What does 2/3 of 2/5 mean?

To understand fractional numbers, you need to first understand numbers.

Numbers are just representations of quantity. Numbers in themselves have little meaning. But, when you provide a unit to any number, they start to make sense. The numbers 1 and 2 are just symbols, but when you say 1 apple or 2 apples, you start to understand that numbers are simply representing the quantity of apples.

Likewise, when you need to represent a quantity of apple that is less than 1, the fractional numbers will help you do the job.

“But why?”, you say, “Why would I ever want to represent a number that is less that 1?”.

It’s like that question you were asked in primary school mathematics, “How will you share a single apple between two friends?” The answer is you cut it in half.

Half (1/2) is a fractional number. It means one part of two.

So to go back to the original question. 2/3 by itself doesn't mean much generally. It's basically just how it reads two thirds (two out of three). So it could mean anything based on the context (unit).

For example: 2/3 points could be a maths test result of a student. In that case, it could mean that student solved two out of three questions, assuming each question carries one point.

Or staying in the realm of apples, “John ate 2/3 of an apple” could mean someone divided the apple into three equal parts and John took and ate two of those divisions.
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