1. What is a Ratio of Three Numbers Calculator?

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

Purpose: It helps in simplifying complex ratios to their most basic form, making them easier to understand and work with in mathematics, chemistry, and various real-world applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a, b, c \) — Original numbers in the ratio
• \( g \) — Greatest common divisor of a, b, and c
• The simplified ratio consists of whole numbers with no common factors

Explanation: The calculator finds the largest number that divides all three input numbers exactly, then divides each term by this GCD to simplify the ratio.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to work with in calculations, comparisons, and when scaling recipes or mixtures. They maintain the same proportional relationship while using smaller 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 numbers by the same power of 10 to convert to integers first.

Q3: How is the GCD calculated?
A: Using the Euclidean algorithm, which efficiently finds the greatest common divisor through successive division.

Q4: What are some practical applications of this?
A: Used in chemistry for empirical formulas, in cooking for recipe scaling, in construction for mixing materials, and in finance for ratio analysis.

Q5: Can this calculator handle more than three numbers?
A: This version handles three numbers, but the same principle applies to ratios with more terms.