Convert Rates

A rate is a ratio (comparison) of two different quantities possessing different units of measure. For example, speed is a measure of distance per unit time – distance is measurable and so is time. More specific examples of units are:

  • Wage: $20 per hour
  • Points per game: 14.5 points per game
  • Speed: 15 kilometers per hour

Let’s analyze this further. Take the example of wage:


Anytime your rate is per one unit of whatever, it’s referred to as a unit rate. Therefore, $40/2 hours isn’t a unit rate, where as $20/1 hour is.

To convert one rate to another, you have to perform two simultaneous conversions. It’s the same process as converting a single unit, except it needs to be performed twice – one conversion each for the numerator and denominator. The videos show several examples of unit rate conversions.

Part 2 and part 3 show examples that are slightly more challenging than those above. One of the questions from Part 2 states:

[Convert] 777 gallons per minute to cubic meters per hour

According to the question, you’re expected to go from gallons to meters. A gallon is a unit of volume while a meter is a unit of length. There’s no clear-path to convert from gallons to meters, so an intermediate step is required.