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Dialogue: 0,0:00:00.81,0:00:03.11,Default,,0000,0000,0000,,Welcome to the presentation\Non dividing fractions.
Dialogue: 0,0:00:03.11,0:00:04.49,Default,,0000,0000,0000,,Let's get started.
Dialogue: 0,0:00:04.49,0:00:06.64,Default,,0000,0000,0000,,So before I give you the\Nintuition-- actually, I might
Dialogue: 0,0:00:06.64,0:00:09.34,Default,,0000,0000,0000,,do that in a different module--\NI'm just going to show you the
Dialogue: 0,0:00:09.34,0:00:11.74,Default,,0000,0000,0000,,mechanics of how you\Ndivide a fraction.
Dialogue: 0,0:00:11.74,0:00:13.74,Default,,0000,0000,0000,,And it turns out that\Nit's actually not much
Dialogue: 0,0:00:13.74,0:00:16.03,Default,,0000,0000,0000,,more difficult than\Nmultiplying fractions.
Dialogue: 0,0:00:16.03,0:00:21.41,Default,,0000,0000,0000,,If I were to ask you, 1/2\Ndivided by 1/2, whenever you
Dialogue: 0,0:00:21.41,0:00:25.11,Default,,0000,0000,0000,,divide by a fraction, or\Nactually, when you divide by
Dialogue: 0,0:00:25.11,0:00:29.96,Default,,0000,0000,0000,,any number, it's the same thing\Nas multiplying by its inverse.
Dialogue: 0,0:00:29.96,0:00:36.67,Default,,0000,0000,0000,,So 1/2 divided by 1/2 is\Nequal to 1/2 times 2/1.
Dialogue: 0,0:00:36.67,0:00:44.99,Default,,0000,0000,0000,,We just inverted--\Ninverse-- the second 1/2.
Dialogue: 0,0:00:44.99,0:00:47.63,Default,,0000,0000,0000,,And we know from the\Nmultiplication module, 1/2
Dialogue: 0,0:00:47.63,0:00:51.11,Default,,0000,0000,0000,,times 2/1, well, that's\Njust equal to 2/2,
Dialogue: 0,0:00:51.11,0:00:53.56,Default,,0000,0000,0000,,or it's equal to 1.
Dialogue: 0,0:00:53.56,0:00:56.02,Default,,0000,0000,0000,,And that makes sense because,\Nactually, any number divided
Dialogue: 0,0:00:56.02,0:00:58.75,Default,,0000,0000,0000,,by itself is equal to 1.
Dialogue: 0,0:00:58.75,0:01:03.22,Default,,0000,0000,0000,,1/2 divided by 1/2 is 1, just\Nlike 5 divided by 5 is 1, just
Dialogue: 0,0:01:03.22,0:01:05.24,Default,,0000,0000,0000,,like 100 divided by 100 is 1.
Dialogue: 0,0:01:05.24,0:01:06.85,Default,,0000,0000,0000,,And this isn't a new principal.
Dialogue: 0,0:01:06.85,0:01:08.97,Default,,0000,0000,0000,,Actually, you were\Nalways doing it.
Dialogue: 0,0:01:16.29,0:01:20.56,Default,,0000,0000,0000,,But isn't this also the\Nsame thing as 2 times the
Dialogue: 0,0:01:20.56,0:01:24.21,Default,,0000,0000,0000,,inverse of 2, which is 1?
Dialogue: 0,0:01:24.21,0:01:24.95,Default,,0000,0000,0000,,I'll show it to you.
Dialogue: 0,0:01:24.95,0:01:26.99,Default,,0000,0000,0000,,Actually, let me give you a\Ncouple more examples to show
Dialogue: 0,0:01:26.99,0:01:31.34,Default,,0000,0000,0000,,that dividing fractions really\Nisn't a new concept, this whole
Dialogue: 0,0:01:31.34,0:01:34.84,Default,,0000,0000,0000,,notion of multiplying\Nby the inverse.
Dialogue: 0,0:01:34.84,0:01:40.54,Default,,0000,0000,0000,,If I were to tell you\Nwhat is 12 divided by 4?
Dialogue: 0,0:01:40.54,0:01:42.65,Default,,0000,0000,0000,,Well, we know the answer to\Nthis, but I'm going to show
Dialogue: 0,0:01:42.65,0:01:50.64,Default,,0000,0000,0000,,you that this is the same\Nthing as 12 times 1/4.
Dialogue: 0,0:01:50.64,0:01:56.23,Default,,0000,0000,0000,,12/1 times 1/4 4 is\N12/4, which is 3.
Dialogue: 0,0:01:56.23,0:01:59.48,Default,,0000,0000,0000,,And 12/4 is really just another\Nway of writing 12 divided by 4,
Dialogue: 0,0:01:59.48,0:02:02.54,Default,,0000,0000,0000,,so it's kind of a long way of\Ngetting to the same point.
Dialogue: 0,0:02:02.54,0:02:04.99,Default,,0000,0000,0000,,But I just wanted to show you\Nthat what we're doing in this
Dialogue: 0,0:02:04.99,0:02:07.97,Default,,0000,0000,0000,,module is nothing new than\Nwhat we've always been doing
Dialogue: 0,0:02:07.97,0:02:09.32,Default,,0000,0000,0000,,when we divide by a number.
Dialogue: 0,0:02:09.32,0:02:11.36,Default,,0000,0000,0000,,Division is the same thing.
Dialogue: 0,0:02:11.36,0:02:14.31,Default,,0000,0000,0000,,Dividing by a number is the\Nsame thing as multiplying by
Dialogue: 0,0:02:14.31,0:02:15.96,Default,,0000,0000,0000,,the inverse of that number.
Dialogue: 0,0:02:15.96,0:02:19.88,Default,,0000,0000,0000,,And just as a review, an\Ninverse, if I have a number
Dialogue: 0,0:02:19.88,0:02:28.07,Default,,0000,0000,0000,,A, the inverse-- inv, short\Nfor inverse-- is 1 over A.
Dialogue: 0,0:02:28.07,0:02:36.29,Default,,0000,0000,0000,,So the inverse of 2/3 is 3/2,\Nor the inverse of 5, because 5
Dialogue: 0,0:02:36.29,0:02:39.67,Default,,0000,0000,0000,,is the same thing as 5/1,\Nso the inverse is 1/5.
Dialogue: 0,0:02:43.32,0:02:46.48,Default,,0000,0000,0000,,So let's do some fraction\Ndivision problems.
Dialogue: 0,0:02:46.48,0:02:49.27,Default,,0000,0000,0000,,\NWhat is 2/3 divided by 5/6?
Dialogue: 0,0:02:56.34,0:03:05.97,Default,,0000,0000,0000,,Well, we know that this is the\Nsame thing as 2/3 times 6/5,
Dialogue: 0,0:03:05.97,0:03:09.23,Default,,0000,0000,0000,,and that's equal to 12/15.
Dialogue: 0,0:03:09.23,0:03:14.57,Default,,0000,0000,0000,,We can divide the numerator and\Ndenominator by 3, that's 4/5.
Dialogue: 0,0:03:14.57,0:03:22.90,Default,,0000,0000,0000,,What is 7/8 divided by 1/4?
Dialogue: 0,0:03:22.90,0:03:30.52,Default,,0000,0000,0000,,Well, that's the same\Nthing as 7/8 times 4/1.
Dialogue: 0,0:03:30.52,0:03:32.82,Default,,0000,0000,0000,,Remember, I just\Nflipped this 1/4.
Dialogue: 0,0:03:32.82,0:03:36.84,Default,,0000,0000,0000,,Divide by 1/4 is the same\Nthing as multiplying by 4/1.
Dialogue: 0,0:03:36.84,0:03:38.23,Default,,0000,0000,0000,,That's all you've got to do.
Dialogue: 0,0:03:38.23,0:03:39.99,Default,,0000,0000,0000,,And then we could use a little\Nshortcut we learned in the
Dialogue: 0,0:03:39.99,0:03:41.48,Default,,0000,0000,0000,,multiplication module.
Dialogue: 0,0:03:41.48,0:03:42.95,Default,,0000,0000,0000,,8 divided by 4 is 2.
Dialogue: 0,0:03:42.95,0:03:44.80,Default,,0000,0000,0000,,4 divided by 4 is 1.
Dialogue: 0,0:03:44.80,0:03:47.45,Default,,0000,0000,0000,,So that equals 7/2.
Dialogue: 0,0:03:47.45,0:03:49.90,Default,,0000,0000,0000,,Or if you wanted to write that\Nas a mixed number, this is, of
Dialogue: 0,0:03:49.90,0:03:51.20,Default,,0000,0000,0000,,course, an improper fraction.
Dialogue: 0,0:03:51.20,0:03:53.44,Default,,0000,0000,0000,,Improper fractions have\Na numerator larger
Dialogue: 0,0:03:53.44,0:03:54.83,Default,,0000,0000,0000,,than the denominator.
Dialogue: 0,0:03:54.83,0:03:58.67,Default,,0000,0000,0000,,If you wanted to write that as\Na mixed number, 2 goes into 7
Dialogue: 0,0:03:58.67,0:04:03.68,Default,,0000,0000,0000,,three times with a remainder\Nof 1, so that's 3 and a half.
Dialogue: 0,0:04:03.68,0:04:04.44,Default,,0000,0000,0000,,You can write it either way.
Dialogue: 0,0:04:04.44,0:04:05.99,Default,,0000,0000,0000,,I tend to keep it this\Nway because it's
Dialogue: 0,0:04:05.99,0:04:07.80,Default,,0000,0000,0000,,easier to deal with.
Dialogue: 0,0:04:07.80,0:04:10.13,Default,,0000,0000,0000,,Let's do a ton of more\Nproblems, or at least as many
Dialogue: 0,0:04:10.13,0:04:13.83,Default,,0000,0000,0000,,more as we can do in the\Nnext four or five minutes.
Dialogue: 0,0:04:13.83,0:04:23.85,Default,,0000,0000,0000,,What's negative 2/3\Ndivided by 5/2?
Dialogue: 0,0:04:23.85,0:04:29.11,Default,,0000,0000,0000,,Once again, that's the same\Nthing as minus 2/3-- whoops--
Dialogue: 0,0:04:29.11,0:04:34.85,Default,,0000,0000,0000,,as minus 2/3 times what?
Dialogue: 0,0:04:34.85,0:04:40.11,Default,,0000,0000,0000,,It's times the inverse of\N5/2, which is 2/5, and
Dialogue: 0,0:04:40.11,0:04:45.63,Default,,0000,0000,0000,,that equals minus 4/15.
Dialogue: 0,0:04:45.63,0:04:52.30,Default,,0000,0000,0000,,What is 3/2 divided by 1/6?
Dialogue: 0,0:04:52.30,0:04:59.85,Default,,0000,0000,0000,,Well, that's just the same\Nthing as 3/2 times 6/1,
Dialogue: 0,0:05:09.61,0:05:11.28,Default,,0000,0000,0000,,I think you might\Nbe getting it now.
Dialogue: 0,0:05:11.28,0:05:12.95,Default,,0000,0000,0000,,Let's see, let's\Ndo a couple more.
Dialogue: 0,0:05:12.95,0:05:16.29,Default,,0000,0000,0000,,And, of course, you can always\Npause, and look at this whole
Dialogue: 0,0:05:16.29,0:05:19.42,Default,,0000,0000,0000,,presentation again, so you can\Nget confused all over again.
Dialogue: 0,0:05:19.42,0:05:27.24,Default,,0000,0000,0000,,Let's see, let's do minus\N5/7 divided by 10/3.
Dialogue: 0,0:05:27.24,0:05:33.88,Default,,0000,0000,0000,,Well, this is the same thing\Nas minus 5/7 times 3/10.
Dialogue: 0,0:05:33.88,0:05:35.42,Default,,0000,0000,0000,,I just multiplied\Nby the inverse.
Dialogue: 0,0:05:35.42,0:05:38.12,Default,,0000,0000,0000,,That's all I keep doing\Nover and over again.
Dialogue: 0,0:05:38.12,0:05:40.18,Default,,0000,0000,0000,,Minus 5 times 3.
Dialogue: 0,0:05:40.18,0:05:42.61,Default,,0000,0000,0000,,Minus 15.
Dialogue: 0,0:05:42.61,0:05:47.35,Default,,0000,0000,0000,,7 times 10 is 70.
Dialogue: 0,0:05:47.35,0:05:49.90,Default,,0000,0000,0000,,If we divide the numerator\Nand the denominator by
Dialogue: 0,0:05:49.90,0:05:56.05,Default,,0000,0000,0000,,5, we get minus 3/14.
Dialogue: 0,0:05:56.05,0:05:57.50,Default,,0000,0000,0000,,We could have also\Njust done it here.
Dialogue: 0,0:05:57.50,0:05:59.89,Default,,0000,0000,0000,,We could have done 5, 2,\Nand we would have gotten
Dialogue: 0,0:05:59.89,0:06:02.51,Default,,0000,0000,0000,,minus 3/14 as well.
Dialogue: 0,0:06:02.51,0:06:05.42,Default,,0000,0000,0000,,Let's do one or two\Nmore problems.
Dialogue: 0,0:06:05.42,0:06:06.63,Default,,0000,0000,0000,,I think you kind of\Nget it, though.
Dialogue: 0,0:06:06.63,0:06:09.60,Default,,0000,0000,0000,,Let's say 1/2\Ndivided by minus 3.
Dialogue: 0,0:06:14.50,0:06:14.96,Default,,0000,0000,0000,,Ah-ha!
Dialogue: 0,0:06:14.96,0:06:17.94,Default,,0000,0000,0000,,So what happens when you take a\Nfraction and you divide it by
Dialogue: 0,0:06:17.94,0:06:19.73,Default,,0000,0000,0000,,a whole number or an integer?
Dialogue: 0,0:06:19.73,0:06:22.97,Default,,0000,0000,0000,,Well, we know any whole number\Ncan be written as a fraction.
Dialogue: 0,0:06:22.97,0:06:29.01,Default,,0000,0000,0000,,This is the same thing as\N1/2 divided by minus 3/1.
Dialogue: 0,0:06:29.01,0:06:33.87,Default,,0000,0000,0000,,And dividing by a fraction is\Nthe same thing as multiplying
Dialogue: 0,0:06:33.87,0:06:37.43,Default,,0000,0000,0000,,by it's inverse.
Dialogue: 0,0:06:37.43,0:06:42.15,Default,,0000,0000,0000,,So the inverse of negative 3/1\Nis negative 1/3, and this
Dialogue: 0,0:06:42.15,0:06:45.20,Default,,0000,0000,0000,,equals negative 1/6.
Dialogue: 0,0:06:45.20,0:06:46.04,Default,,0000,0000,0000,,Let's do it the other way.
Dialogue: 0,0:06:46.04,0:06:51.88,Default,,0000,0000,0000,,What if I had negative\N3 divided by 1/2?
Dialogue: 0,0:06:51.88,0:06:52.50,Default,,0000,0000,0000,,Same thing.
Dialogue: 0,0:06:52.50,0:07:00.37,Default,,0000,0000,0000,,Negative 3 is the same thing as\Nminus 3/1 divided by 1/2, which
Dialogue: 0,0:07:00.37,0:07:07.94,Default,,0000,0000,0000,,is the same thing as minus 3/1\Ntimes 2/1, which is equal to
Dialogue: 0,0:07:07.94,0:07:12.01,Default,,0000,0000,0000,,minus 6/1, which\Nequals minus 6.
Dialogue: 0,0:07:12.01,0:07:15.81,Default,,0000,0000,0000,,\NNow, let me give you a\Nlittle bit of intuition
Dialogue: 0,0:07:17.35,0:07:19.73,Default,,0000,0000,0000,,of why this works.
Dialogue: 0,0:07:19.73,0:07:24.24,Default,,0000,0000,0000,,Let's say I said 2\Ndivided by 1/3.
Dialogue: 0,0:07:24.24,0:07:27.65,Default,,0000,0000,0000,,Well, we know that this\Nis equal to 2/1 times
Dialogue: 0,0:07:27.65,0:07:30.12,Default,,0000,0000,0000,,3/1, which equals 6.
Dialogue: 0,0:07:30.12,0:07:32.70,Default,,0000,0000,0000,,So how does 2, 1/3,\Nand 6 relate?
Dialogue: 0,0:07:32.70,0:07:33.69,Default,,0000,0000,0000,,Well, let's look\Nat it this way.
Dialogue: 0,0:07:33.69,0:07:36.93,Default,,0000,0000,0000,,If I had two pieces of pizza.
Dialogue: 0,0:07:36.93,0:07:38.66,Default,,0000,0000,0000,,I have two pieces of pizza.
Dialogue: 0,0:07:38.66,0:07:41.52,Default,,0000,0000,0000,,Here's my two pieces\Nof pizza right.
Dialogue: 0,0:07:41.52,0:07:42.53,Default,,0000,0000,0000,,Two right here.
Dialogue: 0,0:07:42.53,0:07:45.05,Default,,0000,0000,0000,,So I have two pieces of pizza,\Nand I'm going to divide
Dialogue: 0,0:07:45.05,0:07:48.08,Default,,0000,0000,0000,,them into thirds.
Dialogue: 0,0:07:48.08,0:07:50.60,Default,,0000,0000,0000,,So I'm going to divide\Neach pizza into a third.
Dialogue: 0,0:07:50.60,0:07:52.86,Default,,0000,0000,0000,,I'll draw the little\NMercedes sign.
Dialogue: 0,0:07:52.86,0:07:57.05,Default,,0000,0000,0000,,So I'm dividing each pizza\Ninto a third, right?
Dialogue: 0,0:07:57.05,0:07:58.21,Default,,0000,0000,0000,,How many pieces do I have?
Dialogue: 0,0:07:58.21,0:08:02.92,Default,,0000,0000,0000,,Let's see, 1, 2, 3, 4, 5, 6.
Dialogue: 0,0:08:02.92,0:08:04.80,Default,,0000,0000,0000,,I have 6 pieces.
Dialogue: 0,0:08:04.80,0:08:08.14,Default,,0000,0000,0000,,So you might want to sit and\Nponder that for a little bit,
Dialogue: 0,0:08:08.14,0:08:12.85,Default,,0000,0000,0000,,but I think it might make a\Nlittle bit of sense to you.
Dialogue: 0,0:08:12.85,0:08:17.19,Default,,0000,0000,0000,,Let's do one more just\Nto tire your brain.
Dialogue: 0,0:08:17.19,0:08:25.75,Default,,0000,0000,0000,,If I had negative 7/2 divided\Nby 4/9-- let's pick a negative
Dialogue: 0,0:08:25.75,0:08:30.58,Default,,0000,0000,0000,,4/9-- well, that's the same\Nthing as minus 7/2 times
Dialogue: 0,0:08:30.58,0:08:33.72,Default,,0000,0000,0000,,minus 9/4, right?
Dialogue: 0,0:08:33.72,0:08:37.95,Default,,0000,0000,0000,,I just multiplied by the\Ninverse of negative 4/9.
Dialogue: 0,0:08:37.95,0:08:41.22,Default,,0000,0000,0000,,9 times 7 is equal to--\Nnegative 7 times negative
Dialogue: 0,0:08:41.22,0:08:47.80,Default,,0000,0000,0000,,9 is positive 63,\Nand 2 times 4 is 8.
Dialogue: 0,0:08:47.80,0:08:51.46,Default,,0000,0000,0000,,Hopefully, I think you have a\Ngood idea of how to divide by
Dialogue: 0,0:08:51.46,0:08:55.96,Default,,0000,0000,0000,,a fraction now, and you can\Ntry out the dividing
Dialogue: 0,0:08:55.96,0:08:57.31,Default,,0000,0000,0000,,fractions modules.
Dialogue: 0,0:08:57.31,0:08:58.89,Default,,0000,0000,0000,,Have fun!