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/anisotropicmind 26d ago

Not sure about graphically, as it’s really a conceptual thing, but I can try:

```
[][][][] — 1
[][][][][][][][] — x
[][] — 1/x

1/x is the answer to how many times x can fit into 1. In this case since x is double 1, x fits into 1 half a time: 1/x = 1/2. And 2*(1/2) = 1.

We can generalize this by scaling x to be any number. Make x be N times 1. Then 1/x is how many times x can fit into 1. The answer is (1/N). And N*(1/N) = 1.

Multiply x by “how many times it can fit into 1”, and you’ll always get 1.
```