Scale two units of measurement

On a map every 50 miles is represented as 0.2 centimeters. How many miles is 1.5 centimeters on the map?

The two units of measurement are miles and centimeters.

**Set up a proportion for miles and centimeters. Let the unknown miles be**

**π.**

**$$\boldsymbol{\frac {miles}{centimeters}=\frac {50}{0.2}=\frac {x}{1.5}}$$**

Cross multiply and solve for π

**.**0.2 × π

**= 1.5 × 50****0.2**π

**= 75**

π

**=****375 miles**When setting up a proportion, it is important to have the same units in numerator and denominator.

Explanation on proportion:

In the above example, it is given that 50 miles is 0.2 centimeters. This means that for any given value of miles or centimeters, the ratio of miles:centimeter will always be 50:0.2. Hence,

miles:centimeter = 50:0.2 = unknown miles:1.5

Proportion is a ratio written as a fraction. Similar ratios can be equated as fractions as shown in the solution above.

Try the following:

1. A building architect has created a scale for the height of a building. On the scale 30 feet is represented as 2 inches. How many inches represent 720 feet on the architect's scale?

2. Tara is planning to drive to her cousin's house. On a map the distance between Tara and her cousin's home is 18 centimeters. If 0.4 centimeters on the map represents 3 miles, how many miles will Tara drive from her home to her cousin's home?

3. A small city has two large shopping malls. On the city map the distance between the two shopping malls is 3 inches. If 0.15 inches on the map corresponds to 10 miles, how far apart are the two shopping malls in miles?

**Show/Hide Answers**

1. $${\frac {inches}{feet}=\frac {2}{30}=\frac {x}{720} → {x=48}\ {inches}}$$

2. $${\frac {miles}{centimeters}=\frac {3}{0.4}=\frac {x}{18} → {x=135}\ {miles}}$$

3. $${\frac {miles}{inches}=\frac {10}{0.15}=\frac {x}{3} → {x=200}\ {miles}}$$

3. $${\frac {miles}{inches}=\frac {10}{0.15}=\frac {x}{3} → {x=200}\ {miles}}$$