Fractions, Decimals, and Percentages

ACT Math · Axiom Academy

LESSON Fractions, Decimals, and Percentages The same number, three costumes — plus the one percentage trap that catches almost everyone once Every fraction has a decimal twin and a percentage twin — they all name the same point on the number line. Watch a single marker travel from 0 to 1 : at every position, its fraction name, decimal name, and percentage name are read off together. Fraction → decimal: divide numerator by denominator Decimal → percentage: multiply by 100 2. Percent-Of vs. What-Percent-Of Nearly every ACT percentage question is one of two directions through the same relationship: part = percent × whole . Sometimes the whole and the percent are given and you solve for the part; sometimes the part and the whole are given and you solve for the percent. Same triangle, different missing corner. "What is 20% of 80?" → multiply: . "12 is what percent of 50?" → divide, then scale: . 3. Why +20% Then −20% Doesn't Get You Back to Start This is the single most common percentage trap on the ACT. Intuition says "up 20%, down 20% — that cancels out." It doesn't. The second percentage change applies to the new value, not the original one. Watch the bar grow, then shrink — and notice where it actually lands. A +r then -r pair always nets a LOSS of r^2 — never zero. 4. ACT Question Patterns to Recognize Two phrasings show up over and over. Recognizing the pattern instantly saves you from re-deriving the approach mid-test. Question: 18 is what percent of 40?

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