3.2 Meaning of Percentage

Figure: A percentage is simply how many of 100 equal squares are shaded.

The word “percent” comes from the Latin per centum, meaning “per hundred.” A percentage is simply a fraction (or ratio) whose denominator has been standardized to 100. Writing “x%” means x parts out of every 100 parts of the whole.

x% = (x)/(100)

Percentages are a universal language for comparison because they remove the need to know the actual size of the whole — saying “36% of students passed” lets you compare a class of 50 with a class of 5,000 on equal footing. Every percentage problem, no matter how complicated it looks, is built from just three quantities: the base (the whole, treated as 100%), the part (the portion you’re interested in), and the percentage value itself. Correctly identifying which quantity is the base is 80% of solving any percentage question correctly.

Percentage = (Part)/(Base) × 100