Solve ratios, scale ratios, and find missing values in proportions. Perfect for math homework, aspect ratios, recipe scaling, and proportional calculations with step-by-step solutions.
A ratio is a quantitative relationship between two numbers that describes how many times one value can contain another. Ratios are fundamental mathematical concepts used in countless real-world applications, from cooking and construction to finance and design.
Understanding ratios is essential for proportional reasoning, scaling objects, comparing quantities, and solving practical problems that involve relationships between different values. Ratios provide a standardized way to express and compare relative quantities.
Where A, B, C, and D are the terms of the proportion
Used to solve for missing values in proportions
| Application | Example Ratio | Usage | Calculation |
|---|---|---|---|
| Recipe Scaling | 2 cups : 4 servings | Cooking | Adjust ingredients proportionally |
| Screen Aspect Ratio | 16:9 | Technology | Maintain screen proportions |
| Map Scale | 1:50,000 | Geography | Convert map to real distances |
| Gear Ratios | 3:1 | Engineering | Mechanical advantage calculations |
| Investment Allocation | 60:40 | Finance | Portfolio diversification |
| Paint Mixing | 2:1:3 | Art/Construction | Color consistency |
| Employee Ratio | 1:10 | Management | Staffing decisions |
Cross-Multiplication Method: The most common method for solving proportions. If A:B = C:D, then A×D = B×C. This allows you to solve for any missing value when three values are known.
Unit Rate Method: Find the rate for one unit, then multiply to find the desired quantity. For example, if 3 items cost $6, then 1 item costs $2, so 5 items cost $10.
Scaling Method: Determine the scale factor between ratios by dividing corresponding terms, then apply this factor to find missing values.
Equivalent Fractions: Convert ratios to fractions and use fraction operations to solve problems. The ratio A:B can be written as the fraction A/B.
Enlargement: Multiply both terms of a ratio by the same factor greater than 1. For example, scaling 2:3 by a factor of 4 gives 8:12.
Reduction: Divide both terms of a ratio by the same factor greater than 1, or multiply by a factor less than 1. For example, scaling 10:15 by a factor of 0.5 gives 5:7.5.
Simplification: Reduce ratios to their lowest terms by dividing both terms by their greatest common divisor. For example, 12:18 simplifies to 2:3.
Complex Ratios: Ratios with more than two terms (e.g., 2:3:5) where all relationships must be maintained when scaling.
| Aspect Ratio | Decimal | Common Use | Examples |
|---|---|---|---|
| 1:1 | 1.00 | Square format | Instagram posts, profile pictures |
| 4:3 | 1.33 | Traditional TV | Old computer monitors, slides |
| 3:2 | 1.50 | Photography | 35mm film, DSLR cameras |
| 16:10 | 1.60 | Computer displays | Laptops, wide monitors |
| 5:3 | 1.67 | European film | Some European cinema |
| 16:9 | 1.78 | Widescreen | HDTV, YouTube, modern monitors |
| 21:9 | 2.33 | Ultra-wide | Cinematic, gaming monitors |
Keep Units Consistent: Always ensure that corresponding terms in ratios have the same units. Convert units if necessary before calculating.
Check Your Work: Verify solutions by substituting back into the original ratio to ensure the proportion holds true.
Simplify When Possible: Reduce ratios to their simplest form for easier comparison and understanding.
Use Visual Aids: Draw diagrams or use visual representations to better understand ratio relationships, especially for complex problems.