Fraction to Percent — turn parts into percentages fast
Core idea
A percentage is just a fraction with denominator 100. Divide numerator by denominator, then multiply by 100 and add %.
How it works
For a/b: (a ÷ b) × 100%. For a mixed number w a/b: convert to improper (w·b + a)/b first, then apply the same rule.
- Compute decimal = a ÷ b
- Percentage = decimal × 100
- Append the % symbol
Sanity checks
- 0/b → 0%
- a = b → 100%
- a > b → percentage > 100%
- b = 0 → undefined (division by 0)
Shortcuts
- Halves: 1/2 = 50%
- Quarters: 1/4 = 25%, 3/4 = 75%
- Fifths: ×20 (e.g., 3/5 = 60%)
- Eighths: ×12.5 (e.g., 3/8 = 37.5%)
Pitfalls
- Swapping numerator and denominator
- Rounding too early—keep precision, round for display
- For mixed numbers, forgetting to convert to improper first
Micro‑examples
- 3/4 → 0.75 → 75%
- 2 1/2 → 5/2 = 2.5 → 250%
- 7/4 → 1.75 → 175%
Mini‑FAQ
- Do I need to simplify first? Not required, but it helps intuition
- Repeating decimals? Keep enough digits, then round to 2–3 dp
- Why >100%? Improper fractions represent more than a whole
Action tip
When mental‑math is needed, use friendly anchors: halves (50%), quarters (25/75%), fifths (20/40/60/80%).