Question

the scale on a map is $\frac{1}{5}$ cm = $\frac{2}{5}$ mile. how long is one mile on the map?

Explanation:

Step1: Set up proportion

Let $x$ = map length for 1 mile.
$\frac{\frac{1}{5}\text{ cm}}{\frac{3}{5}\text{ mile}} = \frac{x}{1\text{ mile}}$

Step2: Cross-multiply to solve

$\frac{3}{5}x = \frac{1}{5} \times 1$

Step3: Isolate $x$

$x = \frac{1}{5} \div \frac{3}{5} = \frac{1}{5} \times \frac{5}{3}$

Step4: Simplify the expression

$x = \frac{1 \times 5}{5 \times 3} = \frac{1}{3}$

Answer:

$\frac{1}{3}$ cm