WEBVTT 00:00:00.690 --> 00:00:01.915 - [Voiceover] We're told that Burger Barn 00:00:01.915 --> 00:00:05.734 makes dipping sauce by mixing two spoonfuls of honey 00:00:05.734 --> 00:00:09.313 with one half spoonful of mustard. 00:00:09.313 --> 00:00:11.108 Sandwich Town makes dipping sauce 00:00:11.108 --> 00:00:13.164 by mixing four spoonfuls of honey 00:00:13.164 --> 00:00:16.373 with one spoonful of mustard. 00:00:16.373 --> 00:00:21.362 Which dipping sauce has a stronger mustard flavor? 00:00:21.362 --> 00:00:22.945 So pause this video and see if you can 00:00:22.945 --> 00:00:25.108 work through that on your own. 00:00:25.108 --> 00:00:26.772 All right, now let's think about the ratios 00:00:26.772 --> 00:00:30.831 of honey to mustard at each of these restaurants. 00:00:30.831 --> 00:00:34.159 So first let's think about the scenario with Burger Barn. 00:00:34.159 --> 00:00:37.658 So I'll just say BB for short, for Burger Burn. 00:00:37.658 --> 00:00:39.974 So they have two spoonfuls of honey 00:00:39.974 --> 00:00:42.376 for every one half spoonful of mustard, 00:00:42.376 --> 00:00:44.793 so the ratio of honey to mustard 00:00:44.793 --> 00:00:48.710 in terms of spoonfuls is two spoonfuls of honey 00:00:50.121 --> 00:00:53.371 for every one half spoonful of mustard, 00:00:55.298 --> 00:00:58.618 so this is the ratio of honey to mustard. 00:00:58.618 --> 00:00:59.679 Let me write this. 00:00:59.679 --> 00:01:04.672 This is honey, and this right over here is mustard. 00:01:04.672 --> 00:01:08.839 Now, let's look at Sandwich Town, so I'll call that ST. 00:01:10.626 --> 00:01:12.083 So Sandwich Town makes dipping sauce 00:01:12.083 --> 00:01:14.552 by having four spoonfuls of honey 00:01:14.552 --> 00:01:16.894 for every one spoonful of mustard. 00:01:16.894 --> 00:01:18.996 So the ratio of honey to mustard 00:01:18.996 --> 00:01:22.599 is four spoonfuls to one spoonful, 00:01:22.599 --> 00:01:26.682 so once again, that is honey and that is mustard. 00:01:29.251 --> 00:01:31.870 Now, can we make these equivalent ratios 00:01:31.870 --> 00:01:33.577 or can we compare them somehow? 00:01:33.577 --> 00:01:35.081 Well, let's see. 00:01:35.081 --> 00:01:37.852 We have one half spoonful of mustard here. 00:01:37.852 --> 00:01:39.602 We have one spoon of mustard here, 00:01:39.602 --> 00:01:41.342 so what if we multiplied both the mustard 00:01:41.342 --> 00:01:44.380 and the honey spoonfuls by two? 00:01:44.380 --> 00:01:45.669 That still would be an equivalent ratio 00:01:45.669 --> 00:01:48.053 because we're multiplying by the same amount. 00:01:48.053 --> 00:01:51.934 So if we multiply by two in both situations, 00:01:51.934 --> 00:01:54.571 you have four spoonfuls of honey 00:01:54.571 --> 00:01:57.404 for every one spoonful of mustard. 00:01:59.044 --> 00:02:00.460 Well, that's the exact same ratio 00:02:00.460 --> 00:02:02.157 that we have at Sandwich Town. 00:02:02.157 --> 00:02:04.465 So it actually turns out that they have 00:02:04.465 --> 00:02:07.960 the same concentration of mustard. 00:02:07.960 --> 00:02:11.929 They have the same ratio of honey to mustard. 00:02:11.929 --> 00:02:15.174 Four spoonfuls of honey for every spoonful of mustard 00:02:15.174 --> 00:02:17.434 in either situation. 00:02:17.434 --> 00:02:18.820 Let's do another example. 00:02:18.820 --> 00:02:22.987 So here, we are asked or we are told, we are told, 00:02:25.817 --> 00:02:28.674 Patrick's favorite shade of purple paint 00:02:28.674 --> 00:02:31.343 is made with four ounces of blue paint, 00:02:31.343 --> 00:02:35.510 so underline that in blue, four ounces of blue paint, 00:02:36.784 --> 00:02:39.312 for every three ounces of red paint, 00:02:39.312 --> 00:02:41.610 for every three ounces of red paint. 00:02:41.610 --> 00:02:44.280 So the ratio of blue paint to red paint 00:02:44.280 --> 00:02:47.947 is four ounces of blue, four ounces of blue, 00:02:50.063 --> 00:02:54.063 for every three ounces of red, so four to three. 00:02:55.197 --> 00:02:56.825 Which of the following paint mixtures 00:02:56.825 --> 00:03:00.223 will create the same shade of purple? 00:03:00.223 --> 00:03:01.623 All right, pause this video 00:03:01.623 --> 00:03:04.826 and see if you can figure it out on your own. 00:03:04.826 --> 00:03:06.559 So this is three ounces of blue paint 00:03:06.559 --> 00:03:08.702 mixed with four ounces of red paint. 00:03:08.702 --> 00:03:12.369 Well, this is a ratio here of three to four, 00:03:14.804 --> 00:03:16.739 and even though it's dealing with the same numbers, 00:03:16.739 --> 00:03:18.023 this is a different ratio. 00:03:18.023 --> 00:03:19.238 The order matters. 00:03:19.238 --> 00:03:22.318 This is four ounces of blue for every three ounces of red. 00:03:22.318 --> 00:03:24.489 This is saying three ounces of blue 00:03:24.489 --> 00:03:29.110 for every four ounces of red, so we could rule this one out. 00:03:29.110 --> 00:03:30.890 Eight ounces of blue paint mixed 00:03:30.890 --> 00:03:32.372 with six ounces of red paint. 00:03:32.372 --> 00:03:35.672 So here, this ratio is eight ounces of blue 00:03:35.672 --> 00:03:38.005 for every six ounces of red. 00:03:40.133 --> 00:03:42.252 Well, are these equivalent ratios? 00:03:42.252 --> 00:03:45.153 Well, the difference, or you can go, 00:03:45.153 --> 00:03:48.320 if you multiply by two in either case, 00:03:49.527 --> 00:03:52.056 you will get to eight to six. 00:03:52.056 --> 00:03:55.677 Four times two is eight, three times two is six. 00:03:55.677 --> 00:03:57.917 So this is indeed an equivalent ratio, 00:03:57.917 --> 00:03:59.971 so we would select this one. 00:03:59.971 --> 00:04:02.173 All right, here they say six ounces of blue paint 00:04:02.173 --> 00:04:04.906 mixed with eight ounces of red paint. 00:04:04.906 --> 00:04:08.221 So this is, they've swapped the blues and the red 00:04:08.221 --> 00:04:11.293 relative to this one, so this is a ratio of six to eight, 00:04:11.293 --> 00:04:13.238 so let me write this down. 00:04:13.238 --> 00:04:15.439 So this is a ratio, six ounces of blue paint 00:04:15.439 --> 00:04:18.409 for every eight ounces of red paint. 00:04:18.409 --> 00:04:20.064 So just like we ruled out that first one, 00:04:20.064 --> 00:04:22.001 this is dealing with the same numbers 00:04:22.001 --> 00:04:23.935 but in a different order and the order matters, 00:04:23.935 --> 00:04:25.374 so we'll rule that out. 00:04:25.374 --> 00:04:29.783 20 ounces of blue paint, 20 ounces of blue paint, 00:04:29.783 --> 00:04:33.176 for every 15 ounces of red paint. 00:04:33.176 --> 00:04:35.381 So are these equivalent? 00:04:35.381 --> 00:04:37.319 Well, let's think about it. 00:04:37.319 --> 00:04:41.555 To go from four to 20, you can multiply by five, 00:04:41.555 --> 00:04:44.546 and to go from three to 15, you could multiply by five, 00:04:44.546 --> 00:04:45.999 so we can multiply by the same factor 00:04:45.999 --> 00:04:48.738 to go from four to three to 20 to 15, 00:04:48.738 --> 00:04:51.905 so this is indeed an equivalent ratio. 00:04:53.060 --> 00:04:57.649 12 ounces of blue paint mixed with 16 ounces of red paint. 00:04:57.649 --> 00:04:59.368 All right, so this is a ratio here 00:04:59.368 --> 00:05:03.368 of 12 ounces of blue for every 16 ounces of red. 00:05:04.302 --> 00:05:06.728 So let's think about this. 00:05:06.728 --> 00:05:10.895 To go from four to 12, you would multiply by three. 00:05:14.600 --> 00:05:16.255 Now, if you multiplied three by three, 00:05:16.255 --> 00:05:18.547 you would have a nine here, not a 16, 00:05:18.547 --> 00:05:20.732 so this is definitely not an equivalent ratio. 00:05:20.732 --> 00:05:21.805 Another way of thinking about it, 00:05:21.805 --> 00:05:23.851 you have, in terms of ounces, 00:05:23.851 --> 00:05:26.275 you have more ounces of blue than you have of red 00:05:26.275 --> 00:05:27.827 for any of the equivalent ratios, 00:05:27.827 --> 00:05:30.088 but here you have more ounces of red than blue, 00:05:30.088 --> 00:05:32.005 so once again, another way of realizing 00:05:32.005 --> 00:05:33.440 that that is not equivalent, 00:05:33.440 --> 00:05:37.740 so only B and D are the equivalent mixtures 00:05:37.740 --> 00:05:40.840 that will provide the same shade of purple. 00:05:40.840 --> 00:05:41.875 To have that same shade, 00:05:41.875 --> 00:05:44.441 you need the same ratio of blue to red.