Properties of Circles
Wheels in Motion
Graphing Ratios
Scale Drawings
Putting it Together
Proportions as Ratio
Inverse Proportion
Ohm's Law

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Proportion as Ratio
(Student Copy)

Activity  11:  Proportion as Ratio


Part A

Look at table you completed for Activity 3, Part A.  It looks like this:

Distance (cm)

You found that the distance traveled after five revolutions was about five times the distance traveled after one revolution.  This is an example of a proportion.  If you had a 27" wheel on your bicycle (an outside tire diameter of about 30" or 76 cm), you could say that the wheel rolled 239 cm after one revolution.  The ways you could write this ratio include:

     1:239 (number of revolutions: number of centimeters)
     1 to 239 (number of revolutions to number of centimeters)
The wheel would roll about 5 x 239 or 1195 cm in 5 revolutions.
You can express this as a proportion as follows:
    Image 2
This proportion relates the distance traveled in one revolution of a 27" bicycle wheel to the distance traveled in 5 revolutions.  Notice that the numbers in each fraction are just entries from the table!  It is always possible to write a proportion using two sets of numbers from a ratio table.

Fill in the table above with the measurements for a 27" bicycle wheel.  In the space below, write the proportions that relate the distance traveled in one revolution of a 27" bicycle wheel to the distance traveled in 2, 3, and 4 revolutions.

After completing Activity 6, you should now understand that when a bicycle is in a gear where the chain is connecting a sprocket with 44 teeth in the front to one with 22 teeth in the back, it will travel at the same speed as if you had 50 teeth in the front and 25 in the back.

Write this statement as a proportion in the space below.

Part B

Answer the following using complete sentences:

  1. If you travel 203 miles in 3.5 hours, how far will you travel in 8 hours (assuming you maintain the same speed)?
  2. A pump can pump 48 gallons of water in 3 minutes.  How many gallons can it pump in 45 minutes?  How many gallons can it pump in 2 hours?
  3. A map has a scale of 1/4 inch (which can be written as 0.25 inch) to 20 miles.  How far apart are two towns that are 2 1/2 inches apart on the map?
  4. Ed's Golf Outlet is giving 5 free golf balls with every dozen purchased.  Amy bought twelve dozen golf balls.  How many did she get free?
  5. A stamping machine can make 46 parts in a half hour.  How many parts can it make in an 8-hour shift?
  6. A kilometer is approximately 0.6 miles.  How many miles per hour is a car traveling if it is moving 90 kph (kilometers per hour)?
Part C

Solve the following proportions.  You may wish to refer to Reference Sheet

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Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.

Last updated on 1/30/1999
Comments: egalindo@indiana.edu