Start by naming the mathematical object
A percentage describes a part relative to a stated whole. A fraction preserves an exact number of equal parts. A ratio compares two quantities without declaring their total. These ideas can all be written with a slash or a colon, but their questions are different. The useful first step is to write what each number represents before applying an operation.
Averages need their hidden denominator
A grade percentage divides points earned by points available. GPA divides quality points by course credits. A weighted average divides weighted values by their combined weights. Standard deviation does not average the values directly; it summarizes their distances from their mean. Choosing the denominator is often the entire problem, especially when course credits, group sizes, or assessment totals differ.
Use exact forms when they carry information
The fraction 5/6 is exact even when a display gives 0.8333. Scientific notation separates a coefficient from a power of ten and can communicate significant figures. Reducing 12:20 to 3:5 shows proportional shape, while keeping 12 and 20 preserves an actual count. Keep the form that will make the next decision easier to check.
Check the convention before relying on a result
Schools choose their own grade scales and GPA inclusion rules. Statistics distinguishes a population divisor from a sample divisor. Percentage changes require an old value, while ordinary percentages require a base. A browser calculation can expose the arithmetic, but the syllabus, measurement record, or stated definition supplies the convention that makes the arithmetic relevant.
Keep source values beside the answer
For a study calculation, save the original score, credits, units, scale, and rounding rule. A result can then be reconstructed and challenged without guessing which number was treated as the total. That habit is more valuable than a memorized formula when a score, experiment, or planning estimate is reviewed later.