Ratio Calculator
Quick Examples
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Understanding Ratios
What is a Ratio?
A ratio is a comparison of two quantities showing how many times one value contains or is contained within another. Ratios can be written as a:b, a/b, or "a to b." They're used everywhere from cooking recipes to financial analysis.
Ratios vs Proportions
Ratio
A comparison of two numbers (e.g., 3:4). Represents a relationship between quantities.
Proportion
An equation stating two ratios are equal (e.g., 3:4 = 6:8). Used to solve for unknown values.
Solving Proportions
Cross Multiplication Method
For a proportion a:b = c:d:
a × d = b × c
So if 3:4 = x:20
3 × 20 = 4 × x
60 = 4x
x = 15
Simplifying Ratios
To simplify a ratio, divide both parts by their greatest common divisor (GCD).
Example: Simplify 24:36
Find GCD of 24 and 36 = 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Simplified ratio: 2:3
Real-World Applications
Cooking & Recipes
Scaling recipes up or down while maintaining proportions. Example: 2:3 cups flour to sugar.
Maps & Scale Models
Map scales like 1:100,000 mean 1 cm represents 1 km. Model scales like 1:24 for cars.
Finance
Price-to-earnings ratios, debt-to-income ratios, and other financial metrics.
Mixing & Chemistry
Paint mixing ratios, concrete mixtures, chemical solutions and dilutions.
Common Ratio Examples
| Context | Ratio | Meaning |
|---|---|---|
| Golden Ratio | 1:1.618 | Found in art, architecture, nature |
| Aspect Ratio (HD) | 16:9 | Standard widescreen TV/monitor |
| Photo Ratio | 3:2 | Common DSLR photo format |
| Concrete Mix | 1:2:3 | Cement:Sand:Gravel by volume |
Pro Tip
When comparing ratios, convert them to the same second term or convert to decimals. For example, 3:4 = 0.75 and 2:3 ≈ 0.67, so 3:4 is the larger ratio.
Frequently Asked Questions
How do you solve a proportion with a missing value?
Use cross multiplication. For a:b = c:x, multiply a times x and b times c, then solve. Example: 3:4 = 9:x means 3 times x equals 4 times 9, so 3x = 36, and x = 12. You can verify: 3/4 = 9/12 = 0.75.
How do you simplify a ratio?
Divide both parts by their greatest common divisor (GCD). For 24:36: GCD is 12, so 24/12 : 36/12 = 2:3. For ratios with decimals, first multiply to make whole numbers (0.5:1.5 becomes 5:15 becomes 1:3).
What is the difference between a ratio and a fraction?
A ratio compares two quantities (3:4 means '3 to 4'). A fraction represents part of a whole (3/4 means '3 out of 4'). If 3:4 represents boys to girls, boys are 3/7 of total, not 3/4. Context determines interpretation.
How do you scale a recipe using ratios?
Find the scale factor by dividing your desired amount by the original. For a recipe serving 4 that you want to serve 6: scale factor is 6/4 = 1.5. Multiply ALL ingredients by 1.5. Keep ratios constant for proper taste and texture.