1. What is a Ratio of Three Numbers?

A ratio of three numbers compares the relative sizes of three quantities. It shows the proportional relationship between them in simplest form by dividing each number by their greatest common divisor (GCD).

2. How Does the Calculator Work?

The calculator uses the following process:

Where:

• \( a, b, c \) — The three numbers to compare
• \( GCD \) — Greatest Common Divisor function

Explanation: The calculator finds the largest number that divides all three input numbers without remainder, 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, and finance for comparing quantities, mixing ingredients, creating scale models, and analyzing proportions in data.

4. Using the Calculator

Tips: Enter three positive numbers. The calculator will return the simplified ratio and show the calculation steps. All values must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the numbers is zero?
A: All numbers must be greater than zero. Ratios with zero are undefined.

Q2: Can I use decimal numbers?
A: Yes, the calculator handles decimal numbers. It will find the GCD considering the decimal places.

Q3: What does a ratio of 1:1:1 mean?
A: This means all three quantities are equal in proportion.

Q4: How is this different from percentage?
A: Ratios compare quantities directly, while percentages express one quantity as parts per hundred of another.

Q5: Can this be used for mixing ingredients?
A: Yes, this calculator is useful for determining ingredient proportions in recipes, chemical solutions, and other mixtures.