Question

oscar has a map of the campground where he is staying. the scale shows that 4 inches on the map represents an actual distance of 2 miles. oscars tent is at campsite 4a. what number can you multiply each length on the map by to find the actual distance?

Explanation:

Step1: Calculate the scale factor

We know that 4 inches on the map represents 2 miles in actual distance. To find the number \(x\) (scale factor) such that map distance \(\times x=\) actual distance. Let the map distance be \(d_{m}\) and actual distance be \(d_{a}\). We have the proportion \(\frac{d_{a}}{d_{m}}=x\). Given \(d_{m} = 4\) inches and \(d_{a}=2\) miles. Then \(x=\frac{2}{4}\).

Step2: Simplify the fraction

Simplify \(\frac{2}{4}\). Using the rule \(\frac{a}{b}=\frac{a\div c}{b\div c}\) (where \(c\) is the greatest common divisor of \(a\) and \(b\), here \(c = 2\)). So \(\frac{2\div2}{4\div2}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)