Equations, Ratios, and Proportions
Equations with Two Variables
Ratios and proportions are not only used in arithmetic, but are also commonly used in algebra (and geometry). The definitions are the same as those used in arithmetic.
Ratios
A ratio is a method of comparing two or more numbers or variables. Ratios are written as a:b or in working form, as a fraction.
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is read “ a is to b.” Notice that whatever comes after the “to” goes second or at the bottom of the fraction.
Proportions
Proportions are written as two ratios (fractions) equal to each other.
Example 1: Solve this problem for x.
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First the proportion may be rewritten.
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Now simply multiply each side by y.
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Example 2: Solve this proportion for t.
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Rewrite.
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Cross multiply.
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Divide both sides by r.
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Solving Proportions for Value
Follow the procedures given in Examples 11 and 12 to solve for the unknown.
Example 3: Solve for x.
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Cross multiply.
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Divide both sides by 2.
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