A cookie recipe make one dozen cookies and requires \(\dfrac{2}{3}\) cups of milk.
1. How many cookies can be made with 9 cups of milk?
Solution: 162 cookies
2. What method did you use to solve this problem?
Methods vary. Two methods are described below:
Method 1: Additive Reasoning
If \(\dfrac{2}{3}\) cups of milk makes 12 cookies, then
- 2 times \(\dfrac{2}{3}= \dfrac{4}{3}=1\dfrac{1}{3}\) cups of milk makes \(2(12)=24\) cookies
- 3 times \(\dfrac{2}{3}=\dfrac{6}{3}=2\) cups of milk makes \(3(12)=36\) cookies
- 6 times \(\dfrac{2}{3}=\dfrac{12}{3}=4\) cups of milk makes \(6(12)=72\) cookies
- 13.5 times \(\dfrac{2}{3}= \dfrac{27}{3}=9\) cups of milk makes \(13.5(12)=162\) cookies
Method 2: Division and multiplication
\(\dfrac{9}{\dfrac{2}{3}}\)\(=9(\dfrac{3}{2})=\dfrac{27}{2}=13.5\) dozens of cookies. \(13.5(12)=162\) cookies.
3. Which of the two methods above did you use? Did you use another method?
Return to Explore (Proportional Reasoning)
