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- [Voiceover] We're told that Burger Barn

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makes dipping sauce by[br]mixing two spoonfuls of honey

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with one half spoonful of mustard.

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Sandwich Town makes dipping sauce

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by mixing four spoonfuls of honey

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with one spoonful of mustard.

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Which dipping sauce has a[br]stronger mustard flavor?

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So pause this video and see if you can

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work through that on your own.

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All right, now let's[br]think about the ratios

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of honey to mustard at[br]each of these restaurants.

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So first let's think about[br]the scenario with Burger Barn.

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So I'll just say BB for[br]short, for Burger Burn.

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So they have two spoonfuls of honey

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for every one half spoonful of mustard,

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so the ratio of honey to mustard

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in terms of spoonfuls is[br]two spoonfuls of honey

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for every one half spoonful of mustard,

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so this is the ratio of honey to mustard.

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Let me write this.

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This is honey, and this[br]right over here is mustard.

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Now, let's look at Sandwich[br]Town, so I'll call that ST.

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So Sandwich Town makes dipping sauce

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by having four spoonfuls of honey

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for every one spoonful of mustard.

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So the ratio of honey to mustard

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is four spoonfuls to one spoonful,

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so once again, that is[br]honey and that is mustard.

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Now, can we make these equivalent ratios

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or can we compare them somehow?

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Well, let's see.

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We have one half spoonful of mustard here.

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We have one spoon of mustard here,

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so what if we multiplied both the mustard

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and the honey spoonfuls by two?

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That still would be an equivalent ratio

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because we're multiplying[br]by the same amount.

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So if we multiply by[br]two in both situations,

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you have four spoonfuls of honey

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for every one spoonful of mustard.

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Well, that's the exact same ratio

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that we have at Sandwich Town.

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So it actually turns out that they have

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the same concentration of mustard.

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They have the same ratio[br]of honey to mustard.

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Four spoonfuls of honey for[br]every spoonful of mustard

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in either situation.

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Let's do another example.

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So here, we are asked or[br]we are told, we are told,

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Patrick's favorite shade of purple paint

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is made with four ounces of blue paint,

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so underline that in blue,[br]four ounces of blue paint,

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for every three ounces of red paint,

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for every three ounces of red paint.

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So the ratio of blue paint to red paint

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is four ounces of blue,[br]four ounces of blue,

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for every three ounces[br]of red, so four to three.

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Which of the following paint mixtures

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will create the same shade of purple?

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All right, pause this video

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and see if you can figure[br]it out on your own.

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So this is three ounces of blue paint

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mixed with four ounces of red paint.

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Well, this is a ratio[br]here of three to four,

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and even though it's dealing[br]with the same numbers,

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this is a different ratio.

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The order matters.

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This is four ounces of blue[br]for every three ounces of red.

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This is saying three ounces of blue

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for every four ounces of red,[br]so we could rule this one out.

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Eight ounces of blue paint mixed

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with six ounces of red paint.

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So here, this ratio is[br]eight ounces of blue

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for every six ounces of red.

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Well, are these equivalent ratios?

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Well, the difference, or you can go,

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if you multiply by two in either case,

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you will get to eight to six.

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Four times two is eight,[br]three times two is six.

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So this is indeed an equivalent ratio,

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so we would select this one.

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All right, here they say[br]six ounces of blue paint

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mixed with eight ounces of red paint.

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So this is, they've swapped[br]the blues and the red

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relative to this one, so this[br]is a ratio of six to eight,

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so let me write this down.

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So this is a ratio, six[br]ounces of blue paint

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for every eight ounces of red paint.

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So just like we ruled out that first one,

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this is dealing with the same numbers

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but in a different order[br]and the order matters,

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so we'll rule that out.

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20 ounces of blue paint,[br]20 ounces of blue paint,

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for every 15 ounces of red paint.

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So are these equivalent?

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Well, let's think about it.

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To go from four to 20,[br]you can multiply by five,

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and to go from three to 15,[br]you could multiply by five,

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so we can multiply by the same factor

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to go from four to three to 20 to 15,

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so this is indeed an equivalent ratio.

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12 ounces of blue paint mixed[br]with 16 ounces of red paint.

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All right, so this is a ratio here

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of 12 ounces of blue for[br]every 16 ounces of red.

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So let's think about this.

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To go from four to 12, you[br]would multiply by three.

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Now, if you multiplied three by three,

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you would have a nine here, not a 16,

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so this is definitely[br]not an equivalent ratio.

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Another way of thinking about it,

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you have, in terms of ounces,

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you have more ounces of[br]blue than you have of red

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for any of the equivalent ratios,

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but here you have more[br]ounces of red than blue,

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so once again, another way of realizing

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that that is not equivalent,

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so only B and D are[br]the equivalent mixtures

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that will provide the[br]same shade of purple.

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To have that same shade,

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you need the same ratio of blue to red.