Ratios for recipes

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.

All right, so right now we're gonna think about—well, we're going to have a slightly smaller super cake. 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 eight eggs for a smaller super cake, you could have four eggs. Instead of six cups of flour in our smaller super cake, you could have three cups of flour. Instead of six cups of sugar, you could have three cups of sugar. I'm just taking half of each of these numbers. Instead of two cups of butter, you could have one cup of butter. Instead of six teaspoons of baking soda, you could have three teaspoons of baking soda. And last but not least, instead of two cups of water, you could have one 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 eight eggs, you have six cups of flour. So let me write this down: for every eight eggs, we have six cups of flour. We have six cups of flour, which can be expressed as a ratio. The ratio of eggs to flour is 8 to 6, which is once again interpreted as, for every 8 eggs, I have 6 cups of flour. If I said for every 6 cups of flour, I have 8 eggs, I would have written 6 to 8. So the order here matters. But here I'm saying the ratio of eggs to flour, of eggs to cups of flour, is eight to six. For every eight eggs, I have six cups of flour.

Well, what about for the smaller cake? Well here, for every four eggs, we have three cups of flour. We have three cups of flour. So what would this ratio be? Well, for every four eggs, we have three cups of flour. So the ratio of eggs to flour is four to three. Now, it turns out that these are the exact same ratio. If you have eight eggs for every six cups of flour, or for every eight eggs you have six cups of flour, that's the same thing as for every four eggs you have three cups of flour. What you're just doing is taking each of these numbers and you are dividing it by two.

So you could say the ratio in either case, the ratio of eggs to flour—let me write this down. The ratio of eggs to two cups of flour—let me write it: two cups of flour, in either case is four eggs for every three cups of flour. This is going to be true for either recipe. You have the same ratio. If you have eight eggs here, for every four eggs, you have three 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, and a 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.