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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 = 9 ft 2 × 12 in 1 ft

= 9 ft × 12 in 2 × 1 ft

= 108 in 2

= 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 ) 0.62 miles ( mi )

1 gallon ( gal ) 3.79 liters ( L )

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

80 mi $ 6 × $ 2.50 1 gal × 1 gal 3.79 L × 1 km 0.62 mi

= 80 mi × $ 2 .50 × 1 gal × 1 km $ 6 × 1 gal × 3.79 L × 0.62 mi

= 80 mi × $ 2 .50 × 1 gal × 1 km $ 6 × 1 gal × 3.79 L × 0.62 mi

= 200 km 14.0988 L

14.2 km / L

 

 

 

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