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Ratios and Proportions

Ratios and Proportions. Objective I will solve proportions using reciprocals and cross products. I will use proportions to solve real-life problems. Vocabulary. Proportion - an equation in which one ratio is set equal to another ratio

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Ratios and Proportions

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  1. Ratios and Proportions Objective • I will solve proportions using reciprocals and cross products. • I will use proportions to solve real-life problems.

  2. Vocabulary • Proportion - an equation in which one ratio is set equal to another ratio (Written in the form of , which is read as “a is to b, as c is to d”)

  3. Using the Reciprocal Property Solve the proportion . SOLUTION Write original proportion Use reciprocal property Multiply each side by 4 Simplify

  4. Using the Reciprocal Property Solve the proportion . CHECK Substitute

  5. Using the Cross Product Property Solve the proportion . Write original proportion Use cross product property Simplify Take square root of both sides The solutions are x=-8 and x=8. Check both answers.

  6. Checking Solutions Solve the proportion. Use cross product property Use distributive property Isolate variable term Take square root of both sides

  7. Checking Solutions Check each solution. x = 4: x = -4 The solution x = -4 is extraneous because the check results in a false statement. The correct solution is x = 4.

  8. Proportions in Real-Life Archaeologists excavated three pits containing the clay army. To estimate the number of warriors in Pit 1 shown below, an archaeologist might excavate three sites. The sites at the ends together contain 450 warriors. The site in the central region contains 282 warriors. This 10-meter-wide site is thought to be representative of the 200-meter central region. Estimate the number of warriors in the central region. Then estimate the total number of warriors in Pit 1.

  9. Proportions in Real-Life 282 warriors 62m 240 warriors 210 warriors 10m Central Region 200m 5m 5m SOLUTION Let n represent the number of warriors in the 200-meter central region. You can find the value of n by solving a proportion.

  10. Proportions in Real-Life Number of warriors found Number of meters excavated = Total number of warriors Total number of meters 282 = 10 n 200 The solution is n = 5640, indicating that there are about 5640 warriors in the central region. With the 450 warriors at the ends, that makes a total of about 6090 warriors in Pit 1.

  11. Practice

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