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SOLVING PROPORTIONS USING CROSS PRODUCTS Section 8.5

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Science At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? You’ll find the answer in Example 2. In the Real World Solving Proportions Using Cross Products

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In the proportion =, the products 2 6 and 3 4 are called cross products. Notice that the cross products are equal. This suggests the cross products property. 2323 4646 Science At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? You’ll find the answer in Example 2. In the Real World Solving Proportions Using Cross Products

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NOTE BOOK If = where b and d are nonzero numbers, then ad = bc. abab cdcd Words The cross products of a proportion are equal. Numbers Algebra Cross Products Property 3434 15 20 = 4 15 = 60 3 20 = 60 Solving Proportions Using Cross Products

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Solving a Proportion Using Cross Products Use the cross products property to solve. 2929 3d3d = 2d = 9 3 9 3 2 2d22d2 = d = 13.5 Cross products property. Divide each side by 2. Simplify. Write original proportion. 2929 3d3d = Solving Proportions Using Cross Products

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Writing and Solving a Proportion Science To find the weight w of a 60 pound dog on the moon, as described earlier, write and solve a proportion using the weight of the person. PersonDog 105 17.5 = weight on Earth weight on moon 60 w Cross products property. Divide each side by 105. 105w = 17.5 60 105w 105 17.5 60 105 = w = 10 ANSWER A 60 pound dog would weigh 10 pounds on the moon. Simplify. Solving Proportions Using Cross Products

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Writing and Solving a Proportion Penguins At an aquarium, the ratio of rockhopper penguins to African penguins is 3 to 7. If there are 50 penguins, how many are rockhoppers? SOLUTION First, determine the ratio of rockhoppers to total penguins. 3 10 3 3 + 7 = Set up a proportion to find the number r of rockhoppers. 3 10 = r 50 rockhoppers total penguins For every 10 penguins, 3 are rockhoppers. Solve. 3 10 = r 50 3 50 = 10r 10r 10 3 50 10 = 15 = r Cross products property. Divide each side by 10. Simplify. ANSWER There are 15 rockhoppers at the aquarium. Solving Proportions Using Cross Products

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NOTE BOOK Cross Products Property Solving Proportions Using Cross Products 1.Write proportion Make sure the bottom numbers represent the same item and the top numbers represent the same items. 2. Cross Multiply 3. Divide 4. Write out your answer

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