1 00:00:01,732 --> 00:00:05,300 Today's session is on ratio. 2 00:00:05,300 --> 00:00:07,521 I'm going to explain what a ratio is 3 00:00:07,569 --> 00:00:09,145 and how ratios are used 4 00:00:09,145 --> 00:00:11,175 in different situations. 5 00:00:11,275 --> 00:00:14,538 So to start off with what is a ratio? 6 00:00:14,980 --> 00:00:18,494 Well, a ratio is a way of comparing 7 00:00:18,508 --> 00:00:22,531 amounts of ingredients. 8 00:00:22,531 --> 00:00:25,690 Ratios can be used to compare 9 00:00:25,740 --> 00:00:30,110 weights, money, length and so on. 10 00:00:30,190 --> 00:00:33,200 So if we take this example 11 00:00:33,200 --> 00:00:34,990 we've got a model boat 12 00:00:34,990 --> 00:00:38,050 whose length is 1 metre 13 00:00:38,050 --> 00:00:40,820 and the real boat 14 00:00:40,830 --> 00:00:43,267 whose length is 25 metres. 15 00:00:43,290 --> 00:00:45,014 Then we say the ratio of the 16 00:00:45,014 --> 00:00:48,204 length of the model boat to the real boat 17 00:00:48,204 --> 00:00:51,880 is 1 to 25. 18 00:00:51,900 --> 00:00:54,770 Notice we've just used the numbers 19 00:00:54,770 --> 00:00:57,670 without the unit (metres) 20 00:00:57,670 --> 00:00:59,915 and we've used the colon 21 00:00:59,915 --> 00:01:02,882 to represent the ratio. 22 00:01:03,030 --> 00:01:06,064 Ratios are used to describe quantities 23 00:01:06,064 --> 00:01:08,984 of ingredients in mixtures. 24 00:01:08,984 --> 00:01:11,966 For example, in the pharmaceutical trade 25 00:01:11,966 --> 00:01:14,360 when you're making medicines, 26 00:01:14,360 --> 00:01:16,642 or in the building trade 27 00:01:16,642 --> 00:01:19,410 when you are making cement or mortar, 28 00:01:19,410 --> 00:01:22,486 or at home when you're making up food 29 00:01:22,486 --> 00:01:26,546 you use different quantities in different proportions 30 00:01:26,546 --> 00:01:29,000 and if you don't get them right 31 00:01:29,000 --> 00:01:30,947 then things go wrong. 32 00:01:30,947 --> 00:01:33,830 So it's very important to know 33 00:01:33,830 --> 00:01:39,358 what quantities you've got and in what ratio. 34 00:01:39,358 --> 00:01:41,820 So for example, if we have 35 00:01:41,820 --> 00:01:45,630 mortar for building brick walls. 36 00:01:45,630 --> 00:01:47,550 Mortar is made up by mixing 37 00:01:47,550 --> 00:01:52,778 two parts of cement to seven parts of gravel by volume 38 00:01:52,778 --> 00:01:57,880 and we write that ratio as 2 to 7. 39 00:01:57,880 --> 00:02:00,410 Again notice we've used 40 00:02:00,410 --> 00:02:03,504 the numbers without the units 41 00:02:03,504 --> 00:02:07,268 and the colon to represent the ratio. 42 00:02:07,268 --> 00:02:09,304 When we're making pastry at home, 43 00:02:09,304 --> 00:02:11,381 when we're making pies and tarts, 44 00:02:11,381 --> 00:02:14,157 we mix four ounces of flour 45 00:02:14,157 --> 00:02:17,210 with two ounces of margarine 46 00:02:17,210 --> 00:02:23,040 And that ratio would be 4 to 2. 47 00:02:23,040 --> 00:02:24,309 But in this case, 48 00:02:24,309 --> 00:02:25,899 if you look at the numbers, 49 00:02:25,899 --> 00:02:28,679 they've got a factor of two in common 50 00:02:28,679 --> 00:02:31,085 So we can simplify ratios just in the same 51 00:02:31,085 --> 00:02:33,520 way as we simplify fractions. 52 00:02:33,520 --> 00:02:36,495 We can divide by the common factor, 53 00:02:36,495 --> 00:02:39,280 so we divide 4 by 2 54 00:02:39,280 --> 00:02:42,530 and 2 by 2 to give 1. 55 00:02:42,530 --> 00:02:48,570 So 2 to 1 is the simplest form of the ratio 4 to 2. 56 00:02:48,570 --> 00:02:52,760 But both of the ratios are equivalent, 57 00:02:52,760 --> 00:03:01,920 because the relationship of the numbers involved stays the same. 58 00:03:01,920 --> 00:03:05,620 If we take this example 59 00:03:05,620 --> 00:03:09,860 250 to 150 60 00:03:09,860 --> 00:03:12,580 We can simplify this ratio. 61 00:03:12,580 --> 00:03:15,530 We divide both by 10 62 00:03:15,530 --> 00:03:19,502 to get 25 to 15 63 00:03:19,502 --> 00:03:22,342 And then we can divide both by 5 64 00:03:22,342 --> 00:03:24,813 5 into 25 will give me 5 65 00:03:24,813 --> 00:03:28,276 5 into 15 will give me 3 66 00:03:28,276 --> 00:03:31,986 We can't divide anymore, 67 00:03:31,986 --> 00:03:34,262 so this is the simplest form. 68 00:03:34,262 --> 00:03:37,864 5 to 3 the simplest form of 69 00:03:37,864 --> 00:03:41,467 the ratio 250 to 150. 70 00:03:41,467 --> 00:03:44,310 But all three ratios are equivalent 71 00:03:44,310 --> 00:03:46,881 because the relationship of the numbers 72 00:03:46,881 --> 00:03:50,070 is exactly the same. 73 00:03:50,070 --> 00:03:53,655 In the same way, we can actually 74 00:03:53,655 --> 00:04:00,110 simplify this ratio: 1 to 1.5 75 00:04:00,110 --> 00:04:04,494 In ratios we like to have whole numbers 76 00:04:04,494 --> 00:04:06,094 and in this ratio you can see 77 00:04:06,094 --> 00:04:07,650 that we have a decimal. 78 00:04:07,650 --> 00:04:09,471 To get rid of the decimal 79 00:04:09,471 --> 00:04:11,342 we can multiply both sides of the 80 00:04:11,342 --> 00:04:12,732 ratio by 10 81 00:04:12,732 --> 00:04:16,000 and we still have an equivalent ratio. 82 00:04:16,000 --> 00:04:18,020 Because, again, the relationship 83 00:04:18,020 --> 00:04:19,860 between the numbers is the same. 84 00:04:19,860 --> 00:04:22,588 So we multiply the 1 by 10 85 00:04:22,588 --> 00:04:24,042 you get 10 86 00:04:24,042 --> 00:04:25,536 Multiply 1.5 by 10 87 00:04:25,536 --> 00:04:27,830 you get 15 88 00:04:27,830 --> 00:04:30,288 10 to 15 we can simplify that. 89 00:04:30,288 --> 00:04:33,930 Divide both sides by 5. 90 00:04:33,930 --> 00:04:36,378 5 into 10 gives me 2 91 00:04:36,378 --> 00:04:40,350 5 into 15 will give me 3 92 00:04:40,350 --> 00:04:42,499 2 to 3 is the simplest form 93 00:04:42,499 --> 00:04:46,820 of the ratio 1 to 1.5 94 00:04:46,820 --> 00:04:49,945 Similarly, when we have fractions 95 00:04:49,945 --> 00:04:53,780 If we had this ratio: 96 00:04:53,780 --> 00:04:57,630 a quarter to five-eighths, 97 00:04:57,630 --> 00:04:59,675 it just doesn't look right. 98 00:04:59,675 --> 00:05:01,590 We want to express that ratio 99 00:05:01,590 --> 00:05:03,265 in terms of whole numbers 100 00:05:03,265 --> 00:05:04,770 in its simplest form. 101 00:05:04,770 --> 00:05:10,158 So what we do first is we write both as fractions over 8 102 00:05:10,158 --> 00:05:11,610 in terms of eighths. 103 00:05:11,610 --> 00:05:17,110 A quarter is two eighths 104 00:05:17,110 --> 00:05:21,604 and now the ratio is two eighths to five eighths. 105 00:05:21,604 --> 00:05:23,798 And now it's dead simple 106 00:05:23,798 --> 00:05:27,612 All we have to say is that is 2 to 5. 107 00:05:27,612 --> 00:05:30,656 We multiply both ratios by 8 108 00:05:30,656 --> 00:05:33,470 And 2 to 5 is the simplest ratio 109 00:05:33,470 --> 00:05:37,942 for the ratio a quarter to five-eighths. 110 00:05:37,942 --> 00:05:40,484 But again all three ratios are 111 00:05:40,484 --> 00:05:42,902 equivalent because the relationship 112 00:05:42,902 --> 00:05:45,870 between the numbers is exactly the same. 113 00:05:45,870 --> 00:05:47,950 Moving on, 114 00:05:47,950 --> 00:05:51,040 we must have the numbers in the ratios 115 00:05:51,040 --> 00:05:53,368 having the same units. 116 00:05:53,368 --> 00:05:55,317 So if we have this ratio 117 00:05:55,317 --> 00:06:02,660 15 pence to 3 pounds, 118 00:06:02,660 --> 00:06:07,296 we cannot say that the ratio is 15 to 3 119 00:06:07,296 --> 00:06:12,550 and then simplify that to 5 to 1 120 00:06:12,550 --> 00:06:15,799 Because we didn't start off with 121 00:06:15,799 --> 00:06:18,538 the numbers having the same units 122 00:06:18,538 --> 00:06:21,748 the relationship between the numbers is not the same, 123 00:06:21,748 --> 00:06:23,927 because as I say, 124 00:06:23,927 --> 00:06:26,566 we didn't start off with these numbers 125 00:06:26,566 --> 00:06:29,080 having the same units. 126 00:06:29,080 --> 00:06:31,378 So we must convert the numbers 127 00:06:31,378 --> 00:06:33,097 to the same units 128 00:06:33,097 --> 00:06:36,766 and we choose whichever unit is appropriate 129 00:06:36,766 --> 00:06:38,936 In this case, it's obvious we must 130 00:06:38,936 --> 00:06:41,390 change them to pence. 131 00:06:41,390 --> 00:06:48,870 So we say the ratio is 15 to 300 132 00:06:48,870 --> 00:06:51,910 as there's 300 pence for 3 pounds 133 00:06:51,910 --> 00:06:55,000 and then we simplify as normal. 134 00:06:55,000 --> 00:06:57,100 We divide both sides by five. 135 00:06:57,100 --> 00:06:59,430 5 into 15 is 3 136 00:06:59,430 --> 00:07:02,195 5 into 300 is 60 137 00:07:02,195 --> 00:07:05,560 And then we can divide by 3 138 00:07:05,560 --> 00:07:07,477 3 into 3 is 1 139 00:07:07,477 --> 00:07:10,300 3 into 60 is 20 140 00:07:10,300 --> 00:07:14,580 And notice these two ratios are 141 00:07:14,580 --> 00:07:16,850 not the same, they're vastly different. 142 00:07:16,850 --> 00:07:18,666 They're not equivalent because 143 00:07:18,666 --> 00:07:20,932 the relationship between the numbers 144 00:07:20,932 --> 00:07:23,630 is not the same. 145 00:07:23,630 --> 00:07:25,754 So it's very important in ratios 146 00:07:25,754 --> 00:07:28,478 that you start with numbers 147 00:07:28,478 --> 00:07:30,740 that have the same units. 148 00:07:30,740 --> 00:07:32,011 If they're not, 149 00:07:32,011 --> 00:07:34,053 then you convert them to the same units 150 00:07:34,053 --> 00:07:42,431 and then simplify if appropriate. 151 00:07:42,431 --> 00:07:44,135 As I said before, 152 00:07:44,135 --> 00:07:45,990 ratios are extremely useful 153 00:07:45,990 --> 00:07:48,730 in lots of different circumstances. 154 00:07:48,730 --> 00:07:50,590 They can be used to divide and 155 00:07:50,590 --> 00:07:53,850 share amounts of different quantities 156 00:07:53,850 --> 00:07:57,550 like money, weights, and so on. 157 00:07:57,550 --> 00:08:00,058 So if I take this problem 158 00:08:00,058 --> 00:08:02,906 just say I had an inheritance of £64,000 159 00:08:02,906 --> 00:08:07,180 and it was to be shared between two people 160 00:08:07,180 --> 00:08:09,810 Mrs Sharp and Mr West 161 00:08:09,810 --> 00:08:12,960 in the ratio 5 to 3 162 00:08:12,960 --> 00:08:14,822 What I want you to do is work out 163 00:08:14,822 --> 00:08:18,290 what each one of those gets. 164 00:08:18,290 --> 00:08:21,470 And that's a lot of information to take in 165 00:08:21,470 --> 00:08:22,590 so what I do first is 166 00:08:22,590 --> 00:08:26,010 I start off with a diagram 167 00:08:26,010 --> 00:08:30,745 I've got the total inheritance of £64,000 168 00:08:30,745 --> 00:08:33,632 and I divide it 169 00:08:33,632 --> 00:08:39,770 between Mrs Sharp 170 00:08:39,770 --> 00:08:42,942 and Mr West 171 00:08:42,942 --> 00:08:48,240 in the ratio 5 to 3 172 00:08:48,240 --> 00:08:50,370 And we want to work out 173 00:08:50,370 --> 00:08:52,660 what each gets. 174 00:08:52,660 --> 00:08:55,306 What we do first is we work out 175 00:08:55,306 --> 00:08:57,952 the total number of parts that 176 00:08:57,952 --> 00:09:02,370 their inheritance is split up into. 177 00:09:02,370 --> 00:09:04,976 Well, we use the ratio for that. 178 00:09:04,976 --> 00:09:07,583 It's five parts for Mrs Sharp 179 00:09:07,583 --> 00:09:09,989 and three parts for Mr West 180 00:09:09,989 --> 00:09:12,395 so altogether that is eight parts 181 00:09:12,395 --> 00:09:15,561 Then we work out what the total value 182 00:09:15,561 --> 00:09:18,728 of one part of the inheritance would be. 183 00:09:18,728 --> 00:09:22,818 Now we know that the total inheritance 184 00:09:22,818 --> 00:09:24,580 is £64,000 185 00:09:24,580 --> 00:09:27,450 so one part 186 00:09:27,450 --> 00:09:35,620 equals 64,000 divided by 8 187 00:09:35,620 --> 00:09:41,060 and that is £8000 188 00:09:41,060 --> 00:09:43,280 And then the rest is easy. 189 00:09:43,280 --> 00:09:47,970 All we have to do now is take Mrs Sharp 190 00:09:47,970 --> 00:09:54,416 and she has five parts 191 00:09:54,416 --> 00:10:01,008 and that is 5 multiplied by £8000 192 00:10:01,008 --> 00:10:06,698 which works out to be £40,000 193 00:10:06,698 --> 00:10:11,740 And then Mr West 194 00:10:11,740 --> 00:10:16,210 he has three parts 195 00:10:16,210 --> 00:10:21,870 and that is 3 multiplied by £8000 196 00:10:21,870 --> 00:10:27,536 which is £24,000 197 00:10:27,536 --> 00:10:29,496 An awful lot of money! 198 00:10:29,496 --> 00:10:31,346 But what if I made a mistake? 199 00:10:31,346 --> 00:10:33,602 How can I check my two answers? 200 00:10:33,602 --> 00:10:36,828 How can I check that Mrs Sharp did get £40,000 201 00:10:36,828 --> 00:10:39,285 and Mr West got £24,000? 202 00:10:39,285 --> 00:10:41,742 Well a very simple check 203 00:10:41,742 --> 00:10:45,799 is to add up these two values 204 00:10:45,799 --> 00:10:47,186 and if they add together 205 00:10:47,186 --> 00:10:48,924 to make up the total inheritance 206 00:10:48,924 --> 00:10:52,772 then we think we've done our calculations properly. 207 00:10:52,772 --> 00:10:57,844 So a quick check: 208 00:10:57,844 --> 00:11:13,130 £40,000 plus 24,000 does equal £64,000 209 00:11:13,130 --> 00:11:14,930 For a complete check though 210 00:11:14,930 --> 00:11:17,140 we can take the two amounts 211 00:11:17,140 --> 00:11:20,710 and see that they will actually make an equivalent ratio 212 00:11:20,710 --> 00:11:23,770 to the ratio that we started off with 5:3 213 00:11:23,770 --> 00:11:32,680 So if we take our 40,000 that Mrs Sharp got 214 00:11:32,680 --> 00:11:36,864 and then the 24,000 that Mr West got 215 00:11:36,864 --> 00:11:38,796 and cancel them down, 216 00:11:38,796 --> 00:11:41,218 we cancel by 1000 217 00:11:41,218 --> 00:11:43,789 then we cancel by 4 218 00:11:43,789 --> 00:11:47,630 so that would make 10 to 6 219 00:11:47,630 --> 00:11:50,081 and then cancel by 2 220 00:11:50,081 --> 00:11:53,613 so that will make 5 to 3 221 00:11:53,613 --> 00:11:55,731 We do actually get the same ratio 222 00:11:55,731 --> 00:12:00,239 that we started off with. 223 00:12:00,239 --> 00:12:02,629 We're going to do another example. 224 00:12:02,629 --> 00:12:05,880 It's an example which involves another 225 00:12:05,880 --> 00:12:08,950 mixture: making concrete. 226 00:12:08,950 --> 00:12:13,850 And with this, concrete is made by mixing 227 00:12:13,850 --> 00:12:17,140 gravel, sand and cement 228 00:12:17,140 --> 00:12:21,460 in the ratio 3 to 2 to 1 229 00:12:21,460 --> 00:12:24,871 and in this problem we start with concrete. 230 00:12:24,871 --> 00:12:28,282 The amount of concrete that we are going to make 231 00:12:28,282 --> 00:12:31,260 will be 12 cubic metres. 232 00:12:31,260 --> 00:12:33,942 And what I want to work out 233 00:12:33,942 --> 00:12:36,264 is how much gravel will be needed 234 00:12:36,264 --> 00:12:40,470 to make 12 cubic metres of concrete. 235 00:12:40,470 --> 00:12:46,080 So we start with drawing a diagram 236 00:12:46,080 --> 00:12:49,934 and that represents the concrete 237 00:12:49,934 --> 00:12:51,385 and we know we want to make 238 00:12:51,385 --> 00:12:55,976 12 cubic metres of concrete 239 00:12:55,976 --> 00:12:58,530 and we know it's mixed 240 00:12:58,530 --> 00:13:09,840 by mixing gravel, sand and cement 241 00:13:09,840 --> 00:13:16,950 in the ratio 3 to 2 to 1 242 00:13:16,950 --> 00:13:19,182 And we want to work out 243 00:13:19,182 --> 00:13:23,844 the amount of concrete for 12 cubic metres 244 00:13:23,844 --> 00:13:24,916 Well, first of all, 245 00:13:24,916 --> 00:13:27,798 we work out the total number of parts 246 00:13:27,798 --> 00:13:31,024 our concrete is divided up into 247 00:13:31,024 --> 00:13:33,620 and we use our ratio for that. 248 00:13:33,620 --> 00:13:43,330 It's 3 + 2 + 1 and that equals 6 parts 249 00:13:43,330 --> 00:13:45,298 Now our concrete is divided up 250 00:13:45,298 --> 00:13:47,188 into six parts 251 00:13:47,188 --> 00:13:50,050 So one part must equal 252 00:13:50,050 --> 00:13:56,092 our 12 cubic metres divided by 6 253 00:13:56,092 --> 00:14:01,214 so that's 12 divided by 6 cubic metres 254 00:14:01,214 --> 00:14:05,980 which works out to be 2 cubic metres. 255 00:14:05,980 --> 00:14:07,780 Now we want to work out 256 00:14:07,780 --> 00:14:10,720 how much gravel is needed. 257 00:14:10,720 --> 00:14:13,854 Gravel is represented by 3 parts 258 00:14:13,854 --> 00:14:19,960 so gravel, the amount that we want 259 00:14:19,960 --> 00:14:27,372 equals 3 times 2 cubic metres 260 00:14:27,372 --> 00:14:30,690 which is 6 cubic metres 261 00:14:30,690 --> 00:14:32,362 and that's our answer. 262 00:14:32,362 --> 00:14:34,034 But it's always good to check 263 00:14:34,034 --> 00:14:36,424 and so we try and do the calculation 264 00:14:36,424 --> 00:14:38,510 in a different way 265 00:14:38,510 --> 00:14:40,722 and the way that I'd like to do it 266 00:14:40,722 --> 00:14:42,425 is using fractions. 267 00:14:42,425 --> 00:14:45,135 If we go back to the original diagram 268 00:14:45,135 --> 00:14:50,026 we know that gravel is represented by 3 parts 269 00:14:50,026 --> 00:14:52,863 and the total is 6 270 00:14:52,863 --> 00:14:57,270 so gravel is a half of the total volume 271 00:14:57,270 --> 00:14:59,977 and a half of 12 cubic metres is 272 00:14:59,977 --> 00:15:02,685 6 cubic metres 273 00:15:02,685 --> 00:15:04,637 so our answer is right 274 00:15:04,637 --> 00:15:06,540 we've done a check. 275 00:15:06,540 --> 00:15:11,680 But what if we did a similar problem 276 00:15:11,680 --> 00:15:13,120 and we want to start off 277 00:15:13,120 --> 00:15:15,705 with mixing our concrete 278 00:15:15,705 --> 00:15:18,290 using gravel, sand, and cement 279 00:15:18,290 --> 00:15:23,602 but we don't know the final volume of the concrete 280 00:15:23,602 --> 00:15:26,813 but we do know that we are given 281 00:15:26,813 --> 00:15:29,605 6 cubic metres of sand 282 00:15:29,605 --> 00:15:33,860 and an unlimited supply of gravel and cement. 283 00:15:33,860 --> 00:15:36,332 How much concrete can we make then 284 00:15:36,332 --> 00:15:39,900 if we've got 6 cubic metres of sand? 285 00:15:39,900 --> 00:15:44,292 Alright, we'll start the question or the problem 286 00:15:44,292 --> 00:15:47,270 with a diagram. 287 00:15:47,270 --> 00:15:52,556 We know that the mixture is still the same. 288 00:15:52,556 --> 00:15:54,805 We use the same ratio 289 00:15:54,805 --> 00:15:58,304 gravel to sand to cement 290 00:15:58,304 --> 00:16:04,140 as 3 to 2 to 1 291 00:16:04,140 --> 00:16:05,369 And we know that 292 00:16:05,369 --> 00:16:09,288 we have 6 cubic metres of sand 293 00:16:09,288 --> 00:16:12,174 but we want to work out 294 00:16:12,174 --> 00:16:15,060 how much concrete we can make 295 00:16:15,060 --> 00:16:17,280 with that amount of sand 296 00:16:17,280 --> 00:16:20,580 and unlimited amounts of the other two. 297 00:16:20,580 --> 00:16:23,496 Well, the number of parts that 298 00:16:23,496 --> 00:16:29,210 the concrete is divided up into is still 6 299 00:16:29,210 --> 00:16:32,020 But we know that 2 parts 300 00:16:32,020 --> 00:16:35,018 is 6 cubic metres 301 00:16:35,018 --> 00:16:37,216 because that's what we're given 302 00:16:37,216 --> 00:16:42,090 so 2 parts equals 6 cubic metres. 303 00:16:42,090 --> 00:16:45,130 So 1 part 304 00:16:45,130 --> 00:16:49,440 equals 6 divided by 2 305 00:16:49,440 --> 00:16:54,480 which is 3 cubic metres 306 00:16:54,480 --> 00:16:56,592 Now the total number of parts of 307 00:16:56,592 --> 00:16:58,705 the concrete is divided up into is 6 308 00:16:58,705 --> 00:17:04,425 So the amount of concrete that is produced 309 00:17:04,425 --> 00:17:08,520 is 6 times 3 cubic metres 310 00:17:08,520 --> 00:17:12,470 and that is 18 cubic metres 311 00:17:12,470 --> 00:17:14,651 Again, it's good to check our answer 312 00:17:14,651 --> 00:17:16,302 and we'll do it in a different way 313 00:17:16,302 --> 00:17:18,670 and we'll use fractions again this time. 314 00:17:18,670 --> 00:17:22,100 We look at what we were given. 315 00:17:22,100 --> 00:17:24,400 Sand is represented by 2 parts 316 00:17:24,400 --> 00:17:29,270 and we know it has a volume of 6 cubic metres. 317 00:17:29,270 --> 00:17:34,440 Altogether, there are 6 parts for our concrete. 318 00:17:34,440 --> 00:17:36,780 So the fraction that represents sand 319 00:17:36,780 --> 00:17:39,680 is 2 over 6, which is a third. 320 00:17:39,680 --> 00:17:44,244 So a third of the total amount is 6 cubic metres 321 00:17:44,244 --> 00:17:48,770 So the whole amount of concrete must be 322 00:17:48,770 --> 00:17:51,015 3 times 6 cubic metres 323 00:17:51,015 --> 00:17:54,281 which is 18 cubic metres 324 00:17:54,281 --> 00:17:57,910 Here's another ratio problem involved with ingredients 325 00:17:57,910 --> 00:18:00,254 but this time the ingredients are to make 326 00:18:00,254 --> 00:18:03,299 the Greek food houmous. 327 00:18:03,300 --> 00:18:07,630 It's usually given as a starter 328 00:18:07,630 --> 00:18:10,520 and there are four ingredients: 329 00:18:10,520 --> 00:18:16,290 two cloves of garlic 330 00:18:16,290 --> 00:18:17,714 are combined with 331 00:18:17,714 --> 00:18:24,310 four ounces of chickpeas 332 00:18:24,310 --> 00:18:32,020 and four tablespoonfuls of olive oil. 333 00:18:32,020 --> 00:18:35,136 I sound a little bit like Delia Smith at this point 334 00:18:35,136 --> 00:18:36,955 and the final secret ingredient is 335 00:18:36,955 --> 00:18:46,414 the 5 fluid ounces of tahini paste. 336 00:18:46,414 --> 00:18:48,378 Now when you combine these ingredients 337 00:18:48,378 --> 00:18:54,970 together that's enough for six people 338 00:18:54,970 --> 00:18:57,030 But what if I want to make houmous 339 00:18:57,030 --> 00:18:58,700 for nine people? 340 00:18:58,700 --> 00:19:02,630 What amounts do I have of these four ingredients 341 00:19:02,630 --> 00:19:05,798 to make it for nine people? 342 00:19:05,798 --> 00:19:08,306 Well, we start off with what we've got 343 00:19:08,306 --> 00:19:10,107 and what we know 344 00:19:10,107 --> 00:19:12,569 We've got 2 cloves of garlic 345 00:19:12,569 --> 00:19:15,637 with 4 ounces of chickpeas 346 00:19:15,637 --> 00:19:19,130 4 tablespoonsful of olive oil 347 00:19:19,130 --> 00:19:24,261 and 5 fluid ounces of tahini paste 348 00:19:24,261 --> 00:19:29,283 and that makes enough for six people 349 00:19:29,283 --> 00:19:32,634 What I do next is that I work out 350 00:19:32,634 --> 00:19:34,587 what each of those ingredients 351 00:19:34,587 --> 00:19:37,630 would be for one person. 352 00:19:37,630 --> 00:19:39,203 So I have to divide 353 00:19:39,203 --> 00:19:41,710 each of those numbers by 6 354 00:19:41,710 --> 00:19:45,105 So that's 2 over 6 355 00:19:45,105 --> 00:19:46,802 4 over 6 356 00:19:46,802 --> 00:19:47,651 4 over 6 357 00:19:47,651 --> 00:19:51,220 and 5 over 6 358 00:19:51,220 --> 00:19:54,025 and then we cancel down if we can 359 00:19:54,025 --> 00:19:55,290 In this case we can 360 00:19:55,290 --> 00:19:57,930 that's one third. 361 00:19:57,930 --> 00:20:03,190 Cancel four sixths to two thirds. 362 00:20:03,190 --> 00:20:05,710 And this will be the same. 363 00:20:05,710 --> 00:20:07,873 And the last one just remains the same: 364 00:20:07,873 --> 00:20:09,269 five sixths 365 00:20:09,269 --> 00:20:11,416 And now it's dead easy to work out 366 00:20:11,416 --> 00:20:15,230 what amounts we need for nine people. 367 00:20:15,230 --> 00:20:18,530 All we have to do is multiply by 9 368 00:20:18,530 --> 00:20:21,830 So that's 1/3 multiplied by 9 369 00:20:21,830 --> 00:20:25,405 2/3 multiplied by 9 370 00:20:25,405 --> 00:20:28,980 and another 2/3 multiplied by 9 371 00:20:28,980 --> 00:20:32,390 and then 5/6 multiplied by 9 372 00:20:32,390 --> 00:20:36,002 And we work out these calculations and simplify 373 00:20:36,002 --> 00:20:38,744 3 into 9 is 3 374 00:20:38,744 --> 00:20:39,680 3 into 9 is 3 375 00:20:39,680 --> 00:20:42,630 and then 2 threes are 6. 376 00:20:42,630 --> 00:20:44,345 and this works out to be the same 377 00:20:44,345 --> 00:20:47,650 which is 6 because it's the same calculation 378 00:20:47,650 --> 00:20:50,164 3 into 6 is 2 379 00:20:50,164 --> 00:20:52,400 3 into 9 is 3 380 00:20:52,400 --> 00:20:55,910 5 threes are 15 over 2 381 00:20:55,910 --> 00:21:01,030 which works out to be 7 and a half 382 00:21:01,030 --> 00:21:03,310 So our final answer 383 00:21:03,310 --> 00:21:05,080 for the ingredients 384 00:21:05,080 --> 00:21:10,160 is 3 cloves of garlic 385 00:21:10,160 --> 00:21:13,570 6 ounces of chickpeas 386 00:21:13,570 --> 00:21:16,254 combined with 6 tablespoonfuls of olive oil 387 00:21:16,254 --> 00:21:20,268 and 7 and a half fluid ounces 388 00:21:20,268 --> 00:21:22,418 of tahini paste 389 00:21:22,418 --> 00:21:28,000 And that makes enough houmous for nine people. 390 00:21:28,000 --> 00:21:31,465 In a similar way, 391 00:21:31,465 --> 00:21:36,600 you can use this method in conversion problems 392 00:21:36,600 --> 00:21:41,210 If we had the conversion that 393 00:21:41,210 --> 00:21:50,550 1 pound is the same as 1.65 euros 394 00:21:50,550 --> 00:21:53,592 and I wanted to work out 395 00:21:53,592 --> 00:21:59,680 what 50 euros would be in pence 396 00:21:59,680 --> 00:22:01,790 to the nearest pence 397 00:22:01,790 --> 00:22:07,090 What I like doing first is to work out 398 00:22:07,090 --> 00:22:12,578 what 1 euro is in terms of pence 399 00:22:12,578 --> 00:22:13,982 So I start with 400 00:22:13,982 --> 00:22:22,370 1.65 euros equals 100 pence 401 00:22:22,370 --> 00:22:26,592 One euro would then equal 402 00:22:26,592 --> 00:22:33,404 100 divided by the 1.65 403 00:22:33,404 --> 00:22:35,320 And then to work out 404 00:22:35,320 --> 00:22:39,897 what the 50 euros would be 405 00:22:39,897 --> 00:22:44,387 I multiply this by 50 406 00:22:44,387 --> 00:22:48,920 as 100 over 1.65 multiplied by 50 407 00:22:48,920 --> 00:22:52,908 And that is 5000 408 00:22:52,910 --> 00:22:55,630 divided by the 1.65 409 00:22:55,630 --> 00:22:57,891 Now I am not going to do this by long division. 410 00:22:57,891 --> 00:23:00,152 I'll use my calculator 411 00:23:00,152 --> 00:23:07,342 and I just type in the relevant numbers 412 00:23:07,342 --> 00:23:12,586 5000 divided by 1.65 413 00:23:12,586 --> 00:23:14,484 equals 414 00:23:14,484 --> 00:23:19,596 3030 point 3 0 point 3 0 repeating 415 00:23:19,596 --> 00:23:27,698 So 50 euros equals 3030 pence 416 00:23:27,698 --> 00:23:29,280 to the nearest pence. 417 00:23:29,280 --> 00:23:37,510 Which is 30 pounds and 30p 418 00:23:37,510 --> 00:23:40,930 Well, that's the session finished now on ratio. 419 00:23:40,930 --> 00:23:43,210 Before I finish finally, 420 00:23:43,210 --> 00:23:45,490 what I'd like to do is just remind you 421 00:23:45,490 --> 00:23:49,690 of a few key points about ratio. 422 00:23:49,690 --> 00:23:51,670 First of all, what is a ratio? 423 00:23:51,670 --> 00:23:54,010 Well a ratio is a way of comparing 424 00:23:54,010 --> 00:23:56,810 quantities of a similar type 425 00:23:56,810 --> 00:23:58,731 When you write a ratio down 426 00:23:58,731 --> 00:24:01,500 you use whole numbers 427 00:24:01,500 --> 00:24:04,980 separated by colon. 428 00:24:04,980 --> 00:24:08,474 The numbers should be in the same units. 429 00:24:08,474 --> 00:24:10,091 If they're not, you convert them 430 00:24:10,091 --> 00:24:11,428 to the same units 431 00:24:11,428 --> 00:24:14,465 by using one or the other of the units involved 432 00:24:14,465 --> 00:24:17,050 Just use your nous basically. 433 00:24:17,050 --> 00:24:21,380 And then you simplify as appropriate. 434 00:24:21,380 --> 00:24:23,140 In calculations involved in ratio 435 00:24:23,140 --> 00:24:29,610 it is useful to work out the total number of parts 436 00:24:29,610 --> 00:24:33,230 the quantity is divided up into 437 00:24:33,230 --> 00:24:36,770 and then work out one part represents.