[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.94,0:00:04.56,Default,,0000,0000,0000,,Now that we know a little bit about multiplying positive and negative numbers,
Dialogue: 0,0:00:04.56,0:00:06.65,Default,,0000,0000,0000,,Let's think about how how we can divide them.
Dialogue: 0,0:00:06.65,0:00:08.56,Default,,0000,0000,0000,,Now what you'll see is that it's actually
Dialogue: 0,0:00:08.56,0:00:10.63,Default,,0000,0000,0000,,a very similar methodology.
Dialogue: 0,0:00:10.63,0:00:12.16,Default,,0000,0000,0000,,That if both are positive,
Dialogue: 0,0:00:12.16,0:00:15.46,Default,,0000,0000,0000,,you'll get a positive answer. If one is negative,
Dialogue: 0,0:00:15.46,0:00:18.89,Default,,0000,0000,0000,,or the other, but not both, you'll get a negative answer.
Dialogue: 0,0:00:18.89,0:00:22.54,Default,,0000,0000,0000,,And if both are negative, they'll cancel out and you'll get a positive answer.
Dialogue: 0,0:00:22.54,0:00:26.36,Default,,0000,0000,0000,,But let's apply and I encourage you to pause this video and try these out yourself
Dialogue: 0,0:00:26.36,0:00:29.47,Default,,0000,0000,0000,,and then see if you get the same answer that I'm going to get.
Dialogue: 0,0:00:29.47,0:00:32.84,Default,,0000,0000,0000,,So eight (8) divided by negative two (-2).
Dialogue: 0,0:00:32.84,0:00:35.96,Default,,0000,0000,0000,,So if I just said eight (8) divided by two (2), that would be
Dialogue: 0,0:00:35.96,0:00:40.33,Default,,0000,0000,0000,,a positive four (4), but since exactly one of these two numbers
Dialogue: 0,0:00:40.33,0:00:45.42,Default,,0000,0000,0000,,are negative, this one right over here, the answer is going to be negative.
Dialogue: 0,0:00:45.42,0:00:49.56,Default,,0000,0000,0000,,So eight (8) divided by negative two (-2) is negative four (-4).
Dialogue: 0,0:00:49.56,0:00:53.42,Default,,0000,0000,0000,,Now negative sixteen (-16) divided by positive four (4)--
Dialogue: 0,0:00:53.42,0:00:54.42,Default,,0000,0000,0000,,now be very careful here.
Dialogue: 0,0:00:54.42,0:00:59.73,Default,,0000,0000,0000,,If I just said positive sixteen (16) divided by positive four (4), that would just be four (4).
Dialogue: 0,0:00:59.73,0:01:02.68,Default,,0000,0000,0000,,But because one of these two numbers is negative,
Dialogue: 0,0:01:02.68,0:01:05.12,Default,,0000,0000,0000,,and exactly one of these two numbers is negative,
Dialogue: 0,0:01:05.12,0:01:09.10,Default,,0000,0000,0000,,then I'm going to get a negative answer.
Dialogue: 0,0:01:09.10,0:01:12.17,Default,,0000,0000,0000,,Now I have negative thirty (-30) divided by negative five (-5).
Dialogue: 0,0:01:12.17,0:01:17.28,Default,,0000,0000,0000,,If I just said thirty (30) divided by five (5), I'd get a positive six (6).
Dialogue: 0,0:01:17.28,0:01:20.57,Default,,0000,0000,0000,,And because I have a negative divided by a negative,
Dialogue: 0,0:01:20.57,0:01:25.63,Default,,0000,0000,0000,,the negatives cancel out, so my answer will still be positive six (6)!
Dialogue: 0,0:01:25.63,0:01:27.33,Default,,0000,0000,0000,,And I could even write a positive (+) out there, I don't have to,
Dialogue: 0,0:01:27.33,0:01:30.45,Default,,0000,0000,0000,,but this is a positive six (6).
Dialogue: 0,0:01:30.45,0:01:34.06,Default,,0000,0000,0000,,A negative divided by a negative, just like a negative times a negative,
Dialogue: 0,0:01:34.06,0:01:37.06,Default,,0000,0000,0000,,you're gonna get a positive answer.
Dialogue: 0,0:01:37.06,0:01:39.04,Default,,0000,0000,0000,,Eighteen (18) divided by two (2)!
Dialogue: 0,0:01:39.04,0:01:40.61,Default,,0000,0000,0000,,And this is a little bit of a trick question.
Dialogue: 0,0:01:40.61,0:01:43.93,Default,,0000,0000,0000,,This is what you knew how to do before we even talked about negative numbers:
Dialogue: 0,0:01:43.93,0:01:47.07,Default,,0000,0000,0000,,This is a positive divided by a positive.
Dialogue: 0,0:01:47.07,0:01:49.04,Default,,0000,0000,0000,,Which is going to be a positive.
Dialogue: 0,0:01:49.04,0:01:52.92,Default,,0000,0000,0000,,So that is going to be equal to positive nine (9).
Dialogue: 0,0:01:52.92,0:01:55.77,Default,,0000,0000,0000,,Now we start doing some interesting things,
Dialogue: 0,0:01:55.77,0:01:57.97,Default,,0000,0000,0000,,here's kind of a compound problem.
Dialogue: 0,0:01:57.97,0:02:01.46,Default,,0000,0000,0000,,We have some multiplication and some division going on.
Dialogue: 0,0:02:01.46,0:02:03.70,Default,,0000,0000,0000,,And so first right over here, the way this is written,
Dialogue: 0,0:02:03.70,0:02:06.03,Default,,0000,0000,0000,,we're gonna wanna multiply the numerator out,
Dialogue: 0,0:02:06.03,0:02:07.79,Default,,0000,0000,0000,,and if you're not familiar with this little dot symbol,
Dialogue: 0,0:02:07.79,0:02:10.16,Default,,0000,0000,0000,,it's just another way of writing multiplication.
Dialogue: 0,0:02:10.16,0:02:12.38,Default,,0000,0000,0000,,I could've written this little "x" thing over here
Dialogue: 0,0:02:12.38,0:02:15.63,Default,,0000,0000,0000,,but what you're gonna see in Algebra is that the dot become much more common.
Dialogue: 0,0:02:15.63,0:02:17.36,Default,,0000,0000,0000,,Because the X becomes used for other--
Dialogue: 0,0:02:17.36,0:02:23.38,Default,,0000,0000,0000,,People don't want to confuse it with the letter X
Dialogue: 0,0:02:23.38,0:02:25.58,Default,,0000,0000,0000,,which gets used a lot in Algebra.
Dialogue: 0,0:02:25.58,0:02:27.93,Default,,0000,0000,0000,,That's why they used the dot very often.
Dialogue: 0,0:02:27.93,0:02:31.09,Default,,0000,0000,0000,,So this just says negative seven (-7) times three (3)
Dialogue: 0,0:02:31.09,0:02:33.45,Default,,0000,0000,0000,,in the numerator, and we're gonna take that product
Dialogue: 0,0:02:33.45,0:02:35.60,Default,,0000,0000,0000,,and divide it by negative one (-1).
Dialogue: 0,0:02:35.60,0:02:37.64,Default,,0000,0000,0000,,So the numerator, negative seven (-7) times three (3),
Dialogue: 0,0:02:37.64,0:02:41.44,Default,,0000,0000,0000,,positive seven (7) times three (3) would be twenty-one (21),
Dialogue: 0,0:02:41.44,0:02:45.30,Default,,0000,0000,0000,,but since exactly one of these two are negative,
Dialogue: 0,0:02:45.30,0:02:47.08,Default,,0000,0000,0000,,this is going to be negative twenty-one (-21),
Dialogue: 0,0:02:47.08,0:02:49.73,Default,,0000,0000,0000,,that's gonna be negative twenty-one (-21) over negative one (-1).
Dialogue: 0,0:02:49.73,0:02:51.89,Default,,0000,0000,0000,,And so negative twenty-one (-21) divided by negative one (-1),
Dialogue: 0,0:02:51.89,0:02:54.94,Default,,0000,0000,0000,,negative divided by a negative is going to be a positive.
Dialogue: 0,0:02:54.94,0:02:57.92,Default,,0000,0000,0000,,So this is going to be a positive twenty-one (21).
Dialogue: 0,0:02:57.92,0:02:59.51,Default,,0000,0000,0000,,Let me write all these things down.
Dialogue: 0,0:02:59.51,0:03:03.27,Default,,0000,0000,0000,,So if I were to take a positive divided by a negative,
Dialogue: 0,0:03:03.27,0:03:07.42,Default,,0000,0000,0000,,that's going to be a negative.
Dialogue: 0,0:03:07.42,0:03:11.41,Default,,0000,0000,0000,,If I had a negative divided by a positive,
Dialogue: 0,0:03:11.41,0:03:15.12,Default,,0000,0000,0000,,that's also going to be a negative.
Dialogue: 0,0:03:15.12,0:03:18.02,Default,,0000,0000,0000,,If I have a negative divided by a negative,
Dialogue: 0,0:03:18.02,0:03:20.45,Default,,0000,0000,0000,,that's going to give me a positive,
Dialogue: 0,0:03:20.45,0:03:24.95,Default,,0000,0000,0000,,and if obviously a positive divided by a positive,
Dialogue: 0,0:03:24.95,0:03:27.77,Default,,0000,0000,0000,,that's also going to give me a positive.
Dialogue: 0,0:03:27.77,0:03:29.36,Default,,0000,0000,0000,,Now let's do this last one over here.
Dialogue: 0,0:03:29.36,0:03:30.59,Default,,0000,0000,0000,,This is actually all multiplication,
Dialogue: 0,0:03:30.59,0:03:31.99,Default,,0000,0000,0000,,but it's interesting, because we're multiplying
Dialogue: 0,0:03:31.99,0:03:34.54,Default,,0000,0000,0000,,three (3) things, which we haven't done yet.
Dialogue: 0,0:03:34.54,0:03:37.12,Default,,0000,0000,0000,,And we could just go from left to right over here,
Dialogue: 0,0:03:37.12,0:03:39.40,Default,,0000,0000,0000,,and we could first think about negative two (-2) times
Dialogue: 0,0:03:39.40,0:03:41.09,Default,,0000,0000,0000,,negative seven (-7).
Dialogue: 0,0:03:41.09,0:03:42.63,Default,,0000,0000,0000,,Negative two (-2) times negative seven (-7).
Dialogue: 0,0:03:42.63,0:03:44.04,Default,,0000,0000,0000,,They are both negatives, and
Dialogue: 0,0:03:44.04,0:03:45.09,Default,,0000,0000,0000,,negatives cancel out, so this would give us,
Dialogue: 0,0:03:45.09,0:03:46.84,Default,,0000,0000,0000,,this part right over here,
Dialogue: 0,0:03:46.84,0:03:49.54,Default,,0000,0000,0000,,will give us positive fourteen (14).
Dialogue: 0,0:03:49.54,0:03:51.41,Default,,0000,0000,0000,,And so we're going to multiply positive fourteen (14)
Dialogue: 0,0:03:51.41,0:03:55.21,Default,,0000,0000,0000,,times this negative one (-1), times -1.
Dialogue: 0,0:03:55.21,0:03:57.91,Default,,0000,0000,0000,,Now we have a positive times a negative.
Dialogue: 0,0:03:57.91,0:03:59.59,Default,,0000,0000,0000,,Exactly one of them is negative,
Dialogue: 0,0:03:59.59,0:04:01.47,Default,,0000,0000,0000,,so this is going to be negative answer,
Dialogue: 0,0:04:01.47,0:04:05.02,Default,,0000,0000,0000,,it's gonna give me negative fourteen (-14).
Dialogue: 0,0:04:05.02,0:04:06.09,Default,,0000,0000,0000,,Now let me give you a couple of more,
Dialogue: 0,0:04:06.09,0:04:08.66,Default,,0000,0000,0000,,I guess we could call these trick problems.
Dialogue: 0,0:04:08.66,0:04:12.07,Default,,0000,0000,0000,,What would happen if I had zero (0) divided by
Dialogue: 0,0:04:12.07,0:04:14.25,Default,,0000,0000,0000,,negative five (-5).
Dialogue: 0,0:04:14.25,0:04:16.50,Default,,0000,0000,0000,,Well this is zero negative fifths
Dialogue: 0,0:04:16.50,0:04:19.22,Default,,0000,0000,0000,,So zero divided by anything that's non-zero
Dialogue: 0,0:04:19.22,0:04:22.36,Default,,0000,0000,0000,,is just going to equal to zero.
Dialogue: 0,0:04:22.36,0:04:25.04,Default,,0000,0000,0000,,But what if it were the other way around?
Dialogue: 0,0:04:25.04,0:04:27.37,Default,,0000,0000,0000,,What happens if we said negative five divided by zero?
Dialogue: 0,0:04:27.37,0:04:29.84,Default,,0000,0000,0000,,Well, we don't know what happens when you divide things by zero.
Dialogue: 0,0:04:29.84,0:04:31.52,Default,,0000,0000,0000,,We haven't defined that.
Dialogue: 0,0:04:31.52,0:04:35.25,Default,,0000,0000,0000,,There's arguments for multiple ways to conceptualize this,
Dialogue: 0,0:04:35.25,0:04:38.30,Default,,0000,0000,0000,,so we traditionally do say that this is undefined.
Dialogue: 0,0:04:38.30,0:04:43.21,Default,,0000,0000,0000,,We haven't defined what happens when something is divided by zero.
Dialogue: 0,0:04:43.21,0:04:46.35,Default,,0000,0000,0000,,And similarly, even when we had zero divided by zero,
Dialogue: 0,0:04:46.35,0:04:50.43,Default,,0000,0000,0000,,this is still, this is still, undefined.