is equal to negative and what happens if you have a positive 2 times a negative 2 I think you probably guess this one right as you can tell that these two are pretty much the same thing by the what is it that I believe it's the the transitive property those is no no no I think it's a communicative property I have to remember that but 2 times negative 2 this also equals negative 4 so we have the final rule that a positive times a negative also equals a negative so you see and actually these the second two rules you they're kind of the same thing negative times a positive is a negative or positive times a negative is negative you could you could also say that as when the signs are different and you multiply the two numbers you get a negative number and of course you already know what happens when you have a positive times a positive well that's just a positive so let's review negative times a negative is a positive a negative times a positive is a negative a positive times negative is a negative and positive times each other equals positives I think that last little bit completely confused you maybe I can simplify it for you what if I just told you if you when you're when you're multiplying and they're the same signs same signs that gets you a positive result and different signs different signs gets you a negative result so that would be either a let's say a 1 times 1 is equal to 1 or if I said negative 1 times negative 1 is equal to positive 1 as well or if I said 1 times negative 1 is equal to negative 1 or negative 1 times 1 is equal to negative 1 you see how this the bottom two problems I had two different signs get positive 1 and negative 1 and the top two problems this this one right here both ones are positive and this one right here both ones are negative so let's do a bunch of problems now and hopefully it'll hit the point home and and you also can try to do all the practice problems and also give the hints and give you what rules to use so that that should help you as well so if I said negative 4 times positive 3 well 4 times 3 is 12 and we have a negative and a positive so different signs different signs mean negative so negative 4 times 3 is a negative 12 and that makes sense because we're essentially saying what's negative 4 times itself 3 times so it's like negative 4 plus negative 4 plus negative 4 which is negative 12 if you've seen the video on adding and subtracting negative numbers but you probably should watch first alright let's do another one what if I said minus 2 times minus 7 and you might want to pause the video at any time and see if you know how to do it and then restart it to see what the answer is well 2 times 7 is 14 and we have the same sign here so it's a positive 14 normally we wouldn't have to write the positive but that makes it a little bit more explicit and what if I had let me think 9 times negative 5 well 9 times 5 is 45 and once again the signs are different so it's a negative and then finally what if if I had let me think of some good numbers minus 6 times minus 11 well 6 times 11 is 66 and then it's a negative and negative so it's a positive let me give you a trick problem what is 0 times negative 12 well you might say that the signs are different but 0 is actually neither positive nor negative and 0 times anything is still 0 it doesn't matter if the thing you multiply by is is a negative number or positive number 0 times anything is still 0 so let's see if we can apply these same rules to division it actually turns out the same rules apply if I have 9 divided by negative 3 well first we say well what's 9 divided by 3 well that's 3 and they have different signs positive 9 negative 3 so different signs means a negative 9 divided by negative 3 is equal to negative 3 what is minus 16 divided by 8 well once again 16 divided by 8 is 2 but the signs are different negative 16 divided by positive eight that equals negative two remember different signs will get you a negative result what is minus 54 divided by minus six well 54 divided by six is nine and since both terms the divisor and the dividend are both negative negative 54 and negative six it turns out that the answer is positive remember same signs result in a positive quotient in this in this example we did it before it was product and let's do let's do one more obviously 0 divided by anything is still 0 that's pretty straightforward and of course you can't divide anything by zero that gives you that's undefined let's do one more what is I'm just going to think of random numbers 4 divided by negative 1 well 4 divided by 1 is 4 but the signs are different so it's negative 4 I hope that helps now what I want you to do is actually try as many of these multiplying and dividing negative numbers as you can and you click on hints and it will remind you of which rule to use and if you think about if you and in your own time you might want to actually think about why these rules apply and what it means to multiply a negative number times a positive number and even more interesting what it means to multiply a negative number times a negative number but I think at this point hopefully you are ready to start doing some some problems good luck