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Sec 5-1D. Solve Proportions
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Definitions A Proportion is an equation stating that two ratios or rates are equivalent. 2 5 = 4 10 π π = π π , πβ 0, π β 0 Example, We sell 2 candy bars for $3.00 $ πππππ¦ ππππ = $ πππππ¦ ππππ = $ πππππ¦ ππππ Equivalent ratios have the same value.
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Cross Products We often use CROSS PRODUCTS to solve proportions.
Consider, π π = π π Multiply both sides by bd (common denominator) ππ π π = π π ππ After cross-canceling we are left with ad =bc This is the cross product of the proportion This is the same as multiplying top by bottom across the equal signβ¦cross products!
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Solve this proportion 4 13 = π₯ 39 Use cross products (4)(39) = 13x
4 13 = π₯ 39 Use cross products (4)(39) = 13x 156 = 13x = 13π₯ 13 12 = x
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Solve this proportion 18 eggs cost $3.50. How much would 10 eggs cost?
18 ππππ $3.50 = 10 ππππ π₯ Use cross products 18x = ($3.50)(10) 18x = $35.00 18π₯ 18 = $ x = $1.94 When setting up your proportion, make sure that like items are across from each other
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Solve this proportion A certain vehicle can travel 23 miles on 1 tank of gas. How many gallons will it need to travel 700 miles. Round to the nearest tenth. Set up a proportion. 23 πππππ 1 ππππππ = 700 πππππ π Use cross products 23g = 700 23π 23 = g = 30.4 gallons Miles on top Gallons on bottom
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