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A recipe for oatmeal cookies calls for 2 cups of flour for every 3 cups of oatmeal. How much flour is needed for a big batch of cookies that uses 9 cups of oatmeal? Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
A recipe for oat meal cookies calls for 2 cups of flour for every 3 cups oatmeal. How much flour is required for a big batch which uses 9 cups of oatmeal. So 2 cups of flour for every 3 cups of oatmeal. Now we are going to a situation where we are using 9 cups of oatmeal. I will let you know a couple of different ways we can think about it. One way to think about this is we know if we use 3 cups of oatmeal , we need 2 cups of flour. We do not know how much is required if we use 9 cups of oatmeal If we are going from 3 cups to 9 cups of oatmeal how much more oatmeal we are using? we are using 3 times more , 3 x 3 = 9 If we want to use flour in the same proportion we need to use, 3 times the flour we need flour times 3 ; 2x3 = 6 cups of flour Another way to think about it You can say 2 cups of flour over 3 cups of oatmeal is equal to ? cups of flour over 9 cups of oatmeal. I like the first way of doing it It is common sense. If you triple the oatmeal, you have to triple the flour. Once youset up an equation like this, is to use a little bit of algebra. In cross multiplication, whenever you set a proportion like this, 2 x 9 = ? x 3 or we get 18 = ? x 3 so the number of cups of flour we need to use times 3 needs to be 18. You divide both sides by 3 to get the answer which is 6 So we get ? = 6 cups of flour. You might we wondering cross multiplication does not make sense. If you have setup a proportion like this, why should cross multiplication work. That comes from algebra. I am going to rewirte this part as x to simplify we have 2/3 = x/9. In algebra, all we are saying this quantity over here is equal to this quantity over there. If you do anything to the left , we need to do the same thing to the right to keep it equal. So what can we multiply this by, so that we are left with just "x". So we multiply this times 9, If you multiply right side by 9, you need to multiply the left by 9 for both sides to be equal. on the right hand side the 9 cancel out, you are left with x. On the left hand side, 9*2/3 = 18/3 = 6 So these are all legitimate ways of doing this. For really simple problems like this you can use common sense. If you are increasing oatmeal by 3 times, increase flour also by a factor of 3