1. What is a Ratio Simplification Calculator?

Definition: This calculator simplifies a ratio of three numbers to its smallest whole number form by dividing each term by their greatest common divisor (GCD).

Purpose: It helps in mathematics, engineering, and various sciences to express ratios in their simplest form for easier interpretation and comparison.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a, b, c \) — Original ratio terms
• \( g \) — Greatest common divisor of a, b, and c

Explanation: The calculator finds the largest number that divides all three terms without remainder, then divides each term by this number.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand, compare, and use in further calculations. They represent the same proportional relationship in the smallest whole numbers.

4. Using the Calculator

Tips: Enter three positive whole numbers. The calculator will return the simplified ratio and the GCD used to simplify it.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers have no common divisor other than 1?
A: The ratio is already in simplest form and will be returned unchanged.

Q2: Can I use decimal numbers?
A: This calculator works with whole numbers. For decimals, multiply all terms by the same factor to convert to integers first.

Q3: How is the GCD calculated?
A: Using the Euclidean algorithm, an efficient method for finding the greatest common divisor.

Q4: Can this calculator handle more than three numbers?
A: This version is designed for three numbers, but the same principle applies to ratios with more terms.

Q5: What's the practical use of simplified ratios?
A: Used in recipe scaling, chemical formulas, mixing ratios, financial analysis, and many other proportional applications.