Proportion and Reasoning

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Proportion and Reasoning

• Algebra Review
• Pg. 560 - 561

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• Working with similar geometric figures involves
  ratios and proportions.
• A ratio is an expression that compares two
  quantities by division. You can write the ratio
  of quantity a to quantity b in these three ways
• a to b ab

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• A proportion is a statement of equality between
  two ratios.
• The equality is an example of a
  proportion.
• Proportions are useful for solving problems
  involving comparisons.

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Example Problem

• In a photograph, Dan is 2.5 inches tall and his
  sister Emma is 1.5 inches tall. Dans actual
  height is 70 inches. What is Emmas actual
  height?
• The ratio of Dans height to Emmas height is the
  same in real life as it is in the photo.
• So, let x Emmas height and set up a proportion.

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• Dans height in Dans actual
• photograph height
• Emmas height in Emmas actual
• Photograph height
• Now solve for x.

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• Solve for x.
• Emma is 42 inches tall.

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Example 2

• Some proportions require more algebra to solve.
• Solve

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Assignment

• Pg. 561
• 1-13 all