Ratio Calculator Guide
How the Ratio Calculator Works
A ratio is a comparison between two or more quantities. Ratios show the relative sizes of values and can be written in different forms: a:b, a/b, or "a to b". They're fundamental in cooking, finance, construction, and many other fields.
Different Forms
- 3:4 (colon notation)
- 3/4 (fraction)
- 3 to 4 (words)
Ratios can be simplified like fractions by dividing by the GCF. When two ratios are equal, they form a proportion.
Working with Ratios
Simplifying Ratios
Divide both parts by their greatest common factor (GCF):
Example: 12:18 → divide by 6 → 2:3
Equivalent Ratios
Multiply or divide both parts by the same number:
2:3 = 4:6 = 6:9 = 8:12 (all equivalent)
Solving Proportions
Use cross multiplication when ratios are equal:
If a/b = c/d, then a × d = b × c
Example: 3/4 = x/12 → 3 × 12 = 4 × x → x = 9
Real-World Applications
Cooking & Recipes
Scale ingredients up or down while maintaining proper proportions. A recipe with a 2:3 flour to sugar ratio stays consistent at any size.
Maps & Scale Models
Map scales like 1:50,000 mean 1 cm on the map represents 50,000 cm (500 m) in reality.
Financial Ratios
Price-to-earnings ratios, debt-to-income ratios, and profit margins all use ratio analysis.
Mixing & Solutions
Paint mixing, chemical solutions, and concrete mixtures require precise ratio calculations.