Use the sliders below to perform addition and multipllication of fractions.

The red sliders represent the numerator and denominator of the first fraction. The blue sliders represent the numerator and denominator of the second fraction. Move the sliders to the desired positions for the fractions you are adding or multiplying. Next, move the blue point to the left so that the two squares coincide.
For addition,
The numerator can be found by counting all of the shaded rectangles. The purple ones must be counted twice since they are two overlapping rectangles (one red and one blue). The denominator is found by counting all of the small congruent rectangles.
For multiplication, the answer is:
(all of the purple rectangles) / (total number of small congruent rectangles)