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

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.