[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.74,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.74,0:00:05.19,Default,,0000,0000,0000,,Write 5 and 1/4 as an\Nimproper fraction.
Dialogue: 0,0:00:05.19,0:00:08.77,Default,,0000,0000,0000,,An improper fraction is just\Na pure fraction where the
Dialogue: 0,0:00:08.77,0:00:11.51,Default,,0000,0000,0000,,numerator is greater than\Nthe denominator.
Dialogue: 0,0:00:11.51,0:00:13.27,Default,,0000,0000,0000,,This right here, it's\Nnot a pure fraction.
Dialogue: 0,0:00:13.27,0:00:16.08,Default,,0000,0000,0000,,We have a whole number mixed\Nwith a fraction, so we call
Dialogue: 0,0:00:16.08,0:00:17.72,Default,,0000,0000,0000,,this a mixed number.
Dialogue: 0,0:00:17.72,0:00:20.72,Default,,0000,0000,0000,,So let's think about what 5 and\N1/4 represents, and let me
Dialogue: 0,0:00:20.72,0:00:21.40,Default,,0000,0000,0000,,rewrite it.
Dialogue: 0,0:00:21.40,0:00:27.78,Default,,0000,0000,0000,,So if we're talking about 5 and\N1/4, and you can literally
Dialogue: 0,0:00:27.78,0:00:32.86,Default,,0000,0000,0000,,think of this as 5 and 1/4 or 5\Nplus 1/4, that's what 5 and
Dialogue: 0,0:00:32.86,0:00:34.76,Default,,0000,0000,0000,,1/4 represents.
Dialogue: 0,0:00:34.76,0:00:35.75,Default,,0000,0000,0000,,So let's think about 5.
Dialogue: 0,0:00:35.75,0:00:39.25,Default,,0000,0000,0000,,Five is 5 wholes, or if you're\Nthinking of pie, we could draw
Dialogue: 0,0:00:39.25,0:00:42.71,Default,,0000,0000,0000,,literally five pies.
Dialogue: 0,0:00:42.71,0:00:45.25,Default,,0000,0000,0000,,Let me just cut up the pies\Nfrom the get go into four
Dialogue: 0,0:00:45.25,0:00:48.33,Default,,0000,0000,0000,,pieces since we're dealing\Nwith fourths.
Dialogue: 0,0:00:48.33,0:00:51.75,Default,,0000,0000,0000,,So let me just cut up the\Npies right over here.
Dialogue: 0,0:00:51.75,0:00:54.05,Default,,0000,0000,0000,,So that's one pie right\Nover there.
Dialogue: 0,0:00:54.05,0:00:56.09,Default,,0000,0000,0000,,Let me copy and paste this.
Dialogue: 0,0:00:56.09,0:00:57.90,Default,,0000,0000,0000,,Copy and paste.
Dialogue: 0,0:00:57.90,0:01:04.04,Default,,0000,0000,0000,,So I have two pies, and then I\Nhave three pies, and then I
Dialogue: 0,0:01:04.04,0:01:08.99,Default,,0000,0000,0000,,have four pies, and then\NI have five pies.
Dialogue: 0,0:01:08.99,0:01:11.23,Default,,0000,0000,0000,,So this is what the\N5 represents.
Dialogue: 0,0:01:11.23,0:01:13.57,Default,,0000,0000,0000,,5 literally represents--\Nso let me
Dialogue: 0,0:01:13.57,0:01:14.78,Default,,0000,0000,0000,,circle all of this together.
Dialogue: 0,0:01:14.78,0:01:17.11,Default,,0000,0000,0000,,That is the 5 part\Nright there.
Dialogue: 0,0:01:17.11,0:01:19.68,Default,,0000,0000,0000,,That is what 5 literally\Nrepresents.
Dialogue: 0,0:01:19.68,0:01:22.26,Default,,0000,0000,0000,,It represents five whole pies.
Dialogue: 0,0:01:22.26,0:01:26.85,Default,,0000,0000,0000,,
Dialogue: 0,0:01:26.85,0:01:32.17,Default,,0000,0000,0000,,Now, I have cut up the pies into\Nfour pieces, so you can
Dialogue: 0,0:01:32.17,0:01:35.94,Default,,0000,0000,0000,,imagine each piece represents\Na fourth.
Dialogue: 0,0:01:35.94,0:01:39.70,Default,,0000,0000,0000,,Now, how many pieces do I\Nhave in these five pies?
Dialogue: 0,0:01:39.70,0:01:41.93,Default,,0000,0000,0000,,Well, I have four\Npieces per pie.
Dialogue: 0,0:01:41.93,0:01:50.97,Default,,0000,0000,0000,,
Dialogue: 0,0:01:50.97,0:01:51.79,Default,,0000,0000,0000,,Let me just right it here.
Dialogue: 0,0:01:51.79,0:02:05.38,Default,,0000,0000,0000,,4 pieces per pie times 5 pies\Nis equal to 20 pieces.
Dialogue: 0,0:02:05.38,0:02:09.10,Default,,0000,0000,0000,,Or another way to think of it,\Nsince each piece is a fourth,
Dialogue: 0,0:02:09.10,0:02:14.58,Default,,0000,0000,0000,,this is also equal to 20 times\N1/4, or you could just write
Dialogue: 0,0:02:14.58,0:02:18.75,Default,,0000,0000,0000,,this as being equal to 20/4.
Dialogue: 0,0:02:18.75,0:02:25.64,Default,,0000,0000,0000,,So we have 5 whole pies is\Nequal to 20 fourths.
Dialogue: 0,0:02:25.64,0:02:26.83,Default,,0000,0000,0000,,Let me write it like that.
Dialogue: 0,0:02:26.83,0:02:29.46,Default,,0000,0000,0000,,20 fourths.
Dialogue: 0,0:02:29.46,0:02:35.23,Default,,0000,0000,0000,,Or we could write it as 20/4.
Dialogue: 0,0:02:35.23,0:02:36.70,Default,,0000,0000,0000,,I've kind of done the\Nsame thing twice.
Dialogue: 0,0:02:36.70,0:02:39.02,Default,,0000,0000,0000,,So that's what the five\Npies represent.
Dialogue: 0,0:02:39.02,0:02:43.16,Default,,0000,0000,0000,,20/4 or 20 pieces, where\Neach piece is 1/4.
Dialogue: 0,0:02:43.16,0:02:46.79,Default,,0000,0000,0000,,Now, the 1/4 right here\Nrepresents literally one more
Dialogue: 0,0:02:46.79,0:02:50.27,Default,,0000,0000,0000,,fourth of a pie or one more\Npiece of a pie, so let me draw
Dialogue: 0,0:02:50.27,0:02:51.52,Default,,0000,0000,0000,,another pie here.
Dialogue: 0,0:02:51.52,0:02:54.41,Default,,0000,0000,0000,,
Dialogue: 0,0:02:54.41,0:02:57.09,Default,,0000,0000,0000,,So that is another pie.
Dialogue: 0,0:02:57.09,0:02:59.67,Default,,0000,0000,0000,,Cut it into four pieces.
Dialogue: 0,0:02:59.67,0:03:04.08,Default,,0000,0000,0000,,But this 1/4 only represents\None of these pieces, right?
Dialogue: 0,0:03:04.08,0:03:06.75,Default,,0000,0000,0000,,This is one of the\Nfour pieces.
Dialogue: 0,0:03:06.75,0:03:09.08,Default,,0000,0000,0000,,The denominator tells\Nus how many pieces.
Dialogue: 0,0:03:09.08,0:03:12.14,Default,,0000,0000,0000,,The 1 tells us how many of those\Npieces we're dealing
Dialogue: 0,0:03:12.14,0:03:16.18,Default,,0000,0000,0000,,with, so it's just this\None piece over here.
Dialogue: 0,0:03:16.18,0:03:19.55,Default,,0000,0000,0000,,That right there is the 1/4.
Dialogue: 0,0:03:19.55,0:03:26.10,Default,,0000,0000,0000,,Now, if we write 5 and 1/4,\Nwe just saw that the 5
Dialogue: 0,0:03:26.10,0:03:29.29,Default,,0000,0000,0000,,right here is 20/4.
Dialogue: 0,0:03:29.29,0:03:30.69,Default,,0000,0000,0000,,So we could rewrite this.
Dialogue: 0,0:03:30.69,0:03:31.44,Default,,0000,0000,0000,,Let me write it like this.
Dialogue: 0,0:03:31.44,0:03:44.56,Default,,0000,0000,0000,,5 and 1/4 can be rewritten as\Nthe same thing as 5 plus 1/4,
Dialogue: 0,0:03:44.56,0:03:48.45,Default,,0000,0000,0000,,which is the same thing as--\Nwe just saw that five whole
Dialogue: 0,0:03:48.45,0:03:53.96,Default,,0000,0000,0000,,pies is the same\Nthing as 20/4.
Dialogue: 0,0:03:53.96,0:03:55.65,Default,,0000,0000,0000,,And to see that these are the\Nsame thing, you literally just
Dialogue: 0,0:03:55.65,0:03:57.12,Default,,0000,0000,0000,,divide 4 into 20.
Dialogue: 0,0:03:57.12,0:03:59.70,Default,,0000,0000,0000,,You get 5, and nothing\Nis left over.
Dialogue: 0,0:03:59.70,0:04:03.30,Default,,0000,0000,0000,,So 5 is the same thing as 20/4,\Nand then this plus 1/4
Dialogue: 0,0:04:03.30,0:04:05.05,Default,,0000,0000,0000,,is the same thing as plus 1/4.
Dialogue: 0,0:04:05.05,0:04:10.35,Default,,0000,0000,0000,,So if I have 20 fourths and I\Nadd one more fourth to it, how
Dialogue: 0,0:04:10.35,0:04:12.38,Default,,0000,0000,0000,,many fourths do I have?
Dialogue: 0,0:04:12.38,0:04:14.64,Default,,0000,0000,0000,,Well, I have 21.
Dialogue: 0,0:04:14.64,0:04:17.12,Default,,0000,0000,0000,,I have 21 fourths.
Dialogue: 0,0:04:17.12,0:04:20.74,Default,,0000,0000,0000,,Or another way of thinking about\Nit, this 5 is-- so this
Dialogue: 0,0:04:20.74,0:04:27.99,Default,,0000,0000,0000,,right here is 20\Npieces of pie.
Dialogue: 0,0:04:27.99,0:04:28.77,Default,,0000,0000,0000,,You can even count it.
Dialogue: 0,0:04:28.77,0:04:33.47,Default,,0000,0000,0000,,1, 2, 3, 4, 5, 6, 7, 8, 9, 10,\N11, 12, 13, 14, 15, 16, 17,
Dialogue: 0,0:04:33.47,0:04:34.64,Default,,0000,0000,0000,,18, 19, 20.
Dialogue: 0,0:04:34.64,0:04:36.57,Default,,0000,0000,0000,,But a quicker way is to say,\Nwell, we have five pies.
Dialogue: 0,0:04:36.57,0:04:37.96,Default,,0000,0000,0000,,Each of them have four pieces.
Dialogue: 0,0:04:37.96,0:04:39.82,Default,,0000,0000,0000,,5 times 4 is 20.
Dialogue: 0,0:04:39.82,0:04:46.02,Default,,0000,0000,0000,,This 1/4 right here represents\None piece plus one piece, so
Dialogue: 0,0:04:46.02,0:04:51.06,Default,,0000,0000,0000,,total we're going to\Nhave 21 pieces.
Dialogue: 0,0:04:51.06,0:04:56.15,Default,,0000,0000,0000,,So we have 21 pieces, where each\Npiece is 1/4, so we could
Dialogue: 0,0:04:56.15,0:05:02.03,Default,,0000,0000,0000,,say we have 21 times 1/4 or\N21 fourths pieces of pie.
Dialogue: 0,0:05:02.03,0:05:03.27,Default,,0000,0000,0000,,However you want to\Nthink of it, but
Dialogue: 0,0:05:03.27,0:05:05.49,Default,,0000,0000,0000,,we've solved the problem.
Dialogue: 0,0:05:05.49,0:05:07.33,Default,,0000,0000,0000,,We're at an improper fraction.
Dialogue: 0,0:05:07.33,0:05:09.85,Default,,0000,0000,0000,,We've written 5 and 1/4 as\Nan improper fraction.
Dialogue: 0,0:05:09.85,0:05:13.49,Default,,0000,0000,0000,,Now, I've gone through great\Npains to give you the
Dialogue: 0,0:05:13.49,0:05:17.41,Default,,0000,0000,0000,,intuition of what 5 and 1/4\Nmeans, but there is a fairly
Dialogue: 0,0:05:17.41,0:05:20.71,Default,,0000,0000,0000,,straightforward process for\Ngetting straight to the
Dialogue: 0,0:05:20.71,0:05:21.96,Default,,0000,0000,0000,,improper fraction.
Dialogue: 0,0:05:21.96,0:05:24.51,Default,,0000,0000,0000,,
Dialogue: 0,0:05:24.51,0:05:25.97,Default,,0000,0000,0000,,Let me color code it.
Dialogue: 0,0:05:25.97,0:05:35.15,Default,,0000,0000,0000,,So if you have 5 and 1 over 4,\Nto convert it into an improper
Dialogue: 0,0:05:35.15,0:05:39.02,Default,,0000,0000,0000,,fraction, you're going to keep\Nthe same denominator, so
Dialogue: 0,0:05:39.02,0:05:41.68,Default,,0000,0000,0000,,you're going to have\Nthe over 4 there.
Dialogue: 0,0:05:41.68,0:05:47.22,Default,,0000,0000,0000,,But your numerator is going to\Nbe your numerator of the
Dialogue: 0,0:05:47.22,0:05:48.37,Default,,0000,0000,0000,,fraction part before.
Dialogue: 0,0:05:48.37,0:05:53.51,Default,,0000,0000,0000,,So it's going to be 1 plus your\Nwhole number times your
Dialogue: 0,0:05:53.51,0:05:54.82,Default,,0000,0000,0000,,denominator.
Dialogue: 0,0:05:54.82,0:05:57.62,Default,,0000,0000,0000,,So 1 plus-- or actually, let\Nme do it the way I tend to
Dialogue: 0,0:05:57.62,0:05:58.29,Default,,0000,0000,0000,,think of it.
Dialogue: 0,0:05:58.29,0:06:00.24,Default,,0000,0000,0000,,What I do is I take 4 times 5.
Dialogue: 0,0:06:00.24,0:06:02.70,Default,,0000,0000,0000,,So let me write that down and\NI want to color code it.
Dialogue: 0,0:06:02.70,0:06:12.83,Default,,0000,0000,0000,,4 times 5, and then to that,\NI add this numerator.
Dialogue: 0,0:06:12.83,0:06:16.56,Default,,0000,0000,0000,,So I literally do 4 times 5 plus\N1, which is-- so this is
Dialogue: 0,0:06:16.56,0:06:21.53,Default,,0000,0000,0000,,equal to 4 times 5 is 20, plus\N1 is 21, and then that's over
Dialogue: 0,0:06:21.53,0:06:23.68,Default,,0000,0000,0000,,4, so it's 21/4.
Dialogue: 0,0:06:23.68,0:06:25.41,Default,,0000,0000,0000,,And all of this is kind of\Na fast way to do it.
Dialogue: 0,0:06:25.41,0:06:27.91,Default,,0000,0000,0000,,We're literally doing the exact\Nsame thing that we did
Dialogue: 0,0:06:27.91,0:06:29.42,Default,,0000,0000,0000,,here in kind of a slower way.
Dialogue: 0,0:06:29.42,0:06:33.55,Default,,0000,0000,0000,,We're saying, OK, 5 wholes is\Nthe same thing as 20 fourths,
Dialogue: 0,0:06:33.55,0:06:37.22,Default,,0000,0000,0000,,so you take 5, and I figure that\Nout, 5 times 4, and then
Dialogue: 0,0:06:37.22,0:06:41.87,Default,,0000,0000,0000,,I have one more fourth there, so\N4 times 5 plus 1 gives 21.
Dialogue: 0,0:06:41.87,0:06:42.67,Default,,0000,0000,0000,,