Guides/Reverse percentage
Reverse percentage: find the whole from a part
Forward percent asks “what is 18% of 250?” Reverse percent asks “18% equals 45 — what was the whole?” Shops, tips, and test scores often give you the part and the rate, not the base.
Core formula
- If part = rate × whole, then whole = part ÷ rate.
- Write the rate as a decimal: 18% → 0.18, so whole = 45 ÷ 0.18 = 250.
- Forward direction refresher:percentage of a number.
Worked examples
- Tip known: 20% tip was $16 → bill before tip = 16 ÷ 0.20 = $80.
- Score: 85% of a quiz is 34 points → total points = 34 ÷ 0.85 = 40.
- Sale remainder: after 30% off you paid $70 (70% of original) → original = 70 ÷ 0.70 = $100. Related:original price before discount.
“Percent of” vs “percent off”
Paying 70% of the price is not the same wording as “30% off,” even though the dollars can match. Seepercent off vs percent ofanddiscount math.
Common mistakes
- Dividing by 18 instead of 0.18 (off by 100×).
- Treating “increased by 20% to 120” as divide-by-0.20 instead of divide-by-1.20.
- Stacking percents without converting back to a single factor —compound two-step %.