1. What is a Ratio of Three Numbers?

A ratio of three numbers compares the relative sizes of three quantities. It shows how much of one thing there is compared to two others. Ratios are simplified by dividing all terms by their greatest common divisor (GCD).

2. How Does the Ratio Calculator Work?

The calculator uses the following mathematical process:

Where:

• \( num1, num2, num3 \) — The three numbers to compare
• \( gcd \) — Greatest common divisor of all three numbers

Explanation: The calculator first finds the GCD of all three numbers, then divides each number by this GCD to get the simplified ratio.

3. Importance of Ratio Calculation

Details: Ratios are fundamental in mathematics, science, engineering, finance, and everyday life. They allow comparison of quantities regardless of their absolute size.

4. Using the Calculator

Tips: Enter three positive numbers in the input fields. The calculator will determine their GCD and display the simplified ratio.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the numbers is zero?
A: All numbers must be positive for ratio calculation. Zero would make the ratio meaningless.

Q2: Can I use decimal numbers?
A: Yes, the calculator handles decimal numbers, though ratios are often expressed with whole numbers.

Q3: What if the numbers have no common divisor?
A: If the GCD is 1, the ratio is already in its simplest form.

Q4: How is this different from a percentage?
A: Ratios compare quantities directly, while percentages express a part of a whole (100%).

Q5: Where are three-number ratios used?
A: Common in mixing compounds (chemistry), color models (RGB), and financial analysis (three-way comparisons).