Comparing Fractions — the 80/20
To compare fractions, either convert to a common denominator and compare numerators, or convert to decimals. The calculator shows both.
How it works
- Find the LCD of all denominators.
- Rewrite each a/b as (a×k)/(b×k) with the LCD.
- Compare numerators; greater numerator means greater fraction.
- Optionally verify by decimal or percent.
Sanity checks
- Same denominators → larger numerator is larger.
- Same numerators → smaller denominator is larger.
- 1/2 ≈ 0.5; 3/4 ≈ 0.75, so 3/4 > 1/2.
Shortcuts
- Two fractions: use cross‑multiplication (ad vs bc).
- Use benchmark fractions (1/2, 1/4, 3/4) to estimate quickly.
- Convert mixed numbers to improper before comparing.
Pitfalls
- Comparing parts separately (numerator vs denominator) without context.
- Arithmetic slips when finding the LCD or multiplying.
- Not simplifying before comparing similar fractions.
Micro‑examples
- 3/4 vs 5/8 → LCD 8 → 6/8 vs 5/8 → 3/4 is larger.
- 1/3 vs 2/5 → cross‑multiply: 1×5=5, 2×3=6 → 2/5 > 1/3.
- 1/2, 2/3, 3/5 → order: 1/2 < 3/5 < 2/3.
Mini‑FAQ
- Decimals vs fractions? Both valid; decimals are handy for quick checks.
- Do I need the LCD? For exact comparison by numerators—yes.
- How about negatives? More negative means smaller; apply rules to absolute values, then sign.
Action tip
Enter your fractions and click compare—the tool will order them, show simplified forms, decimals, and a clear step‑by‑step.