ACT Math Percentage Increase and Decrease: Apply the Same Formula for Both

Percentage change=(New-Old)/Old×100%. This single formula works for increases, decreases, and everything between. Example increase: Price increased from $10 to $12. Percentage=(12-10)/10×100%=20% increase. Example decrease: Price decreased from $20 to $15. Percentage=(15-20)/20×100%=-25% decrease. The negative sign indicates a decrease. This one formula eliminates the need to memorize separate increase and decrease formulas, reducing errors and confusion.

Key insight: The denominator is always the starting (original) value. This consistency is crucial. If you reverse it (using new value as denominator), you get the wrong answer.

Mistake 1: Using the new value instead of the old value as the denominator. "Percentage=(12-10)/12×100%" is wrong. Always use the original value in the denominator. Mistake 2: Forgetting to multiply by 100% (or by 100 and add %). If you get 0.20, that's 20%, not 0.20. Mistake 3: Misidentifying which value is "new" and which is "old." Read the question carefully: "From 2020 to 2021" means 2020 is old, 2021 is new. Reversing them gives opposite sign and wrong magnitude.

Build a reference card with the formula and examples of both increase and decrease. Reference it daily until you can apply the formula without looking.

Problem 1: Salary increased from $40,000 to $50,000. Percentage=(50,000-40,000)/40,000×100%=25% increase. Problem 2: Price decreased from $80 to $60. Percentage=(60-80)/80×100%=-25% decrease. Problem 3: Population went from 5,000 to 6,000. Percentage=(6,000-5,000)/5,000×100%=20% increase. Problem 4: Inventory decreased from 200 units to 150 units. Percentage=(150-200)/200×100%=-25% decrease. Problem 5: Value increased from $15 to $18. Percentage=(18-15)/15×100%=20% increase. Solve all five, clearly labeling the old value, new value, and percent change (with sign indicating increase or decrease).

Find five percentage increase/decrease problems from a practice test. Apply the formula to each, being careful with numerator and denominator placement. By the fifth problem, you should calculate percentage change accurately and quickly.

Percentage problems appear on most ACT Math tests, particularly in word problems and data contexts. Students who master the universal percentage formula pick up 1 point on the math section because one formula eliminates the confusion of trying to remember separate increase and decrease methods.

Drill the formula daily this week. Each day, solve five percentage increase/decrease problems. By test day, you should calculate any percentage change in under 30 seconds.