0:00:01.732,0:00:05.300 Today's session is on ratio. 0:00:05.300,0:00:07.521 I'm going to explain what a ratio is 0:00:07.569,0:00:09.145 and how ratios are used 0:00:09.145,0:00:11.175 in different situations. 0:00:11.275,0:00:14.538 So to start off with what is a ratio? 0:00:14.980,0:00:18.494 Well, a ratio is a way of comparing 0:00:18.508,0:00:22.531 amounts of ingredients. 0:00:22.531,0:00:25.690 Ratios can be used to compare 0:00:25.740,0:00:30.110 weights, money, length and so on. 0:00:30.190,0:00:33.200 So if we take this example 0:00:33.200,0:00:34.990 we've got a model boat 0:00:34.990,0:00:38.050 whose length is 1 metre 0:00:38.050,0:00:40.820 and the real boat 0:00:40.830,0:00:43.267 whose length is 25 metres. 0:00:43.290,0:00:45.014 Then we say the ratio of the 0:00:45.014,0:00:48.204 length of the model boat to the real boat 0:00:48.204,0:00:51.880 is 1 to 25. 0:00:51.900,0:00:54.770 Notice we've just used the numbers 0:00:54.770,0:00:57.670 without the unit (metres) 0:00:57.670,0:00:59.915 and we've used the colon 0:00:59.915,0:01:02.882 to represent the ratio. 0:01:03.030,0:01:06.064 Ratios are used to describe quantities 0:01:06.064,0:01:08.984 of ingredients in mixtures. 0:01:08.984,0:01:11.966 For example, in the[br]pharmaceutical trade 0:01:11.966,0:01:14.360 when you're making medicines, 0:01:14.360,0:01:16.642 or in the building trade 0:01:16.642,0:01:19.410 when you are making cement or mortar, 0:01:19.410,0:01:22.486 or at home when you're making up food 0:01:22.486,0:01:26.546 you use different quantities[br]in different proportions 0:01:26.546,0:01:29.000 and if you don't get them right 0:01:29.000,0:01:30.947 then things go wrong. 0:01:30.947,0:01:33.830 So it's very important to know 0:01:33.830,0:01:39.358 what quantities you've got and[br]in what ratio. 0:01:39.358,0:01:41.820 So for example, if we have 0:01:41.820,0:01:45.630 mortar for building brick walls. 0:01:45.630,0:01:47.550 Mortar is made up by mixing 0:01:47.550,0:01:52.778 two parts of cement to [br]seven parts of gravel by volume 0:01:52.778,0:01:57.880 and we write that ratio as 2 to 7. 0:01:57.880,0:02:00.410 Again notice we've used 0:02:00.410,0:02:03.504 the numbers without the units 0:02:03.504,0:02:07.268 and the colon to represent the ratio. 0:02:07.268,0:02:09.304 When we're making pastry at home, 0:02:09.304,0:02:11.381 when we're making pies and tarts, 0:02:11.381,0:02:14.157 we mix four ounces of flour 0:02:14.157,0:02:17.210 with two ounces of margarine 0:02:17.210,0:02:23.040 And that ratio would be 4 to 2. 0:02:23.040,0:02:24.309 But in this case, 0:02:24.309,0:02:25.899 if you look at the numbers, 0:02:25.899,0:02:28.679 they've got a factor of two in common 0:02:28.679,0:02:31.085 So we can simplify ratios just in the same 0:02:31.085,0:02:33.520 way as we simplify fractions. 0:02:33.520,0:02:36.495 We can divide by the common factor, 0:02:36.495,0:02:39.280 so we divide 4 by 2 0:02:39.280,0:02:42.530 and 2 by 2 to give 1. 0:02:42.530,0:02:48.570 So 2 to 1 is the simplest form[br]of the ratio 4 to 2. 0:02:48.570,0:02:52.760 But both of the ratios are equivalent, 0:02:52.760,0:03:01.920 because the relationship of the numbers[br]involved stays the same. 0:03:01.920,0:03:05.620 If we take this example 0:03:05.620,0:03:09.860 250 to 150 0:03:09.860,0:03:12.580 We can simplify this ratio. 0:03:12.580,0:03:15.530 We divide both by 10 0:03:15.530,0:03:19.502 to get 25 to 15 0:03:19.502,0:03:22.342 And then we can divide both by 5 0:03:22.342,0:03:24.813 5 into 25 will give me 5 0:03:24.813,0:03:28.276 5 into 15 will give me 3 0:03:28.276,0:03:31.986 We can't divide anymore, 0:03:31.986,0:03:34.262 so this is the simplest form. 0:03:34.262,0:03:37.864 5 to 3 the simplest form of 0:03:37.864,0:03:41.467 the ratio 250 to 150. 0:03:41.467,0:03:44.310 But all three ratios are equivalent 0:03:44.310,0:03:46.881 because the relationship of the numbers 0:03:46.881,0:03:50.070 is exactly the same. 0:03:50.070,0:03:53.655 In the same way, we can actually 0:03:53.655,0:04:00.110 simplify this ratio: 1 to 1.5 0:04:00.110,0:04:04.494 In ratios we like to have whole numbers 0:04:04.494,0:04:06.094 and in this ratio you can see 0:04:06.094,0:04:07.650 that we have a decimal. 0:04:07.650,0:04:09.471 To get rid of the decimal 0:04:09.471,0:04:11.342 we can multiply both sides of the 0:04:11.342,0:04:12.732 ratio by 10 0:04:12.732,0:04:16.000 and we still have an equivalent ratio. 0:04:16.000,0:04:18.020 Because, again, the relationship 0:04:18.020,0:04:19.860 between the numbers is the same. 0:04:19.860,0:04:22.588 So we multiply the 1 by 10 0:04:22.588,0:04:24.042 you get 10 0:04:24.042,0:04:25.536 Multiply 1.5 by 10 0:04:25.536,0:04:27.830 you get 15 0:04:27.830,0:04:30.288 10 to 15 we can simplify that. 0:04:30.288,0:04:33.930 Divide both sides by 5. 0:04:33.930,0:04:36.378 5 into 10 gives me 2 0:04:36.378,0:04:40.350 5 into 15 will give me 3 0:04:40.350,0:04:42.499 2 to 3 is the simplest form 0:04:42.499,0:04:46.820 of the ratio 1 to 1.5 0:04:46.820,0:04:49.945 Similarly, when we have fractions 0:04:49.945,0:04:53.780 If we had this ratio: 0:04:53.780,0:04:57.630 a quarter to five-eighths, 0:04:57.630,0:04:59.675 it just doesn't look right. 0:04:59.675,0:05:01.590 We want to express that ratio 0:05:01.590,0:05:03.265 in terms of whole numbers 0:05:03.265,0:05:04.770 in its simplest form. 0:05:04.770,0:05:10.158 So what we do first is we write[br]both as fractions over 8 0:05:10.158,0:05:11.610 in terms of eighths. 0:05:11.610,0:05:17.110 A quarter is two eighths 0:05:17.110,0:05:21.604 and now the ratio is two eighths to five eighths. 0:05:21.604,0:05:23.798 And now it's dead simple 0:05:23.798,0:05:27.612 All we have to say is that is 2 to 5. 0:05:27.612,0:05:30.656 We multiply both ratios by 8 0:05:30.656,0:05:33.470 And 2 to 5 is the simplest ratio 0:05:33.470,0:05:37.942 for the ratio a quarter to five-eighths. 0:05:37.942,0:05:40.484 But again all three ratios are 0:05:40.484,0:05:42.902 equivalent because the relationship 0:05:42.902,0:05:45.870 between the numbers is exactly the same. 0:05:45.870,0:05:47.950 Moving on, 0:05:47.950,0:05:51.040 we must have the numbers [br]in the ratios 0:05:51.040,0:05:53.368 having the same units. 0:05:53.368,0:05:55.317 So if we have this ratio 0:05:55.317,0:06:02.660 15 pence to 3 pounds, 0:06:02.660,0:06:07.296 we cannot say that the ratio is 15 to 3 0:06:07.296,0:06:12.550 and then simplify that to 5 to 1 0:06:12.550,0:06:15.799 Because we didn't start off with 0:06:15.799,0:06:18.538 the numbers having the same units 0:06:18.538,0:06:21.748 the relationship between[br]the numbers is not the same, 0:06:21.748,0:06:23.927 because as I say, 0:06:23.927,0:06:26.566 we didn't start off with these numbers 0:06:26.566,0:06:29.080 having the same units. 0:06:29.080,0:06:31.378 So we must convert the numbers 0:06:31.378,0:06:33.097 to the same units 0:06:33.097,0:06:36.766 and we choose whichever unit is [br]appropriate 0:06:36.766,0:06:38.936 [br]In this case, it's obvious we must 0:06:38.936,0:06:41.390 change them to pence. 0:06:41.390,0:06:48.870 So we say the ratio is 15 to 300 0:06:48.870,0:06:51.910 as there's 300 pence for 3 pounds 0:06:51.910,0:06:55.000 and then we simplify as normal. 0:06:55.000,0:06:57.100 We divide both sides by five. 0:06:57.100,0:06:59.430 5 into 15 is 3 0:06:59.430,0:07:02.195 5 into 300 is 60 0:07:02.195,0:07:05.560 And then we can divide by 3 0:07:05.560,0:07:07.477 3 into 3 is 1 0:07:07.477,0:07:10.300 3 into 60 is 20 0:07:10.300,0:07:14.580 And notice these two ratios are 0:07:14.580,0:07:16.850 not the same, they're vastly different. 0:07:16.850,0:07:18.666 They're not equivalent because 0:07:18.666,0:07:20.932 the relationship between the numbers 0:07:20.932,0:07:23.630 is not the same. 0:07:23.630,0:07:25.754 So it's very important in ratios 0:07:25.754,0:07:28.478 that you start with numbers 0:07:28.478,0:07:30.740 that have the same units. 0:07:30.740,0:07:32.011 If they're not, 0:07:32.011,0:07:34.053 then you convert them to the same units 0:07:34.053,0:07:42.431 and then simplify if appropriate. 0:07:42.431,0:07:44.135 As I said before, 0:07:44.135,0:07:45.990 ratios are extremely useful 0:07:45.990,0:07:48.730 in lots of different circumstances. 0:07:48.730,0:07:50.590 They can be used to divide and 0:07:50.590,0:07:53.850 share amounts of different quantities 0:07:53.850,0:07:57.550 like money, weights, and so on. 0:07:57.550,0:08:00.058 So if I take this problem 0:08:00.058,0:08:02.906 just say I had an inheritance of £64,000 0:08:02.906,0:08:07.180 and it was to be shared between two people 0:08:07.180,0:08:09.810 Mrs Sharp and Mr West 0:08:09.810,0:08:12.960 in the ratio 5 to 3 0:08:12.960,0:08:14.822 What I want you to do is work out 0:08:14.822,0:08:18.290 what each one of those gets. 0:08:18.290,0:08:21.470 And that's a lot of information to take in 0:08:21.470,0:08:22.590 so what I do first is 0:08:22.590,0:08:26.010 I start off with a diagram 0:08:26.010,0:08:30.745 I've got the total inheritance of £64,000 0:08:30.745,0:08:33.632 and I divide it 0:08:33.632,0:08:39.770 between Mrs Sharp 0:08:39.770,0:08:42.942 and Mr West 0:08:42.942,0:08:48.240 in the ratio 5 to 3 0:08:48.240,0:08:50.370 And we want to work out 0:08:50.370,0:08:52.660 what each gets. 0:08:52.660,0:08:55.306 What we do first is we work out 0:08:55.306,0:08:57.952 the total number of parts that 0:08:57.952,0:09:02.370 their inheritance is split up into. 0:09:02.370,0:09:04.976 Well, we use the ratio for that. 0:09:04.976,0:09:07.583 It's five parts for Mrs Sharp 0:09:07.583,0:09:09.989 and three parts for Mr West 0:09:09.989,0:09:12.395 so altogether that is eight parts 0:09:12.395,0:09:15.561 Then we work out what the total value 0:09:15.561,0:09:18.728 of one part of the inheritance would be. 0:09:18.728,0:09:22.818 Now we know that the total inheritance 0:09:22.818,0:09:24.580 is £64,000 0:09:24.580,0:09:27.450 so one part 0:09:27.450,0:09:35.620 equals 64,000 divided by 8 0:09:35.620,0:09:41.060 and that is £8000 0:09:41.060,0:09:43.280 And then the rest is easy. 0:09:43.280,0:09:47.970 All we have to do now is[br]take Mrs Sharp 0:09:47.970,0:09:54.416 and she has five parts 0:09:54.416,0:10:01.008 and that is 5 multiplied by £8000 0:10:01.008,0:10:06.698 which works out to be £40,000 0:10:06.698,0:10:11.740 And then Mr West 0:10:11.740,0:10:16.210 he has three parts 0:10:16.210,0:10:21.870 and that is 3 multiplied by £8000 0:10:21.870,0:10:27.536 which is £24,000 0:10:27.536,0:10:29.496 An awful lot of money! 0:10:29.496,0:10:31.346 But what if I made a mistake? 0:10:31.346,0:10:33.602 How can I check my two answers? 0:10:33.602,0:10:36.828 How can I check that Mrs Sharp did get [br]£40,000 0:10:36.828,0:10:39.285 and Mr West got £24,000? 0:10:39.285,0:10:41.742 Well a very simple check 0:10:41.742,0:10:45.799 is to add up these two values 0:10:45.799,0:10:47.186 and if they add together 0:10:47.186,0:10:48.924 to make up the total inheritance 0:10:48.924,0:10:52.772 then we think we've done our [br]calculations properly. 0:10:52.772,0:10:57.844 So a quick check: 0:10:57.844,0:11:13.130 £40,000 plus 24,000 does equal £64,000 0:11:13.130,0:11:14.930 For a complete check though 0:11:14.930,0:11:17.140 we can take the two amounts 0:11:17.140,0:11:20.710 and see that they will actually make an[br]equivalent ratio 0:11:20.710,0:11:23.770 to the ratio that we started off with 5:3 0:11:23.770,0:11:32.680 So if we take our 40,000 that [br]Mrs Sharp got 0:11:32.680,0:11:36.864 and then the 24,000 that Mr West got 0:11:36.864,0:11:38.796 and cancel them down, 0:11:38.796,0:11:41.218 we cancel by 1000 0:11:41.218,0:11:43.789 then we cancel by 4 0:11:43.789,0:11:47.630 so that would make 10 to 6 0:11:47.630,0:11:50.081 and then cancel by 2 0:11:50.081,0:11:53.613 so that will make 5 to 3 0:11:53.613,0:11:55.731 We do actually get the same ratio 0:11:55.731,0:12:00.239 that we started off with. 0:12:00.239,0:12:02.629 We're going to do another example. 0:12:02.629,0:12:05.880 It's an example which involves another 0:12:05.880,0:12:08.950 mixture: making concrete. 0:12:08.950,0:12:13.850 And with this, concrete is made by mixing 0:12:13.850,0:12:17.140 gravel, sand and cement 0:12:17.140,0:12:21.460 in the ratio 3 to 2 to 1 0:12:21.460,0:12:24.871 and in this problem we[br]start with concrete. 0:12:24.871,0:12:28.282 The amount of concrete[br]that we are going to make 0:12:28.282,0:12:31.260 will be 12 cubic metres. 0:12:31.260,0:12:33.942 And what I want to work out 0:12:33.942,0:12:36.264 is how much gravel will be needed 0:12:36.264,0:12:40.470 to make 12 cubic metres of concrete. 0:12:40.470,0:12:46.080 So we start with drawing a diagram 0:12:46.080,0:12:49.934 and that represents the concrete 0:12:49.934,0:12:51.385 and we know we want to make 0:12:51.385,0:12:55.976 12 cubic metres of concrete 0:12:55.976,0:12:58.530 and we know it's mixed 0:12:58.530,0:13:09.840 by mixing gravel, sand and cement 0:13:09.840,0:13:16.950 in the ratio 3 to 2 to 1 0:13:16.950,0:13:19.182 And we want to work out 0:13:19.182,0:13:23.844 the amount of concrete for 12 cubic metres 0:13:23.844,0:13:24.916 Well, first of all, 0:13:24.916,0:13:27.798 we work out the total number of parts 0:13:27.798,0:13:31.024 our concrete is divided up into 0:13:31.024,0:13:33.620 and we use our ratio for that. 0:13:33.620,0:13:43.330 It's 3 + 2 + 1 and that equals 6 parts 0:13:43.330,0:13:45.298 Now our concrete is divided up 0:13:45.298,0:13:47.188 into six parts 0:13:47.188,0:13:50.050 So one part must equal 0:13:50.050,0:13:56.092 our 12 cubic metres divided by 6 0:13:56.092,0:14:01.214 so that's 12 divided by 6 cubic metres 0:14:01.214,0:14:05.980 which works out to be 2 cubic metres. 0:14:05.980,0:14:07.780 Now we want to work out 0:14:07.780,0:14:10.720 how much gravel is needed. 0:14:10.720,0:14:13.854 Gravel is represented by 3 parts 0:14:13.854,0:14:19.960 so gravel, the amount that we want 0:14:19.960,0:14:27.372 equals 3 times 2 cubic metres 0:14:27.372,0:14:30.690 which is 6 cubic metres 0:14:30.690,0:14:32.362 and that's our answer. 0:14:32.362,0:14:34.034 But it's always good to check 0:14:34.034,0:14:36.424 and so we try and do the calculation 0:14:36.424,0:14:38.510 in a different way 0:14:38.510,0:14:40.722 and the way that I'd like to do it 0:14:40.722,0:14:42.425 is using fractions. 0:14:42.425,0:14:45.135 If we go back to the original diagram 0:14:45.135,0:14:50.026 we know that gravel is represented[br]by 3 parts 0:14:50.026,0:14:52.863 and the total is 6 0:14:52.863,0:14:57.270 so gravel is a half of[br]the total volume 0:14:57.270,0:14:59.977 and a half of 12 cubic metres is 0:14:59.977,0:15:02.685 6 cubic metres 0:15:02.685,0:15:04.637 so our answer is right 0:15:04.637,0:15:06.540 we've done a check. 0:15:06.540,0:15:11.680 But what if we did a similar problem 0:15:11.680,0:15:13.120 and we want to start off 0:15:13.120,0:15:15.705 with mixing our concrete 0:15:15.705,0:15:18.290 using gravel, sand, and cement 0:15:18.290,0:15:23.602 but we don't know the final volume of[br]the concrete 0:15:23.602,0:15:26.813 but we do know that we are given 0:15:26.813,0:15:29.605 6 cubic metres of sand 0:15:29.605,0:15:33.860 and an unlimited supply of[br]gravel and cement. 0:15:33.860,0:15:36.332 How much concrete can we make then 0:15:36.332,0:15:39.900 if we've got 6 cubic metres of sand? 0:15:39.900,0:15:44.292 Alright, we'll start the[br]question or the problem 0:15:44.292,0:15:47.270 with a diagram. 0:15:47.270,0:15:52.556 We know that the mixture is[br]still the same. 0:15:52.556,0:15:54.805 We use the same ratio 0:15:54.805,0:15:58.304 gravel to sand to cement 0:15:58.304,0:16:04.140 as 3 to 2 to 1 0:16:04.140,0:16:05.369 And we know that 0:16:05.369,0:16:09.288 we have 6 cubic metres of sand 0:16:09.288,0:16:12.174 but we want to work out 0:16:12.174,0:16:15.060 how much concrete we can make 0:16:15.060,0:16:17.280 with that amount of sand 0:16:17.280,0:16:20.580 and unlimited amounts of the other two. 0:16:20.580,0:16:23.496 Well, the number of parts that 0:16:23.496,0:16:29.210 the concrete is divided up into is still 6 0:16:29.210,0:16:32.020 But we know that 2 parts 0:16:32.020,0:16:35.018 is 6 cubic metres 0:16:35.018,0:16:37.216 because that's what we're given 0:16:37.216,0:16:42.090 so 2 parts equals 6 cubic metres. 0:16:42.090,0:16:45.130 So 1 part 0:16:45.130,0:16:49.440 equals 6 divided by 2 0:16:49.440,0:16:54.480 which is 3 cubic metres 0:16:54.480,0:16:56.592 Now the total number of parts of 0:16:56.592,0:16:58.705 the concrete is divided up into is 6 0:16:58.705,0:17:04.425 So the amount of concrete that is produced 0:17:04.425,0:17:08.520 is 6 times 3 cubic metres 0:17:08.520,0:17:12.470 and that is 18 cubic metres 0:17:12.470,0:17:14.651 Again, it's good to check our answer 0:17:14.651,0:17:16.302 and we'll do it in a different way 0:17:16.302,0:17:18.670 and we'll use fractions again this time. 0:17:18.670,0:17:22.100 We look at what we were given. 0:17:22.100,0:17:24.400 Sand is represented by 2 parts 0:17:24.400,0:17:29.270 and we know it has a volume [br]of 6 cubic metres. 0:17:29.270,0:17:34.440 Altogether, there are 6 parts[br]for our concrete. 0:17:34.440,0:17:36.780 So the fraction that represents sand 0:17:36.780,0:17:39.680 is 2 over 6, which is a third. 0:17:39.680,0:17:44.244 So a third of the total amount is [br]6 cubic metres 0:17:44.244,0:17:48.770 So the whole amount of concrete must be 0:17:48.770,0:17:51.015 3 times 6 cubic metres 0:17:51.015,0:17:54.281 which is 18 cubic metres 0:17:54.281,0:17:57.910 Here's another ratio problem involved[br]with ingredients 0:17:57.910,0:18:00.254 but this time the ingredients are to make 0:18:00.254,0:18:03.299 the Greek food houmous. 0:18:03.300,0:18:07.630 It's usually given as a starter 0:18:07.630,0:18:10.520 and there are four ingredients: 0:18:10.520,0:18:16.290 two cloves of garlic 0:18:16.290,0:18:17.714 are combined with 0:18:17.714,0:18:24.310 four ounces of chickpeas 0:18:24.310,0:18:32.020 and four tablespoonfuls[br]of olive oil. 0:18:32.020,0:18:35.136 I sound a little bit like[br]Delia Smith at this point 0:18:35.136,0:18:36.955 and the final secret ingredient is 0:18:36.955,0:18:46.414 the 5 fluid ounces of tahini paste. 0:18:46.414,0:18:48.378 Now when you combine these ingredients 0:18:48.378,0:18:54.970 together that's enough for six people 0:18:54.970,0:18:57.030 But what if I want to make houmous 0:18:57.030,0:18:58.700 for nine people? 0:18:58.700,0:19:02.630 What amounts do I have of these four[br]ingredients 0:19:02.630,0:19:05.798 to make it for nine people? 0:19:05.798,0:19:08.306 Well, we start off with what we've got 0:19:08.306,0:19:10.107 and what we know 0:19:10.107,0:19:12.569 We've got 2 cloves of garlic 0:19:12.569,0:19:15.637 with 4 ounces of chickpeas 0:19:15.637,0:19:19.130 4 tablespoonsful of olive oil 0:19:19.130,0:19:24.261 and 5 fluid ounces of tahini paste 0:19:24.261,0:19:29.283 and that makes enough for six people 0:19:29.283,0:19:32.634 What I do next is that I work out 0:19:32.634,0:19:34.587 what each of those ingredients 0:19:34.587,0:19:37.630 would be for one person. 0:19:37.630,0:19:39.203 So I have to divide 0:19:39.203,0:19:41.710 each of those numbers by 6 0:19:41.710,0:19:45.105 So that's 2 over 6 0:19:45.105,0:19:46.802 4 over 6 0:19:46.802,0:19:47.651 4 over 6 0:19:47.651,0:19:51.220 and 5 over 6 0:19:51.220,0:19:54.025 and then we cancel down if we can 0:19:54.025,0:19:55.290 In this case we can 0:19:55.290,0:19:57.930 that's one third. 0:19:57.930,0:20:03.190 Cancel four sixths to two thirds. 0:20:03.190,0:20:05.710 And this will be the same. 0:20:05.710,0:20:07.873 And the last one just remains the same: 0:20:07.873,0:20:09.269 five sixths 0:20:09.269,0:20:11.416 And now it's dead easy to work out 0:20:11.416,0:20:15.230 what amounts we need for nine people. 0:20:15.230,0:20:18.530 All we have to do is multiply by 9 0:20:18.530,0:20:21.830 So that's 1/3 multiplied by 9 0:20:21.830,0:20:25.405 2/3 multiplied by 9 0:20:25.405,0:20:28.980 and another 2/3 multiplied by 9 0:20:28.980,0:20:32.390 and then 5/6 multiplied by 9 0:20:32.390,0:20:36.002 And we work out these[br]calculations and simplify 0:20:36.002,0:20:38.744 3 into 9 is 3 0:20:38.744,0:20:39.680 3 into 9 is 3 0:20:39.680,0:20:42.630 and then 2 threes are 6. 0:20:42.630,0:20:44.345 and this works out to be the same 0:20:44.345,0:20:47.650 which is 6 because it's the same [br]calculation 0:20:47.650,0:20:50.164 3 into 6 is 2 0:20:50.164,0:20:52.400 3 into 9 is 3 0:20:52.400,0:20:55.910 5 threes are 15 over 2 0:20:55.910,0:21:01.030 which works out to be 7 and a half 0:21:01.030,0:21:03.310 So our final answer 0:21:03.310,0:21:05.080 for the ingredients 0:21:05.080,0:21:10.160 is 3 cloves of garlic 0:21:10.160,0:21:13.570 6 ounces of chickpeas 0:21:13.570,0:21:16.254 combined with 6 tablespoonfuls[br]of olive oil 0:21:16.254,0:21:20.268 and 7 and a half fluid ounces 0:21:20.268,0:21:22.418 of tahini paste 0:21:22.418,0:21:28.000 And that makes enough[br]houmous for nine people. 0:21:28.000,0:21:31.465 In a similar way, 0:21:31.465,0:21:36.600 you can use this method in conversion [br]problems 0:21:36.600,0:21:41.210 If we had the conversion that 0:21:41.210,0:21:50.550 1 pound is the same as 1.65 euros 0:21:50.550,0:21:53.592 and I wanted to work out 0:21:53.592,0:21:59.680 what 50 euros would be in pence 0:21:59.680,0:22:01.790 to the nearest pence 0:22:01.790,0:22:07.090 What I like doing first is to work out 0:22:07.090,0:22:12.578 what 1 euro is in terms of pence 0:22:12.578,0:22:13.982 So I start with 0:22:13.982,0:22:22.370 1.65 euros equals 100 pence 0:22:22.370,0:22:26.592 One euro would then equal 0:22:26.592,0:22:33.404 100 divided by the 1.65 0:22:33.404,0:22:35.320 And then to work out 0:22:35.320,0:22:39.897 what the 50 euros would be 0:22:39.897,0:22:44.387 I multiply this by 50 0:22:44.387,0:22:48.920 as 100 over 1.65 multiplied by 50 0:22:48.920,0:22:52.908 And that is 5000 0:22:52.910,0:22:55.630 divided by the 1.65 0:22:55.630,0:22:57.891 Now I am not going to do this by[br]long division. 0:22:57.891,0:23:00.152 I'll use my calculator 0:23:00.152,0:23:07.342 and I just type in the relevant numbers 0:23:07.342,0:23:12.586 5000 divided by 1.65 0:23:12.586,0:23:14.484 equals 0:23:14.484,0:23:19.596 3030 point 3 0 point 3 0 repeating 0:23:19.596,0:23:27.698 So 50 euros equals 3030 pence 0:23:27.698,0:23:29.280 to the nearest pence. 0:23:29.280,0:23:37.510 Which is 30 pounds and 30p 0:23:37.510,0:23:40.930 Well, that's the session finished [br]now on ratio. 0:23:40.930,0:23:43.210 Before I finish finally, 0:23:43.210,0:23:45.490 what I'd like to do is just remind you 0:23:45.490,0:23:49.690 of a few key points about ratio. 0:23:49.690,0:23:51.670 First of all, what is a ratio? 0:23:51.670,0:23:54.010 Well a ratio is a way of comparing 0:23:54.010,0:23:56.810 quantities of a similar type 0:23:56.810,0:23:58.731 When you write a ratio down 0:23:58.731,0:24:01.500 you use whole numbers 0:24:01.500,0:24:04.980 separated by colon. 0:24:04.980,0:24:08.474 The numbers should be in the[br]same units. 0:24:08.474,0:24:10.091 If they're not, you convert them 0:24:10.091,0:24:11.428 to the same units 0:24:11.428,0:24:14.465 by using one or the other of the [br]units involved 0:24:14.465,0:24:17.050 Just use your nous basically. 0:24:17.050,0:24:21.380 And then you simplify as appropriate. 0:24:21.380,0:24:23.140 In calculations involved in ratio 0:24:23.140,0:24:29.610 it is useful to work out the total [br]number of parts 0:24:29.610,0:24:33.230 the quantity is divided up into 0:24:33.230,0:24:36.770 and then work out one part represents.