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Video transcript

so right over here we have the recipe for super cake which you want to make for your guests that are coming over for dinner tonight but this recipe right over here this is for 32 people this would serve 32 folks but you only have 16 guests coming over so if you only have 16 guests coming over what should be your ingredients here how much of each of these ingredients should you have and I encourage you to pause the video and think about it alright so right now we're gonna think about well we're gonna have a slightly smaller super cake smaller super super cake and you might have reasoned that look if we're going to have half as many guests then each of the ingredients we should just have half as much and you would be right instead of 8 eggs for a smaller super cake you could have 4 eggs instead of 6 cups of flour and our smaller super cake you could have 3 cups of flour instead of 6 cups of sugar you could have 3 cups of sugar I'm just taking half of each of these numbers instead of 2 cups of butter you could have 1 cup of butter instead of 6 teaspoons of baking soda you could have 3 teaspoons of baking soda and last but not least instead of 2 cups of water you could have 1 cup of water now this will work and this is actually how you should adjust recipes but there's something interesting about what's similar about these two recipes the recipe for the main super cake that feeds 32 people and the recipe for the smaller super cake and that's the notion of ratios the ratios between ingredients or the ratio of how much of an ingredient you need for a given guest so for example you can see here that for every 8 eggs you have 6 cups of flour so let me write this down so for every 8 eggs we have 6 cups of flour we six cups of flour which is can be expressed as a ratio of the ratio of eggs to flour is eight to six which is once again interpreted it is for every eight eggs I have six cups of flour if I said for every six cups of flour I have eight eggs I would have written six to eight so the order here matters but here I'm saying the ratio of eggs to flour of eggs 2 cups of flour is 8 to 6 for every 8 eggs I have 6 cups of flour well what about for the smaller cake well here for for every 4 eggs for every 4 eggs we have 3 cups of flour we have 3 cups of flour so what would this ratio be well for every 4 eggs we have 3 cups of flour so the ratio of eggs to flour is 4 to 3 now it turns out that these are the exact same ratio if you have 8 eggs for every 6 cups of flour or for every 8 eggs you have 6 cups of flour that's the same thing as for every 4 eggs you have 3 cups of flour what you're just doing is taking each of these numbers and you are dividing it by 2 so you could say the ratio and either case the ratio of eggs to flour let me write this down the ratio of eggs eggs to 2 cups of flour let me write 2 cups of flour cups of flour in either case is is 4 eggs for every 3 cups of flour this is going to be true for either recipe you have the same ratio if you have 8 eggs here so for every 4 eggs you have 3 cups of flour well that means you're going to have six cups of flour and so this is why ratios are helpful this recipe has a different number of eggs a different number of cups of flour different number of cups of sugar but the ratios between the ingredients are the same and so you will be able to have a cake that tastes the same that essentially is the same cake but just is a different size