Math & homework

Student and homework helpers: fraction arithmetic, greatest common factor and least common multiple, mean/median/mode, standard deviation, quadratic formula, slope and intercept, Pythagorean theorem, triangle and circle area, and percentage change. Classroom estimates — verify significant figures and show your work for graded assignments.

A calculated answer is most useful when you already have one of your own to check against, so work the problem first and use these tools to confirm it. A few distinctions come up repeatedly. Mean, median, and mode answer different questions, and the median is the more honest summary when a few extreme values would drag the average; standard deviation has separate sample and population forms, and using the wrong one on a small dataset changes the result. Percentage change is not symmetric — a rise of 50 percent followed by a fall of 50 percent leaves you below where you started. The quadratic formula returns two roots, and whether both are valid depends on the problem, since a negative length or time usually is not.