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Ratio Calculator 3 Numbers Simplifier

Ratio Simplification Formula:

\[ a : b : c = \frac{a}{g} : \frac{b}{g} : \frac{c}{g} \]

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1. What is a 3-Number Ratio Simplifier?

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

Purpose: It helps in reducing complex ratios to simpler forms for easier interpretation and comparison in mathematics, finance, chemistry, and other fields.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a : b : c = \frac{a}{g} : \frac{b}{g} : \frac{c}{g} \]

Where:

Explanation: The calculator finds the largest number that divides all three terms exactly, then divides each term by this GCD to get the simplified ratio.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand, compare, and use in calculations. They maintain the same proportional relationship while using smaller numbers.

4. Using the Calculator

Tips: Enter three positive numbers in the ratio you want to simplify. The calculator will show the simplified ratio and the GCD used.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers have decimals?
A: The calculator handles decimal inputs, but the simplified ratio will be in decimal form unless you multiply by a factor to make all numbers integers first.

Q2: Can I simplify more than three numbers?
A: This calculator is designed for three numbers, but the same principle applies to ratios with more terms.

Q3: What if my numbers have different units?
A: The calculator assumes all numbers are in the same unit. Convert all terms to the same unit before simplifying.

Q4: How is the GCD calculated?
A: The calculator uses the Euclidean algorithm to find the greatest common divisor of the three numbers.

Q5: What if I get 1:1:1 as the simplified ratio?
A: This means all three original numbers were equal, or their ratio was already in simplest form with equal terms.

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