Musical Chairs

Suppose a, b, and c are whole numbers not equal to zero. Also, suppose   a > b > c. What can you say about each of these fractions?

If possible, tell which of the following is larger. Justify your thinking.

(Reprinted with permission from Developing Number Sense in the Middle Grades, Addenda Series Grades 5-8, copyright 1991 by the National Council of Teachers of Mathematics. All rights reserved.)

Extension:
Let’s say a, b, and c are integers instead of whole numbers. Do any of your conclusions change? How? Why?

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