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About This Calculator
Ratios express the relative size between two or more quantities and appear constantly in cooking, construction, finance, and science. This calculator simplifies ratios, solves for missing values in proportions, and scales quantities up or down while maintaining the original relationship. Understanding ratios is essential for tasks like mixing concrete at the correct strength or converting recipe portions for different serving sizes.
Quick Tips
- 1 Simplify ratios like fractions — divide both sides by their GCF.
- 2 To scale a ratio, multiply or divide both parts by the same number.
- 3 Ratios can have more than two parts — 2:3:5 splits 10 into 2, 3, and 5.
Example Calculation
A recipe calls for flour to sugar in 5:2 ratio, you have 750g of flour.
Sugar needed: 300g | Total mixture: 1,050g | Flour: 71.4%, Sugar: 28.6%
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.
Frequently Asked Questions
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.
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.
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.
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.