Ratio Calculator

How to Simplify and Solve Ratios

A ratio compares two quantities, showing how many times one value contains another. Ratios are written as A:B or A/B and appear everywhere from recipes and maps to finance and engineering. Understanding how to simplify and solve ratios is a core math skill.

Simplifying a Ratio

To simplify a ratio A:B, find the greatest common factor (GCF) of A and B, then divide both numbers by it. For example, the ratio 12:18 simplifies to 2:3 because the GCF of 12 and 18 is 6, and 12 ÷ 6 = 2, 18 ÷ 6 = 3. A ratio is in its simplest form when the two values share no common factor other than 1.

Converting a Ratio to a Fraction or Decimal

A ratio A:B is equivalent to the fraction A/B. To convert it to a decimal, divide the numerator by the denominator. For example, the ratio 3:4 equals the fraction 3/4, which equals the decimal 0.75. This is useful when you need to compare ratios or use them in further calculations.

Solving a Proportion (A:B = X:C)

A proportion states that two ratios are equal. To solve for X in A:B = X:C, use cross-multiplication: X = (A × C) ÷ B. For example, if 2:3 = X:9, then X = (2 × 9) ÷ 3 = 6. This is the same principle used in scaling recipes, converting map distances, and calculating currency conversions.

Common Ratio Uses

• Cooking: Recipe ratios like 2:3 for water to rice keep proportions consistent when scaling.
• Finance: Financial ratios like debt-to-income or price-to-earnings compare two monetary values.
• Maps & models: Scale ratios (1:25,000) relate distances on a map to real-world distances.
• Engineering: Gear ratios, aspect ratios, and mixing ratios rely on simplified proportions.

Worked Examples

Here are a few examples that show the process. To simplify 24:36, the GCF is 12, so 24 ÷ 12 = 2 and 36 ÷ 12 = 3, giving 2:3. To convert 5:8 to a decimal, compute 5 ÷ 8 = 0.625. To solve 4:7 = X:21, cross-multiply: X = (4 × 21) ÷ 7 = 12. The calculator performs all three of these calculations at once and shows the working so you can verify each step.