What percent is X of Y?

The formula

Percentage = part ÷ whole × 100. For a test score of 42 out of 50, 42 ÷ 50 = 0.84, and 0.84 × 100 = 84%.

Which number is the whole?

The whole is the number that comes after “of” in the question. In “what percent of the budget is rent?”, the budget is the whole. In “what percent of rent is the utility bill?”, rent is the whole. Swapping them is the most common mistake, and the answers are very different: 350 is 12.5% of 2,800, while 2,800 is 800% of 350.

If the question compares an old value with a new one (“by what percent did it grow?”), you want percentage change instead. That divides the change by the old value rather than dividing one value by the other.

When the answer is over 100%

A result above 100% means the part is larger than the whole. That’s normal when the “whole” is a target or a previous figure: selling 130 units against a target of 100 is 130% of target. It signals a mistake only when the part is supposed to be a piece of the whole, such as students who passed out of students who sat the test.

Dividing by zero

If the whole is 0, there’s no answer. No number multiplied by 0 gives a non-zero part, so the calculator tells you this instead of showing an error code.