NumberTally Ratio Calculator
Simplify ratios and solve proportions in seconds. Reduce a ratio like 12:18 to lowest terms (with an optional third part), or find the missing value in a proportion like 2:3 = 6:x — with every step shown.
Solves a:b = c:x — leave exactly one box empty.
Splits the amount into shares proportional to a:b (or a:b:c).
Advanced options
Simplifying with the GCD
A ratio is in lowest terms when its parts share no common divisor but 1. Divide every part by the greatest common divisor — 12:18 shares GCD 6, so it reduces to 2:3. The steps box shows the Euclidean algorithm finding that GCD.
Cross-multiplication for proportions
If a:b = c:x, then a·x = b·c, so x = b·c/a. Scaling a recipe, converting currencies, map distances — all the same trick.
Frequently Asked Questions
What is a ratio?
A comparison of two or more quantities, written a:b. It tells you how many of one thing per unit of another.
How do you simplify a ratio?
Divide all parts by their greatest common divisor. 12:18 → GCD 6 → 2:3.
What is a proportion?
An equation stating two ratios are equal, like 2:3 = 6:9. Proportions let you solve for a missing value.
How does cross-multiplication work?
For a/b = c/d, multiply diagonally: a·d = b·c. Then isolate the unknown — one division finishes it.
What is the greatest common factor (GCF)?
The largest number dividing all given numbers evenly. Same thing as the GCD — the two names are interchangeable.