Ratios are recipes for relationships — flour to water, cement to sand, width to height. This page does the three things ratios need: simplify to lowest terms, solve the missing term of a proportion, and scale everything up or down.
Simplifying: same relationship, smallest numbers
18:24 and 3:4 say the same thing; the second just says it cleanly. Divide both sides by their greatest common factor (6 here) and you're done. Decimals work too — 2.5:4 gets lifted to 25:40 and lands at 5:8, with the calculator showing exactly what it multiplied and divided.
Proportions: cross-multiply and conquer
A proportion claims two ratios are equal: 3:4 = 9:x. Cross-multiplication turns the claim into an equation — 3x = 36, so x = 12. This one move solves map scales, unit prices, drug dilutions, and every "if 3 workers take 4 days…" puzzle (mind the inverse ones, though — more workers means fewer days).
Scaling: recipes, mixes, models
The scaling table multiplies your ratio through ×0.5 to ×10, keeping the relationship fixed while the quantities move — a 2:3 mix serving four becomes 4:6 for eight. Three-part ratios like concrete's classic 1:2:3 follow the same logic; scale each term by the same factor. For the part-of-whole view of the same math, see the fraction calculator, and for screen dimensions specifically, the aspect-ratio version of this problem has its own tool.
Ratio vs rate vs fraction
A ratio compares parts (3:4), a fraction names a share of the whole (3⁄7 of the mix is flour), and a rate compares different units (km per hour). Keeping the three straight prevents most word-problem wrecks — and percent, the fourth sibling, lives in the percentage calculator.
All math exact until display rounding at 4 decimals.