Unit Analysis

Unit analysis means using the rules of multiplying and reducing fractions to solve problems involving different units.

Example 1:

A desk is 4 1/2 feet long. Find the length of the desk in inches.

There are 12 inches in 1 foot. Write this relationship as a fraction, and multiply it by the given length.

4 1/2 ft * 12 in/1 ft = 54 in

Note that you can cancel the unit "ft" just as though it were a number being multiplied.

Example 2:

A car can drive 80 miles on $6 worth of gasoline. If 1 gallon of gasoline costs $2.50, find how far the car can travel in kilometers on 1 liter of gasoline.

To solve this problem you need to know some conversions.

1 kilometer (km) approximately equal to 0.62 miles (mi)

1 gallon (gal) approximately equal to 3.79 liters (L)

Write all the conversions as fractions, so that the unwanted units will cancel.

long equation resulting in 5.5 km/L