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
• A unit rate has demonimator 1.
• We use rates to compare items for a
“better buy” and for other comparisons in
general.

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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?

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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?

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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

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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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