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Ratio and Proportion

Ratio and Proportion. Find and simplify the ratio of two numbers. Use properties to solve real-life problems. Warm Up. Ratios in the Real World. What are some examples of ratios used in real-life?

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Ratio and Proportion

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  1. Ratio and Proportion Find and simplify the ratio of two numbers. Use properties to solve real-life problems.

  2. Warm Up

  3. Ratios in the Real World • What are some examples of ratios used in real-life? • In this lesson, you will learn about ratios in geometry and review techniques you can use to solve geometric and real-life problems with ratios.

  4. Vocabulary • Ratio a to b • If a and b are two quantities that are measured in the same units, then the ratio of “a to b” is or a : b. • Proportion • An equation that equates two ratios • Extremes • In the proportion a and d are the extremes • Means • In the proportion b and c are the means

  5. Simplifying Ratios • To simplify ratios with unlike units, convert to like units so that the units divide out. • Then simplify the fraction if possible.

  6. On Your Own The perimeter of rectangle JKLM is 56 cm. The ratio of JK:KL is 4:3. Find the length and width of the rectangle.

  7. Properties of Proportions • Cross Product Property The product of the extremes equals the product of the means. • Reciprocal Property If 2 ratios are equal, then their reciprocals are also equal.

  8. Additional Properties of Proportions • If , then • If , then

  9. Manipulating Proportions

  10. Using Proportions

  11. On Your Own

  12. Solving Proportions • Solve the proportion 1. 2. • On Your Own

  13. Using Proportions • The ratio of width to length of a rectangle is 7 : 10. The width of the rectangle is 91 cm. Write and solve a proportion to find the length. • The ratio of the two acute angles in a right triangle is 5 : 13. What is the measure of each angle in the right triangle?

  14. Closure • Describe two ways to solve a proportion.

  15. Lesson Check

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