SOLVING PROPORTIONS USING CROSS PRODUCTS Section 8.5
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
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 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
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 = 4 15 = = 60 Solving Proportions Using Cross Products
Solving a Proportion Using Cross Products Use the cross products property to solve d3d = 2d = d22d2 = d = 13.5 Cross products property. Divide each side by 2. Simplify. Write original proportion d3d = Solving Proportions Using Cross Products
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 = weight on Earth weight on moon 60 w Cross products property. Divide each side by w = w = w = 10 ANSWER A 60 pound dog would weigh 10 pounds on the moon. Simplify. Solving Proportions Using Cross Products
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 = Set up a proportion to find the number r of rockhoppers = r 50 rockhoppers total penguins For every 10 penguins, 3 are rockhoppers. Solve = r = 10r 10r = 15 = r Cross products property. Divide each side by 10. Simplify. ANSWER There are 15 rockhoppers at the aquarium. Solving Proportions Using Cross Products
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