POTD Ratio and Proportion by myh13361

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									                   POTD                                  Ratio and Proportion
• If 3 apples cost $4, how much will 6            • To find ratios and rates
  apples cost?                                    • To solve proportions




               Definitions
• A ratio is a comparison of two numbers.                        Example
• The ratio of a to b can be written three
  ways:                  a                        • Which is the best
            a to b a :b                             buy?
                          b
• If a and b have different units, the ratio is   • Find the unit
  called a rate.                                    rates to support
                                                    your answer.
• A unit rate has demonimator 1.
• We use rates to compare items for a
  “better buy” and for other comparisons in
  general.




                                                                                1
         More with Unit rates
                                                               Conversions
• The formula “d=rt” requires a unit rate for r.
                                                   • Conversion factors are another place
• In 2004, Lance Armonstrong won the Tour            that unit rates are used.
  de France.
                                                   • Multiplying by conversion factors to
• He completed the 3391 km course in 83.6
  hours.                                             change one rate to another is called
                                                     “Dimensional Analysis.”
• Write an equation that represents this.
• Find the unit rate.                              • We will do this with speeds.
• Use this to predict how long it would take
  for him to travel 185 km.




                Examples                                         Examples
 • A snail travels 3 feet per day.                 • A car travels 60 miles per hour.
 • How many inches per minute is this?             • How many feet per second is this?



 • Another snail travels 0.5 feet per hour.        • Another car travels 44 feet per second.
 • How many inches per day is this?                • How many miles per hour is this?




                                                                                               2
              Examples
                                                        Proportions
• 5 gorbles is equal to 1 zorble.
• 3 zorbles are equal to 2 borbles.     • A proportion is an             Solve:
                                          equation that states
                                          two ratios are equal.           x 5
• You have 20 gorbles.                                                     =
                                        • We solve this with              9 6
• How many borbles is this equal to?      cross multiplication.
                                            – We could also
• You have 8 borbles.                         multiply both sides by
                                              the LCD.
• How many gorbles is this equal to?




              Examples                                    Example
    Solve:                     Solve:   •   A box of cereal weighs 354 grams.
    x 9                       x !11     •   It contains 20 grams of fat.
     =                          =
    3 8                       5   3     •   A serving size is 55 grams of cereal.
                                        •   How many grams of fat are in one
                                            serving?




                                                                                    3
      Multi-step proportions                    Literal Equations
• Solve:                              • A literal equation is an equation that
                                        contains two or more variables.
x+4 x!2                3
                         =
                           5
   =                                    – Formulas are literal equations.
 5   7                w+6 w!4
                                      • You can solve for a variable in a literal
                                        equation by using the inverse operation
                                        steps.




                Examples                  Transforming Equations
 Solve for w:          Solve for h:    Solve for x:                  Solve for y:

P = 2l + 2w                   1       2x ! 3y = !6                2x ! 3y = !6
                           A = bh
                              2




                                                                                    4
Most Common Example Ever          Ratio and Proportion
                           • To find ratios and rates
                           • To solve proportions

                           • Homework:
                             – Starts on page 145
                             – See assignment sheet




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