[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.73,0:00:05.30,Default,,0000,0000,0000,,Today's session is on ratio.
Dialogue: 0,0:00:05.30,0:00:07.52,Default,,0000,0000,0000,,I'm going to explain what a ratio is
Dialogue: 0,0:00:07.57,0:00:09.14,Default,,0000,0000,0000,,and how ratios are used
Dialogue: 0,0:00:09.14,0:00:11.18,Default,,0000,0000,0000,,in different situations.
Dialogue: 0,0:00:11.28,0:00:14.54,Default,,0000,0000,0000,,So to start off with what is a ratio?
Dialogue: 0,0:00:14.98,0:00:18.49,Default,,0000,0000,0000,,Well, a ratio is a way of comparing
Dialogue: 0,0:00:18.51,0:00:22.53,Default,,0000,0000,0000,,amounts of ingredients.
Dialogue: 0,0:00:22.53,0:00:25.69,Default,,0000,0000,0000,,Ratios can be used to compare
Dialogue: 0,0:00:25.74,0:00:30.11,Default,,0000,0000,0000,,weights, money, length and so on.
Dialogue: 0,0:00:30.19,0:00:33.20,Default,,0000,0000,0000,,So if we take this example
Dialogue: 0,0:00:33.20,0:00:34.99,Default,,0000,0000,0000,,we've got a model boat
Dialogue: 0,0:00:34.99,0:00:38.05,Default,,0000,0000,0000,,whose length is 1 metre
Dialogue: 0,0:00:38.05,0:00:40.82,Default,,0000,0000,0000,,and the real boat
Dialogue: 0,0:00:40.83,0:00:43.27,Default,,0000,0000,0000,,whose length is 25 metres.
Dialogue: 0,0:00:43.29,0:00:45.01,Default,,0000,0000,0000,,Then we say the ratio of the
Dialogue: 0,0:00:45.01,0:00:48.20,Default,,0000,0000,0000,,length of the model boat to the real boat
Dialogue: 0,0:00:48.20,0:00:51.88,Default,,0000,0000,0000,,is 1 to 25.
Dialogue: 0,0:00:51.90,0:00:54.77,Default,,0000,0000,0000,,Notice we've just used the numbers
Dialogue: 0,0:00:54.77,0:00:57.67,Default,,0000,0000,0000,,without the unit (metres)
Dialogue: 0,0:00:57.67,0:00:59.92,Default,,0000,0000,0000,,and we've used the colon
Dialogue: 0,0:00:59.92,0:01:02.88,Default,,0000,0000,0000,,to represent the ratio.
Dialogue: 0,0:01:03.03,0:01:06.06,Default,,0000,0000,0000,,Ratios are used to describe quantities
Dialogue: 0,0:01:06.06,0:01:08.98,Default,,0000,0000,0000,,of ingredients in mixtures.
Dialogue: 0,0:01:08.98,0:01:11.97,Default,,0000,0000,0000,,For example, in the\Npharmaceutical trade
Dialogue: 0,0:01:11.97,0:01:14.36,Default,,0000,0000,0000,,when you're making medicines,
Dialogue: 0,0:01:14.36,0:01:16.64,Default,,0000,0000,0000,,or in the building trade
Dialogue: 0,0:01:16.64,0:01:19.41,Default,,0000,0000,0000,,when you are making cement or mortar,
Dialogue: 0,0:01:19.41,0:01:22.49,Default,,0000,0000,0000,,or at home when you're making up food
Dialogue: 0,0:01:22.49,0:01:26.55,Default,,0000,0000,0000,,you use different quantities\Nin different proportions
Dialogue: 0,0:01:26.55,0:01:29.00,Default,,0000,0000,0000,,and if you don't get them right
Dialogue: 0,0:01:29.00,0:01:30.95,Default,,0000,0000,0000,,then things go wrong.
Dialogue: 0,0:01:30.95,0:01:33.83,Default,,0000,0000,0000,,So it's very important to know
Dialogue: 0,0:01:33.83,0:01:39.36,Default,,0000,0000,0000,,what quantities you've got and\Nin what ratio.
Dialogue: 0,0:01:39.36,0:01:41.82,Default,,0000,0000,0000,,So for example, if we have
Dialogue: 0,0:01:41.82,0:01:45.63,Default,,0000,0000,0000,,mortar for building brick walls.
Dialogue: 0,0:01:45.63,0:01:47.55,Default,,0000,0000,0000,,Mortar is made up by mixing
Dialogue: 0,0:01:47.55,0:01:52.78,Default,,0000,0000,0000,,two parts of cement to \Nseven parts of gravel by volume
Dialogue: 0,0:01:52.78,0:01:57.88,Default,,0000,0000,0000,,and we write that ratio as 2 to 7.
Dialogue: 0,0:01:57.88,0:02:00.41,Default,,0000,0000,0000,,Again notice we've used
Dialogue: 0,0:02:00.41,0:02:03.50,Default,,0000,0000,0000,,the numbers without the units
Dialogue: 0,0:02:03.50,0:02:07.27,Default,,0000,0000,0000,,and the colon to represent the ratio.
Dialogue: 0,0:02:07.27,0:02:09.30,Default,,0000,0000,0000,,When we're making pastry at home,
Dialogue: 0,0:02:09.30,0:02:11.38,Default,,0000,0000,0000,,when we're making pies and tarts,
Dialogue: 0,0:02:11.38,0:02:14.16,Default,,0000,0000,0000,,we mix four ounces of flour
Dialogue: 0,0:02:14.16,0:02:17.21,Default,,0000,0000,0000,,with two ounces of margarine
Dialogue: 0,0:02:17.21,0:02:23.04,Default,,0000,0000,0000,,And that ratio would be 4 to 2.
Dialogue: 0,0:02:23.04,0:02:24.31,Default,,0000,0000,0000,,But in this case,
Dialogue: 0,0:02:24.31,0:02:25.90,Default,,0000,0000,0000,,if you look at the numbers,
Dialogue: 0,0:02:25.90,0:02:28.68,Default,,0000,0000,0000,,they've got a factor of two in common
Dialogue: 0,0:02:28.68,0:02:31.08,Default,,0000,0000,0000,,So we can simplify ratios just in the same
Dialogue: 0,0:02:31.08,0:02:33.52,Default,,0000,0000,0000,,way as we simplify fractions.
Dialogue: 0,0:02:33.52,0:02:36.50,Default,,0000,0000,0000,,We can divide by the common factor,
Dialogue: 0,0:02:36.50,0:02:39.28,Default,,0000,0000,0000,,so we divide 4 by 2
Dialogue: 0,0:02:39.28,0:02:42.53,Default,,0000,0000,0000,,and 2 by 2 to give 1.
Dialogue: 0,0:02:42.53,0:02:48.57,Default,,0000,0000,0000,,So 2 to 1 is the simplest form\Nof the ratio 4 to 2.
Dialogue: 0,0:02:48.57,0:02:52.76,Default,,0000,0000,0000,,But both of the ratios are equivalent,
Dialogue: 0,0:02:52.76,0:03:01.92,Default,,0000,0000,0000,,because the relationship of the numbers\Ninvolved stays the same.
Dialogue: 0,0:03:01.92,0:03:05.62,Default,,0000,0000,0000,,If we take this example
Dialogue: 0,0:03:05.62,0:03:09.86,Default,,0000,0000,0000,,250 to 150
Dialogue: 0,0:03:09.86,0:03:12.58,Default,,0000,0000,0000,,We can simplify this ratio.
Dialogue: 0,0:03:12.58,0:03:15.53,Default,,0000,0000,0000,,We divide both by 10
Dialogue: 0,0:03:15.53,0:03:19.50,Default,,0000,0000,0000,,to get 25 to 15
Dialogue: 0,0:03:19.50,0:03:22.34,Default,,0000,0000,0000,,And then we can divide both by 5
Dialogue: 0,0:03:22.34,0:03:24.81,Default,,0000,0000,0000,,5 into 25 will give me 5
Dialogue: 0,0:03:24.81,0:03:28.28,Default,,0000,0000,0000,,5 into 15 will give me 3
Dialogue: 0,0:03:28.28,0:03:31.99,Default,,0000,0000,0000,,We can't divide anymore,
Dialogue: 0,0:03:31.99,0:03:34.26,Default,,0000,0000,0000,,so this is the simplest form.
Dialogue: 0,0:03:34.26,0:03:37.86,Default,,0000,0000,0000,,5 to 3 the simplest form of
Dialogue: 0,0:03:37.86,0:03:41.47,Default,,0000,0000,0000,,the ratio 250 to 150.
Dialogue: 0,0:03:41.47,0:03:44.31,Default,,0000,0000,0000,,But all three ratios are equivalent
Dialogue: 0,0:03:44.31,0:03:46.88,Default,,0000,0000,0000,,because the relationship of the numbers
Dialogue: 0,0:03:46.88,0:03:50.07,Default,,0000,0000,0000,,is exactly the same.
Dialogue: 0,0:03:50.07,0:03:53.66,Default,,0000,0000,0000,,In the same way, we can actually
Dialogue: 0,0:03:53.66,0:04:00.11,Default,,0000,0000,0000,,simplify this ratio: 1 to 1.5
Dialogue: 0,0:04:00.11,0:04:04.49,Default,,0000,0000,0000,,In ratios we like to have whole numbers
Dialogue: 0,0:04:04.49,0:04:06.09,Default,,0000,0000,0000,,and in this ratio you can see
Dialogue: 0,0:04:06.09,0:04:07.65,Default,,0000,0000,0000,,that we have a decimal.
Dialogue: 0,0:04:07.65,0:04:09.47,Default,,0000,0000,0000,,To get rid of the decimal
Dialogue: 0,0:04:09.47,0:04:11.34,Default,,0000,0000,0000,,we can multiply both sides of the
Dialogue: 0,0:04:11.34,0:04:12.73,Default,,0000,0000,0000,,ratio by 10
Dialogue: 0,0:04:12.73,0:04:16.00,Default,,0000,0000,0000,,and we still have an equivalent ratio.
Dialogue: 0,0:04:16.00,0:04:18.02,Default,,0000,0000,0000,,Because, again, the relationship
Dialogue: 0,0:04:18.02,0:04:19.86,Default,,0000,0000,0000,,between the numbers is the same.
Dialogue: 0,0:04:19.86,0:04:22.59,Default,,0000,0000,0000,,So we multiply the 1 by 10
Dialogue: 0,0:04:22.59,0:04:24.04,Default,,0000,0000,0000,,you get 10
Dialogue: 0,0:04:24.04,0:04:25.54,Default,,0000,0000,0000,,Multiply 1.5 by 10
Dialogue: 0,0:04:25.54,0:04:27.83,Default,,0000,0000,0000,,you get 15
Dialogue: 0,0:04:27.83,0:04:30.29,Default,,0000,0000,0000,,10 to 15 we can simplify that.
Dialogue: 0,0:04:30.29,0:04:33.93,Default,,0000,0000,0000,,Divide both sides by 5.
Dialogue: 0,0:04:33.93,0:04:36.38,Default,,0000,0000,0000,,5 into 10 gives me 2
Dialogue: 0,0:04:36.38,0:04:40.35,Default,,0000,0000,0000,,5 into 15 will give me 3
Dialogue: 0,0:04:40.35,0:04:42.50,Default,,0000,0000,0000,,2 to 3 is the simplest form
Dialogue: 0,0:04:42.50,0:04:46.82,Default,,0000,0000,0000,,of the ratio 1 to 1.5
Dialogue: 0,0:04:46.82,0:04:49.94,Default,,0000,0000,0000,,Similarly, when we have fractions
Dialogue: 0,0:04:49.94,0:04:53.78,Default,,0000,0000,0000,,If we had this ratio:
Dialogue: 0,0:04:53.78,0:04:57.63,Default,,0000,0000,0000,,a quarter to five-eighths,
Dialogue: 0,0:04:57.63,0:04:59.68,Default,,0000,0000,0000,,it just doesn't look right.
Dialogue: 0,0:04:59.68,0:05:01.59,Default,,0000,0000,0000,,We want to express that ratio
Dialogue: 0,0:05:01.59,0:05:03.26,Default,,0000,0000,0000,,in terms of whole numbers
Dialogue: 0,0:05:03.26,0:05:04.77,Default,,0000,0000,0000,,in its simplest form.
Dialogue: 0,0:05:04.77,0:05:10.16,Default,,0000,0000,0000,,So what we do first is we write\Nboth as fractions over 8
Dialogue: 0,0:05:10.16,0:05:11.61,Default,,0000,0000,0000,,in terms of eighths.
Dialogue: 0,0:05:11.61,0:05:17.11,Default,,0000,0000,0000,,A quarter is two eighths
Dialogue: 0,0:05:17.11,0:05:21.60,Default,,0000,0000,0000,,and now the ratio is two eighths to five eighths.
Dialogue: 0,0:05:21.60,0:05:23.80,Default,,0000,0000,0000,,And now it's dead simple
Dialogue: 0,0:05:23.80,0:05:27.61,Default,,0000,0000,0000,,All we have to say is that is 2 to 5.
Dialogue: 0,0:05:27.61,0:05:30.66,Default,,0000,0000,0000,,We multiply both ratios by 8
Dialogue: 0,0:05:30.66,0:05:33.47,Default,,0000,0000,0000,,And 2 to 5 is the simplest ratio
Dialogue: 0,0:05:33.47,0:05:37.94,Default,,0000,0000,0000,,for the ratio a quarter to five-eighths.
Dialogue: 0,0:05:37.94,0:05:40.48,Default,,0000,0000,0000,,But again all three ratios are
Dialogue: 0,0:05:40.48,0:05:42.90,Default,,0000,0000,0000,,equivalent because the relationship
Dialogue: 0,0:05:42.90,0:05:45.87,Default,,0000,0000,0000,,between the numbers is exactly the same.
Dialogue: 0,0:05:45.87,0:05:47.95,Default,,0000,0000,0000,,Moving on,
Dialogue: 0,0:05:47.95,0:05:51.04,Default,,0000,0000,0000,,we must have the numbers \Nin the ratios
Dialogue: 0,0:05:51.04,0:05:53.37,Default,,0000,0000,0000,,having the same units.
Dialogue: 0,0:05:53.37,0:05:55.32,Default,,0000,0000,0000,,So if we have this ratio
Dialogue: 0,0:05:55.32,0:06:02.66,Default,,0000,0000,0000,,15 pence to 3 pounds,
Dialogue: 0,0:06:02.66,0:06:07.30,Default,,0000,0000,0000,,we cannot say that the ratio is 15 to 3
Dialogue: 0,0:06:07.30,0:06:12.55,Default,,0000,0000,0000,,and then simplify that to 5 to 1
Dialogue: 0,0:06:12.55,0:06:15.80,Default,,0000,0000,0000,,Because we didn't start off with
Dialogue: 0,0:06:15.80,0:06:18.54,Default,,0000,0000,0000,,the numbers having the same units
Dialogue: 0,0:06:18.54,0:06:21.75,Default,,0000,0000,0000,,the relationship between\Nthe numbers is not the same,
Dialogue: 0,0:06:21.75,0:06:23.93,Default,,0000,0000,0000,,because as I say,
Dialogue: 0,0:06:23.93,0:06:26.57,Default,,0000,0000,0000,,we didn't start off with these numbers
Dialogue: 0,0:06:26.57,0:06:29.08,Default,,0000,0000,0000,,having the same units.
Dialogue: 0,0:06:29.08,0:06:31.38,Default,,0000,0000,0000,,So we must convert the numbers
Dialogue: 0,0:06:31.38,0:06:33.10,Default,,0000,0000,0000,,to the same units
Dialogue: 0,0:06:33.10,0:06:36.77,Default,,0000,0000,0000,,and we choose whichever unit is \Nappropriate
Dialogue: 0,0:06:36.77,0:06:38.94,Default,,0000,0000,0000,,\NIn this case, it's obvious we must
Dialogue: 0,0:06:38.94,0:06:41.39,Default,,0000,0000,0000,,change them to pence.
Dialogue: 0,0:06:41.39,0:06:48.87,Default,,0000,0000,0000,,So we say the ratio is 15 to 300
Dialogue: 0,0:06:48.87,0:06:51.91,Default,,0000,0000,0000,,as there's 300 pence for 3 pounds
Dialogue: 0,0:06:51.91,0:06:55.00,Default,,0000,0000,0000,,and then we simplify as normal.
Dialogue: 0,0:06:55.00,0:06:57.10,Default,,0000,0000,0000,,We divide both sides by five.
Dialogue: 0,0:06:57.10,0:06:59.43,Default,,0000,0000,0000,,5 into 15 is 3
Dialogue: 0,0:06:59.43,0:07:02.20,Default,,0000,0000,0000,,5 into 300 is 60
Dialogue: 0,0:07:02.20,0:07:05.56,Default,,0000,0000,0000,,And then we can divide by 3
Dialogue: 0,0:07:05.56,0:07:07.48,Default,,0000,0000,0000,,3 into 3 is 1
Dialogue: 0,0:07:07.48,0:07:10.30,Default,,0000,0000,0000,,3 into 60 is 20
Dialogue: 0,0:07:10.30,0:07:14.58,Default,,0000,0000,0000,,And notice these two ratios are
Dialogue: 0,0:07:14.58,0:07:16.85,Default,,0000,0000,0000,,not the same, they're vastly different.
Dialogue: 0,0:07:16.85,0:07:18.67,Default,,0000,0000,0000,,They're not equivalent because
Dialogue: 0,0:07:18.67,0:07:20.93,Default,,0000,0000,0000,,the relationship between the numbers
Dialogue: 0,0:07:20.93,0:07:23.63,Default,,0000,0000,0000,,is not the same.
Dialogue: 0,0:07:23.63,0:07:25.75,Default,,0000,0000,0000,,So it's very important in ratios
Dialogue: 0,0:07:25.75,0:07:28.48,Default,,0000,0000,0000,,that you start with numbers
Dialogue: 0,0:07:28.48,0:07:30.74,Default,,0000,0000,0000,,that have the same units.
Dialogue: 0,0:07:30.74,0:07:32.01,Default,,0000,0000,0000,,If they're not,
Dialogue: 0,0:07:32.01,0:07:34.05,Default,,0000,0000,0000,,then you convert them to the same units
Dialogue: 0,0:07:34.05,0:07:42.43,Default,,0000,0000,0000,,and then simplify if appropriate.
Dialogue: 0,0:07:42.43,0:07:44.14,Default,,0000,0000,0000,,As I said before,
Dialogue: 0,0:07:44.14,0:07:45.99,Default,,0000,0000,0000,,ratios are extremely useful
Dialogue: 0,0:07:45.99,0:07:48.73,Default,,0000,0000,0000,,in lots of different circumstances.
Dialogue: 0,0:07:48.73,0:07:50.59,Default,,0000,0000,0000,,They can be used to divide and
Dialogue: 0,0:07:50.59,0:07:53.85,Default,,0000,0000,0000,,share amounts of different quantities
Dialogue: 0,0:07:53.85,0:07:57.55,Default,,0000,0000,0000,,like money, weights, and so on.
Dialogue: 0,0:07:57.55,0:08:00.06,Default,,0000,0000,0000,,So if I take this problem
Dialogue: 0,0:08:00.06,0:08:02.91,Default,,0000,0000,0000,,just say I had an inheritance of £64,000
Dialogue: 0,0:08:02.91,0:08:07.18,Default,,0000,0000,0000,,and it was to be shared between two people
Dialogue: 0,0:08:07.18,0:08:09.81,Default,,0000,0000,0000,,Mrs Sharp and Mr West
Dialogue: 0,0:08:09.81,0:08:12.96,Default,,0000,0000,0000,,in the ratio 5 to 3
Dialogue: 0,0:08:12.96,0:08:14.82,Default,,0000,0000,0000,,What I want you to do is work out
Dialogue: 0,0:08:14.82,0:08:18.29,Default,,0000,0000,0000,,what each one of those gets.
Dialogue: 0,0:08:18.29,0:08:21.47,Default,,0000,0000,0000,,And that's a lot of information to take in
Dialogue: 0,0:08:21.47,0:08:22.59,Default,,0000,0000,0000,,so what I do first is
Dialogue: 0,0:08:22.59,0:08:26.01,Default,,0000,0000,0000,,I start off with a diagram
Dialogue: 0,0:08:26.01,0:08:30.74,Default,,0000,0000,0000,,I've got the total inheritance of £64,000
Dialogue: 0,0:08:30.74,0:08:33.63,Default,,0000,0000,0000,,and I divide it
Dialogue: 0,0:08:33.63,0:08:39.77,Default,,0000,0000,0000,,between Mrs Sharp
Dialogue: 0,0:08:39.77,0:08:42.94,Default,,0000,0000,0000,,and Mr West
Dialogue: 0,0:08:42.94,0:08:48.24,Default,,0000,0000,0000,,in the ratio 5 to 3
Dialogue: 0,0:08:48.24,0:08:50.37,Default,,0000,0000,0000,,And we want to work out
Dialogue: 0,0:08:50.37,0:08:52.66,Default,,0000,0000,0000,,what each gets.
Dialogue: 0,0:08:52.66,0:08:55.31,Default,,0000,0000,0000,,What we do first is we work out
Dialogue: 0,0:08:55.31,0:08:57.95,Default,,0000,0000,0000,,the total number of parts that
Dialogue: 0,0:08:57.95,0:09:02.37,Default,,0000,0000,0000,,their inheritance is split up into.
Dialogue: 0,0:09:02.37,0:09:04.98,Default,,0000,0000,0000,,Well, we use the ratio for that.
Dialogue: 0,0:09:04.98,0:09:07.58,Default,,0000,0000,0000,,It's five parts for Mrs Sharp
Dialogue: 0,0:09:07.58,0:09:09.99,Default,,0000,0000,0000,,and three parts for Mr West
Dialogue: 0,0:09:09.99,0:09:12.40,Default,,0000,0000,0000,,so altogether that is eight parts
Dialogue: 0,0:09:12.40,0:09:15.56,Default,,0000,0000,0000,,Then we work out what the total value
Dialogue: 0,0:09:15.56,0:09:18.73,Default,,0000,0000,0000,,of one part of the inheritance would be.
Dialogue: 0,0:09:18.73,0:09:22.82,Default,,0000,0000,0000,,Now we know that the total inheritance
Dialogue: 0,0:09:22.82,0:09:24.58,Default,,0000,0000,0000,,is £64,000
Dialogue: 0,0:09:24.58,0:09:27.45,Default,,0000,0000,0000,,so one part
Dialogue: 0,0:09:27.45,0:09:35.62,Default,,0000,0000,0000,,equals 64,000 divided by 8
Dialogue: 0,0:09:35.62,0:09:41.06,Default,,0000,0000,0000,,and that is £8000
Dialogue: 0,0:09:41.06,0:09:43.28,Default,,0000,0000,0000,,And then the rest is easy.
Dialogue: 0,0:09:43.28,0:09:47.97,Default,,0000,0000,0000,,All we have to do now is\Ntake Mrs Sharp
Dialogue: 0,0:09:47.97,0:09:54.42,Default,,0000,0000,0000,,and she has five parts
Dialogue: 0,0:09:54.42,0:10:01.01,Default,,0000,0000,0000,,and that is 5 multiplied by £8000
Dialogue: 0,0:10:01.01,0:10:06.70,Default,,0000,0000,0000,,which works out to be £40,000
Dialogue: 0,0:10:06.70,0:10:11.74,Default,,0000,0000,0000,,And then Mr West
Dialogue: 0,0:10:11.74,0:10:16.21,Default,,0000,0000,0000,,he has three parts
Dialogue: 0,0:10:16.21,0:10:21.87,Default,,0000,0000,0000,,and that is 3 multiplied by £8000
Dialogue: 0,0:10:21.87,0:10:27.54,Default,,0000,0000,0000,,which is £24,000
Dialogue: 0,0:10:27.54,0:10:29.50,Default,,0000,0000,0000,,An awful lot of money!
Dialogue: 0,0:10:29.50,0:10:31.35,Default,,0000,0000,0000,,But what if I made a mistake?
Dialogue: 0,0:10:31.35,0:10:33.60,Default,,0000,0000,0000,,How can I check my two answers?
Dialogue: 0,0:10:33.60,0:10:36.83,Default,,0000,0000,0000,,How can I check that Mrs Sharp did get \N£40,000
Dialogue: 0,0:10:36.83,0:10:39.28,Default,,0000,0000,0000,,and Mr West got £24,000?
Dialogue: 0,0:10:39.28,0:10:41.74,Default,,0000,0000,0000,,Well a very simple check
Dialogue: 0,0:10:41.74,0:10:45.80,Default,,0000,0000,0000,,is to add up these two values
Dialogue: 0,0:10:45.80,0:10:47.19,Default,,0000,0000,0000,,and if they add together
Dialogue: 0,0:10:47.19,0:10:48.92,Default,,0000,0000,0000,,to make up the total inheritance
Dialogue: 0,0:10:48.92,0:10:52.77,Default,,0000,0000,0000,,then we think we've done our \Ncalculations properly.
Dialogue: 0,0:10:52.77,0:10:57.84,Default,,0000,0000,0000,,So a quick check:
Dialogue: 0,0:10:57.84,0:11:13.13,Default,,0000,0000,0000,,£40,000 plus 24,000 does equal £64,000
Dialogue: 0,0:11:13.13,0:11:14.93,Default,,0000,0000,0000,,For a complete check though
Dialogue: 0,0:11:14.93,0:11:17.14,Default,,0000,0000,0000,,we can take the two amounts
Dialogue: 0,0:11:17.14,0:11:20.71,Default,,0000,0000,0000,,and see that they will actually make an\Nequivalent ratio
Dialogue: 0,0:11:20.71,0:11:23.77,Default,,0000,0000,0000,,to the ratio that we started off with 5:3
Dialogue: 0,0:11:23.77,0:11:32.68,Default,,0000,0000,0000,,So if we take our 40,000 that \NMrs Sharp got
Dialogue: 0,0:11:32.68,0:11:36.86,Default,,0000,0000,0000,,and then the 24,000 that Mr West got
Dialogue: 0,0:11:36.86,0:11:38.80,Default,,0000,0000,0000,,and cancel them down,
Dialogue: 0,0:11:38.80,0:11:41.22,Default,,0000,0000,0000,,we cancel by 1000
Dialogue: 0,0:11:41.22,0:11:43.79,Default,,0000,0000,0000,,then we cancel by 4
Dialogue: 0,0:11:43.79,0:11:47.63,Default,,0000,0000,0000,,so that would make 10 to 6
Dialogue: 0,0:11:47.63,0:11:50.08,Default,,0000,0000,0000,,and then cancel by 2
Dialogue: 0,0:11:50.08,0:11:53.61,Default,,0000,0000,0000,,so that will make 5 to 3
Dialogue: 0,0:11:53.61,0:11:55.73,Default,,0000,0000,0000,,We do actually get the same ratio
Dialogue: 0,0:11:55.73,0:12:00.24,Default,,0000,0000,0000,,that we started off with.
Dialogue: 0,0:12:00.24,0:12:02.63,Default,,0000,0000,0000,,We're going to do another example.
Dialogue: 0,0:12:02.63,0:12:05.88,Default,,0000,0000,0000,,It's an example which involves another
Dialogue: 0,0:12:05.88,0:12:08.95,Default,,0000,0000,0000,,mixture: making concrete.
Dialogue: 0,0:12:08.95,0:12:13.85,Default,,0000,0000,0000,,And with this, concrete is made by mixing
Dialogue: 0,0:12:13.85,0:12:17.14,Default,,0000,0000,0000,,gravel, sand and cement
Dialogue: 0,0:12:17.14,0:12:21.46,Default,,0000,0000,0000,,in the ratio 3 to 2 to 1
Dialogue: 0,0:12:21.46,0:12:24.87,Default,,0000,0000,0000,,and in this problem we\Nstart with concrete.
Dialogue: 0,0:12:24.87,0:12:28.28,Default,,0000,0000,0000,,The amount of concrete\Nthat we are going to make
Dialogue: 0,0:12:28.28,0:12:31.26,Default,,0000,0000,0000,,will be 12 cubic metres.
Dialogue: 0,0:12:31.26,0:12:33.94,Default,,0000,0000,0000,,And what I want to work out
Dialogue: 0,0:12:33.94,0:12:36.26,Default,,0000,0000,0000,,is how much gravel will be needed
Dialogue: 0,0:12:36.26,0:12:40.47,Default,,0000,0000,0000,,to make 12 cubic metres of concrete.
Dialogue: 0,0:12:40.47,0:12:46.08,Default,,0000,0000,0000,,So we start with drawing a diagram
Dialogue: 0,0:12:46.08,0:12:49.93,Default,,0000,0000,0000,,and that represents the concrete
Dialogue: 0,0:12:49.93,0:12:51.38,Default,,0000,0000,0000,,and we know we want to make
Dialogue: 0,0:12:51.38,0:12:55.98,Default,,0000,0000,0000,,12 cubic metres of concrete
Dialogue: 0,0:12:55.98,0:12:58.53,Default,,0000,0000,0000,,and we know it's mixed
Dialogue: 0,0:12:58.53,0:13:09.84,Default,,0000,0000,0000,,by mixing gravel, sand and cement
Dialogue: 0,0:13:09.84,0:13:16.95,Default,,0000,0000,0000,,in the ratio 3 to 2 to 1
Dialogue: 0,0:13:16.95,0:13:19.18,Default,,0000,0000,0000,,And we want to work out
Dialogue: 0,0:13:19.18,0:13:23.84,Default,,0000,0000,0000,,the amount of concrete for 12 cubic metres
Dialogue: 0,0:13:23.84,0:13:24.92,Default,,0000,0000,0000,,Well, first of all,
Dialogue: 0,0:13:24.92,0:13:27.80,Default,,0000,0000,0000,,we work out the total number of parts
Dialogue: 0,0:13:27.80,0:13:31.02,Default,,0000,0000,0000,,our concrete is divided up into
Dialogue: 0,0:13:31.02,0:13:33.62,Default,,0000,0000,0000,,and we use our ratio for that.
Dialogue: 0,0:13:33.62,0:13:43.33,Default,,0000,0000,0000,,It's 3 + 2 + 1 and that equals 6 parts
Dialogue: 0,0:13:43.33,0:13:45.30,Default,,0000,0000,0000,,Now our concrete is divided up
Dialogue: 0,0:13:45.30,0:13:47.19,Default,,0000,0000,0000,,into six parts
Dialogue: 0,0:13:47.19,0:13:50.05,Default,,0000,0000,0000,,So one part must equal
Dialogue: 0,0:13:50.05,0:13:56.09,Default,,0000,0000,0000,,our 12 cubic metres divided by 6
Dialogue: 0,0:13:56.09,0:14:01.21,Default,,0000,0000,0000,,so that's 12 divided by 6 cubic metres
Dialogue: 0,0:14:01.21,0:14:05.98,Default,,0000,0000,0000,,which works out to be 2 cubic metres.
Dialogue: 0,0:14:05.98,0:14:07.78,Default,,0000,0000,0000,,Now we want to work out
Dialogue: 0,0:14:07.78,0:14:10.72,Default,,0000,0000,0000,,how much gravel is needed.
Dialogue: 0,0:14:10.72,0:14:13.85,Default,,0000,0000,0000,,Gravel is represented by 3 parts
Dialogue: 0,0:14:13.85,0:14:19.96,Default,,0000,0000,0000,,so gravel, the amount that we want
Dialogue: 0,0:14:19.96,0:14:27.37,Default,,0000,0000,0000,,equals 3 times 2 cubic metres
Dialogue: 0,0:14:27.37,0:14:30.69,Default,,0000,0000,0000,,which is 6 cubic metres
Dialogue: 0,0:14:30.69,0:14:32.36,Default,,0000,0000,0000,,and that's our answer.
Dialogue: 0,0:14:32.36,0:14:34.03,Default,,0000,0000,0000,,But it's always good to check
Dialogue: 0,0:14:34.03,0:14:36.42,Default,,0000,0000,0000,,and so we try and do the calculation
Dialogue: 0,0:14:36.42,0:14:38.51,Default,,0000,0000,0000,,in a different way
Dialogue: 0,0:14:38.51,0:14:40.72,Default,,0000,0000,0000,,and the way that I'd like to do it
Dialogue: 0,0:14:40.72,0:14:42.42,Default,,0000,0000,0000,,is using fractions.
Dialogue: 0,0:14:42.42,0:14:45.14,Default,,0000,0000,0000,,If we go back to the original diagram
Dialogue: 0,0:14:45.14,0:14:50.03,Default,,0000,0000,0000,,we know that gravel is represented\Nby 3 parts
Dialogue: 0,0:14:50.03,0:14:52.86,Default,,0000,0000,0000,,and the total is 6
Dialogue: 0,0:14:52.86,0:14:57.27,Default,,0000,0000,0000,,so gravel is a half of\Nthe total volume
Dialogue: 0,0:14:57.27,0:14:59.98,Default,,0000,0000,0000,,and a half of 12 cubic metres is
Dialogue: 0,0:14:59.98,0:15:02.68,Default,,0000,0000,0000,,6 cubic metres
Dialogue: 0,0:15:02.68,0:15:04.64,Default,,0000,0000,0000,,so our answer is right
Dialogue: 0,0:15:04.64,0:15:06.54,Default,,0000,0000,0000,,we've done a check.
Dialogue: 0,0:15:06.54,0:15:11.68,Default,,0000,0000,0000,,But what if we did a similar problem
Dialogue: 0,0:15:11.68,0:15:13.12,Default,,0000,0000,0000,,and we want to start off
Dialogue: 0,0:15:13.12,0:15:15.70,Default,,0000,0000,0000,,with mixing our concrete
Dialogue: 0,0:15:15.70,0:15:18.29,Default,,0000,0000,0000,,using gravel, sand, and cement
Dialogue: 0,0:15:18.29,0:15:23.60,Default,,0000,0000,0000,,but we don't know the final volume of\Nthe concrete
Dialogue: 0,0:15:23.60,0:15:26.81,Default,,0000,0000,0000,,but we do know that we are given
Dialogue: 0,0:15:26.81,0:15:29.60,Default,,0000,0000,0000,,6 cubic metres of sand
Dialogue: 0,0:15:29.60,0:15:33.86,Default,,0000,0000,0000,,and an unlimited supply of\Ngravel and cement.
Dialogue: 0,0:15:33.86,0:15:36.33,Default,,0000,0000,0000,,How much concrete can we make then
Dialogue: 0,0:15:36.33,0:15:39.90,Default,,0000,0000,0000,,if we've got 6 cubic metres of sand?
Dialogue: 0,0:15:39.90,0:15:44.29,Default,,0000,0000,0000,,Alright, we'll start the\Nquestion or the problem
Dialogue: 0,0:15:44.29,0:15:47.27,Default,,0000,0000,0000,,with a diagram.
Dialogue: 0,0:15:47.27,0:15:52.56,Default,,0000,0000,0000,,We know that the mixture is\Nstill the same.
Dialogue: 0,0:15:52.56,0:15:54.80,Default,,0000,0000,0000,,We use the same ratio
Dialogue: 0,0:15:54.80,0:15:58.30,Default,,0000,0000,0000,,gravel to sand to cement
Dialogue: 0,0:15:58.30,0:16:04.14,Default,,0000,0000,0000,,as 3 to 2 to 1
Dialogue: 0,0:16:04.14,0:16:05.37,Default,,0000,0000,0000,,And we know that
Dialogue: 0,0:16:05.37,0:16:09.29,Default,,0000,0000,0000,,we have 6 cubic metres of sand
Dialogue: 0,0:16:09.29,0:16:12.17,Default,,0000,0000,0000,,but we want to work out
Dialogue: 0,0:16:12.17,0:16:15.06,Default,,0000,0000,0000,,how much concrete we can make
Dialogue: 0,0:16:15.06,0:16:17.28,Default,,0000,0000,0000,,with that amount of sand
Dialogue: 0,0:16:17.28,0:16:20.58,Default,,0000,0000,0000,,and unlimited amounts of the other two.
Dialogue: 0,0:16:20.58,0:16:23.50,Default,,0000,0000,0000,,Well, the number of parts that
Dialogue: 0,0:16:23.50,0:16:29.21,Default,,0000,0000,0000,,the concrete is divided up into is still 6
Dialogue: 0,0:16:29.21,0:16:32.02,Default,,0000,0000,0000,,But we know that 2 parts
Dialogue: 0,0:16:32.02,0:16:35.02,Default,,0000,0000,0000,,is 6 cubic metres
Dialogue: 0,0:16:35.02,0:16:37.22,Default,,0000,0000,0000,,because that's what we're given
Dialogue: 0,0:16:37.22,0:16:42.09,Default,,0000,0000,0000,,so 2 parts equals 6 cubic metres.
Dialogue: 0,0:16:42.09,0:16:45.13,Default,,0000,0000,0000,,So 1 part
Dialogue: 0,0:16:45.13,0:16:49.44,Default,,0000,0000,0000,,equals 6 divided by 2
Dialogue: 0,0:16:49.44,0:16:54.48,Default,,0000,0000,0000,,which is 3 cubic metres
Dialogue: 0,0:16:54.48,0:16:56.59,Default,,0000,0000,0000,,Now the total number of parts of
Dialogue: 0,0:16:56.59,0:16:58.70,Default,,0000,0000,0000,,the concrete is divided up into is 6
Dialogue: 0,0:16:58.70,0:17:04.42,Default,,0000,0000,0000,,So the amount of concrete that is produced
Dialogue: 0,0:17:04.42,0:17:08.52,Default,,0000,0000,0000,,is 6 times 3 cubic metres
Dialogue: 0,0:17:08.52,0:17:12.47,Default,,0000,0000,0000,,and that is 18 cubic metres
Dialogue: 0,0:17:12.47,0:17:14.65,Default,,0000,0000,0000,,Again, it's good to check our answer
Dialogue: 0,0:17:14.65,0:17:16.30,Default,,0000,0000,0000,,and we'll do it in a different way
Dialogue: 0,0:17:16.30,0:17:18.67,Default,,0000,0000,0000,,and we'll use fractions again this time.
Dialogue: 0,0:17:18.67,0:17:22.10,Default,,0000,0000,0000,,We look at what we were given.
Dialogue: 0,0:17:22.10,0:17:24.40,Default,,0000,0000,0000,,Sand is represented by 2 parts
Dialogue: 0,0:17:24.40,0:17:29.27,Default,,0000,0000,0000,,and we know it has a volume \Nof 6 cubic metres.
Dialogue: 0,0:17:29.27,0:17:34.44,Default,,0000,0000,0000,,Altogether, there are 6 parts\Nfor our concrete.
Dialogue: 0,0:17:34.44,0:17:36.78,Default,,0000,0000,0000,,So the fraction that represents sand
Dialogue: 0,0:17:36.78,0:17:39.68,Default,,0000,0000,0000,,is 2 over 6, which is a third.
Dialogue: 0,0:17:39.68,0:17:44.24,Default,,0000,0000,0000,,So a third of the total amount is \N6 cubic metres
Dialogue: 0,0:17:44.24,0:17:48.77,Default,,0000,0000,0000,,So the whole amount of concrete must be
Dialogue: 0,0:17:48.77,0:17:51.02,Default,,0000,0000,0000,,3 times 6 cubic metres
Dialogue: 0,0:17:51.02,0:17:54.28,Default,,0000,0000,0000,,which is 18 cubic metres
Dialogue: 0,0:17:54.28,0:17:57.91,Default,,0000,0000,0000,,Here's another ratio problem involved\Nwith ingredients
Dialogue: 0,0:17:57.91,0:18:00.25,Default,,0000,0000,0000,,but this time the ingredients are to make
Dialogue: 0,0:18:00.25,0:18:03.30,Default,,0000,0000,0000,,the Greek food houmous.
Dialogue: 0,0:18:03.30,0:18:07.63,Default,,0000,0000,0000,,It's usually given as a starter
Dialogue: 0,0:18:07.63,0:18:10.52,Default,,0000,0000,0000,,and there are four ingredients:
Dialogue: 0,0:18:10.52,0:18:16.29,Default,,0000,0000,0000,,two cloves of garlic
Dialogue: 0,0:18:16.29,0:18:17.71,Default,,0000,0000,0000,,are combined with
Dialogue: 0,0:18:17.71,0:18:24.31,Default,,0000,0000,0000,,four ounces of chickpeas
Dialogue: 0,0:18:24.31,0:18:32.02,Default,,0000,0000,0000,,and four tablespoonfuls\Nof olive oil.
Dialogue: 0,0:18:32.02,0:18:35.14,Default,,0000,0000,0000,,I sound a little bit like\NDelia Smith at this point
Dialogue: 0,0:18:35.14,0:18:36.96,Default,,0000,0000,0000,,and the final secret ingredient is
Dialogue: 0,0:18:36.96,0:18:46.41,Default,,0000,0000,0000,,the 5 fluid ounces of tahini paste.
Dialogue: 0,0:18:46.41,0:18:48.38,Default,,0000,0000,0000,,Now when you combine these ingredients
Dialogue: 0,0:18:48.38,0:18:54.97,Default,,0000,0000,0000,,together that's enough for six people
Dialogue: 0,0:18:54.97,0:18:57.03,Default,,0000,0000,0000,,But what if I want to make houmous
Dialogue: 0,0:18:57.03,0:18:58.70,Default,,0000,0000,0000,,for nine people?
Dialogue: 0,0:18:58.70,0:19:02.63,Default,,0000,0000,0000,,What amounts do I have of these four\Ningredients
Dialogue: 0,0:19:02.63,0:19:05.80,Default,,0000,0000,0000,,to make it for nine people?
Dialogue: 0,0:19:05.80,0:19:08.31,Default,,0000,0000,0000,,Well, we start off with what we've got
Dialogue: 0,0:19:08.31,0:19:10.11,Default,,0000,0000,0000,,and what we know
Dialogue: 0,0:19:10.11,0:19:12.57,Default,,0000,0000,0000,,We've got 2 cloves of garlic
Dialogue: 0,0:19:12.57,0:19:15.64,Default,,0000,0000,0000,,with 4 ounces of chickpeas
Dialogue: 0,0:19:15.64,0:19:19.13,Default,,0000,0000,0000,,4 tablespoonsful of olive oil
Dialogue: 0,0:19:19.13,0:19:24.26,Default,,0000,0000,0000,,and 5 fluid ounces of tahini paste
Dialogue: 0,0:19:24.26,0:19:29.28,Default,,0000,0000,0000,,and that makes enough for six people
Dialogue: 0,0:19:29.28,0:19:32.63,Default,,0000,0000,0000,,What I do next is that I work out
Dialogue: 0,0:19:32.63,0:19:34.59,Default,,0000,0000,0000,,what each of those ingredients
Dialogue: 0,0:19:34.59,0:19:37.63,Default,,0000,0000,0000,,would be for one person.
Dialogue: 0,0:19:37.63,0:19:39.20,Default,,0000,0000,0000,,So I have to divide
Dialogue: 0,0:19:39.20,0:19:41.71,Default,,0000,0000,0000,,each of those numbers by 6
Dialogue: 0,0:19:41.71,0:19:45.10,Default,,0000,0000,0000,,So that's 2 over 6
Dialogue: 0,0:19:45.10,0:19:46.80,Default,,0000,0000,0000,,4 over 6
Dialogue: 0,0:19:46.80,0:19:47.65,Default,,0000,0000,0000,,4 over 6
Dialogue: 0,0:19:47.65,0:19:51.22,Default,,0000,0000,0000,,and 5 over 6
Dialogue: 0,0:19:51.22,0:19:54.02,Default,,0000,0000,0000,,and then we cancel down if we can
Dialogue: 0,0:19:54.02,0:19:55.29,Default,,0000,0000,0000,,In this case we can
Dialogue: 0,0:19:55.29,0:19:57.93,Default,,0000,0000,0000,,that's one third.
Dialogue: 0,0:19:57.93,0:20:03.19,Default,,0000,0000,0000,,Cancel four sixths to two thirds.
Dialogue: 0,0:20:03.19,0:20:05.71,Default,,0000,0000,0000,,And this will be the same.
Dialogue: 0,0:20:05.71,0:20:07.87,Default,,0000,0000,0000,,And the last one just remains the same:
Dialogue: 0,0:20:07.87,0:20:09.27,Default,,0000,0000,0000,,five sixths
Dialogue: 0,0:20:09.27,0:20:11.42,Default,,0000,0000,0000,,And now it's dead easy to work out
Dialogue: 0,0:20:11.42,0:20:15.23,Default,,0000,0000,0000,,what amounts we need for nine people.
Dialogue: 0,0:20:15.23,0:20:18.53,Default,,0000,0000,0000,,All we have to do is multiply by 9
Dialogue: 0,0:20:18.53,0:20:21.83,Default,,0000,0000,0000,,So that's 1/3 multiplied by 9
Dialogue: 0,0:20:21.83,0:20:25.40,Default,,0000,0000,0000,,2/3 multiplied by 9
Dialogue: 0,0:20:25.40,0:20:28.98,Default,,0000,0000,0000,,and another 2/3 multiplied by 9
Dialogue: 0,0:20:28.98,0:20:32.39,Default,,0000,0000,0000,,and then 5/6 multiplied by 9
Dialogue: 0,0:20:32.39,0:20:36.00,Default,,0000,0000,0000,,And we work out these\Ncalculations and simplify
Dialogue: 0,0:20:36.00,0:20:38.74,Default,,0000,0000,0000,,3 into 9 is 3
Dialogue: 0,0:20:38.74,0:20:39.68,Default,,0000,0000,0000,,3 into 9 is 3
Dialogue: 0,0:20:39.68,0:20:42.63,Default,,0000,0000,0000,,and then 2 threes are 6.
Dialogue: 0,0:20:42.63,0:20:44.34,Default,,0000,0000,0000,,and this works out to be the same
Dialogue: 0,0:20:44.34,0:20:47.65,Default,,0000,0000,0000,,which is 6 because it's the same \Ncalculation
Dialogue: 0,0:20:47.65,0:20:50.16,Default,,0000,0000,0000,,3 into 6 is 2
Dialogue: 0,0:20:50.16,0:20:52.40,Default,,0000,0000,0000,,3 into 9 is 3
Dialogue: 0,0:20:52.40,0:20:55.91,Default,,0000,0000,0000,,5 threes are 15 over 2
Dialogue: 0,0:20:55.91,0:21:01.03,Default,,0000,0000,0000,,which works out to be 7 and a half
Dialogue: 0,0:21:01.03,0:21:03.31,Default,,0000,0000,0000,,So our final answer
Dialogue: 0,0:21:03.31,0:21:05.08,Default,,0000,0000,0000,,for the ingredients
Dialogue: 0,0:21:05.08,0:21:10.16,Default,,0000,0000,0000,,is 3 cloves of garlic
Dialogue: 0,0:21:10.16,0:21:13.57,Default,,0000,0000,0000,,6 ounces of chickpeas
Dialogue: 0,0:21:13.57,0:21:16.25,Default,,0000,0000,0000,,combined with 6 tablespoonfuls\Nof olive oil
Dialogue: 0,0:21:16.25,0:21:20.27,Default,,0000,0000,0000,,and 7 and a half fluid ounces
Dialogue: 0,0:21:20.27,0:21:22.42,Default,,0000,0000,0000,,of tahini paste
Dialogue: 0,0:21:22.42,0:21:28.00,Default,,0000,0000,0000,,And that makes enough\Nhoumous for nine people.
Dialogue: 0,0:21:28.00,0:21:31.46,Default,,0000,0000,0000,,In a similar way,
Dialogue: 0,0:21:31.46,0:21:36.60,Default,,0000,0000,0000,,you can use this method in conversion \Nproblems
Dialogue: 0,0:21:36.60,0:21:41.21,Default,,0000,0000,0000,,If we had the conversion that
Dialogue: 0,0:21:41.21,0:21:50.55,Default,,0000,0000,0000,,1 pound is the same as 1.65 euros
Dialogue: 0,0:21:50.55,0:21:53.59,Default,,0000,0000,0000,,and I wanted to work out
Dialogue: 0,0:21:53.59,0:21:59.68,Default,,0000,0000,0000,,what 50 euros would be in pence
Dialogue: 0,0:21:59.68,0:22:01.79,Default,,0000,0000,0000,,to the nearest pence
Dialogue: 0,0:22:01.79,0:22:07.09,Default,,0000,0000,0000,,What I like doing first is to work out
Dialogue: 0,0:22:07.09,0:22:12.58,Default,,0000,0000,0000,,what 1 euro is in terms of pence
Dialogue: 0,0:22:12.58,0:22:13.98,Default,,0000,0000,0000,,So I start with
Dialogue: 0,0:22:13.98,0:22:22.37,Default,,0000,0000,0000,,1.65 euros equals 100 pence
Dialogue: 0,0:22:22.37,0:22:26.59,Default,,0000,0000,0000,,One euro would then equal
Dialogue: 0,0:22:26.59,0:22:33.40,Default,,0000,0000,0000,,100 divided by the 1.65
Dialogue: 0,0:22:33.40,0:22:35.32,Default,,0000,0000,0000,,And then to work out
Dialogue: 0,0:22:35.32,0:22:39.90,Default,,0000,0000,0000,,what the 50 euros would be
Dialogue: 0,0:22:39.90,0:22:44.39,Default,,0000,0000,0000,,I multiply this by 50
Dialogue: 0,0:22:44.39,0:22:48.92,Default,,0000,0000,0000,,as 100 over 1.65 multiplied by 50
Dialogue: 0,0:22:48.92,0:22:52.91,Default,,0000,0000,0000,,And that is 5000
Dialogue: 0,0:22:52.91,0:22:55.63,Default,,0000,0000,0000,,divided by the 1.65
Dialogue: 0,0:22:55.63,0:22:57.89,Default,,0000,0000,0000,,Now I am not going to do this by\Nlong division.
Dialogue: 0,0:22:57.89,0:23:00.15,Default,,0000,0000,0000,,I'll use my calculator
Dialogue: 0,0:23:00.15,0:23:07.34,Default,,0000,0000,0000,,and I just type in the relevant numbers
Dialogue: 0,0:23:07.34,0:23:12.59,Default,,0000,0000,0000,,5000 divided by 1.65
Dialogue: 0,0:23:12.59,0:23:14.48,Default,,0000,0000,0000,,equals
Dialogue: 0,0:23:14.48,0:23:19.60,Default,,0000,0000,0000,,3030 point 3 0 point 3 0 repeating
Dialogue: 0,0:23:19.60,0:23:27.70,Default,,0000,0000,0000,,So 50 euros equals 3030 pence
Dialogue: 0,0:23:27.70,0:23:29.28,Default,,0000,0000,0000,,to the nearest pence.
Dialogue: 0,0:23:29.28,0:23:37.51,Default,,0000,0000,0000,,Which is 30 pounds and 30p
Dialogue: 0,0:23:37.51,0:23:40.93,Default,,0000,0000,0000,,Well, that's the session finished \Nnow on ratio.
Dialogue: 0,0:23:40.93,0:23:43.21,Default,,0000,0000,0000,,Before I finish finally,
Dialogue: 0,0:23:43.21,0:23:45.49,Default,,0000,0000,0000,,what I'd like to do is just remind you
Dialogue: 0,0:23:45.49,0:23:49.69,Default,,0000,0000,0000,,of a few key points about ratio.
Dialogue: 0,0:23:49.69,0:23:51.67,Default,,0000,0000,0000,,First of all, what is a ratio?
Dialogue: 0,0:23:51.67,0:23:54.01,Default,,0000,0000,0000,,Well a ratio is a way of comparing
Dialogue: 0,0:23:54.01,0:23:56.81,Default,,0000,0000,0000,,quantities of a similar type
Dialogue: 0,0:23:56.81,0:23:58.73,Default,,0000,0000,0000,,When you write a ratio down
Dialogue: 0,0:23:58.73,0:24:01.50,Default,,0000,0000,0000,,you use whole numbers
Dialogue: 0,0:24:01.50,0:24:04.98,Default,,0000,0000,0000,,separated by colon.
Dialogue: 0,0:24:04.98,0:24:08.47,Default,,0000,0000,0000,,The numbers should be in the\Nsame units.
Dialogue: 0,0:24:08.47,0:24:10.09,Default,,0000,0000,0000,,If they're not, you convert them
Dialogue: 0,0:24:10.09,0:24:11.43,Default,,0000,0000,0000,,to the same units
Dialogue: 0,0:24:11.43,0:24:14.46,Default,,0000,0000,0000,,by using one or the other of the \Nunits involved
Dialogue: 0,0:24:14.46,0:24:17.05,Default,,0000,0000,0000,,Just use your nous basically.
Dialogue: 0,0:24:17.05,0:24:21.38,Default,,0000,0000,0000,,And then you simplify as appropriate.
Dialogue: 0,0:24:21.38,0:24:23.14,Default,,0000,0000,0000,,In calculations involved in ratio
Dialogue: 0,0:24:23.14,0:24:29.61,Default,,0000,0000,0000,,it is useful to work out the total \Nnumber of parts
Dialogue: 0,0:24:29.61,0:24:33.23,Default,,0000,0000,0000,,the quantity is divided up into
Dialogue: 0,0:24:33.23,0:24:36.77,Default,,0000,0000,0000,,and then work out one part represents.