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Dialogue: 0,0:00:00.94,0:00:03.53,Default,,0000,0000,0000,,Welcome to the presentation\Non multiplying and
Dialogue: 0,0:00:03.53,0:00:05.27,Default,,0000,0000,0000,,dividing negative numbers.
Dialogue: 0,0:00:05.27,0:00:06.75,Default,,0000,0000,0000,,Let's get started.
Dialogue: 0,0:00:06.75,0:00:08.92,Default,,0000,0000,0000,,I think you're going to find\Nthat multiplying and dividing
Dialogue: 0,0:00:08.92,0:00:10.73,Default,,0000,0000,0000,,negative numbers are a lot\Neasier than it might
Dialogue: 0,0:00:10.76,0:00:13.87,Default,,0000,0000,0000,,look initially. You just have to\Nremember a couple of rules.
Dialogue: 0,0:00:13.87,0:00:16.17,Default,,0000,0000,0000,,And I am going to teach probably \Nin the future like I'm actually going
Dialogue: 0,0:00:16.17,0:00:20.84,Default,,0000,0000,0000,,to give you more intuition on\Nwhy there rules work.
Dialogue: 0,0:00:20.99,0:00:25.22,Default,,0000,0000,0000,,So the basic rules are when you\Nmultiply two negative numbers,
Dialogue: 0,0:00:25.22,0:00:31.79,Default,,0000,0000,0000,,so let's say I had negative\N2 times negative 2.
Dialogue: 0,0:00:31.79,0:00:33.97,Default,,0000,0000,0000,,First you just look at each\Nof the numbers as if there
Dialogue: 0,0:00:33.97,0:00:35.24,Default,,0000,0000,0000,,was no negative sign.
Dialogue: 0,0:00:35.24,0:00:40.15,Default,,0000,0000,0000,,Well you say well, 2\Ntimes 2 that equals 4.
Dialogue: 0,0:00:40.15,0:00:42.67,Default,,0000,0000,0000,,And it turns out that if you\Nhave a negative times a
Dialogue: 0,0:00:42.67,0:00:45.18,Default,,0000,0000,0000,,negative, that that\Nequals a positive.
Dialogue: 0,0:00:45.18,0:00:47.71,Default,,0000,0000,0000,,So let's write that\Nfirst rule down.
Dialogue: 0,0:00:47.71,0:00:54.28,Default,,0000,0000,0000,,A negative times a negative\Nequals a positive.
Dialogue: 0,0:00:56.85,0:01:01.89,Default,,0000,0000,0000,,\NWhat if it was negative\N2 times positive 2?
Dialogue: 0,0:01:01.89,0:01:04.77,Default,,0000,0000,0000,,Well in this case, let's\Nfirst of all look at the
Dialogue: 0,0:01:04.77,0:01:06.06,Default,,0000,0000,0000,,two numbers without signs.
Dialogue: 0,0:01:06.06,0:01:10.17,Default,,0000,0000,0000,,We know that 2 times 2 is 4.
Dialogue: 0,0:01:10.17,0:01:13.74,Default,,0000,0000,0000,,But here we have a negative\Ntimes a positive 2, and it
Dialogue: 0,0:01:13.74,0:01:15.91,Default,,0000,0000,0000,,turns out that when you\Nmultiply a negative times a
Dialogue: 0,0:01:15.91,0:01:18.92,Default,,0000,0000,0000,,positive you get a negative.
Dialogue: 0,0:01:18.92,0:01:20.26,Default,,0000,0000,0000,,So that's another rule.
Dialogue: 0,0:01:20.26,0:01:29.01,Default,,0000,0000,0000,,Negative times positive\Nis equal to negative.
Dialogue: 0,0:01:29.01,0:01:34.79,Default,,0000,0000,0000,,What happens if you have a\Npositive 2 times a negative 2?
Dialogue: 0,0:01:34.79,0:01:37.14,Default,,0000,0000,0000,,I think you'll probably guess\Nthis one right, as you can tell
Dialogue: 0,0:01:37.14,0:01:41.17,Default,,0000,0000,0000,,that these two are pretty much\Nthe same thing by, I believe
Dialogue: 0,0:01:41.17,0:01:44.80,Default,,0000,0000,0000,,it's the transitive property --\Nno, no I think it's the
Dialogue: 0,0:01:44.80,0:01:45.86,Default,,0000,0000,0000,,communicative property.
Dialogue: 0,0:01:45.86,0:01:47.70,Default,,0000,0000,0000,,I have to remember that.
Dialogue: 0,0:01:47.70,0:01:51.78,Default,,0000,0000,0000,,But 2 times negative 2, this\Nalso equals negative 4.
Dialogue: 0,0:01:51.78,0:01:57.64,Default,,0000,0000,0000,,So we have the final rule that\Na positive times a negative
Dialogue: 0,0:01:57.64,0:01:58.98,Default,,0000,0000,0000,,also equals the negative.
Dialogue: 0,0:01:58.98,0:02:01.49,Default,,0000,0000,0000,,\NAnd actually these second\Ntwo rules, they're kind
Dialogue: 0,0:02:03.98,0:02:04.99,Default,,0000,0000,0000,,of the same thing.
Dialogue: 0,0:02:04.99,0:02:07.57,Default,,0000,0000,0000,,A negative times a positive\Nis a negative, or a positive
Dialogue: 0,0:02:07.57,0:02:09.14,Default,,0000,0000,0000,,times a negative is negative.
Dialogue: 0,0:02:09.14,0:02:13.73,Default,,0000,0000,0000,,You could also say that as when\Nthe signs are different and
Dialogue: 0,0:02:13.73,0:02:16.40,Default,,0000,0000,0000,,you multiply the two numbers,\Nyou get a negative number.
Dialogue: 0,0:02:16.40,0:02:18.89,Default,,0000,0000,0000,,And of course, you already know\Nwhat happens when you have a
Dialogue: 0,0:02:18.89,0:02:21.55,Default,,0000,0000,0000,,positive times a positive.
Dialogue: 0,0:02:21.55,0:02:22.84,Default,,0000,0000,0000,,Well that's just a positive.
Dialogue: 0,0:02:22.84,0:02:23.90,Default,,0000,0000,0000,,So let's review.
Dialogue: 0,0:02:23.90,0:02:27.97,Default,,0000,0000,0000,,Negative times a\Nnegative is a positive.
Dialogue: 0,0:02:27.97,0:02:30.39,Default,,0000,0000,0000,,A negative times a\Npositive is a negative.
Dialogue: 0,0:02:30.39,0:02:32.73,Default,,0000,0000,0000,,A positive times a\Nnegative is a negative.
Dialogue: 0,0:02:32.73,0:02:36.29,Default,,0000,0000,0000,,And positive times each\Nother equals positive.
Dialogue: 0,0:02:36.29,0:02:39.98,Default,,0000,0000,0000,,I think that last little bit\Ncompletely confused you.
Dialogue: 0,0:02:39.98,0:02:42.27,Default,,0000,0000,0000,,Maybe I can simplify\Nit for you.
Dialogue: 0,0:02:42.27,0:02:46.35,Default,,0000,0000,0000,,What if I just told you if when\Nyou're multiplying and they're
Dialogue: 0,0:02:46.35,0:02:55.18,Default,,0000,0000,0000,,the same signs that gets\Nyou a positive result.
Dialogue: 0,0:02:55.18,0:02:57.84,Default,,0000,0000,0000,,\NAnd different signs gets\Nyou a negative result.
Dialogue: 0,0:03:11.01,0:03:17.78,Default,,0000,0000,0000,,So that would be either, let's\Nsay a 1 times 1 is equal to 1,
Dialogue: 0,0:03:17.78,0:03:22.12,Default,,0000,0000,0000,,or if I said negative 1 times\Nnegative 1 is equal to
Dialogue: 0,0:03:22.12,0:03:23.51,Default,,0000,0000,0000,,positive 1 as well.
Dialogue: 0,0:03:23.51,0:03:29.15,Default,,0000,0000,0000,,Or if I said 1 times negative\N1 is equal to negative 1, or
Dialogue: 0,0:03:29.15,0:03:32.60,Default,,0000,0000,0000,,negative 1 times 1 is\Nequal to negative 1.
Dialogue: 0,0:03:32.60,0:03:36.13,Default,,0000,0000,0000,,You see how on the bottom two\Nproblems I had two different
Dialogue: 0,0:03:36.13,0:03:38.59,Default,,0000,0000,0000,,signs, positive 1\Nand negative 1?
Dialogue: 0,0:03:38.59,0:03:41.12,Default,,0000,0000,0000,,And the top two problems,\Nthis one right here
Dialogue: 0,0:03:41.12,0:03:42.68,Default,,0000,0000,0000,,both 1s are positive.
Dialogue: 0,0:03:42.68,0:03:45.97,Default,,0000,0000,0000,,And this one right here\Nboth 1s are negative.
Dialogue: 0,0:03:45.97,0:03:49.11,Default,,0000,0000,0000,,So let's do a bunch of problems\Nnow, and hopefully it'll hit
Dialogue: 0,0:03:49.11,0:03:51.51,Default,,0000,0000,0000,,the point home, and you also\Ncould try to do along the
Dialogue: 0,0:03:51.51,0:03:56.20,Default,,0000,0000,0000,,practice problems and also give\Nthe hints and give you what rules to you so that should help you as well
Dialogue: 0,0:04:02.86,0:04:06.75,Default,,0000,0000,0000,,So if I said negative 4 times\Npositive 3, well 4 times
Dialogue: 0,0:04:06.75,0:04:11.82,Default,,0000,0000,0000,,3 is 12, and we have a\Nnegative and a positive.
Dialogue: 0,0:04:11.82,0:04:15.67,Default,,0000,0000,0000,,So different signs\Nmean negative.
Dialogue: 0,0:04:15.67,0:04:19.06,Default,,0000,0000,0000,,So negative 4 times\N3 is a negative 12.
Dialogue: 0,0:04:19.06,0:04:21.31,Default,,0000,0000,0000,,That makes sense because we're\Nessentially saying what's
Dialogue: 0,0:04:21.31,0:04:25.07,Default,,0000,0000,0000,,negative 4 times itself three\Ntimes, so it's like negative 4
Dialogue: 0,0:04:25.07,0:04:27.80,Default,,0000,0000,0000,,plus negative 4 plus negative\N4, which is negative 12.
Dialogue: 0,0:04:27.80,0:04:31.12,Default,,0000,0000,0000,,If you've seen the video on\Nadding and subtracting negative
Dialogue: 0,0:04:31.12,0:04:34.20,Default,,0000,0000,0000,,numbers, you probably\Nshould watch first.
Dialogue: 0,0:04:34.20,0:04:35.21,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:04:35.21,0:04:40.43,Default,,0000,0000,0000,,What if I said minus\N2 times minus 7.
Dialogue: 0,0:04:40.43,0:04:42.47,Default,,0000,0000,0000,,And you might want to pause the\Nvideo at any time to see if you
Dialogue: 0,0:04:42.47,0:04:44.03,Default,,0000,0000,0000,,know how to do it and\Nthen restart it to see
Dialogue: 0,0:04:44.03,0:04:45.42,Default,,0000,0000,0000,,what the answer is.
Dialogue: 0,0:04:45.42,0:04:51.19,Default,,0000,0000,0000,,Well, 2 times 7 is 14, and we\Nhave the same sign here, so
Dialogue: 0,0:04:51.19,0:04:53.53,Default,,0000,0000,0000,,it's a positive 14 -- normally\Nyou wouldn't have to write the
Dialogue: 0,0:04:53.53,0:04:56.93,Default,,0000,0000,0000,,positive but that makes it a\Nlittle bit more explicit.
Dialogue: 0,0:04:56.93,0:05:05.88,Default,,0000,0000,0000,,And what if I had -- let me\Nthink -- 9 times negative 5.
Dialogue: 0,0:05:05.88,0:05:08.80,Default,,0000,0000,0000,,Well, 9 times 5 is 45.
Dialogue: 0,0:05:08.80,0:05:13.66,Default,,0000,0000,0000,,And once again, the signs are\Ndifferent so it's a negative.
Dialogue: 0,0:05:13.66,0:05:18.01,Default,,0000,0000,0000,,And then finally what if it I\Nhad -- let me think of some
Dialogue: 0,0:05:18.01,0:05:24.54,Default,,0000,0000,0000,,good numbers -- minus\N6 times minus 11.
Dialogue: 0,0:05:24.54,0:05:29.73,Default,,0000,0000,0000,,Well, 6 times 11 is 66 and\Nthen it's a negative and
Dialogue: 0,0:05:29.73,0:05:31.72,Default,,0000,0000,0000,,negative, it's a positive.
Dialogue: 0,0:05:31.72,0:05:32.91,Default,,0000,0000,0000,,Let me give you a\Ntrick problem.
Dialogue: 0,0:05:32.91,0:05:39.10,Default,,0000,0000,0000,,What is 0 times negative 12?
Dialogue: 0,0:05:39.10,0:05:42.74,Default,,0000,0000,0000,,Well, you might say that the\Nsigns are different, but
Dialogue: 0,0:05:42.74,0:05:46.46,Default,,0000,0000,0000,,0 is actually neither\Npositive nor negative.
Dialogue: 0,0:05:46.46,0:05:48.32,Default,,0000,0000,0000,,And 0 times anything\Nis still 0.
Dialogue: 0,0:05:48.32,0:05:52.08,Default,,0000,0000,0000,,It doesn't matter if the thing\Nyou multiply it by is a
Dialogue: 0,0:05:52.08,0:05:53.65,Default,,0000,0000,0000,,negative number or\Na positive number.
Dialogue: 0,0:05:53.65,0:05:57.63,Default,,0000,0000,0000,,0 times anything is still 0.
Dialogue: 0,0:05:57.63,0:06:00.02,Default,,0000,0000,0000,,So let's see if we can apply\Nthese same rules to division.
Dialogue: 0,0:06:00.02,0:06:03.08,Default,,0000,0000,0000,,It actually turns out that\Nthe same rules apply.
Dialogue: 0,0:06:03.08,0:06:09.03,Default,,0000,0000,0000,,If I have 9 divided\Nby negative 3.
Dialogue: 0,0:06:09.03,0:06:11.82,Default,,0000,0000,0000,,Well, first we say\Nwhat's 9 divided by 3?
Dialogue: 0,0:06:11.82,0:06:13.64,Default,,0000,0000,0000,,Well that's 3.
Dialogue: 0,0:06:13.64,0:06:17.92,Default,,0000,0000,0000,,And they have different signs,\Npositive 9, negative 3.
Dialogue: 0,0:06:17.92,0:06:22.19,Default,,0000,0000,0000,,So different signs\Nmeans a negative.
Dialogue: 0,0:06:22.19,0:06:27.52,Default,,0000,0000,0000,,9 divided by negative 3\Nis equal to negative 3.
Dialogue: 0,0:06:27.52,0:06:33.83,Default,,0000,0000,0000,,What is minus 16 divided by 8?
Dialogue: 0,0:06:33.83,0:06:37.79,Default,,0000,0000,0000,,Well, once again, 16\Ndivided by 8 is 2, but
Dialogue: 0,0:06:37.79,0:06:39.37,Default,,0000,0000,0000,,the signs are different.
Dialogue: 0,0:06:39.37,0:06:44.83,Default,,0000,0000,0000,,Negative 16 divided by positive\N8, that equals negative 2.
Dialogue: 0,0:06:44.83,0:06:49.14,Default,,0000,0000,0000,,Remember, different signs will\Nget you a negative result.
Dialogue: 0,0:06:49.14,0:07:00.50,Default,,0000,0000,0000,,What is minus 54\Ndivided by minus 6?
Dialogue: 0,0:07:00.50,0:07:04.32,Default,,0000,0000,0000,,Well, 54 divided by 6 is 9.
Dialogue: 0,0:07:04.32,0:07:09.05,Default,,0000,0000,0000,,And since both terms, the\Ndivisor and the dividend, are
Dialogue: 0,0:07:11.47,0:07:13.89,Default,,0000,0000,0000,,both negative -- negative 54\Nand negative 6 -- it turns out
Dialogue: 0,0:07:13.93,0:07:18.19,Default,,0000,0000,0000,,that the answer is positive.\NRemember, same signs
Dialogue: 0,0:07:18.19,0:07:18.98,Default,,0000,0000,0000,,result in a positive sign.
Dialogue: 0,0:07:22.47,0:07:24.73,Default,,0000,0000,0000,,Let's do one more.
Dialogue: 0,0:07:24.73,0:07:30.50,Default,,0000,0000,0000,,Obviously, 0 divided by\Nanything is still 0.
Dialogue: 0,0:07:30.50,0:07:31.51,Default,,0000,0000,0000,,That's pretty straightforward.
Dialogue: 0,0:07:31.51,0:07:33.20,Default,,0000,0000,0000,,And of course, you can't\Ndivide anything by 0
Dialogue: 0,0:07:33.20,0:07:36.21,Default,,0000,0000,0000,,-- that's undefined.
Dialogue: 0,0:07:36.21,0:07:38.42,Default,,0000,0000,0000,,Let's do one more.
Dialogue: 0,0:07:38.42,0:07:41.89,Default,,0000,0000,0000,,What is -- I'm just going to\Nthink of random numbers --
Dialogue: 0,0:07:41.89,0:07:44.93,Default,,0000,0000,0000,,4 divided by negative 1?
Dialogue: 0,0:07:44.93,0:07:50.61,Default,,0000,0000,0000,,Well, 4 divided by 1 is 4,\Nbut the signs are different.
Dialogue: 0,0:07:50.61,0:07:53.13,Default,,0000,0000,0000,,So it's negative 4.
Dialogue: 0,0:07:53.13,0:07:54.41,Default,,0000,0000,0000,,I hope that helps.
Dialogue: 0,0:07:54.41,0:07:56.86,Default,,0000,0000,0000,,Now what I want you to do is\Nactually try
Dialogue: 0,0:07:56.86,0:08:01.38,Default,,0000,0000,0000,,as many of these multiplying and dividing\Nnegative numbers as you can.
Dialogue: 0,0:08:01.38,0:08:03.01,Default,,0000,0000,0000,,And you click on hints\N
Dialogue: 0,0:08:03.01,0:08:04.26,Default,,0000,0000,0000,,and it'll remind you of which rule to use.
Dialogue: 0,0:08:04.26,0:08:09.44,Default,,0000,0000,0000,,In your own time you might want\Nto actually think about
Dialogue: 0,0:08:09.46,0:08:11.46,Default,,0000,0000,0000,,why these rules apply and what it\Nmeans
Dialogue: 0,0:08:11.46,0:08:15.32,Default,,0000,0000,0000,,to multiply a negative number times a positive number.
Dialogue: 0,0:08:15.32,0:08:16.98,Default,,0000,0000,0000,,And even more interesting, what\Nit means
Dialogue: 0,0:08:16.98,0:08:20.23,Default,,0000,0000,0000,,to multiply a negative number times a negative number.
Dialogue: 0,0:08:20.23,0:08:23.22,Default,,0000,0000,0000,,But I think at this point,\N
Dialogue: 0,0:08:23.22,0:08:27.16,Default,,0000,0000,0000,,hopefully, you are ready to start doing some problems.
Dialogue: 0,0:08:27.16,0:08:29.02,Default,,0000,0000,0000,,Good luck.