Chapter 7 Proportional Reasoning Section 7.1 The Concept of

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Chapter 7Proportional Reasoning

• Section 7.1
• The Concept of Ratio

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Definition of Ratio

• A ratio is an ordered pair of numbers used to
  show a comparison between like or unlike
  quantities, written x to y,
• x , x y, or x y (y ? 0).
• Y
• Example
• A certain football team won 9 of the twelve
  games they played last season. Write the ratio
  of
• wins to games played (part to whole)
• games played to losses (whole to part)
• wins to losses (part to part)

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Equivalent Ratios

• Two ratios are equivalent ratios if their
  respective fractions are equivalent or if the
  quotients of the respective terms are the same.
• Example
• Katrina makes 8 free throws every 10 attempts.
  At this rate, how many free throws can she expect
  to make in 15 attempts? 20 attempts? 75
  attempts?

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Rates

• A rate is a ratio comparing quantities that
  involve different units. The word per is often
  used to describe rates.
• Rates of speed, time
• Unit price

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Example

• A recipe for biscuit mix calls for 8 cups of
  flour, 1 1/3 cups of nonfat dry milk, and 5
  tablespoons of baking powder, along with other
  ingredients. If you had only 6 cups of flour,
  what would be the comparable amounts of nonfat
  dry milk and baking soda?

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Example

• Alisha finds that she uses 12 gallons of gasoline
  for every 250 miles that she drives. Her friend
  Nicole uses about 15 gallons of gasoline for
  every 300 miles that she drives.
• Who gets the better gasoline mileage and why?