Algebra I Recipe: Problem Solving Using Ratios and Proportions

A. Definitions

1. ratio – two quantities measured in the same unit (a fraction)
2. proportion – an equation with two ratios set equal to each other
• Extremes: "a" and "d"
• Means: "b" and "c"

B. Facts about Ratios and Proportions

1. If two ratios are equal, then their reciprocals are equal.
• Example: If   then 
2. To solve a proportion, cross-multiply OR the product of the extremes is equal to the product of the means.
• Example: If , then ad = bc.
3. If an "x²" term is obtained after cross-multiplying, solve by factoring or using the quadratic formula.

Practice Problems