Work with fractions confidently
Core idea
Fractions are ratios of integers. The suite helps you add, subtract, compare, convert, and simplify them with exact math and clear steps.
How it works
- Operations: find LCD for +/−; use cross‑multiply rules for compare.
- Conversions: decimals ↔ fractions, percentages, ratios, mixed ↔ improper.
- Simplification: GCD reduction to lowest terms everywhere.
Sanity checks
- Denominators are never 0 and remain positive.
- Results reduce to lowest terms; mixed forms are consistent with improper.
- Back‑conversion (to decimal/percent) matches within display rounding.
Shortcuts
- Memorize common families: halves, thirds, quarters, fifths, eighths.
- Use GCD/LCD to shrink work before doing arithmetic.
- Convert mixed to improper for × and ÷ to avoid borrowing mistakes.
Pitfalls
- Adding unlike denominators without converting.
- Dropping signs or placing the sign on the denominator.
- Rounding values instead of display outputs.
Micro‑examples
- 3/4 + 1/2 → LCD 4 → 3/4 + 2/4 = 5/4 = 1 1/4
- 0.125 → 125/1000 → 1/8
- 5/4 → 1 1/4 → 125%
Mini‑FAQ
- Why LCD for addition? It aligns part sizes so numerators add meaningfully.
- Do all decimals convert? Yes—terminating or repeating → exact fraction.
- Is simplest form unique? Yes, with a positive denominator.
Action tip
Use the Quick Fraction Calculator to sanity‑check; then jump into the specific tool that matches your task for detailed steps.