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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.sstatic.net/s7gBZ.png [2]: https://i.sstatic.net/OxDvn.png [3]: https://i.sstatic.net/0frgX.png

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  • $\begingroup$ Converting improper fractions into mixed fractions might help. e.g. $\frac{4}{3}=1\frac{1}{3}$ $\endgroup$
    – Aman Kushwaha
    Commented Aug 28, 2021 at 3:53
  • $\begingroup$ Just add extra white spaces. Each block of white should be the same size. Then cut and shade them all in the same way, for each fraction. They will be separated, but close enough to get the idea. $\endgroup$
    – Bafs
    Commented Aug 28, 2021 at 7:03
  • $\begingroup$ Related, perhaps helpful: math.stackexchange.com/questions/1127483/… $\endgroup$
    – Ethan Bolker
    Commented Aug 29, 2021 at 13:59

1 Answer 1

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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.

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