Now, I can visualize how a/b*a/d=ab/cd for partial fractions, but I can't for the life of me visualize how they can work for multiplying an improper fraction anywhere (i.e. either multiplying a partial fraction with an improper one or two improper fractions).
Let's say, 1/5x2/3. Let's visualize it to get a good idea of what I'm talking about. [enter image description here][1] Now, let's "overlay" the denominator 3, by cutting that 5 up into 3 parts, making it 5*3. [enter image description here][2] And now, let's get 2/3 of 1/5. [enter image description here][3]
Now, as you can see, the shaded in "overlaid" part is 2/3x1/5, or 2/15. However, I want to know how this could apply to both multiplying partial fractions with improper fractions (e.g. 1/3*4/3) and also two improper fractions. I feel like both have a different way of how they work. Thank you. [1]: https://i.stack.imgur.com/s7gBZ.png [2]: https://i.stack.imgur.com/OxDvn.png [3]: https://i.stack.imgur.com/0frgX.png
The thick green segments indicate the unit lengths in the indicated directions. The figures on the right indicate the "value" of the indicated square or rectangle.