Reduce any ratio to its lowest terms, or find the missing value in A:B = C:X.
Divide both terms of the ratio by their greatest common divisor (GCD). Simplifying 8:12 — the GCD of 8 and 12 is 4, so dividing both terms by 4 gives 2:3, the lowest-terms form of the same ratio.
A proportion sets two ratios equal to each other, like A:B = C:X. Cross-multiplication gives A × X = B × C, so X = (B × C) / A. This lets you find a missing fourth value any time you already know three of the four numbers in a proportional relationship — a very common real-world task, like scaling a recipe or a map.
Related, but not identical. A fraction represents a part of a whole — 3/4 of one pizza. A ratio compares two separate quantities that don't have to add up to any single whole — a 3:2 ratio of flour to sugar in a recipe describes two different ingredients, not two parts of one total amount. Ratios are often written and calculated in fraction form, which is exactly why the two concepts get conflated, even though conceptually a ratio is a comparison and a fraction is a portion.
The Fraction Calculator handles arithmetic directly on fractions — adding, subtracting, multiplying, and dividing two fractions together. This tool instead handles ratio-specific tasks: reducing a ratio to its lowest terms, and solving a proportion for a missing value. Use the Fraction Calculator when you need to combine two fractions; use this tool when you're comparing quantities or scaling a proportion.
Worked example: simplifying 8:12 gives 2:3 (dividing both by their GCD, 4). Solving the proportion 2:3 = 10:X: X = (3 × 10) / 2 = 30/2 = 15 — check: 2:3 and 10:15 both reduce to the same 2:3 ratio.