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A specific shade of orange paint calls for two parts, yellow and three parts red Katie uses 3 cups of yellow paint and 4 cups of red paint to make orange paint. Is this a proportional relationship explain

Let's break down the problem to check whether the relationship between the yellow and red paint is proportional.

### Problem:
- The correct ratio for the orange paint mixture is **2 parts yellow to 3 parts red**.
- Catie uses **3 cups of yellow paint and 4 cups of red paint**.

### Step 1: Express the Ratio for the Required Mixture
The ratio of yellow to red paint for the specific shade of orange paint is \( 2:3 \). This means for every 2 parts of yellow paint, 3 parts of red paint are required.

### Step 2: Express the Ratio of What Catie Used
Catie uses 3 cups of yellow and 4 cups of red, so the ratio of yellow to red paint she used is \( 3:4 \).

### Step 3: Compare the Ratios
Now we compare the required ratio \( \frac{2}{3} \) with the ratio Catie used \( \frac{3}{4} \).

\[
\frac{2}{3} \neq \frac{3}{4}
\]

Since \( \frac{2}{3} \neq \frac{3}{4} \), the two ratios are not equal.

### Conclusion:
Catie's mixture of yellow and red paint is not in the same proportion as the required 2:3 ratio, so the relationship is not proportional.

Would you like more details on proportional relationships or further examples?

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Here are five follow-up questions to deepen your understanding:

1. What does it mean for two ratios to be proportional?
2. How could Catie adjust her mixture to create a proportional orange paint with the 2:3 ratio?
3. What mathematical operation can be used to check if two ratios are proportional?
4. Can you think of other real-world examples where proportional relationships are important?
5. If Catie used 5 cups of red paint, how many cups of yellow would she need to maintain the correct ratio?

**Tip:** When checking for proportionality, you can always cross-multiply to see if the ratios are equal!

A specific shade of orange paint calls for two parts yellow and three parts red. Catie uses 3 cups of yellow paint and 4 cups of red paint to make orange paint. Is this a proportional relationship? Explain.

Explore the problem of mixing paint with a 2:3 ratio of yellow to red. Catie uses 3 cups of yellow and 4 cups of red paint—find out if the proportions match. This problem helps students understand ratios and proportions, perfect for Grades 6-8.

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