Why is there a need to simplify fractions?
To clarify communication and to avoid misunderstandings.
For one thing, it is a spelling (or grammar) -like rule.
Why do we spell school like that ("school") instead of skule? Why is "cat" spelled with a "c" rather than a "k"?
Why do we end a sentence starting with the word "Why" by putting a question mark?
Why do we end one sentence with a period and also start the next with a capital?
The reason we have spelling and punctuation 'rules' is to clarify communication and to avoid misunderstandings.
We simplify fractions for the same reason. To clarify communication and to avoid misunderstandings.
If you and I do some complicated arithmetic and you get
(We didn't. You got
And what if Sam got
(Sam also got