Ratio Calculator
Simplify ratios, solve proportions, and compare ratio relationships
Calculate Ratios
Results
Example Calculations
Simplifying a Ratio
Problem: Simplify the ratio 12:18
Step 1: Find GCD of 12 and 18
Step 2: GCD(12, 18) = 6
Step 3: Divide both terms by 6
Step 4: 12 ÷ 6 = 2, 18 ÷ 6 = 3
Answer: 2:3
Solving a Proportion
Problem: If 3:4 = 9:x, find x
Cross multiply: 3 × x = 4 × 9
Solve: 3x = 36, so x = 12
Answer: x = 12
Ratio Applications
Recipe Scaling
Adjust ingredient quantities proportionally
Example: 2:3 cups ratio
Financial Analysis
Compare financial metrics and ratios
Example: Debt-to-equity ratio
Map Scales
Convert between map and real distances
Example: 1:50,000 scale
Ratio Tips
Always simplify ratios to lowest terms
Use GCD to find the simplest form
Cross multiplication solves proportions
Units must be consistent when comparing
Understanding Ratios
What is a Ratio?
A ratio is a comparison between two or more quantities. It shows the relative size of one quantity compared to another. Ratios can be written in several forms: as fractions (3/4), with colons (3:4), or as words ("3 to 4").
Simplifying Ratios
To simplify a ratio, divide both terms by their Greatest Common Divisor (GCD). This gives you the simplest form of the ratio, making it easier to understand and work with.
Real-World Applications
- •Cooking and baking recipes
- •Financial analysis and business metrics
- •Scale drawings and maps
- •Speed, density, and other rate calculations
Types of Ratios
Part-to-Part Ratio
Compares different parts of a whole (boys:girls = 3:2)
Part-to-Whole Ratio
Compares a part to the total (boys:total students = 3:5)
Rate Ratio
Compares different units (miles:hour, cost:item)
Golden Ratio: A special ratio (≈1.618) found in nature, art, and architecture, considered aesthetically pleasing.