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Are either of these proportional relationships? Explain why or why not.
This is asking about the temperature and the inches to centimeters questions.

To determine whether the relationships shown are proportional, we need to check if there is a constant ratio between the two quantities in each set of data (inches to centimeters).

### Analyzing the "Inches to Centimeters" Relationship:

The relationship between inches and centimeters is typically a proportional one. The conversion factor is:
\[
1 \text{ inch} = 2.54 \text{ cm}
\]

Let's check if the provided conversions maintain this constant ratio.

#### Given Data:
1. **10 inches** corresponds to **25.4 cm**.
2. **8 inches** corresponds to **20.32 cm**.
3. **3.5 inches** corresponds to **8.89 cm**.

#### Checking the Ratios:

For the relationship to be proportional, the ratio of centimeters to inches should be the same in all cases:

1. \[
\text{Ratio} = \frac{25.4 \text{ cm}}{10 \text{ in}} = 2.54 \text{ cm per inch}
\]

2. \[
\text{Ratio} = \frac{20.32 \text{ cm}}{8 \text{ in}} = 2.54 \text{ cm per inch}
\]

3. \[
\text{Ratio} = \frac{8.89 \text{ cm}}{3.5 \text{ in}} \approx 2.54 \text{ cm per inch}
\]

Since all three ratios are equal to 2.54, this confirms that the relationship between inches and centimeters is indeed proportional.

### Conclusion:
The inches to centimeters relationship is proportional because the ratio (2.54) remains constant across all values.

Would you like more details or have any questions?

### Further Questions to Explore:
1. What is the meaning of a proportional relationship in mathematics?
2. Can you provide an example of a non-proportional relationship?
3. How do you convert from centimeters to inches?
4. Are there other real-life examples of proportional relationships?
5. What would happen if the ratios were not equal in a dataset like this?

**Tip:** A proportional relationship always involves a constant multiplier between two quantities.

Are either of these proportional relationships? Explain why or why not. This is asking about the temperature and the inches to centimeters questions.

Explore whether the conversion from inches to centimeters represents a proportional relationship. Detailed analysis shows that the ratio of 2.54 remains constant, confirming proportionality. This is a suitable math problem for students in Grades 6-8.

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