1. What is a Ratio Calculator For 2 Numbers?

Definition: This calculator simplifies a ratio of two numbers to its lowest terms by dividing both numbers by their greatest common divisor (GCD).

Purpose: It helps in simplifying ratios for mathematics, engineering, cooking recipes, and other applications where simplified ratios are needed.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — First number in the ratio
• \( b \) — Second number in the ratio
• \( \gcd(a,b) \) — Greatest common divisor of a and b

Explanation: The GCD is found using the Euclidean algorithm, then both numbers are divided by this GCD to get the simplified ratio.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand and work with, especially in proportional calculations, scaling recipes, or creating mixtures.

4. Using the Calculator

Tips: Enter two positive integers (whole numbers greater than 0) to get their simplified ratio. The calculator will show both the GCD and the simplified ratio.

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: Can this calculator handle very large numbers?
A: Yes, within PHP's integer limits (typically up to 2,147,483,647 on 32-bit systems).

Q3: What if the numbers are prime relative to each other?
A: If the GCD is 1, the ratio is already in simplest form and will be returned unchanged.

Q4: Can I use this for more than two numbers?
A: This calculator is designed for two numbers only. For more numbers, you would need to find the GCD of all numbers.

Q5: What's the practical use of simplified ratios?
A: Simplified ratios are used in mixing chemicals, scaling recipes, creating color mixtures, and many other proportional applications.