Ratio Calculator — quick guide
1) Core idea
Ratios compare quantities (a:b). You can simplify, solve proportions a:b = c:x, compute scale factors, and generate equivalents.
2) How this tool works
- Simplify: reduce by GCD; supports two or three terms.
- Proportion: solves a:b = c:x via x = (b × c)/a.
- Scale: factor = scaled/original; outputs simplified ratio and percentage.
- Equivalents: lists multiples of the simplified base ratio.
3) Sanity checks
- 12:18 → 2:3 (GCD 6).
- 2:3 = 8:x → x = 12 by cross‑multiplication.
- Scale 5 → 15 gives factor 3:1; new 8 → 24.
4) Shortcuts that help
- Normalize decimals by scaling to integers before GCD.
- Keep units consistent when forming ratios.
- For equivalence lists, multiply the simplified ratio by 1..N.
5) Common pitfalls
- Division by zero in proportions (ensure a and b ≠ 0).
- Order reversal: a:b ≠ b:a unless explicitly inverted.
- Mixing decimals and integers without scaling for GCD.
6) Micro-examples
- 3:4 equivalents → 3:4 = 6:8 = 9:12 …
- 10:25 → 2:5.
- Scale 7→14 (2×), new 9 → 18.
7) Mini-FAQ
- Three-term ratios? Supported in simplify; GCD reduces all parts.
- Decimals? Converted to integers internally for accurate GCD.
- Rounding? Results shown rounded for readability; math uses full precision.
8) Action tip
Write ratios with units (e.g., cm:cm) and keep term order consistent across equalities.