Ratio Calculator

A ratio is a comparison between two or more quantities, showing how many times one value contains another. It's expressed as a:b or a/b, where a and b are the quantities being compared.

Types of Ratios:

• Simple Ratio: Compares two quantities (e.g., 3:4)
• Compound Ratio: Compares more than two quantities (e.g., 2:3:5)
• Part-to-Part: Compares parts of a whole (e.g., boys:girls)
• Part-to-Whole: Compares a part to the total (e.g., boys:total students)

Ratio Properties:

• Simplification: Divide both terms by their GCD
• Equivalent Ratios: Ratios that represent the same relationship
• Proportion: Two ratios that are equal (a:b = c:d)
• Cross Multiplication: a × d = b × c in proportions

Common Examples:

• 12:8 = 3:2 (simplified by dividing by 4)
• 1:2 = 0.5 = 50%
• 3:4 = 3/4 = 0.75 = 75%
• Golden ratio: 1:1.618 (approximately 5:8)

Applications:

• Recipe scaling and cooking
• Financial analysis and ratios
• Architecture and design proportions
• Statistics and probability
• Engineering and technical calculations
• Art and photography composition