Simplify a ratio or solve a proportion.
Reduce any ratio to its lowest terms, or find the missing value in A:B = C:D. See the decimal, the percentage split and equivalent ratios instantly.
Your numbers
What this means
Equivalent ratios
| Scale | A | B | As A : B |
|---|
How ratios work
Understanding Ratios
A ratio compares two or more quantities, showing their relative sizes. The ratio 3:4 means for every 3 units of the first quantity, there are 4 units of the second. Ratios can be written as 3:4, 3/4, or "3 to 4." They are used in recipes, maps, scale models, and financial analysis.
Simplifying Ratios
To simplify a ratio, divide both numbers by their greatest common factor (GCF). For example, 12:18 → divide both by 6 → 2:3. A simplified ratio uses the smallest whole numbers possible while maintaining the same relationship between the quantities.
Solving Proportions
A proportion states that two ratios are equal: A/B = C/D. To find a missing value, cross-multiply: A × D = B × C. If A:B = 3:4 and C = 6, then D = (B × C) / A = (4 × 6) / 3 = 8. This technique is fundamental in scaling, unit conversion, and similar triangles.
Ratios in Everyday Life
Recipes use ratios (2 cups flour : 1 cup sugar). Maps use scale ratios (1:50,000). Financial ratios (debt-to-income, price-to-earnings) guide investment decisions. Mixing solutions, converting units, and resizing images all rely on maintaining correct ratios.
Common questions
How do I convert a ratio to a percentage?
For a ratio A:B, the percentage of A is A/(A+B) × 100. For example, 3:4 → 3/7 × 100 ≈ 42.9% for A and 4/7 × 100 ≈ 57.1% for B.
Can ratios have decimals?
Ratios are typically expressed as whole numbers. If your ratio has decimals, multiply both sides by a power of 10 to eliminate them, then simplify. For example, 1.5:2.5 → 15:25 → 3:5.
What is a proportion?
A proportion is an equation stating that two ratios are equal, such as 1/2 = 3/6. Proportions are used to solve for unknown values when the relationship between quantities is known.
How do ratios relate to fractions?
A ratio A:B can be written as the fraction A/B. However, ratios compare parts to parts, while fractions often represent parts to whole. The ratio 3:4 is the fraction 3/4, but the parts are 3/7 and 4/7 of the total.
Results are exact for whole-number inputs. Decimal inputs are scaled to whole numbers before simplifying, so very long decimals may round.