Pre-Algebra: Chapter 9-1
Ratio and Rate
Ratio is the term used to describe 2 numbers expressed as a fraction. We can say 4/5, 4:5, 4 of 5 or 4 out of 5. They all mean the same thing.
Ratio is the comparison of 2 numbers with the same units, like 3 of 6 race cars.
Rate is the comparison of a fraction with numbers of varying units like 300 miles for 6 hours or 50 miles per hour. Rate always has differing units in the answer.
Unit rate is the amount of someting per unit amount. Unit amount means “per ounce or per mile”.
Here is a good link from Purplemath.
Algebra: Chapter 10-1
Simplifying Rational Expressions
A rationale expression is a quotient of 2 polynomials. A rationale expression always indicated division. A rationale expression is in SIMPLEST FORM when the numerator and denominator have NO common factor other than 1 or -1.
To simplify rationale expressions, you may have to factor the numerator and denominator.
See this page for some good examples.