Making life easier.
Reducing a fraction to its smallest terms (e.g., 4/8 -> 1/2).
Mathematicians value elegance. The simplest answer is usually the best answer.
Divide top and bottom by the Greatest Common Factor.
Plain English: Imagine a pizza cut into 8 slices. If you eat 4 slices, you ate 4/8 of the pizza. But it's easier to just say you ate 'half' (1/2). Simplifying makes numbers smaller and easier to handle without changing the amount.
Real-world example: Woodworking instructions. They won't say 'cut 2/4 of an inch.' They say '1/2 inch.'
Dividing the top number but forgetting to divide the bottom number. You must treat them equally!