[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.33,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.33,0:00:02.90,Default,,0000,0000,0000,,Let's add some rational\Nnumbers.
Dialogue: 0,0:00:02.90,0:00:05.35,Default,,0000,0000,0000,,And I'm using that word because\Nthat's the word that
Dialogue: 0,0:00:05.35,0:00:08.64,Default,,0000,0000,0000,,this book uses, but in more\Npopular terminology we'll be
Dialogue: 0,0:00:08.64,0:00:10.48,Default,,0000,0000,0000,,adding fractions.
Dialogue: 0,0:00:10.48,0:00:14.10,Default,,0000,0000,0000,,So let's just go through all\Nof these, actually, just to
Dialogue: 0,0:00:14.10,0:00:15.08,Default,,0000,0000,0000,,see all of the examples.
Dialogue: 0,0:00:15.08,0:00:19.66,Default,,0000,0000,0000,,So first we're going to\Nhave 3/7 plus 2/7.
Dialogue: 0,0:00:19.66,0:00:22.84,Default,,0000,0000,0000,,Our denominators are the same,\Nso we can just add the
Dialogue: 0,0:00:22.84,0:00:24.07,Default,,0000,0000,0000,,numerators.
Dialogue: 0,0:00:24.07,0:00:28.48,Default,,0000,0000,0000,,So our denominator is\N7, 3 plus 2 is 5.
Dialogue: 0,0:00:28.48,0:00:31.06,Default,,0000,0000,0000,,That is a.
Dialogue: 0,0:00:31.06,0:00:31.96,Default,,0000,0000,0000,,Let me do every other.
Dialogue: 0,0:00:31.96,0:00:33.29,Default,,0000,0000,0000,,It would take forever\Nto do all of them.
Dialogue: 0,0:00:33.29,0:00:36.55,Default,,0000,0000,0000,,Not forever, but just more time\Nthan I want to spend.
Dialogue: 0,0:00:36.55,0:00:42.86,Default,,0000,0000,0000,,So c is 5/16 plus 5/12.
Dialogue: 0,0:00:42.86,0:00:44.90,Default,,0000,0000,0000,,Our denominators are\Nnot the same.
Dialogue: 0,0:00:44.90,0:00:47.70,Default,,0000,0000,0000,,We have to find a common\Ndenominator, which has to be
Dialogue: 0,0:00:47.70,0:00:50.45,Default,,0000,0000,0000,,the least common-- it actually\Ncould be any common multiple
Dialogue: 0,0:00:50.45,0:00:52.05,Default,,0000,0000,0000,,of these, but for simplicity\Nlet's do the
Dialogue: 0,0:00:52.05,0:00:53.77,Default,,0000,0000,0000,,least common multiple.
Dialogue: 0,0:00:53.77,0:00:56.15,Default,,0000,0000,0000,,So what's the smallest number\Nthat's a multiple
Dialogue: 0,0:00:56.15,0:00:58.22,Default,,0000,0000,0000,,of both 16 and 12?
Dialogue: 0,0:00:58.22,0:01:01.70,Default,,0000,0000,0000,,So let's see, 16 times 2\Nis 32, not there yet.
Dialogue: 0,0:01:01.70,0:01:03.66,Default,,0000,0000,0000,,Times 3, 48.
Dialogue: 0,0:01:03.66,0:01:04.60,Default,,0000,0000,0000,,That seems to work.
Dialogue: 0,0:01:04.60,0:01:06.99,Default,,0000,0000,0000,,12 goes into 48 four times.
Dialogue: 0,0:01:06.99,0:01:09.73,Default,,0000,0000,0000,,So let's use 48 as our\Ncommon denominator.
Dialogue: 0,0:01:09.73,0:01:13.96,Default,,0000,0000,0000,,
Dialogue: 0,0:01:13.96,0:01:19.42,Default,,0000,0000,0000,,So we had to multiply 16 times 3\Nto get to 48, so we're going
Dialogue: 0,0:01:19.42,0:01:23.89,Default,,0000,0000,0000,,to have to multiply\Nthis 5 times 3.
Dialogue: 0,0:01:23.89,0:01:25.67,Default,,0000,0000,0000,,We're just multiplying the\Nnumerator and the denominator
Dialogue: 0,0:01:25.67,0:01:28.09,Default,,0000,0000,0000,,by the same number, so we're\Nnot really changing it.
Dialogue: 0,0:01:28.09,0:01:31.37,Default,,0000,0000,0000,,So 5 times 3 is 15.
Dialogue: 0,0:01:31.37,0:01:36.85,Default,,0000,0000,0000,,And then to get from this 12 to\Nthis 48 right there, we had
Dialogue: 0,0:01:36.85,0:01:38.89,Default,,0000,0000,0000,,to multiply times 4.
Dialogue: 0,0:01:38.89,0:01:42.17,Default,,0000,0000,0000,,So then to get to 5 to this\Nnumerator over here, we have
Dialogue: 0,0:01:42.17,0:01:44.12,Default,,0000,0000,0000,,to multiply times 4.
Dialogue: 0,0:01:44.12,0:01:46.69,Default,,0000,0000,0000,,5 times 4 is 20.
Dialogue: 0,0:01:46.69,0:01:49.98,Default,,0000,0000,0000,,Now we have the same\Ndenominator.
Dialogue: 0,0:01:49.98,0:01:54.18,Default,,0000,0000,0000,,So this is going to be equal\Nto, our denominator is 48.
Dialogue: 0,0:01:54.18,0:02:01.15,Default,,0000,0000,0000,,And so we can add 15 plus\N20, which is 35.
Dialogue: 0,0:02:01.15,0:02:02.67,Default,,0000,0000,0000,,And can we reduce this?
Dialogue: 0,0:02:02.67,0:02:04.95,Default,,0000,0000,0000,,Let's see, 5 does\Nnot go into 48.
Dialogue: 0,0:02:04.95,0:02:06.62,Default,,0000,0000,0000,,7 does not go into 48.
Dialogue: 0,0:02:06.62,0:02:08.33,Default,,0000,0000,0000,,It looks like we're all done.
Dialogue: 0,0:02:08.33,0:02:13.94,Default,,0000,0000,0000,,Let's do e right there.
Dialogue: 0,0:02:13.94,0:02:19.79,Default,,0000,0000,0000,,8/25 plus 7 over 10.
Dialogue: 0,0:02:19.79,0:02:23.57,Default,,0000,0000,0000,,Once again, we don't have\Na common denominator.
Dialogue: 0,0:02:23.57,0:02:25.85,Default,,0000,0000,0000,,But we can solve that.
Dialogue: 0,0:02:25.85,0:02:28.89,Default,,0000,0000,0000,,Let's make, let's see, 50 is the\Nsmallest number that both
Dialogue: 0,0:02:28.89,0:02:29.80,Default,,0000,0000,0000,,of these go into.
Dialogue: 0,0:02:29.80,0:02:32.34,Default,,0000,0000,0000,,25 times 2, so that's 50.
Dialogue: 0,0:02:32.34,0:02:37.05,Default,,0000,0000,0000,,8 over 25, to go to 50\Nwe multiply by 2.
Dialogue: 0,0:02:37.05,0:02:39.99,Default,,0000,0000,0000,,So the 8, we're going to\Nhave to multiply by 2.
Dialogue: 0,0:02:39.99,0:02:42.64,Default,,0000,0000,0000,,So it's going to\Nbe 16 over 50.
Dialogue: 0,0:02:42.64,0:02:45.94,Default,,0000,0000,0000,,And then the 7 over 10,\Nwe're going to want
Dialogue: 0,0:02:45.94,0:02:47.93,Default,,0000,0000,0000,,to put it over 50.
Dialogue: 0,0:02:47.93,0:02:51.75,Default,,0000,0000,0000,,We multiply the 10 times\N5, so we have to
Dialogue: 0,0:02:51.75,0:02:54.60,Default,,0000,0000,0000,,multiply the 7 times 5.
Dialogue: 0,0:02:54.60,0:02:57.72,Default,,0000,0000,0000,,So it's going to\Nbe 35 over 50.
Dialogue: 0,0:02:57.72,0:03:01.56,Default,,0000,0000,0000,,Now that our denominators are\Nthe same, we have it over 50.
Dialogue: 0,0:03:01.56,0:03:05.55,Default,,0000,0000,0000,,16 plus 35, what is that?
Dialogue: 0,0:03:05.55,0:03:10.69,Default,,0000,0000,0000,,10 plus 35 is 45,\Nplus 6 is 51.
Dialogue: 0,0:03:10.69,0:03:14.77,Default,,0000,0000,0000,,So it is 51 over 50.
Dialogue: 0,0:03:14.77,0:03:16.99,Default,,0000,0000,0000,,Problem g.
Dialogue: 0,0:03:16.99,0:03:19.70,Default,,0000,0000,0000,,Let me do it in a new color.
Dialogue: 0,0:03:19.70,0:03:22.41,Default,,0000,0000,0000,,Problem g.
Dialogue: 0,0:03:22.41,0:03:28.47,Default,,0000,0000,0000,,So here we have 7 over 15-- I'll\Nwrite the second one in a
Dialogue: 0,0:03:28.47,0:03:33.53,Default,,0000,0000,0000,,different color--\Nplus 2 over 9.
Dialogue: 0,0:03:33.53,0:03:35.62,Default,,0000,0000,0000,,Once again, the denominators\Nare different.
Dialogue: 0,0:03:35.62,0:03:37.49,Default,,0000,0000,0000,,Find a common denominator.
Dialogue: 0,0:03:37.49,0:03:41.54,Default,,0000,0000,0000,,What is the smallest number that\Nboth 15 and 9 go into?
Dialogue: 0,0:03:41.54,0:03:43.26,Default,,0000,0000,0000,,Let's see, 15 times 2 is 30.
Dialogue: 0,0:03:43.26,0:03:44.94,Default,,0000,0000,0000,,Nope, not divisible by 9.
Dialogue: 0,0:03:44.94,0:03:47.67,Default,,0000,0000,0000,,15 times 3 is 45, that works.
Dialogue: 0,0:03:47.67,0:03:50.22,Default,,0000,0000,0000,,45 is divisible by 9.
Dialogue: 0,0:03:50.22,0:03:52.59,Default,,0000,0000,0000,,So we use 45.
Dialogue: 0,0:03:52.59,0:03:59.81,Default,,0000,0000,0000,,15 times 3 is 45, so\N7 times 3 is 21.
Dialogue: 0,0:03:59.81,0:04:02.85,Default,,0000,0000,0000,,These two fractions\Nare equivalent.
Dialogue: 0,0:04:02.85,0:04:06.68,Default,,0000,0000,0000,,Plus we're going over 45.
Dialogue: 0,0:04:06.68,0:04:11.52,Default,,0000,0000,0000,,To get from 9 to 45, we have\Nto multiply times 5.
Dialogue: 0,0:04:11.52,0:04:14.42,Default,,0000,0000,0000,,So to get our numerator\Nover here, we have to
Dialogue: 0,0:04:14.42,0:04:15.98,Default,,0000,0000,0000,,multiply it times 5.
Dialogue: 0,0:04:15.98,0:04:18.42,Default,,0000,0000,0000,,So 2 times 5 is 10.
Dialogue: 0,0:04:18.42,0:04:22.42,Default,,0000,0000,0000,,2/9 is the same thing\Nas 10/45.
Dialogue: 0,0:04:22.42,0:04:24.71,Default,,0000,0000,0000,,So now we can add.
Dialogue: 0,0:04:24.71,0:04:27.13,Default,,0000,0000,0000,,We're adding fractions of 45.
Dialogue: 0,0:04:27.13,0:04:33.13,Default,,0000,0000,0000,,21 plus 10 is 31,\Nand we are done.
Dialogue: 0,0:04:33.13,0:04:36.90,Default,,0000,0000,0000,,Let's do one more problem down\Nhere, a word problem.
Dialogue: 0,0:04:36.90,0:04:40.07,Default,,0000,0000,0000,,Nadia, Peter and Ian are pooling\Ntheir money to buy a
Dialogue: 0,0:04:40.07,0:04:41.64,Default,,0000,0000,0000,,gallon of ice cream.
Dialogue: 0,0:04:41.64,0:04:44.63,Default,,0000,0000,0000,,Nadia's the oldest and gets\Nthe greatest allowance.
Dialogue: 0,0:04:44.63,0:04:49.74,Default,,0000,0000,0000,,She contributes 1/2 the cost.\NSo Nadia is contributing 1/2
Dialogue: 0,0:04:49.74,0:04:53.75,Default,,0000,0000,0000,,the cost. So that is\NNadia right there.
Dialogue: 0,0:04:53.75,0:04:58.85,Default,,0000,0000,0000,,Ian is next oldest and\Ncontributes 1/3 of the cost.
Dialogue: 0,0:04:58.85,0:05:02.28,Default,,0000,0000,0000,,So Ian contributes 1/3.
Dialogue: 0,0:05:02.28,0:05:03.82,Default,,0000,0000,0000,,That is Ian.
Dialogue: 0,0:05:03.82,0:05:06.36,Default,,0000,0000,0000,,Peter, the youngest, gets the\Nsmallest allowance and
Dialogue: 0,0:05:06.36,0:05:13.73,Default,,0000,0000,0000,,contributes 1/4 of the cost.\NSo Peter gives 1/4 of the
Dialogue: 0,0:05:13.73,0:05:17.56,Default,,0000,0000,0000,,cost. Peter contributes\N1/4 of cost.
Dialogue: 0,0:05:17.56,0:05:19.92,Default,,0000,0000,0000,,They figure that this will\Nbe enough money.
Dialogue: 0,0:05:19.92,0:05:22.48,Default,,0000,0000,0000,,When they get to the checkout,\Nthey realize that they forgot
Dialogue: 0,0:05:22.48,0:05:24.00,Default,,0000,0000,0000,,about sales tax and\Nworry there will
Dialogue: 0,0:05:24.00,0:05:25.34,Default,,0000,0000,0000,,not be enough money.
Dialogue: 0,0:05:25.34,0:05:28.37,Default,,0000,0000,0000,,Amazingly, they have exactly\Nthe right amount of money.
Dialogue: 0,0:05:28.37,0:05:32.46,Default,,0000,0000,0000,,What fraction of the cost of\Nice cream was added as tax?
Dialogue: 0,0:05:32.46,0:05:35.64,Default,,0000,0000,0000,,Well, let's see, if we add 1/2\Nplus 1/3, plus 1/4 of the
Dialogue: 0,0:05:35.64,0:05:37.64,Default,,0000,0000,0000,,cost, let's see what we get.
Dialogue: 0,0:05:37.64,0:05:41.10,Default,,0000,0000,0000,,So we have to find a common\Ndenominator, some number that
Dialogue: 0,0:05:41.10,0:05:44.25,Default,,0000,0000,0000,,is the least common multiple\Nof 2, 3, and 4.
Dialogue: 0,0:05:44.25,0:05:46.97,Default,,0000,0000,0000,,And let's see, 4, it would\Nhave to be 12, right?
Dialogue: 0,0:05:46.97,0:05:49.15,Default,,0000,0000,0000,,12 is divisible by 2, it's\Ndivisible by 3, and it's
Dialogue: 0,0:05:49.15,0:05:50.40,Default,,0000,0000,0000,,divisible by 4.
Dialogue: 0,0:05:50.40,0:05:56.48,Default,,0000,0000,0000,,So 1/2 is the same\Nthing as 6/12.
Dialogue: 0,0:05:56.48,0:05:58.75,Default,,0000,0000,0000,,2 times 6 is 12.
Dialogue: 0,0:05:58.75,0:06:00.42,Default,,0000,0000,0000,,1 times 6 is 6.
Dialogue: 0,0:06:00.42,0:06:01.24,Default,,0000,0000,0000,,These are equivalent.
Dialogue: 0,0:06:01.24,0:06:03.72,Default,,0000,0000,0000,,6 is 1/2 of 12.
Dialogue: 0,0:06:03.72,0:06:09.44,Default,,0000,0000,0000,,1/3, if we use 12 as a common\Ndenominator, to go from 3 to
Dialogue: 0,0:06:09.44,0:06:11.57,Default,,0000,0000,0000,,12 you have to multiply by 4.
Dialogue: 0,0:06:11.57,0:06:14.19,Default,,0000,0000,0000,,So you take that 4 and\Nyou multiply it by 1.
Dialogue: 0,0:06:14.19,0:06:17.62,Default,,0000,0000,0000,,4/12 is the same thing as 1/3.
Dialogue: 0,0:06:17.62,0:06:24.28,Default,,0000,0000,0000,,And then 1/4, if you use your\Ndenominator 12, to go from 4
Dialogue: 0,0:06:24.28,0:06:27.41,Default,,0000,0000,0000,,to 12 you have to multiply by\N3, so multiply the numerator
Dialogue: 0,0:06:27.41,0:06:30.08,Default,,0000,0000,0000,,by 3 as well, you get 3.
Dialogue: 0,0:06:30.08,0:06:31.36,Default,,0000,0000,0000,,So let's add these.
Dialogue: 0,0:06:31.36,0:06:36.66,Default,,0000,0000,0000,,So 6/12 plus 4/12, plus 3/12 is\Ngoing to be equal to-- our
Dialogue: 0,0:06:36.66,0:06:40.67,Default,,0000,0000,0000,,denominator's going to be 12--\Nit's going to be 6 plus 4,
Dialogue: 0,0:06:40.67,0:06:47.56,Default,,0000,0000,0000,,plus 3, which is equal to 6 plus\N4 is 10, plus 3 is 13.
Dialogue: 0,0:06:47.56,0:06:50.98,Default,,0000,0000,0000,,So it's going to be\Nequal to 13/12.
Dialogue: 0,0:06:50.98,0:06:53.00,Default,,0000,0000,0000,,And this is as an improper\Nfraction.
Dialogue: 0,0:06:53.00,0:06:55.95,Default,,0000,0000,0000,,Or we could say that this is the\Nsame thing, this is equal
Dialogue: 0,0:06:55.95,0:07:02.88,Default,,0000,0000,0000,,to 12/12 plus 1/12, or we could\Nsay the same thing as
Dialogue: 0,0:07:02.88,0:07:04.42,Default,,0000,0000,0000,,12/12 is just 1, right?
Dialogue: 0,0:07:04.42,0:07:05.77,Default,,0000,0000,0000,,12 divided by 12 is 1.
Dialogue: 0,0:07:05.77,0:07:10.05,Default,,0000,0000,0000,,So this is 1 and 1/12.
Dialogue: 0,0:07:10.05,0:07:13.95,Default,,0000,0000,0000,,So when they pool their money,\Nthey get 1 and 1/12 of the
Dialogue: 0,0:07:13.95,0:07:19.18,Default,,0000,0000,0000,,price of the ice cream that\Nthey want to buy.
Dialogue: 0,0:07:19.18,0:07:21.48,Default,,0000,0000,0000,,So they say what fraction of\Nthe cost of ice cream was
Dialogue: 0,0:07:21.48,0:07:22.31,Default,,0000,0000,0000,,added as tax?
Dialogue: 0,0:07:22.31,0:07:24.62,Default,,0000,0000,0000,,This is the exact amount that\Nthey needed to pay.
Dialogue: 0,0:07:24.62,0:07:29.74,Default,,0000,0000,0000,,So clearly, 1 is the non-taxed\Nprice of the ice cream, so
Dialogue: 0,0:07:29.74,0:07:32.76,Default,,0000,0000,0000,,this 1/12 was the amount\Nadded as tax.
Dialogue: 0,0:07:32.76,0:07:35.74,Default,,0000,0000,0000,,So the answer to the question\Nis 1/12 of the price
Dialogue: 0,0:07:35.74,0:07:39.29,Default,,0000,0000,0000,,was added as tax.
Dialogue: 0,0:07:39.29,0:07:39.47,Default,,0000,0000,0000,,