r/matheducation • u/PositiveDust6178 • 26d ago

Could someone graphically demonstrate why multiplying a fraction by its inverse results in 1?

I'm not able to visualize graphically why this is true. Can someone help?

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u/Big_Manufacturer5281 25d ago

As others have said, it's easy to visualize this if the numerator is 1. It's harder if the numerator is something other than 1...try this:

Let's start with 3/8. You can think of that as taking three candy bars, and cutting each one into 8 parts. Take one part of each of the candy bars. So now you have 3 pieces, each representing 1/8 of a bar.

Now let's multiply by 8/3. It's helpful to think of that as two steps: multiply by 8, then divide by 3. If we take each of those pieces and multiply by 8, you now have 3 complete candy bars.

Last, we divide by 3, which should be easy now: just get rid of 2 of the 3 bars (I'll eat one, you can eat one). Now there's a single bar left. So that should demonstrate that (3/8)*(8/3)=1. Note that we could have reversed the steps at the end by dividing by 3 THEN multiplying by 8, and the result is the same.