Adding and Subtracting Fractions

Use the sliders below to perform addition and subtraction of fractions

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Megan Yanes, Created with GeoGebra

Move the red sliders to show 1/2.  Move the blue sliders to show 2/5.  Now move the blue point to the left so that the two squares coincide.  

1.  How many of the small congruent rectangles are red?  (Hint:  the purple ones count too)  

2.  How many are blue? (Same hint as above)  

3.  How many are there total?  (Shaded and unshaded)

4.  How do the answers to questions 1-3 relate to the sum of these two fractions?

5.  How many red, non-purple rectangles are there?

6.  How many blue, non-purple rectangles are there?

7.  How do the answers to questions 6 and 7 relate to the difference of these two fractions?

8.  Come up with a rule for adding fractions and a rule for subtracting tfractions using this tool.