Proper Fraction Fury
Suppose you start with a proper fraction (where the numerator is less than the denominator), and you add 1 to the numerator and to the denominator. For example, if you started with 2/ 3, then you'd get
Is this procedure of adding 1 to the numerator and the denominator the same as adding the number 1 to the original fraction? Explain your reasoning.
Try several examples (with proper fractions), comparing the sizes of the original fraction and the new fraction. What do you notice?
Give a general explanation for what you observe. In other words, compare the sizes of
(Source: Insights in Arithmetic and Geometry, Sybilla Beckmann, University of Georgia, Department of Mathematics, 1998.)

Related External Resources 
Visual Fractions [ java applet ]
A series of java programs using number lines to help visualize fractions and the operations on them.
No Matter What Shape Your Fractions are In
A geometric approach to fractions.
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