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 mathematical process:

Where:

• \( a, b, c \) — The original numbers in the ratio
• \( \gcd(a,b,c) \) — The greatest common divisor of all three numbers

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

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to work with and understand. They are essential in fields like chemistry (stoichiometry), cooking (recipe scaling), and engineering (gear ratios).

4. Using the Calculator

Tips: Enter three positive numbers. The calculator will return the simplified ratio in whole numbers when possible. For decimal results, it will maintain the same proportional relationship.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers have decimals?
A: The calculator works with decimal numbers. It will find the greatest common divisor and simplify the ratio while maintaining the decimal proportions.

Q2: Can I simplify more than three numbers?
A: This calculator is designed for three numbers, but the same principle applies to any number of values in a ratio.

Q3: What if my simplified ratio still has decimals?
A: This means your original numbers don't share a whole number common divisor. The simplified version maintains the exact same proportion.

Q4: Why is ratio simplification important?
A: Simplified ratios are easier to understand, compare, and use in calculations. They represent the same relationship in the simplest terms possible.

Q5: Can I use this for negative numbers?
A: The calculator only accepts positive numbers since ratios typically represent positive quantities.