Working With Ratios

A ratio a:b compares two quantities — it has no units. Simplifying by the GCD (e.g., 8:12 → 2:3) makes ratios easier to read and compare, and equivalent ratios (2:3 = 4:6 = 6:9) are produced by scaling both terms by the same factor.

Ratios, Decimals, and Percentages

Every ratio corresponds to a decimal (a ÷ b) and a percentage (a ÷ b × 100). A 2:3 ratio is 0.6667, or 66.7% — useful when converting recipes, mixes, or financial relationships between forms.

Solving Proportions

Proportions state that two ratios are equal: A/B = C/D. Cross-multiplication gives D = B × C ÷ A. This is the standard technique for scaling recipes, resizing images proportionally, and unit conversions.