Ratios and Rates

it compares 2 quantities using division 

When a ratio compares 2 quantities with unlike units, it is called a rate.

Examples: miles per gallon, cents per pound, dollars per movie ticket

A ratio is not a rate if it compares 2 quantities of similar measurement.

Examples: teachers/students are similar

red counters/yellow counters are similar

The first quantity on top, the second quantity on the bottom in a

Example: A car travels 270 miles on 10 gallons of gas:

 $\frac{270}{10}$  you will divide the numerator (top) by the denominator (bottom):  270  $\div$  10 gives us:   $\frac{27\ miles}{1\ gallon}$  

Our rate in simplest form is 27 miles per 1 gallon of gas

 $\frac{3\ chaperones}{15\ students}$  

there are 3 chaperones for every 15 students


This is not a rate because it compares similar units of measurement.  In simplest form (by dividing numerator by the denominator) is  $\frac{1\ chaperone}{5\ students}$