Glossary
percent change
A percent change is the amount of change divided by the value you started from, written as a percent: (new − old) ÷ old × 100.
A percent change measures how much a value rose or fell, as a share of where it started. Find the amount of change (new minus old), divide it by the original value, and multiply by 100. A price that goes from $80 to $92 changed by $12, and 12 ÷ 80 = 0.15, a 15% increase. The denominator is the original value, and that is where the mistakes live. Dividing by the new value instead gives 12 ÷ 92 ≈ 13%, which is a different quantity — the change relative to where it ended, not where it began. Reporting the raw change (12) as if it were a percent is the second common error. To reverse the question — find the original price after a known percent increase — divide the final value by 1 plus the rate, so $75 after a 25% increase came from 75 ÷ 1.25 = $60.
Taught in
Related terms
- ratio — A ratio compares two quantities by division, written with a colon or as a fraction — 2 to 3 means two parts of one thing for every three of another.
- simple interest — Simple interest is I = Prt — principal × rate × time — where the rate is a decimal and the time is in the rate's units.
Source: OpenStax Prealgebra, Elementary Algebra and College Algebra, first editions (CC BY 4.0); NIST SP 811 (units). Each definition restates the two Mathematics guides in this exam, which carry the per-source citations on their own pages. (OpenStax 1e and NIST SP 811 accessed 2026-10-07)