[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.30,0:00:03.05,Default,,0000,0000,0000,,- [Voiceover] Let's say that\Nwe have the fraction 9/10,
Dialogue: 0,0:00:03.05,0:00:08.05,Default,,0000,0000,0000,,and I want to add to\Nthat the fraction 1/6.
Dialogue: 0,0:00:09.57,0:00:13.04,Default,,0000,0000,0000,,What is this, what is this going to equal?
Dialogue: 0,0:00:13.84,0:00:14.83,Default,,0000,0000,0000,,So when you first look at this, you say,
Dialogue: 0,0:00:14.83,0:00:16.60,Default,,0000,0000,0000,,"Oh, I have different denominators here.
Dialogue: 0,0:00:16.60,0:00:18.60,Default,,0000,0000,0000,,It's not obvious how I add these."
Dialogue: 0,0:00:18.60,0:00:21.04,Default,,0000,0000,0000,,And you'd be right and the way to actually
Dialogue: 0,0:00:21.04,0:00:23.55,Default,,0000,0000,0000,,move forward is to find\Na common denominator,
Dialogue: 0,0:00:23.55,0:00:26.18,Default,,0000,0000,0000,,to convert both of these fractions into
Dialogue: 0,0:00:26.18,0:00:28.54,Default,,0000,0000,0000,,fractions that have a common denominator.
Dialogue: 0,0:00:28.54,0:00:30.50,Default,,0000,0000,0000,,So how do you think about\Na common denominator?
Dialogue: 0,0:00:30.50,0:00:32.12,Default,,0000,0000,0000,,Well, a common denominator's\Ngonna have to be
Dialogue: 0,0:00:32.12,0:00:36.48,Default,,0000,0000,0000,,a common multiple of these two\Ndenominators of 10 and six.
Dialogue: 0,0:00:36.48,0:00:38.64,Default,,0000,0000,0000,,So what's a common multiple of 10 and six?
Dialogue: 0,0:00:38.64,0:00:41.44,Default,,0000,0000,0000,,And it's usually simplest to\Nfind the least common multiple,
Dialogue: 0,0:00:41.44,0:00:43.50,Default,,0000,0000,0000,,and a good way of doing that\Nis start with the larger
Dialogue: 0,0:00:43.50,0:00:47.31,Default,,0000,0000,0000,,denominator here, 10, and say,\Nokay is 10 divisible by six?
Dialogue: 0,0:00:47.95,0:00:50.98,Default,,0000,0000,0000,,No. Okay, now, is 20 divisible by six?
Dialogue: 0,0:00:51.59,0:00:56.00,Default,,0000,0000,0000,,No. Is 30 divisible by six?\NYes. 30 is divisible by six.
Dialogue: 0,0:00:56.00,0:00:57.72,Default,,0000,0000,0000,,So I'm just going through\Nthe multiples of 10
Dialogue: 0,0:00:57.72,0:00:59.56,Default,,0000,0000,0000,,and saying, "Well what is\Nthe smallest multiple of 10
Dialogue: 0,0:00:59.56,0:01:03.64,Default,,0000,0000,0000,,that is divisible by six?"\NAnd that's going to be 30.
Dialogue: 0,0:01:03.64,0:01:05.64,Default,,0000,0000,0000,,So I could rewrite both of these fractions
Dialogue: 0,0:01:05.64,0:01:07.60,Default,,0000,0000,0000,,as something over 30.
Dialogue: 0,0:01:07.60,0:01:10.30,Default,,0000,0000,0000,,So nine over 10. How would I write that as
Dialogue: 0,0:01:10.30,0:01:11.90,Default,,0000,0000,0000,,something over 30? Well I multiply
Dialogue: 0,0:01:11.90,0:01:15.98,Default,,0000,0000,0000,,the denominator, I'm multiplying\Nthe denominator by three.
Dialogue: 0,0:01:17.07,0:01:19.62,Default,,0000,0000,0000,,So I've just multiplied\Nthe denominator by three.
Dialogue: 0,0:01:19.62,0:01:22.09,Default,,0000,0000,0000,,So if I don't want to change\Nthe value of the fraction,
Dialogue: 0,0:01:22.09,0:01:23.59,Default,,0000,0000,0000,,I have to do the same\Nthing to the numerator.
Dialogue: 0,0:01:23.59,0:01:26.19,Default,,0000,0000,0000,,I have to multiply that by three as well
Dialogue: 0,0:01:26.100,0:01:29.85,Default,,0000,0000,0000,,because now I'm just multiplying\Nthe numerator by three
Dialogue: 0,0:01:29.85,0:01:31.43,Default,,0000,0000,0000,,and the denominator by three,\Nand that doesn't change
Dialogue: 0,0:01:31.43,0:01:32.95,Default,,0000,0000,0000,,the value of the fraction.
Dialogue: 0,0:01:32.95,0:01:35.75,Default,,0000,0000,0000,,So nine times three is 27.
Dialogue: 0,0:01:35.75,0:01:38.55,Default,,0000,0000,0000,,So once again, 9/10 and 27/30
Dialogue: 0,0:01:38.55,0:01:40.96,Default,,0000,0000,0000,,represent the same number.
Dialogue: 0,0:01:40.96,0:01:43.56,Default,,0000,0000,0000,,I've just written it now\Nwith a denominator of 30,
Dialogue: 0,0:01:43.56,0:01:45.63,Default,,0000,0000,0000,,and that's useful because\NI can also write 1/6
Dialogue: 0,0:01:45.63,0:01:49.10,Default,,0000,0000,0000,,with a denominator of 30. Let's do that.
Dialogue: 0,0:01:49.10,0:01:51.62,Default,,0000,0000,0000,,So 1/6 is what over 30?
Dialogue: 0,0:01:51.62,0:01:52.72,Default,,0000,0000,0000,,I encourage you to pause the video
Dialogue: 0,0:01:52.72,0:01:53.85,Default,,0000,0000,0000,,and try to think about it.
Dialogue: 0,0:01:53.85,0:01:56.15,Default,,0000,0000,0000,,So what did we do go from six to 30?
Dialogue: 0,0:01:56.15,0:01:59.25,Default,,0000,0000,0000,,We had to multiply by five.
Dialogue: 0,0:01:59.91,0:02:01.63,Default,,0000,0000,0000,,So if we multiply the denominator by five,
Dialogue: 0,0:02:01.63,0:02:04.62,Default,,0000,0000,0000,,we have to multiply the\Nnumerator by five as well,
Dialogue: 0,0:02:04.62,0:02:09.62,Default,,0000,0000,0000,,so one times five, one times five is five.
Dialogue: 0,0:02:11.01,0:02:13.75,Default,,0000,0000,0000,,So 9/10 is the same thing as 27/30,
Dialogue: 0,0:02:13.75,0:02:16.45,Default,,0000,0000,0000,,and 1/6 is the same thing as 5/30.
Dialogue: 0,0:02:16.45,0:02:20.23,Default,,0000,0000,0000,,And now we can add, now we can add
Dialogue: 0,0:02:20.23,0:02:21.82,Default,,0000,0000,0000,,and it's fairly straightforward.
Dialogue: 0,0:02:21.82,0:02:23.27,Default,,0000,0000,0000,,We have a certain number of 30ths,
Dialogue: 0,0:02:23.27,0:02:25.34,Default,,0000,0000,0000,,added to another number of 30ths,
Dialogue: 0,0:02:25.34,0:02:30.06,Default,,0000,0000,0000,,so 27/30 + 5/30, well that's going to be
Dialogue: 0,0:02:30.06,0:02:35.06,Default,,0000,0000,0000,,27, that's going to be 27 plus five,
Dialogue: 0,0:02:35.47,0:02:40.20,Default,,0000,0000,0000,,plus five, plus 5/30,
Dialogue: 0,0:02:41.18,0:02:43.58,Default,,0000,0000,0000,,plus 5/30, which of course
Dialogue: 0,0:02:43.58,0:02:47.36,Default,,0000,0000,0000,,going to be equal to 32/30.
Dialogue: 0,0:02:47.36,0:02:50.78,Default,,0000,0000,0000,,32 over 30, and
Dialogue: 0,0:02:50.78,0:02:54.32,Default,,0000,0000,0000,,if we want, we could try\Nto reduce this fraction.
Dialogue: 0,0:02:54.80,0:02:56.80,Default,,0000,0000,0000,,We have a common factor of 32 and 30,
Dialogue: 0,0:02:56.80,0:03:00.20,Default,,0000,0000,0000,,they're both divisible by two.
Dialogue: 0,0:03:00.20,0:03:03.50,Default,,0000,0000,0000,,So if we divide the numerator\Nand the denominator by two,
Dialogue: 0,0:03:03.50,0:03:06.12,Default,,0000,0000,0000,,numerator divided by two is 16,
Dialogue: 0,0:03:06.12,0:03:08.90,Default,,0000,0000,0000,,denominator divided by two is 15.
Dialogue: 0,0:03:09.45,0:03:12.64,Default,,0000,0000,0000,,So, this is the same thing\Nas 16/15, and if I wanted
Dialogue: 0,0:03:12.64,0:03:16.22,Default,,0000,0000,0000,,to write this as a mixed\Nnumber, 15 goes into 16 one time
Dialogue: 0,0:03:16.22,0:03:17.57,Default,,0000,0000,0000,,with a remainder one.
Dialogue: 0,0:03:17.57,0:03:20.26,Default,,0000,0000,0000,,So this is the same thing as 1 1/15.
Dialogue: 0,0:03:20.80,0:03:22.53,Default,,0000,0000,0000,,Let's do another example.
Dialogue: 0,0:03:22.53,0:03:27.02,Default,,0000,0000,0000,,Let's say that we wanted\Nto add, we wanted to add
Dialogue: 0,0:03:27.02,0:03:31.88,Default,,0000,0000,0000,,1/2 to
Dialogue: 0,0:03:31.88,0:03:36.88,Default,,0000,0000,0000,,to 11/12, to 11 over 12.
Dialogue: 0,0:03:36.89,0:03:38.03,Default,,0000,0000,0000,,And I encourage you to pause the video
Dialogue: 0,0:03:38.03,0:03:40.86,Default,,0000,0000,0000,,and see if you could work this out.
Dialogue: 0,0:03:40.86,0:03:42.50,Default,,0000,0000,0000,,Well like we saw before, we wanna find
Dialogue: 0,0:03:42.50,0:03:43.88,Default,,0000,0000,0000,,a common denominator.
Dialogue: 0,0:03:43.88,0:03:45.10,Default,,0000,0000,0000,,If these had the same denominator,
Dialogue: 0,0:03:45.10,0:03:46.26,Default,,0000,0000,0000,,we could just add them immediately,
Dialogue: 0,0:03:46.26,0:03:48.53,Default,,0000,0000,0000,,but we wanna find a common denominator
Dialogue: 0,0:03:48.53,0:03:50.22,Default,,0000,0000,0000,,because right now they're not the same.
Dialogue: 0,0:03:50.90,0:03:53.47,Default,,0000,0000,0000,,Well what we wanna find is a multiple,
Dialogue: 0,0:03:53.47,0:03:55.79,Default,,0000,0000,0000,,a common multiple of\Ntwo and 12, and ideally
Dialogue: 0,0:03:55.79,0:03:58.16,Default,,0000,0000,0000,,we'll find the lowest common\Nmultiple of two and 12,
Dialogue: 0,0:03:58.16,0:04:00.26,Default,,0000,0000,0000,,and just like we did before,\Nlet's start with the larger
Dialogue: 0,0:04:00.26,0:04:01.90,Default,,0000,0000,0000,,of the two numbers, 12.
Dialogue: 0,0:04:01.90,0:04:05.29,Default,,0000,0000,0000,,Now we could just say\Nwell 12 times one is 12,
Dialogue: 0,0:04:05.29,0:04:07.95,Default,,0000,0000,0000,,so that we could view that\Nas the lowest multiple of 12.
Dialogue: 0,0:04:07.95,0:04:10.63,Default,,0000,0000,0000,,And is that divisible by two? Yeah, sure.
Dialogue: 0,0:04:10.63,0:04:12.79,Default,,0000,0000,0000,,12 is divisible by two.
Dialogue: 0,0:04:12.79,0:04:15.86,Default,,0000,0000,0000,,So 12 is actually the least\Ncommon multiple of two and 12,
Dialogue: 0,0:04:15.86,0:04:17.21,Default,,0000,0000,0000,,so we could write both of these
Dialogue: 0,0:04:17.21,0:04:19.01,Default,,0000,0000,0000,,fractions as something over 12.
Dialogue: 0,0:04:19.01,0:04:21.62,Default,,0000,0000,0000,,So 1/2 is what over 12?
Dialogue: 0,0:04:21.62,0:04:24.45,Default,,0000,0000,0000,,Well to go from two to\N12, you multiply by six,
Dialogue: 0,0:04:24.45,0:04:27.10,Default,,0000,0000,0000,,so we'll also multiply\Nthe numerator by six.
Dialogue: 0,0:04:27.10,0:04:30.59,Default,,0000,0000,0000,,Now we see 1/2, and 6/12,\Nthese are the same thing.
Dialogue: 0,0:04:30.59,0:04:33.95,Default,,0000,0000,0000,,One is half of two, six is half of 12.
Dialogue: 0,0:04:34.91,0:04:38.48,Default,,0000,0000,0000,,And how would we write\N11/12 as something over 12?
Dialogue: 0,0:04:38.48,0:04:40.86,Default,,0000,0000,0000,,Well it's already written\Nas something over 12,
Dialogue: 0,0:04:40.86,0:04:43.26,Default,,0000,0000,0000,,11/12 already has 12 in the denominator,
Dialogue: 0,0:04:43.26,0:04:45.03,Default,,0000,0000,0000,,so we don't have to change that.
Dialogue: 0,0:04:45.62,0:04:48.27,Default,,0000,0000,0000,,11/12, and now we're ready to add.
Dialogue: 0,0:04:48.60,0:04:51.35,Default,,0000,0000,0000,,So this is going to be equal to six,
Dialogue: 0,0:04:52.52,0:04:55.82,Default,,0000,0000,0000,,this is going to be equal to six plus 11,
Dialogue: 0,0:04:56.51,0:05:01.51,Default,,0000,0000,0000,,six plus 11 over 12.
Dialogue: 0,0:05:02.38,0:05:06.02,Default,,0000,0000,0000,,Over 12. We have 6/12 plus 11/12,
Dialogue: 0,0:05:06.02,0:05:09.32,Default,,0000,0000,0000,,it's gonna be six plus 11 over 12,
Dialogue: 0,0:05:10.73,0:05:15.09,Default,,0000,0000,0000,,which is equal to, six plus 11 is 17/12.
Dialogue: 0,0:05:15.09,0:05:16.50,Default,,0000,0000,0000,,If we wanted to write\Nit as a mixed number,
Dialogue: 0,0:05:16.50,0:05:19.49,Default,,0000,0000,0000,,that is what, 12 goes\Ninto 17 one time with
Dialogue: 0,0:05:19.49,0:05:24.49,Default,,0000,0000,0000,,a remainder of five, so 1 5/12.
Dialogue: 0,0:05:24.53,0:05:25.71,Default,,0000,0000,0000,,Let's do one more of these.
Dialogue: 0,0:05:25.71,0:05:29.01,Default,,0000,0000,0000,,This is strangely fun. Alright.
Dialogue: 0,0:05:29.01,0:05:31.04,Default,,0000,0000,0000,,Let's say that we wanted to add,
Dialogue: 0,0:05:31.52,0:05:35.89,Default,,0000,0000,0000,,We're gonna add 3/4 to,
Dialogue: 0,0:05:36.50,0:05:40.58,Default,,0000,0000,0000,,we're gonna add 3/4 to 1/5.
Dialogue: 0,0:05:41.41,0:05:43.97,Default,,0000,0000,0000,,To one over five.
Dialogue: 0,0:05:43.97,0:05:44.66,Default,,0000,0000,0000,,What is this going to be?
Dialogue: 0,0:05:44.66,0:05:46.16,Default,,0000,0000,0000,,And once again, pause the video and
Dialogue: 0,0:05:46.16,0:05:47.87,Default,,0000,0000,0000,,see if you could work it out.
Dialogue: 0,0:05:47.87,0:05:49.29,Default,,0000,0000,0000,,Well we have different denominators here,
Dialogue: 0,0:05:49.29,0:05:52.05,Default,,0000,0000,0000,,and we wanna find, we wanna rewrite these
Dialogue: 0,0:05:52.05,0:05:53.46,Default,,0000,0000,0000,,so they have the same denominators,
Dialogue: 0,0:05:53.46,0:05:54.79,Default,,0000,0000,0000,,so we have to find a common multiple,
Dialogue: 0,0:05:54.79,0:05:57.10,Default,,0000,0000,0000,,ideally the least common multiple.
Dialogue: 0,0:05:57.10,0:05:59.74,Default,,0000,0000,0000,,So what's the least common\Nmultiple of four and five?
Dialogue: 0,0:06:00.55,0:06:01.86,Default,,0000,0000,0000,,Well let's start with the larger number,
Dialogue: 0,0:06:01.86,0:06:04.72,Default,,0000,0000,0000,,and let's look at its\Nmultiples and keep increasing
Dialogue: 0,0:06:04.72,0:06:07.06,Default,,0000,0000,0000,,them until we get one\Nthat's divisible by four.
Dialogue: 0,0:06:07.06,0:06:10.06,Default,,0000,0000,0000,,So five is not divisible by four.
Dialogue: 0,0:06:10.06,0:06:13.62,Default,,0000,0000,0000,,10 is not divisible by four,\Nor perfectly divisible by four
Dialogue: 0,0:06:13.62,0:06:14.70,Default,,0000,0000,0000,,is what we care about.
Dialogue: 0,0:06:14.70,0:06:17.06,Default,,0000,0000,0000,,15 is not perfectly divisible by four.
Dialogue: 0,0:06:17.06,0:06:20.76,Default,,0000,0000,0000,,20 is divisible by four, in\Nfact, that is five times four.
Dialogue: 0,0:06:20.76,0:06:23.51,Default,,0000,0000,0000,,That is 20. So what we\Ncould do is, we could write
Dialogue: 0,0:06:23.51,0:06:27.46,Default,,0000,0000,0000,,both of these fractions as\Nhaving 20 in the denominator,
Dialogue: 0,0:06:27.46,0:06:28.71,Default,,0000,0000,0000,,or 20 as the denominator.
Dialogue: 0,0:06:29.45,0:06:32.27,Default,,0000,0000,0000,,So we could write 3/4\Nis something over 20.
Dialogue: 0,0:06:32.100,0:06:35.32,Default,,0000,0000,0000,,So to go from four to\N20 in the denominator,
Dialogue: 0,0:06:35.32,0:06:36.95,Default,,0000,0000,0000,,we multiplied by five.
Dialogue: 0,0:06:36.95,0:06:38.47,Default,,0000,0000,0000,,So we also do that to the numerator.
Dialogue: 0,0:06:38.47,0:06:41.40,Default,,0000,0000,0000,,We multiply by three times five to get 15.
Dialogue: 0,0:06:41.40,0:06:44.18,Default,,0000,0000,0000,,All I did to go from four\Nto 20, multiplied by five.
Dialogue: 0,0:06:44.18,0:06:45.82,Default,,0000,0000,0000,,So I have to do the same\Nthing to the numerator,
Dialogue: 0,0:06:45.82,0:06:47.74,Default,,0000,0000,0000,,three times five is 15.
Dialogue: 0,0:06:47.74,0:06:52.66,Default,,0000,0000,0000,,3/4 is the same thing\Nas 15/20, and over here.
Dialogue: 0,0:06:52.66,0:06:55.00,Default,,0000,0000,0000,,1/5. What is that over 20?
Dialogue: 0,0:06:55.00,0:06:58.36,Default,,0000,0000,0000,,Well to go from five to 20,\Nyou have to multiply by four.
Dialogue: 0,0:06:58.36,0:06:59.100,Default,,0000,0000,0000,,So we have to do the same\Nthing to the numerator.
Dialogue: 0,0:06:59.100,0:07:03.86,Default,,0000,0000,0000,,I have to multiply this\Nnumerator times four to get 4/20.
Dialogue: 0,0:07:04.45,0:07:07.18,Default,,0000,0000,0000,,So now I've rewritten this\Ninstead of 3/4 plus 1/5,
Dialogue: 0,0:07:07.18,0:07:10.82,Default,,0000,0000,0000,,it's now written as 15/20 plus 4/20.
Dialogue: 0,0:07:10.82,0:07:12.97,Default,,0000,0000,0000,,And what is that going to be?
Dialogue: 0,0:07:12.97,0:07:17.93,Default,,0000,0000,0000,,Well that's going to be\N15 plus four is 19/20.
Dialogue: 0,0:07:17.93,0:07:22.02,Default,,0000,0000,0000,,19/20, and we're done.