Ratio Calculator
Ratio - Solve mathematical problems with step-by-step solutions.
Ratio Calculator
Simplify and Solve Proportions
Ratios & Proportions
- A ratio compares two quantities. Simplifying a ratio means reducing it to its smallest integer terms.
- A proportion is an equation stating that two ratios are equal. This calculator solves for the missing value 'x' in the proportion A : B = C : x using the formula: x = (C * B) / A.
How the Ratio Calculator Works
A ratio is a comparison between two or more quantities. Ratios show the relative sizes of values and can be written in different forms: a:b, a/b, or "a to b". They're fundamental in cooking, finance, construction, and many other fields.
Different Forms
- 3:4 (colon notation)
- 3/4 (fraction)
- 3 to 4 (words)
Ratios can be simplified like fractions by dividing by the GCF. When two ratios are equal, they form a proportion.
Working with Ratios
Simplifying Ratios
Divide both parts by their greatest common factor (GCF):
Example: 12:18 → divide by 6 → 2:3
Equivalent Ratios
Multiply or divide both parts by the same number:
2:3 = 4:6 = 6:9 = 8:12 (all equivalent)
Solving Proportions
Use cross multiplication when ratios are equal:
If a/b = c/d, then a × d = b × c
Example: 3/4 = x/12 → 3 × 12 = 4 × x → x = 9
Real-World Applications
Cooking & Recipes
Scale ingredients up or down while maintaining proper proportions. A recipe with a 2:3 flour to sugar ratio stays consistent at any size.
Maps & Scale Models
Map scales like 1:50,000 mean 1 cm on the map represents 50,000 cm (500 m) in reality.
Financial Ratios
Price-to-earnings ratios, debt-to-income ratios, and profit margins all use ratio analysis.
Mixing & Solutions
Paint mixing, chemical solutions, and concrete mixtures require precise ratio calculations.
Frequently Asked Questions
Related Math Calculators
Basic Calculator
A simple calculator for basic arithmetic operations including addition, subtraction, multiplication, and division.
Percentage Calculator
Calculate percentages, percentage changes, discounts, and more with our comprehensive percentage calculator.
Scientific Calculator
An advanced calculator with trigonometric, logarithmic, exponential, and memory functions.
Series And Sequence Calculator
Series And Sequence - Solve mathematical problems with step-by-step solutions.
Absolute Value Calculator
Calculate the absolute value of any number or expression.
Algebra Calculator
Solve algebraic equations and expressions with step-by-step solutions.