Certainly! The reason you don't need to change 4 dozen to 48 and then divide by 1 1/2 is because we are trying to find the amount of flour needed for just 1 dozen cookies, not 4 dozen.
When we have a recipe that calls for a certain amount of ingredient for a specific number of items, we can use proportional reasoning to find out how much of that ingredient we would need for a different number of items.
In this case, the recipe is originally given for 4 dozen cookies, which means it is designed to make 4 groups of 12 cookies each. So, to find the amount of flour needed for just 1 dozen cookies, we need to think about how the number of cookies changes relative to the amount of flour.
Since we are dividing the number of cookies by 4 (from 4 dozen to 1 dozen), we also need to divide the amount of flour by 4 to maintain that proportional relationship. This is why we divide 1 1/2 cups of flour by 4, which gives us 3/2 divided by 4.
By simplifying the fraction division, we get (3/2) x (1/4) = 3/8. This means that for 1 dozen cookies, you will need 3/8 cups of flour, or when expressed as a mixed number, 8/3 cups of flour.
So, the correct amount of flour needed for 1 dozen cookies is 8/3 cups.