1. What is a 3 Number Ratio Simplifier?

Definition: This calculator simplifies a ratio of three numbers by dividing each term by their greatest common divisor (GCD).

Purpose: It helps find the simplest form of a three-term ratio, making it easier to understand and work with proportions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a, b, c \) — Original numbers in the ratio
• \( gcd(a,b,c) \) — Greatest common divisor of all three numbers

Explanation: The calculator finds the largest number that divides all three terms evenly, then divides each term by this number.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand, compare, and use in calculations. They represent the same proportional relationship in their simplest form.

4. Using the Calculator

Tips: Enter three positive integers. The calculator will display both 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 its simplest form and will be returned unchanged.

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

Q3: How is the GCD calculated for three numbers?
A: First find GCD of two numbers, then find GCD of that result with the third number.

Q4: What's the practical use of simplifying ratios?
A: Useful in recipes, construction mixes, chemical formulas, and any proportional scaling applications.

Q5: Can this calculator handle more than three numbers?
A: This version is designed for three numbers only, but the same principle applies to larger sets.