How to Calculate Percentages
What is a Percentage?
A percentage is a number expressed as a fraction of 100. The word comes from the Latin 'per centum', meaning 'by the hundred'. Percentages are used to express how large or small one quantity is relative to another quantity.
Common Percentage Formulas
Finding the percentage:
Example: 20 is what percent of 80?
(20 ÷ 80) × 100 = 25%
Finding the value:
Example: What is 15% of 80?
(15 ÷ 100) × 80 = 12
Finding the original value:
Example: 12 is 15% of what number?
12 ÷ (15 ÷ 100) = 80
Percentage increase/decrease:
Example: From 80 to 100:
((100 - 80) ÷ 80) × 100 = 25% increase
Confession: I once tipped 42 % at a diner because I read the receipt wrong. The waiter loved me; my wallet cried. Five minutes with the right percentage shortcut would’ve saved lunch money for a week. Let’s make sure that never happens to you.
1-Minute Cheat Sheet 🚀
| Need it now? | Do this |
|---|---|
| Formula | % = (Part ÷ Whole) × 100 |
| Find the Part | (% × Whole) ÷ 100 |
| Find the Whole | Part ÷ (% ÷ 100) |
Sticky-note these three and you’re already 80 % better than yesterday.
Quick Story: The Concert Ticket Mix-Up 🎸
Two friends bought tickets—one at $75, one with a 20 % student discount. My buddy asked, “How much did I save?” Brain freeze!
Part = ?
Whole = $75
% = 20 → (20 ÷ 100) × 75 = $15 savings.
Now he owes me popcorn for doing the math on the train.
Step-by-Step Walk-Through
Identify the Whole
– Original price, total points, or full population.Grab the Part or %
– Sale discount, test score, battery level—whatever chunk you’re eyeing.Plug & Chug
Part ÷ Whole → multiply by 100. Done. Calculator welcome, sanity preserved.
Example: Exam Score
You scored 42 out of 50.
% = (42 ÷ 50) × 100 = 84 %. Smash that “B” with pride.
Visual Hack 🎨 (Use in your notes)
Draw a pizza: whole pie = 100 %. Shade the slice you’ve eaten. Suddenly “25 %” looks as tasty as mozzarella.
Everyday Scenarios & Mini-Calculations
| Scenario | Math in 10 sec | Result |
|---|---|---|
| Black-Friday 30 % off $120 | 0.30 × 120 | $36 off → Pay $84 |
| Battery drops from 100 % to 37 % | 100 – 37 | 63 % used |
| Restaurant bill $48 + 18 % tip | 0.18 × 48 | $8.64 tip |
Pro tip: Round the bill to nearest $10 for mental math, then adjust—waiters forgive pennies.
Watch-Out Zone ⚠️
Percent of vs. Percent increase
– 20 % of $50 ≠ 20 % increase from $50 (which is $10 added).Stacking Discounts
– 50 % + 20 % off isn’t 70 %—it’s 50 % first, then 20 % of the new subtotal.Over-100 % Results
– Scores can exceed 100 % with bonus points. Perfectly legal in math land.
Pull Quote
“Percentages are just fractions wearing fancy cologne.” —My stats professor, mid-lecture yawn
Mental-Math Hacks You’ll Actually Use
Move the Decimal – 10 % off? Shift it left one place. 20 %? Double the 10 %.
Complement Trick – Want 15 % tip? Find 10 % (easy), plus half of that. Boom.
Cross-Multiplication for Unknowns – a/b = x/100 → x = (a × 100)/b. Saves phone battery.
Nerd Corner (Optional but Geek-Approved)
Percent Error = |Actual − Expected| ÷ Expected × 100
Compound Percent Change = [(1 + p₁)(1 + p₂)… − 1] × 100
Index Numbers (CPI, etc.) rely on chained percentages—economy’s secret language.
Feel-Good Challenge
Grab your latest grocery receipt. Pick any item, calculate how much you’d save with a 12 % coupon, and drop the number in the comments. Funniest product wins a virtual high-five emoji.
Remember: Next time you stand at a cash register, calculator panic = obsolete.
