1. What is Ratio Simplification?

Ratio simplification is the process of reducing a ratio of two integers to its simplest form by dividing both numbers 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:

• \( a \) — First integer
• \( b \) — Second integer
• \( \gcd(a,b) \) — Greatest common divisor of a and b

Explanation: The calculator first finds the GCD of the two numbers, then divides both numbers by this GCD to get the simplified ratio.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to work with in mathematics, engineering, cooking, and many other fields. They help in comparing quantities directly and are essential for proportional reasoning.

4. Using the Calculator

Tips: Enter two positive integers. The calculator will show both the simplified ratio and the GCD used to simplify it. Both numbers must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter non-integer values?
A: The calculator only accepts positive integers. Decimal values will be truncated to integers.

Q2: What happens if I enter two identical numbers?
A: The simplified ratio will always be 1:1 when both numbers are equal.

Q3: Can this calculator handle very large numbers?
A: Yes, within PHP's integer limits (typically up to 2^31-1 or 2^63-1 depending on your system).

Q4: What's the difference between ratio and fraction?
A: A ratio compares two quantities, while a fraction represents a part of a whole. However, they can often be converted between each other.

Q5: How is this different from reducing fractions?
A: The mathematical process is identical, but ratios are typically written with a colon (:) rather than as a fraction.