Originally Posted by

**Euclid Alexandria** Hi, Quick, I was away from the forums (and math classes) for a while, and this is one of the posts I still have questions about.

After Random's correction, I can see that your fractions (with a common denominator) are relevant to my fractions. I checked the rest of your fractions and they're also clearly relevant. They also make a briefer explanation than my analogy (I'm an intuitive thinker and a writer, so I often think in analogous terms, which obviously aren't the briefest terms in this case).

However, if I were presented with a similar question as the one posed in my original post, I would not be able to easily recreate an explanation similar to yours. This is because I can't see how you came to the conclusion that using 120 for a common denominator would be a good idea, nor can I see how you decided on what numerators to use (without the long and laborious process of filling a page with trial-and-error solutions, in which case an analogous answer would be much simpler in practice).

Could you please explain the thinking process by which you came up with your explanation of why $\displaystyle \frac{1}{5}$ is the smallest fraction?