[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.73,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.73,0:00:02.91,Default,,0000,0000,0000,,Sarah has $48.
Dialogue: 0,0:00:02.91,0:00:07.05,Default,,0000,0000,0000,,She wants to save 1/3 of\Nher money for a trip.
Dialogue: 0,0:00:07.05,0:00:09.99,Default,,0000,0000,0000,,How many dollars should\Nshe set aside?
Dialogue: 0,0:00:09.99,0:00:13.53,Default,,0000,0000,0000,,So we essentially want to think\Nabout what 1/3 of 48 is.
Dialogue: 0,0:00:13.53,0:00:16.17,Default,,0000,0000,0000,,Use 48 as the denominator\Nand find an
Dialogue: 0,0:00:16.17,0:00:19.48,Default,,0000,0000,0000,,equivalent fraction to 1/3.
Dialogue: 0,0:00:19.48,0:00:22.07,Default,,0000,0000,0000,,So what they want us to do in\Nthis problem is they want us
Dialogue: 0,0:00:22.07,0:00:26.50,Default,,0000,0000,0000,,to say, OK, we want 1/3 of her\Nmoney, but we want to write
Dialogue: 0,0:00:26.50,0:00:30.53,Default,,0000,0000,0000,,this as an equivalent fraction\Nwhere we have 48 in the
Dialogue: 0,0:00:30.53,0:00:31.10,Default,,0000,0000,0000,,denominator.
Dialogue: 0,0:00:31.10,0:00:36.59,Default,,0000,0000,0000,,So this is equal to something,\Nsome blank up here.
Dialogue: 0,0:00:36.59,0:00:39.42,Default,,0000,0000,0000,,This is equal to something\Nover 48.
Dialogue: 0,0:00:39.42,0:00:44.12,Default,,0000,0000,0000,,So how can we get it to that\Nsomething over 48?
Dialogue: 0,0:00:44.12,0:00:46.16,Default,,0000,0000,0000,,So let's think about what\Nthis means for a second.
Dialogue: 0,0:00:46.16,0:00:50.43,Default,,0000,0000,0000,,So 1/3, if we were to draw\N1/3, it looks like this.
Dialogue: 0,0:00:50.43,0:00:55.98,Default,,0000,0000,0000,,You could imagine a box\Nor a pie, I guess.
Dialogue: 0,0:00:55.98,0:01:00.69,Default,,0000,0000,0000,,So let's say that this is my\Npie, and I have it split into
Dialogue: 0,0:01:00.69,0:01:01.84,Default,,0000,0000,0000,,three pieces.
Dialogue: 0,0:01:01.84,0:01:04.86,Default,,0000,0000,0000,,So let me split it into\Nthree even pieces.
Dialogue: 0,0:01:04.86,0:01:09.02,Default,,0000,0000,0000,,And 1/3 is one of those\Nthree pieces.
Dialogue: 0,0:01:09.02,0:01:11.55,Default,,0000,0000,0000,,That is what 1/3 means.
Dialogue: 0,0:01:11.55,0:01:15.14,Default,,0000,0000,0000,,Now, if we want express this as\Na fraction over 48, how can
Dialogue: 0,0:01:15.14,0:01:15.74,Default,,0000,0000,0000,,we do that?
Dialogue: 0,0:01:15.74,0:01:17.22,Default,,0000,0000,0000,,Well, we're going to\Nhave to split this
Dialogue: 0,0:01:17.22,0:01:19.28,Default,,0000,0000,0000,,thing into 48 pieces.
Dialogue: 0,0:01:19.28,0:01:22.35,Default,,0000,0000,0000,,How can we split something\Ninto 48?
Dialogue: 0,0:01:22.35,0:01:28.54,Default,,0000,0000,0000,,Well, 3 times 16 is 48, so if we\Nsplit each of these into 16
Dialogue: 0,0:01:28.54,0:01:30.81,Default,,0000,0000,0000,,pieces-- and it's going\Nto be hard to draw
Dialogue: 0,0:01:30.81,0:01:32.30,Default,,0000,0000,0000,,here, but you can imagine.
Dialogue: 0,0:01:32.30,0:01:38.13,Default,,0000,0000,0000,,Let's see, you split it into\Ntwo, now we've split it into
Dialogue: 0,0:01:38.13,0:01:42.62,Default,,0000,0000,0000,,four, now you split\Nit into eight.
Dialogue: 0,0:01:42.62,0:01:44.28,Default,,0000,0000,0000,,You're just going to end up with\Na bunch of lines here,
Dialogue: 0,0:01:44.28,0:01:47.36,Default,,0000,0000,0000,,but you can imagine, you can\Njust split each of these.
Dialogue: 0,0:01:47.36,0:01:51.12,Default,,0000,0000,0000,,If you split each of these into\Nenough, you would have 16
Dialogue: 0,0:01:51.12,0:01:54.14,Default,,0000,0000,0000,,pieces, so those would\Nbe 16 right there.
Dialogue: 0,0:01:54.14,0:01:58.05,Default,,0000,0000,0000,,You would have 16 right there\Nand you have 16 right there.
Dialogue: 0,0:01:58.05,0:01:59.74,Default,,0000,0000,0000,,And I can just keep doing it.
Dialogue: 0,0:01:59.74,0:02:01.28,Default,,0000,0000,0000,,Let me do it in the\Ngreen over here.
Dialogue: 0,0:02:01.28,0:02:05.78,Default,,0000,0000,0000,,So if we just kept splitting\Nit up, we would get 48,
Dialogue: 0,0:02:05.78,0:02:09.05,Default,,0000,0000,0000,,because you have this first\Nthird would be 16 pieces, the
Dialogue: 0,0:02:09.05,0:02:11.70,Default,,0000,0000,0000,,second third would be 16,\Nand then this third
Dialogue: 0,0:02:11.70,0:02:13.82,Default,,0000,0000,0000,,third would be 16 pieces.
Dialogue: 0,0:02:13.82,0:02:16.47,Default,,0000,0000,0000,,Altogether, you would\Nhave 48 pieces.
Dialogue: 0,0:02:16.47,0:02:19.11,Default,,0000,0000,0000,,Now, that 1/3, what does\Nthat represent?
Dialogue: 0,0:02:19.11,0:02:23.23,Default,,0000,0000,0000,,Well, that represents\N16 of the 48.
Dialogue: 0,0:02:23.23,0:02:26.45,Default,,0000,0000,0000,,It represents these\N16 right here.
Dialogue: 0,0:02:26.45,0:02:31.37,Default,,0000,0000,0000,,It represents these 16 right\Nthere, so 1 over 3 is the
Dialogue: 0,0:02:31.37,0:02:33.09,Default,,0000,0000,0000,,exact same thing.
Dialogue: 0,0:02:33.09,0:02:41.12,Default,,0000,0000,0000,,So 1 over 3 is the exact same\Nthing as 16 over 48.
Dialogue: 0,0:02:41.12,0:02:43.42,Default,,0000,0000,0000,,Now, we did it just by thinking\Nabout it kind of
Dialogue: 0,0:02:43.42,0:02:48.89,Default,,0000,0000,0000,,intuitively what 1/3 of 48 is,\Nbut one way to do it more-- I
Dialogue: 0,0:02:48.89,0:02:53.60,Default,,0000,0000,0000,,guess a process for doing it--\Nwe would say, well, look, to
Dialogue: 0,0:02:53.60,0:02:58.84,Default,,0000,0000,0000,,get the denominator, the bottom\Nnumber, from 3 to 48,
Dialogue: 0,0:02:58.84,0:03:02.02,Default,,0000,0000,0000,,we multiply by 16.
Dialogue: 0,0:03:02.02,0:03:04.79,Default,,0000,0000,0000,,3 times 16 is 48.
Dialogue: 0,0:03:04.79,0:03:07.76,Default,,0000,0000,0000,,And that's literally the process\Nof going from 3 pieces
Dialogue: 0,0:03:07.76,0:03:08.96,Default,,0000,0000,0000,,to 48 pieces.
Dialogue: 0,0:03:08.96,0:03:11.46,Default,,0000,0000,0000,,We have to multiply by 16.
Dialogue: 0,0:03:11.46,0:03:14.50,Default,,0000,0000,0000,,We have to turn each of our\Npieces into 16 pieces.
Dialogue: 0,0:03:14.50,0:03:15.99,Default,,0000,0000,0000,,That's what we did.
Dialogue: 0,0:03:15.99,0:03:20.03,Default,,0000,0000,0000,,Now, you can't just multiply\Nonly the denominator by 16.
Dialogue: 0,0:03:20.03,0:03:24.65,Default,,0000,0000,0000,,You have to multiply the\Nnumerator by the same number.
Dialogue: 0,0:03:24.65,0:03:29.75,Default,,0000,0000,0000,,And so if each of my pieces\Nnow become 16 pieces, then
Dialogue: 0,0:03:29.75,0:03:32.73,Default,,0000,0000,0000,,that one piece will\Nnow become 16.
Dialogue: 0,0:03:32.73,0:03:36.37,Default,,0000,0000,0000,,So one way to think about it,\Nyou just say, well, 3 times 16
Dialogue: 0,0:03:36.37,0:03:41.92,Default,,0000,0000,0000,,is 48, so 1 times 16 will be my\Nnumerator, so it'll be 16.
Dialogue: 0,0:03:41.92,0:03:45.18,Default,,0000,0000,0000,,So 1/3 is equal to 16/48.
Dialogue: 0,0:03:45.18,0:03:47.04,Default,,0000,0000,0000,,And another way you could think\Nabout it, which you'll
Dialogue: 0,0:03:47.04,0:03:53.93,Default,,0000,0000,0000,,learn in more detail later on,\Nis we want 1/3 of 48, right?
Dialogue: 0,0:03:53.93,0:04:00.06,Default,,0000,0000,0000,,That's how much she wants to\Nsave. 1/3 of 48 is equal to
Dialogue: 0,0:04:00.06,0:04:03.95,Default,,0000,0000,0000,,1/3 times 48.
Dialogue: 0,0:04:03.95,0:04:08.13,Default,,0000,0000,0000,,And when you multiply-- let me\Nwrite it like this-- 1/3 times
Dialogue: 0,0:04:08.13,0:04:13.37,Default,,0000,0000,0000,,48, and you could rewrite\N48 as a fraction 48/1.
Dialogue: 0,0:04:13.37,0:04:16.51,Default,,0000,0000,0000,,It literally represents\N48 wholes.
Dialogue: 0,0:04:16.51,0:04:18.38,Default,,0000,0000,0000,,And when you multiply fractions,\Nyou can just
Dialogue: 0,0:04:18.38,0:04:20.47,Default,,0000,0000,0000,,multiply the numerators.
Dialogue: 0,0:04:20.47,0:04:25.37,Default,,0000,0000,0000,,So this is equal to 48 over--\Nand then you just multiply the
Dialogue: 0,0:04:25.37,0:04:26.30,Default,,0000,0000,0000,,denominators.
Dialogue: 0,0:04:26.30,0:04:29.97,Default,,0000,0000,0000,,48/3, 1 times 48 is 48.
Dialogue: 0,0:04:29.97,0:04:31.56,Default,,0000,0000,0000,,We'll see this in more\Ndetail in the future.
Dialogue: 0,0:04:31.56,0:04:33.48,Default,,0000,0000,0000,,Don't worry about it\Nif it confuses you.
Dialogue: 0,0:04:33.48,0:04:38.35,Default,,0000,0000,0000,,In the denominator, 3 times 1 is\N3, and 48 divided by 3, or
Dialogue: 0,0:04:38.35,0:04:41.32,Default,,0000,0000,0000,,48/3, is equal to 16.
Dialogue: 0,0:04:41.32,0:04:47.96,Default,,0000,0000,0000,,So 1/3 of 48 is 16,\Nor 16/48 is 1/3.
Dialogue: 0,0:04:47.96,0:04:50.31,Default,,0000,0000,0000,,Hopefully, that make\Nsense to you.