Rates

The relationship ^a/_b of two quantities a and b that are measured in different units.  For example, a car that travels 100 miles in 2 hours has an average RATE of speed of:

^{50 miles}/_{1 hour}  or 50 miles per hour

Ratios

a comparison of two quantities or numbers that are measured in the same units.  A ratio can be expressed as:
1)  ^a/_b
2)  a:b    
3)  a to b
Recipe ingredients are often expressed as ratios to a unit of measure such as a cup or tablespoon.

Proportions

A proportion is an equation that balances two ratios, rates, or fractions, using an equals sign.  You can solve for unit rates (e.g. miles per gallon, price per pound, etc.) and other rate/ratio problems using proportions.  Proportions can be solved using cross-multiplication, aka the "cross-product rule." 

For example:

A car travels 240 miles in 6 hours.  What is the average speed in miles per hour (mph)?

Set up the proportion and use the cross-product rule. You can read the following proportion as "240 miles is to 6 hours, what m miles is to one hour":

Answer:   40 mph

DO NOW:

1) A car travels 840 miles in 14 hours.  Set up a proportion and express the solution as a unit rate.

2) There are 10 boys in a class of 25.  Express the ratio of boys to girls in lowest terms.