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Welcome to the presentation[br]on multiplying and

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dividing negative numbers.

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Let's get started.

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I think you're going to find[br]that multiplying and dividing

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negative numbers are a lot[br]easier than it might

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look initially. You just have to[br]remember a couple of rules.

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And I am going to teach probably [br]in the future like I'm actually going

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to give you more intuition on[br]why there rules work.

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So the basic rules are when you[br]multiply two negative numbers,

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so let's say I had negative[br]2 times negative 2.

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First you just look at each[br]of the numbers as if there

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was no negative sign.

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Well you say well, 2[br]times 2 that equals 4.

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And it turns out that if you[br]have a negative times a

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negative, that that[br]equals a positive.

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So let's write that[br]first rule down.

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A negative times a negative[br]equals a positive.

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[br]What if it was negative[br]2 times positive 2?

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Well in this case, let's[br]first of all look at the

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two numbers without signs.

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We know that 2 times 2 is 4.

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But here we have a negative[br]times a positive 2, and it

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turns out that when you[br]multiply a negative times a

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positive you get a negative.

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So that's another rule.

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Negative times positive[br]is equal to negative.

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What happens if you have a[br]positive 2 times a negative 2?

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I think you'll probably guess[br]this one right, as you can tell

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that these two are pretty much[br]the same thing by, I believe

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it's the transitive property --[br]no, no I think it's the

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communicative property.

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I have to remember that.

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But 2 times negative 2, this[br]also equals negative 4.

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So we have the final rule that[br]a positive times a negative

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also equals the negative.

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[br]And actually these second[br]two rules, they're kind

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of the same thing.

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A negative times a positive[br]is a negative, or a positive

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times a negative is negative.

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You could also say that as when[br]the signs are different and

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you multiply the two numbers,[br]you get a negative number.

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And of course, you already know[br]what happens when you have a

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positive times a positive.

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Well that's just a positive.

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So let's review.

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Negative times a[br]negative is a positive.

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A negative times a[br]positive is a negative.

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A positive times a[br]negative is a negative.

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And positive times each[br]other equals positive.

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I think that last little bit[br]completely confused you.

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Maybe I can simplify[br]it for you.

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What if I just told you if when[br]you're multiplying and they're

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the same signs that gets[br]you a positive result.

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[br]And different signs gets[br]you a negative result.

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So that would be either, let's[br]say a 1 times 1 is equal to 1,

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or if I said negative 1 times[br]negative 1 is equal to

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positive 1 as well.

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Or if I said 1 times negative[br]1 is equal to negative 1, or

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negative 1 times 1 is[br]equal to negative 1.

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You see how on the bottom two[br]problems I had two different

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signs, positive 1[br]and negative 1?

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And the top two problems,[br]this one right here

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both 1s are positive.

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And this one right here[br]both 1s are negative.

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So let's do a bunch of problems[br]now, and hopefully it'll hit

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the point home, and you also[br]could try to do along the

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practice problems and also give[br]the hints and give you what rules to you so that should help you as well

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So if I said negative 4 times[br]positive 3, well 4 times

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3 is 12, and we have a[br]negative and a positive.

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So different signs[br]mean negative.

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So negative 4 times[br]3 is a negative 12.

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That makes sense because we're[br]essentially saying what's

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negative 4 times itself three[br]times, so it's like negative 4

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plus negative 4 plus negative[br]4, which is negative 12.

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If you've seen the video on[br]adding and subtracting negative

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numbers, you probably[br]should watch first.

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Let's do another one.

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What if I said minus[br]2 times minus 7.

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And you might want to pause the[br]video at any time to see if you

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know how to do it and[br]then restart it to see

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what the answer is.

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Well, 2 times 7 is 14, and we[br]have the same sign here, so

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it's a positive 14 -- normally[br]you wouldn't have to write the

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positive but that makes it a[br]little bit more explicit.

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And what if I had -- let me[br]think -- 9 times negative 5.

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Well, 9 times 5 is 45.

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And once again, the signs are[br]different so it's a negative.

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And then finally what if it I[br]had -- let me think of some

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good numbers -- minus[br]6 times minus 11.

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Well, 6 times 11 is 66 and[br]then it's a negative and

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negative, it's a positive.

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Let me give you a[br]trick problem.

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What is 0 times negative 12?

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Well, you might say that the[br]signs are different, but

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0 is actually neither[br]positive nor negative.

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And 0 times anything[br]is still 0.

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It doesn't matter if the thing[br]you multiply it by is a

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negative number or[br]a positive number.

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0 times anything is still 0.

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So let's see if we can apply[br]these same rules to division.

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It actually turns out that[br]the same rules apply.

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If I have 9 divided[br]by negative 3.

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Well, first we say[br]what's 9 divided by 3?

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Well that's 3.

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And they have different signs,[br]positive 9, negative 3.

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So different signs[br]means a negative.

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9 divided by negative 3[br]is equal to negative 3.

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What is minus 16 divided by 8?

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Well, once again, 16[br]divided by 8 is 2, but

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the signs are different.

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Negative 16 divided by positive[br]8, that equals negative 2.

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Remember, different signs will[br]get you a negative result.

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What is minus 54[br]divided by minus 6?

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Well, 54 divided by 6 is 9.

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And since both terms, the[br]divisor and the dividend, are

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both negative -- negative 54[br]and negative 6 -- it turns out

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that the answer is positive.[br]Remember, same signs

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result in a positive sign.

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Let's do one more.

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Obviously, 0 divided by[br]anything is still 0.

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That's pretty straightforward.

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And of course, you can't[br]divide anything by 0

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-- that's undefined.

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Let's do one more.

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What is -- I'm just going to[br]think of random numbers --

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4 divided by negative 1?

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Well, 4 divided by 1 is 4,[br]but the signs are different.

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So it's negative 4.

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I hope that helps.

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Now what I want you to do is[br]actually try

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as many of these multiplying and dividing[br]negative numbers as you can.

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And you click on hints[br]

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and it'll remind you of which rule to use.

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In your own time you might want[br]to actually think about

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why these rules apply and what it[br]means

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to multiply a negative number times a positive number.

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And even more interesting, what[br]it means

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to multiply a negative number times a negative number.

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But I think at this point,[br]

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hopefully, you are ready to start doing some problems.

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Good luck.