Learn about Multiplying and dividing negative numbers Video

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Learn about Multiplying and dividing negative numbers

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 of rules and I'm going to teach probably in a future like I'm actually going to give you more intuition on why this rules work. But first let me just talk to teach you the basic rules. So the basic rules are when you multiply two negative numbers let say I had -2 x -2 first you just look at each of the numbers as if there was no negative sign. Well you say well 2 x 2 that equals 4 and it turns out that if you have negative times the negative that that equals a positive so let's write that first rule down. A negative x a negative equals a positive. What if it was -2 x +2? Well in this case let's first of all look at the two numbers without sign we know that 2 x 2 is 4 but here we have a negative times a +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 happen is you have a +2 x -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? I believe is the transitive property. No, I think it’s a communicative property I have to remember that. But 2 x -2 this also equals -4 so we have the final rule that a positive time a negative also equals a negative. So you see and actually this second to rule they're kind of the same thing, you know, negative times a positive is a negative or positive times a negative is a negative. You could also say that as when the designs 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 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 to each other equals positive. I think that last little bit completely confuse you. Maybe I can simplify it for you. What if I just told you when you're multiplying and there are the same signs that gets you a positive result and different gets you a negative result? So that would be either a, let say a 1 x 1 is equal to 1 or if I said -1 x -1 is equal to +1 as well or I said 1 x -1 is equal to -1 or -1 x 1 is equal to -1. You see how in this the bottom two problems I had two different signs that +1 and -1 and the top two problems this one right here are both one’s are positive and this one right here are both ones are negative. So let's do a bunch of problem now and hopefully it will hit the point home and you are also could try to do or you can practice problems and also give the hints and give you what rules to use so that should help you as well. So if I said -4 x +3 well 4 x 3 is 12 and we have a negative and a positive so different signs, different signs mean negative. So -4 x 3 is a -12 and that make sense because we’re essentially saying what's -4 time itself three times so it’s like -4 + -4 + -4 which is -12. If you'd seen the video on adding and subtracting negative numbers that you should probably should watch first. And let's do another one. What if I said -2 x -7—and you might want to pause a video at anytime to see if you know how to do it and then restart it to see what the answer is. Well 2 x 7 is 14 and we have the same signs here so it’s a +14 normally you wouldn’t have to write the positive but that’s makes a little bit more explicit. And what if I had—let me think 9 x -5? Well 9 x 5 is 45 and once again the signs are different so that’s a negative. And then finally what if I had -6 x -11? Well 6 x 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 x -12? Well you might say that the signs are different but zero is actually neither positive nor negative and zero times anything is still zero it doesn’t matter if the thing you multiply it by is a negative number of a positive number. Zero times anything is still zero. So let see if we can apply the same rules of division. Its actually turns out the same rules apply. If I have 9 ÷ -3 well first we say well what 9 ÷ 3 well that’s 3 and they have different signs +9 and -3. so different signs means a negative. 9 ÷ -3 is equal to -3. What is -16 ÷ 8? Once again 16 ÷ 8 is 2 but the signs are different, -16 ÷ +8 that equals -2, remember difference signs will get you in negative result. What is -54 ÷ -6? Well 54 ÷ 6 is 9 and since both terms the divisor and the dividend are both negative -54 and -6 it turns out that the answer is positive. Remember same signs result in a positive quotient in this example we did before it was product. And let's do one more. Obviously zero divided by anything is still zero that’s pretty straight forward 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 ÷ -1? Well 4 ÷ 1 is 4 but the signs are different so it’s -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 remember it remind you of which rule to use and if you think about 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 the 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 problems. Good luck.

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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 of rules and I'm going to teach probably in a future like I'm actually going to give you more intuition on why this rules work. But first let me just talk to teach you the basic rules. So the basic rules are when you multiply two negative numbers let say I had -2 x -2 first you just look at each of the numbers as if there was no negative sign. Well you say well 2 x 2 that equals 4 and it turns out that if you have negative times the negative that that equals a positive so let's write that first rule down.

A negative x a negative equals a positive. What if it was -2 x +2? Well in this case let's first of all look at the two numbers without sign we know that 2 x 2 is 4 but here we have a negative times a +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 happen is you have a +2 x -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? I believe is the transitive property. No, I think it’s a communicative property I have to remember that.

But 2 x -2 this also equals -4 so we have the final rule that a positive time a negative also equals a negative. So you see and actually this second to rule they're kind of the same thing, you know, negative times a positive is a negative or positive times a negative is a negative. You could also say that as when the designs 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 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 to each other equals positive. I think that last little bit completely confuse you. Maybe I can simplify it for you. What if I just told you when you're multiplying and there are the same signs that gets you a positive result and different gets you a negative result? So that would be either a, let say a 1 x 1 is equal to 1 or if I said -1 x -1 is equal to +1 as well or I said 1 x -1 is equal to -1 or -1 x 1 is equal to -1. You see how in this the bottom two problems I had two different signs that +1 and -1 and the top two problems this one right here are both one’s are positive and this one right here are both ones are negative.

So let's do a bunch of problem now and hopefully it will hit the point home and you are also could try to do or you can practice problems and also give the hints and give you what rules to use so that should help you as well. So if I said -4 x +3 well 4 x 3 is 12 and we have a negative and a positive so different signs, different signs mean negative. So -4 x 3 is a -12 and that make sense because we’re essentially saying what's -4 time itself three times so it’s like -4 + -4 + -4 which is -12. If you'd seen the video on adding and subtracting negative numbers that you should probably should watch first.

And let's do another one. What if I said -2 x -7—and you might want to pause a video at anytime to see if you know how to do it and then restart it to see what the answer is. Well 2 x 7 is 14 and we have the same signs here so it’s a +14 normally you wouldn’t have to write the positive but that’s makes a little bit more explicit. And what if I had—let me think 9 x -5? Well 9 x 5 is 45 and once again the signs are different so that’s a negative.

And then finally what if I had -6 x -11? Well 6 x 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 x -12? Well you might say that the signs are different but zero is actually neither positive nor negative and zero times anything is still zero it doesn’t matter if the thing you multiply it by is a negative number of a positive number. Zero times anything is still zero.

So let see if we can apply the same rules of division. Its actually turns out the same rules apply. If I have 9 ÷ -3 well first we say well what 9 ÷ 3 well that’s 3 and they have different signs +9 and -3. so different signs means a negative. 9 ÷ -3 is equal to -3. What is -16 ÷ 8? Once again 16 ÷ 8 is 2 but the signs are different, -16 ÷ +8 that equals -2, remember difference signs will get you in negative result. What is -54 ÷ -6? Well 54 ÷ 6 is 9 and since both terms the divisor and the dividend are both negative -54 and -6 it turns out that the answer is positive. Remember same signs result in a positive quotient in this example we did before it was product.

And let's do one more. Obviously zero divided by anything is still zero that’s pretty straight forward 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 ÷ -1? Well 4 ÷ 1 is 4 but the signs are different so it’s -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 remember it remind you of which rule to use and if you think about 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 the 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 problems. Good luck.

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