When converting from one unit to another, we multiply a quantity by a conversion factor. A conversion factor is a fraction equivalent to 1, so multiplying it by a quantity doesn't change its actual measure. However, the fraction certainly doesn't look like it's equal to one (at least not until you inspect it). The expressions in the numerator and denominator are equal quantities, but measured in different units. During unit conversion, units are also canceled out when they appear in both the numerator and the denominator. To illustrate this idea, let's convert 1.5 feet into inches, using the fact that 1 foot is equivalent to 12 inches.

Create fraction multiplication 


Multiply numbers, multiply units 


Units of feet cancel 


Our Solution 
A unit rate is a ratio between two quantities with different units. For examples, speed is a unit rate, because it is the ratio between distance traveled and the time taken to travel that distance. There are two different types of units that make up this ratio, distance and time. Another characteristic of a unit rate is that a unit rate has a denominator of 1. Let's think about speed again: we wouldn't normally say that a car travels 120 miles per 2 hours. Instead, we simplify the ratio to 1 hour, and say 60 miles per hour.
When converting unit rates, we need to make use of multiple conversion factors: as many conversion factors needed to convert from one quantity to another for every unit involved in our unit rate. Let's work more with miles per hour, and convert 60 miles per hour into feet per second. We'll need to convert miles to kilometers, but also hours to seconds. Let's first list our conversion factors:




This conversion factor cancels miles 


The second conversion factor cancels hours 


Multiply all fractions, noting canceled units 


Divide 316800 by 3600, for a denominator of 1 


Our Solution 