To proceed with the calculations, let's assume you've measured the length of the trip on the map to be 1 inch. Given the scale where \( \frac{1}{4} \) inch equals 100 miles, here's how you can calculate the total distance:

### Step-by-Step Calculation:

1. **Understand the Scale**:
   - \( \frac{1}{4} \) inch on the map represents 100 miles.

2. **Set Up the Proportion**:
   - You measured 1 inch on the map. We want to find the number of miles this corresponds to.

   \[
   \text{Distance in miles} = \text{Measured Length in inches} \times \left(\frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}}\right)
   \]

3. **Perform the Calculation**:
   - Plug in 1 inch for the measured length:

   \[
   \text{Distance in miles} = 1 \text{ inch} \times \left(\frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}}\right)
   \]

   - Simplify the fraction \( \frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}} \):

   \[
   \frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}} = 100 \text{ miles} \times 4 = 400 \text{ miles}
   \]

   - Thus, 1 inch on the map corresponds to 400 miles.

### Final Answer:

If the length of the trip on the map is 1 inch, the actual distance represented by that length would be **400 miles**.

Do you have any other questions or need further details? Here are some follow-up questions to consider:

1. What if the measured length were 2 inches? How would the distance change?
2. How can you verify that your measurement and calculation are correct?
3. How would you handle a different map scale, such as \( \frac{1}{8} \) inch equals 100 miles?
4. Could you convert the final distance from miles to kilometers?
5. What tools would you use to ensure accurate measurements on the map?

**Tip:** Always keep a calculator handy for scale conversions, especially when dealing with fractions and large distances!

Learn how to calculate distances on a map using scale and proportion with this detailed step-by-step guide. Understand how to convert map measurements to actual distances, including using proportion formulas. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation