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1 Math Solving Proportions

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2 Vocabulary ► Proportion—an equation that shows that two ratios are equivalent. ► Cross Product—the product of the numerator of one ratio and the denominator of the other ratio.

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3 Notes ► 1=3 1 x 6 is a cross product. 262 x 3 is a cross product. ► The cross products of a proportion are equal. ► Two ratios form a proportion if their cross products are equal.

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4 Determine whether each pair of ratios form a proportion. a. 8/10 and 4/5 b. 9/4 and 11/6 c. 6/14 and 9/21 d. 15/12 and 9/6 e. $2.48/4oz and $3.72/6 oz f. 125 mi/5.7 gal and 120 mi/5.6 gal

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5 Example ► Before dinner, Mohammed solved 8 math problems in 12 minutes. After dinner, he solved 2 problems in 3 minutes. Is the number of problems he solve proportional to the time?

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6 Example ► Determine if the quantities $30 for 12 gallons of gasoline and $10 for 4 gallons are proportional.

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7 Notes ► Solving the proportion—Process of using cross products to find a missing term in a proportion. ► Solving a proportion is similar to solving an equation.

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Example x = 4 9 6 x 6 = 9 4 (Cross multiply) 6x = 36 (Solve for the variable) 6x = 36 (Divide to undo multiplication 6 6 6 6 x = 6 8

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9 Examples a. 5/8 = 18/x b. 9/15 = k/18 c. 3.5/14 = 6/n d. 4.6/w = 4/5

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10 Solve each proportion. a. 5 /15 = 15/w b. 2 4/13 = a/26 c. y /7 = 16/28 d. 1 8/x = 3/36 e. 52/8 = m/9 f. 3/u = 5/15 g. 20/b = 70/28 h. 650/6.5 = z/5

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