RATIO AND PROPORTION
Activity 12: An Example of Inverse Proportion
Introduction:Think back to earlier lessons in this unit and answer the following questions:
Because these are all direct proportions, both either increase together or decrease together. More specifically, they increase or decrease at the same rate.
There are other quantities that are also related in a different way. Consider the following variables:
How are they related? What happens to the quantities on the right when those on the left increase? When one quantity increases, the other decreases.
This table of weight and distance is not of direct proportions because as weight increases, distance decreases (distance would increase if these were directly proportional).
Students should say that as weight increases, distance decreases.
In the second table of Part B, W2 X D2 = 600 in each case.
Closing DiscussionHow can you tell when a relationship between two numbers is a direct proportion, an inverse proportion, or not a proportion at all? If dividing values in corresponding columns of a table always gives the same number, there is a direct proportion. If multiplying values in the corresponding columns of a table always gives the same number, there is a direct proportion. Otherwise, there is no proportion.
Think of a situation where two quantities both increase but are not in direct proportion. Explain. An example of such a proportion is your height over time. Both the amount of time and your height increase, but you do not grow at the same rate over your lifetime.
Think of a situation where one quantity goes up while another goes down but the two quantities are not an inverse proportion. Explain. An example of this type of proportion is your ability to run over a long distance. As the amount of distance increases, you run more and more slowly, but your running speed decreases at a faster rate than the rate of increase in distance.
Activity 13: Solving Inverse Proportions
Introduction:At this point, you should have realized that in an inverse proportion, the two terms of each ratio (the numerator and denominator if the ratio is written as a fraction) always multiply to give the same value. Suppose you think it will take you 6 hours to paint your room by yourself without stopping. We can write this as:
Let's try one more example. Suppose Tom and Vickie are working together on a term paper. Tom, who can type 30 words per minute, can type the paper in 2.6 hours. If Vickie, who can type 22 words per minute, decides to help Tom by working on the second part of the paper, how long will it take the two of them working together to type the paper? We can write a fraction representing Tom working alone.
Closing DiscussionLook back to question 2 of Part B. Compare the different ways that each group solved the problem. Did all groups get the same answer? Was one way faster? Which of the procedures used is easiest to remember? Answers will vary
Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.
Last updated on 1/30/1999