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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.
ExamplesExamples:
4/x = 16/3

10/y = 5/24

(3x)/4 = 5/6

(2x)/(3x - 2) = 4/5

x/(x+6) = 3/x




G Redden

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