Problem: A receipe for 4 dozen cookies requires 1 1/2 cups of flour. How much flour is needed for 1 dozen?

work: 4 divided by 1 1/2 = 4/1 x 3/2 =
4/1 x 2/3 = 8/3 cups of flour

Can you explain why i don't need to change 4 dozen to 48 and then divide by 1 1/2?

It's simpler to work with dozens than with 48. (Too many numbers)

You know you'll only need one fourth as much flour for one dozen cookies.

Let's work it this way. Cross multiply and solve for x.

4 / (1 1/2) = 1 / x

4x = 1 1/2

x = (1 1/2) / 4

x = 3/2 * 1/4

x = 3/8 cup

thanks!

You're welcome.

27

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.