Identify the scale factor if the length of a model train is ½ inch and the length of the train itself is 3 feet.  Select ALL that apply.

Identify the scale factor if the length of a model train is ½ inch and the length of the train itself is 3 feet.  Select ALL that apply.

1 inch = 6 feet

inch = 6 feet

inch = 3 feet

1 inch = 3 feet

To identify the scale factor between the model train and the actual train, we need to compare their corresponding lengths.

**Given:**

- Length of the model train: \( \frac{1}{2} \) inch
- Length of the actual train: 3 feet

**Step 1: Convert the actual train's length to inches.**

Since 1 foot = 12 inches, 3 feet = \( 3 \times 12 = 36 \) inches.

**Step 2: Calculate the scale factor.**

The scale factor is the ratio of the model train length to the actual train length:
\[
\text{Scale Factor} = \frac{\text{Length of Model Train}}{\text{Length of Actual Train}} = \frac{\frac{1}{2} \text{ inch}}{36 \text{ inches}} = \frac{1}{2 \times 36} = \frac{1}{72}
\]

This means the scale factor is \( \frac{1}{72} \), which implies that:

- **1 inch on the model represents 72 inches on the actual train.**

**Now, let's compare this with the options:**

- **Option 1:** \( 1 \text{ inch} = 6 \text{ feet} \)
  - Convert 6 feet to inches: \( 6 \times 12 = 72 \) inches.
  - This matches our scale factor of \( \frac{1}{72} \).

- **Option 2:** \( \text{inch} = 6 \text{ feet} \)
  - This option seems incomplete and cannot be evaluated.

- **Option 3:** \( \text{inch} = 3 \text{ feet} \)
  - This option is also incomplete.

- **Option 4:** \( 1 \text{ inch} = 3 \text{ feet} \)
  - Convert 3 feet to inches: \( 3 \times 12 = 36 \) inches.
  - This represents a scale factor of \( \frac{1}{36} \), which does not match our calculated scale factor.

**Conclusion:**
The correct scale factor is represented by **Option 1**: \( 1 \text{ inch} = 6 \text{ feet} \).

Would you like more details or have any questions? 

Here are 5 related questions to explore further:

1. How do you calculate a scale factor when both measurements are in different units?
2. What is the importance of converting units before finding the scale factor?
3. How would the scale factor change if the actual train were 4 feet long instead of 3 feet?
4. Can a scale factor ever be greater than 1? What would that imply?
5. How would you interpret the scale if the model train were larger than the actual train?

**Tip:** Always ensure both quantities are in the same unit before calculating the scale factor to avoid errors.

Learn how to identify the scale factor between a model train and an actual train, given their lengths of ½ inch and 3 feet respectively. This problem involves unit conversion and ratio calculation. Suitable for students in Grades 6-8.

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