1. What is Ratio Simplification?

Ratio simplification is the process of reducing a ratio to its smallest whole number terms by dividing all parts of the ratio by their greatest common divisor (GCD). This makes ratios easier to understand and compare.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( a, b, c \) — The three numbers in the ratio
• \( g \) — The greatest common divisor of a, b, and c
• \( r \) — The simplified ratio

Explanation: The calculator finds the largest number that divides evenly into all three input numbers, then divides each number by this GCD to produce the simplified ratio.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to work with in mathematical calculations, comparisons, and real-world applications like mixing ingredients, financial ratios, or scaling measurements.

4. Using the Calculator

Tips: Enter three positive whole numbers. 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 decimals?
A: This calculator works with whole numbers. For decimals, multiply all numbers by the same power of 10 to make them whole numbers before simplifying.

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

Q3: What if my numbers are already in simplest form?
A: The calculator will return the same ratio with a GCD of 1.

Q4: What's the difference between ratio and fraction?
A: A ratio compares quantities, while a fraction represents a part of a whole. Ratios can compare more than two quantities.

Q5: Can the simplified ratio have decimal numbers?
A: Typically, simplified ratios use whole numbers. If the GCD doesn't divide evenly, you may need to scale up the numbers first.