# RATL 1 | Lesson 3 | Explore (Solution: Proportional Reasoning)

## Proportional Reasoning

A cookie recipe make one dozen cookies and requires $$\Large \frac{2}{3}$$ cups of milk.

1.  How many cookies can be made with 9 cups of milk?

2.  What method did you use to solve this problem?

Methods vary.  Two methods are described below:

If $$\frac{2}{3}$$ cups of milk makes 12 cookies, then

• 2 times $$\frac{2}{3}= \frac{4}{3}=1\frac{1}{3}$$ cups of milk makes $$2(12)=24$$ cookies
• 3 times $$\frac{2}{3}=\frac{6}{3}=2$$ cups of milk makes $$3(12)=36$$ cookies
• 6 times $$\frac{2}{3}=\frac{12}{3}=4$$ cups of milk makes $$6(12)=72$$ cookies
• 13.5 times $$\frac{2}{3}= \frac{27}{3}=9$$ cups of milk makes $$13.5(12)=162$$ cookies

Method 2: Division and multiplication

$$\Large\frac{9}{\frac{2}{3}}$$$$=9(\frac{3}{2})=\frac{27}{2}=13.5$$ dozens of cookies. $$13.5(12)=162$$ cookies.

3.  Which of the two methods above did you use?   Did you use another method?

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