Problem 20 The scale on a map of Ohio says ... [FREE SOLUTION] (2024)

Short Answer

Proportions

Proportions are mathematical equations that show two ratios are equivalent. This is key in scaling problems, like our map scale problem. In this exercise, we set up a proportion to relate the map distance to the real distance. A common example is \( \frac{2 \text{ inches}}{35 \text{ miles}} = \frac{14 \text{ inches}}{x \text{ miles}} \). Here, 14 inches on the map relate to a real-life distance we need to find. Proportions help maintain consistency between the map and actual distances, making it easy to calculate unknown values.

Distance Calculation

Calculating distance on a map involves understanding the scale, and using it to find real-world measurements. Here, the scale states 2 inches equals 35 miles. To find the distance between Cleveland and Cincinnati, we set up the proportion mentioned earlier. Using proportions, we can solve for the real-world distance easily. Let's break it down in steps: identify the scale, set up a proportion, cross-multiply, and solve for the unknown distance. This method assures that our calculations are accurate and verifiable.

Cross Multiplication

Cross multiplication is a method to solve proportions. It involves multiplying the numerator of one ratio by the denominator of the other ratio. For our exercise, we have the proportion \( \frac{2 \text{ inches}}{35 \text{ miles}} = \frac{14 \text{ inches}}{x \text{ miles}} \). We cross-multiply to get 2 \( \times \) x = 35 \( \times \) 14. This simplifies to 2x = 490. Finally, we solve for x by dividing both sides by 2, resulting in x = 245 miles. Cross multiplication keeps calculations straightforward and manageable.

Map Reading

Map reading is a crucial skill that involves interpreting symbols and scales to determine distances and directions. Understanding the given scale on a map is the first step, as it converts map measurements into real-world distances. In our example, the scale tells us that 2 inches is equal to 35 miles. This allows us to set up a proportion to find the distance between cities. By correctly applying ratios and proportions, we can accurately interpret map data to navigate and understand geographic locations.