Fractions, Decimals, and Percents

GRE Quantitative · Axiom Academy

LESSON Fractions, Decimals, Percents One number, three costumes — and the exact moves that convert between them, fast enough for the GRE clock. Picture Fraction , Decimal , and Percent as three corners of a triangle, with the same value — here — riding around it. Each edge is one mechanical move: divide the numerator by the denominator to land on the decimal, multiply by 100 (shift the decimal point two places right) to land on the percent, or write over 100 and reduce to go straight back to a fraction. Fraction → Decimal: divide top by bottom Decimal → Percent: multiply by 100 Conversion gets you INTO a form — but the GRE also tests what you do once you're there. Fraction arithmetic has three fixed rules, and "percent of a number" is just multiplication in disguise. Same denominator: add the numerators, keep the denominator. . Different denominators: find a common one first. Multiply numerators together, multiply denominators together, then reduce. . Multiply by the reciprocal of the second fraction. . Convert the percent to a decimal, then multiply. What is 20% of 50? . . A price moves from \ 120: change =120-100=20 , so percent change . On the actual test, you don't have time to long-divide by hand. Memorize the common fraction–decimal–percent triples below so they're instant recall — then watch the single trap that catches almost everyone at least once: successive percent changes don't cancel.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.