Ratio Calculator
Simplify, Compare & Calculate Ratios
Example for Simplify Ratio:
Input: 16:24
Result: 16:24 = 2:3
About Ratios
A ratio shows the relative sizes of two or more values. Ratios can be expressed in several ways:
- Simplest Form: Divide both sides by their greatest common divisor
- Proportion: Two ratios are equal (A:B = C:D)
- Cross Multiplication: A × D = B × C for proportional ratios
- Applications: Recipes, maps, scale drawings, financial ratios
Frequently Asked Questions (FAQs)
A ratio is a comparison of two or more quantities that indicates their relative sizes. It can be expressed as A:B or A/B.
To simplify a ratio, divide both numbers by their greatest common divisor (GCD). Example: 16:24 simplifies to 2:3 (both divided by 8).
Equal ratios form a proportion. If A:B = C:D, then A × D = B × C (cross multiplication). This means the two ratios represent the same relationship.
Add the ratio parts to get the total parts. Divide the quantity by total parts to get value per part. Multiply each ratio part by this value.
Ratios are used in recipes (ingredient proportions), maps (scale), finance (debt-to-income ratio), and mixing solutions.
Ratio Calculation Methods
Simplifying Ratios
- Find GCD of both numbers
- Divide both numbers by GCD
- Express in simplest integer form
Comparing Ratios
- Convert ratios to decimals
- Cross multiply for fractions
- Check if A × D = B × C
Finding Missing Values
- Use cross multiplication
- A:B = C:x ⇒ A × x = B × C
- Solve for unknown variable
Dividing Quantities
- Add ratio parts
- Find value per part
- Multiply each part
Tip: Always simplify ratios to their lowest terms for easier comparison and calculation.
