[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.69,0:00:01.92,Default,,0000,0000,0000,,- [Voiceover] We're told that Burger Barn
Dialogue: 0,0:00:01.92,0:00:05.73,Default,,0000,0000,0000,,makes dipping sauce by\Nmixing two spoonfuls of honey
Dialogue: 0,0:00:05.73,0:00:09.31,Default,,0000,0000,0000,,with one half spoonful of mustard.
Dialogue: 0,0:00:09.31,0:00:11.11,Default,,0000,0000,0000,,Sandwich Town makes dipping sauce
Dialogue: 0,0:00:11.11,0:00:13.16,Default,,0000,0000,0000,,by mixing four spoonfuls of honey
Dialogue: 0,0:00:13.16,0:00:16.37,Default,,0000,0000,0000,,with one spoonful of mustard.
Dialogue: 0,0:00:16.37,0:00:21.36,Default,,0000,0000,0000,,Which dipping sauce has a\Nstronger mustard flavor?
Dialogue: 0,0:00:21.36,0:00:22.94,Default,,0000,0000,0000,,So pause this video and see if you can
Dialogue: 0,0:00:22.94,0:00:25.11,Default,,0000,0000,0000,,work through that on your own.
Dialogue: 0,0:00:25.11,0:00:26.77,Default,,0000,0000,0000,,All right, now let's\Nthink about the ratios
Dialogue: 0,0:00:26.77,0:00:30.83,Default,,0000,0000,0000,,of honey to mustard at\Neach of these restaurants.
Dialogue: 0,0:00:30.83,0:00:34.16,Default,,0000,0000,0000,,So first let's think about\Nthe scenario with Burger Barn.
Dialogue: 0,0:00:34.16,0:00:37.66,Default,,0000,0000,0000,,So I'll just say BB for\Nshort, for Burger Burn.
Dialogue: 0,0:00:37.66,0:00:39.97,Default,,0000,0000,0000,,So they have two spoonfuls of honey
Dialogue: 0,0:00:39.97,0:00:42.38,Default,,0000,0000,0000,,for every one half spoonful of mustard,
Dialogue: 0,0:00:42.38,0:00:44.79,Default,,0000,0000,0000,,so the ratio of honey to mustard
Dialogue: 0,0:00:44.79,0:00:48.71,Default,,0000,0000,0000,,in terms of spoonfuls is\Ntwo spoonfuls of honey
Dialogue: 0,0:00:50.12,0:00:53.37,Default,,0000,0000,0000,,for every one half spoonful of mustard,
Dialogue: 0,0:00:55.30,0:00:58.62,Default,,0000,0000,0000,,so this is the ratio of honey to mustard.
Dialogue: 0,0:00:58.62,0:00:59.68,Default,,0000,0000,0000,,Let me write this.
Dialogue: 0,0:00:59.68,0:01:04.67,Default,,0000,0000,0000,,This is honey, and this\Nright over here is mustard.
Dialogue: 0,0:01:04.67,0:01:08.84,Default,,0000,0000,0000,,Now, let's look at Sandwich\NTown, so I'll call that ST.
Dialogue: 0,0:01:10.63,0:01:12.08,Default,,0000,0000,0000,,So Sandwich Town makes dipping sauce
Dialogue: 0,0:01:12.08,0:01:14.55,Default,,0000,0000,0000,,by having four spoonfuls of honey
Dialogue: 0,0:01:14.55,0:01:16.89,Default,,0000,0000,0000,,for every one spoonful of mustard.
Dialogue: 0,0:01:16.89,0:01:18.100,Default,,0000,0000,0000,,So the ratio of honey to mustard
Dialogue: 0,0:01:18.100,0:01:22.60,Default,,0000,0000,0000,,is four spoonfuls to one spoonful,
Dialogue: 0,0:01:22.60,0:01:26.68,Default,,0000,0000,0000,,so once again, that is\Nhoney and that is mustard.
Dialogue: 0,0:01:29.25,0:01:31.87,Default,,0000,0000,0000,,Now, can we make these equivalent ratios
Dialogue: 0,0:01:31.87,0:01:33.58,Default,,0000,0000,0000,,or can we compare them somehow?
Dialogue: 0,0:01:33.58,0:01:35.08,Default,,0000,0000,0000,,Well, let's see.
Dialogue: 0,0:01:35.08,0:01:37.85,Default,,0000,0000,0000,,We have one half spoonful of mustard here.
Dialogue: 0,0:01:37.85,0:01:39.60,Default,,0000,0000,0000,,We have one spoon of mustard here,
Dialogue: 0,0:01:39.60,0:01:41.34,Default,,0000,0000,0000,,so what if we multiplied both the mustard
Dialogue: 0,0:01:41.34,0:01:44.38,Default,,0000,0000,0000,,and the honey spoonfuls by two?
Dialogue: 0,0:01:44.38,0:01:45.67,Default,,0000,0000,0000,,That still would be an equivalent ratio
Dialogue: 0,0:01:45.67,0:01:48.05,Default,,0000,0000,0000,,because we're multiplying\Nby the same amount.
Dialogue: 0,0:01:48.05,0:01:51.93,Default,,0000,0000,0000,,So if we multiply by\Ntwo in both situations,
Dialogue: 0,0:01:51.93,0:01:54.57,Default,,0000,0000,0000,,you have four spoonfuls of honey
Dialogue: 0,0:01:54.57,0:01:57.40,Default,,0000,0000,0000,,for every one spoonful of mustard.
Dialogue: 0,0:01:59.04,0:02:00.46,Default,,0000,0000,0000,,Well, that's the exact same ratio
Dialogue: 0,0:02:00.46,0:02:02.16,Default,,0000,0000,0000,,that we have at Sandwich Town.
Dialogue: 0,0:02:02.16,0:02:04.46,Default,,0000,0000,0000,,So it actually turns out that they have
Dialogue: 0,0:02:04.46,0:02:07.96,Default,,0000,0000,0000,,the same concentration of mustard.
Dialogue: 0,0:02:07.96,0:02:11.93,Default,,0000,0000,0000,,They have the same ratio\Nof honey to mustard.
Dialogue: 0,0:02:11.93,0:02:15.17,Default,,0000,0000,0000,,Four spoonfuls of honey for\Nevery spoonful of mustard
Dialogue: 0,0:02:15.17,0:02:17.43,Default,,0000,0000,0000,,in either situation.
Dialogue: 0,0:02:17.43,0:02:18.82,Default,,0000,0000,0000,,Let's do another example.
Dialogue: 0,0:02:18.82,0:02:22.99,Default,,0000,0000,0000,,So here, we are asked or\Nwe are told, we are told,
Dialogue: 0,0:02:25.82,0:02:28.67,Default,,0000,0000,0000,,Patrick's favorite shade of purple paint
Dialogue: 0,0:02:28.67,0:02:31.34,Default,,0000,0000,0000,,is made with four ounces of blue paint,
Dialogue: 0,0:02:31.34,0:02:35.51,Default,,0000,0000,0000,,so underline that in blue,\Nfour ounces of blue paint,
Dialogue: 0,0:02:36.78,0:02:39.31,Default,,0000,0000,0000,,for every three ounces of red paint,
Dialogue: 0,0:02:39.31,0:02:41.61,Default,,0000,0000,0000,,for every three ounces of red paint.
Dialogue: 0,0:02:41.61,0:02:44.28,Default,,0000,0000,0000,,So the ratio of blue paint to red paint
Dialogue: 0,0:02:44.28,0:02:47.95,Default,,0000,0000,0000,,is four ounces of blue,\Nfour ounces of blue,
Dialogue: 0,0:02:50.06,0:02:54.06,Default,,0000,0000,0000,,for every three ounces\Nof red, so four to three.
Dialogue: 0,0:02:55.20,0:02:56.82,Default,,0000,0000,0000,,Which of the following paint mixtures
Dialogue: 0,0:02:56.82,0:03:00.22,Default,,0000,0000,0000,,will create the same shade of purple?
Dialogue: 0,0:03:00.22,0:03:01.62,Default,,0000,0000,0000,,All right, pause this video
Dialogue: 0,0:03:01.62,0:03:04.83,Default,,0000,0000,0000,,and see if you can figure\Nit out on your own.
Dialogue: 0,0:03:04.83,0:03:06.56,Default,,0000,0000,0000,,So this is three ounces of blue paint
Dialogue: 0,0:03:06.56,0:03:08.70,Default,,0000,0000,0000,,mixed with four ounces of red paint.
Dialogue: 0,0:03:08.70,0:03:12.37,Default,,0000,0000,0000,,Well, this is a ratio\Nhere of three to four,
Dialogue: 0,0:03:14.80,0:03:16.74,Default,,0000,0000,0000,,and even though it's dealing\Nwith the same numbers,
Dialogue: 0,0:03:16.74,0:03:18.02,Default,,0000,0000,0000,,this is a different ratio.
Dialogue: 0,0:03:18.02,0:03:19.24,Default,,0000,0000,0000,,The order matters.
Dialogue: 0,0:03:19.24,0:03:22.32,Default,,0000,0000,0000,,This is four ounces of blue\Nfor every three ounces of red.
Dialogue: 0,0:03:22.32,0:03:24.49,Default,,0000,0000,0000,,This is saying three ounces of blue
Dialogue: 0,0:03:24.49,0:03:29.11,Default,,0000,0000,0000,,for every four ounces of red,\Nso we could rule this one out.
Dialogue: 0,0:03:29.11,0:03:30.89,Default,,0000,0000,0000,,Eight ounces of blue paint mixed
Dialogue: 0,0:03:30.89,0:03:32.37,Default,,0000,0000,0000,,with six ounces of red paint.
Dialogue: 0,0:03:32.37,0:03:35.67,Default,,0000,0000,0000,,So here, this ratio is\Neight ounces of blue
Dialogue: 0,0:03:35.67,0:03:38.00,Default,,0000,0000,0000,,for every six ounces of red.
Dialogue: 0,0:03:40.13,0:03:42.25,Default,,0000,0000,0000,,Well, are these equivalent ratios?
Dialogue: 0,0:03:42.25,0:03:45.15,Default,,0000,0000,0000,,Well, the difference, or you can go,
Dialogue: 0,0:03:45.15,0:03:48.32,Default,,0000,0000,0000,,if you multiply by two in either case,
Dialogue: 0,0:03:49.53,0:03:52.06,Default,,0000,0000,0000,,you will get to eight to six.
Dialogue: 0,0:03:52.06,0:03:55.68,Default,,0000,0000,0000,,Four times two is eight,\Nthree times two is six.
Dialogue: 0,0:03:55.68,0:03:57.92,Default,,0000,0000,0000,,So this is indeed an equivalent ratio,
Dialogue: 0,0:03:57.92,0:03:59.97,Default,,0000,0000,0000,,so we would select this one.
Dialogue: 0,0:03:59.97,0:04:02.17,Default,,0000,0000,0000,,All right, here they say\Nsix ounces of blue paint
Dialogue: 0,0:04:02.17,0:04:04.91,Default,,0000,0000,0000,,mixed with eight ounces of red paint.
Dialogue: 0,0:04:04.91,0:04:08.22,Default,,0000,0000,0000,,So this is, they've swapped\Nthe blues and the red
Dialogue: 0,0:04:08.22,0:04:11.29,Default,,0000,0000,0000,,relative to this one, so this\Nis a ratio of six to eight,
Dialogue: 0,0:04:11.29,0:04:13.24,Default,,0000,0000,0000,,so let me write this down.
Dialogue: 0,0:04:13.24,0:04:15.44,Default,,0000,0000,0000,,So this is a ratio, six\Nounces of blue paint
Dialogue: 0,0:04:15.44,0:04:18.41,Default,,0000,0000,0000,,for every eight ounces of red paint.
Dialogue: 0,0:04:18.41,0:04:20.06,Default,,0000,0000,0000,,So just like we ruled out that first one,
Dialogue: 0,0:04:20.06,0:04:22.00,Default,,0000,0000,0000,,this is dealing with the same numbers
Dialogue: 0,0:04:22.00,0:04:23.94,Default,,0000,0000,0000,,but in a different order\Nand the order matters,
Dialogue: 0,0:04:23.94,0:04:25.37,Default,,0000,0000,0000,,so we'll rule that out.
Dialogue: 0,0:04:25.37,0:04:29.78,Default,,0000,0000,0000,,20 ounces of blue paint,\N20 ounces of blue paint,
Dialogue: 0,0:04:29.78,0:04:33.18,Default,,0000,0000,0000,,for every 15 ounces of red paint.
Dialogue: 0,0:04:33.18,0:04:35.38,Default,,0000,0000,0000,,So are these equivalent?
Dialogue: 0,0:04:35.38,0:04:37.32,Default,,0000,0000,0000,,Well, let's think about it.
Dialogue: 0,0:04:37.32,0:04:41.56,Default,,0000,0000,0000,,To go from four to 20,\Nyou can multiply by five,
Dialogue: 0,0:04:41.56,0:04:44.55,Default,,0000,0000,0000,,and to go from three to 15,\Nyou could multiply by five,
Dialogue: 0,0:04:44.55,0:04:45.100,Default,,0000,0000,0000,,so we can multiply by the same factor
Dialogue: 0,0:04:45.100,0:04:48.74,Default,,0000,0000,0000,,to go from four to three to 20 to 15,
Dialogue: 0,0:04:48.74,0:04:51.90,Default,,0000,0000,0000,,so this is indeed an equivalent ratio.
Dialogue: 0,0:04:53.06,0:04:57.65,Default,,0000,0000,0000,,12 ounces of blue paint mixed\Nwith 16 ounces of red paint.
Dialogue: 0,0:04:57.65,0:04:59.37,Default,,0000,0000,0000,,All right, so this is a ratio here
Dialogue: 0,0:04:59.37,0:05:03.37,Default,,0000,0000,0000,,of 12 ounces of blue for\Nevery 16 ounces of red.
Dialogue: 0,0:05:04.30,0:05:06.73,Default,,0000,0000,0000,,So let's think about this.
Dialogue: 0,0:05:06.73,0:05:10.90,Default,,0000,0000,0000,,To go from four to 12, you\Nwould multiply by three.
Dialogue: 0,0:05:14.60,0:05:16.26,Default,,0000,0000,0000,,Now, if you multiplied three by three,
Dialogue: 0,0:05:16.26,0:05:18.55,Default,,0000,0000,0000,,you would have a nine here, not a 16,
Dialogue: 0,0:05:18.55,0:05:20.73,Default,,0000,0000,0000,,so this is definitely\Nnot an equivalent ratio.
Dialogue: 0,0:05:20.73,0:05:21.80,Default,,0000,0000,0000,,Another way of thinking about it,
Dialogue: 0,0:05:21.80,0:05:23.85,Default,,0000,0000,0000,,you have, in terms of ounces,
Dialogue: 0,0:05:23.85,0:05:26.28,Default,,0000,0000,0000,,you have more ounces of\Nblue than you have of red
Dialogue: 0,0:05:26.28,0:05:27.83,Default,,0000,0000,0000,,for any of the equivalent ratios,
Dialogue: 0,0:05:27.83,0:05:30.09,Default,,0000,0000,0000,,but here you have more\Nounces of red than blue,
Dialogue: 0,0:05:30.09,0:05:32.00,Default,,0000,0000,0000,,so once again, another way of realizing
Dialogue: 0,0:05:32.00,0:05:33.44,Default,,0000,0000,0000,,that that is not equivalent,
Dialogue: 0,0:05:33.44,0:05:37.74,Default,,0000,0000,0000,,so only B and D are\Nthe equivalent mixtures
Dialogue: 0,0:05:37.74,0:05:40.84,Default,,0000,0000,0000,,that will provide the\Nsame shade of purple.
Dialogue: 0,0:05:40.84,0:05:41.88,Default,,0000,0000,0000,,To have that same shade,
Dialogue: 0,0:05:41.88,0:05:44.44,Default,,0000,0000,0000,,you need the same ratio of blue to red.