Simplify ratios and solve ratio proportions instantly.
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Simplified ratio
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As fraction: — · As decimal: —
The Ratio Calculator simplifies ratios to their lowest terms and solves proportions of the form A:B = C:D. In Simplify mode, enter two numbers and the calculator divides both by their Greatest Common Divisor to produce the simplest form. In Proportion mode, enter any three of A, B, C, or D and the calculator solves for the fourth using cross-multiplication.
Simplified A:B = A ÷ GCD(A,B) : B ÷ GCD(A,B)
If A:B = C:D, then A × D = B × C
Solving for any one variable is straightforward algebra. For D: D = (B × C) ÷ A. For A: A = (B × D) ÷ C. And so on.
Simplify 24:36: GCD(24, 36) = 12. Simplified = 24÷12 : 36÷12 = 2:3.
Simplify 100:250: GCD(100, 250) = 50. Simplified = 2:5.
Solve 3:4 = 9:D: D = (4 × 9) ÷ 3 = 36 ÷ 3 = 12. So 3:4 = 9:12.
Solve A:5 = 10:25: A = (5 × 10) ÷ 25 = 50 ÷ 25 = 2. So 2:5 = 10:25.
Ratios are everywhere. Recipes use them (2 cups flour : 1 cup water). Maps use them (1:50000 means 1 cm on the map = 50,000 cm in reality). Finance uses them (price-to-earnings ratio, debt-to-income ratio). Photography uses them (16:9 aspect ratio). Chemistry uses them (mole ratios in reactions). Understanding ratios lets you reason about all of these domains with a single mathematical tool.
In academics, ratios appear most often in word problems, geometry (similar figures have proportional sides), and statistics (odds and relative risk). The cross-multiplication technique for solving proportions is one of the most practically useful math skills you can master — it lets you solve any "if X corresponds to Y, what does Z correspond to?" problem in seconds.
Divide both sides by their Greatest Common Divisor (GCD). Example: 12:18 has GCD(12,18)=6, so 12:18 = 2:3.
Use cross-multiplication. For A:B = C:D, the value of D = (B × C) ÷ A. Example: 3:4 = 9:D → D = (4 × 9) ÷ 3 = 12.
For A:B, the percentage of A to the total is A ÷ (A+B) × 100. Example: 3:5 → 3/(3+5) × 100 = 37.5%.
A ratio compares two quantities (A:B), while a fraction represents one quantity as parts of another (A/B). They are mathematically related: A:B = A/B as a fraction.
Yes. A ratio like 2:3:5 compares three quantities. Simplify by dividing all three by their common GCD. Example: 4:6:10 → 2:3:5.
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