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Now that we know a little bit about multiplying positive and negative numbers,
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Let's think about how how we can divide them.
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Now what you'll see is that it's actually
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a very similar methodology.
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That if both are positive,
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you'll get a positive answer. If one is negative,
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or the other, but not both, you'll get a negative answer.
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And if both are negative, they'll cancel out and you'll get a positive answer.
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But let's apply and I encourage you to pause this video and try these out yourself
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and then see if you get the same answer that I'm going to get.
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So eight (8) divided by negative two (-2).
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So if I just said eight (8) divided by two (2), that would be
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a positive four (4), but since exactly one of these two numbers
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are negative, this one right over here, the answer is going to be negative.
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So eight (8) divided by negative two (-2) is negative four (-4).
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Now negative sixteen (-16) divided by positive four (4)--
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now be very careful here.
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If I just said positive sixteen (16) divided by positive four (4), that would just be four (4).
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But because one of these two numbers is negative,
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and exactly one of these two numbers is negative,
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then I'm going to get a negative answer.
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Now I have negative thirty (-30) divided by negative five (-5).
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If I just said thirty (30) divided by five (5), I'd get a positive six (6).
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And because I have a negative divided by a negative,
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the negatives cancel out, so my answer will still be positive six (6)!
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And I could even write a positive (+) out there, I don't have to,
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but this is a positive six (6).
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A negative divided by a negative, just like a negative times a negative,
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you're gonna get a positive answer.
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Eighteen (18) divided by two (2)!
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And this is a little bit of a trick question.
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This is what you knew how to do before we even talked about negative numbers:
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This is a positive divided by a positive.
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Which is going to be a positive.
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So that is going to be equal to positive nine (9).
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Now we start doing some interesting things,
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here's kind of a compound problem.
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We have some multiplication and some division going on.
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And so first right over here, the way this is written,
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we're gonna wanna multiply the numerator out,
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and if you're not familiar with this little dot symbol,
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it's just another way of writing multiplication.
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I could've written this little "x" thing over here
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but what you're gonna see in Algebra is that the dot become much more common.
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Because the X becomes used for other--
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People don't want to confuse it with the letter X
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which gets used a lot in Algebra.
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That's why they used the dot very often.
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So this just says negative seven (-7) times three (3)
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in the numerator, and we're gonna take that product
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and divide it by negative one (-1).
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So the numerator, negative seven (-7) times three (3),
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positive seven (7) times three (3) would be twenty-one (21),
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but since exactly one of these two are negative,
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this is going to be negative twenty-one (-21),
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that's gonna be negative twenty-one (-21) over negative one (-1).
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And so negative twenty-one (-21) divided by negative one (-1),
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negative divided by a negative is going to be a positive.
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So this is going to be a positive twenty-one (21).
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Let me write all these things down.
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So if I were to take a positive divided by a negative,
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that's going to be a negative.
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If I had a negative divided by a positive,
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that's also going to be a negative.
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If I have a negative divided by a negative,
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that's going to give me a positive,
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and if obviously a positive divided by a positive,
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that's also going to give me a positive.
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Now let's do this last one over here.
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This is actually all multiplication,
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but it's interesting, because we're multiplying
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three (3) things, which we haven't done yet.
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And we could just go from left to right over here,
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and we could first think about negative two (-2) times
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negative seven (-7).
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Negative two (-2) times negative seven (-7).
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They are both negatives, and
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negatives cancel out, so this would give us,
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this part right over here,
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will give us positive fourteen (14).
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And so we're going to multiply positive fourteen (14)
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times this negative one (-1), times -1.
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Now we have a positive times a negative.
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Exactly one of them is negative,
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so this is going to be negative answer,
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it's gonna give me negative fourteen (-14).
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Now let me give you a couple of more,
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I guess we could call these trick problems.
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What would happen if I had zero (0) divided by
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negative five (-5).
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Well this is zero negative fifths
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So zero divided by anything that's non-zero
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is just going to equal to zero.
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But what if it were the other way around?
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What happens if we said negative five divided by zero?
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Well, we don't know what happens when you divide things by zero.
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We haven't defined that.
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There's arguments for multiple ways to conceptualize this,
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so we traditionally do say that this is undefined.
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We haven't defined what happens when something is divided by zero.
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And similarly, even when we had zero divided by zero,
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this is still, this is still, undefined.