1. What is a Ratio Calculator for Two 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 find the simplest form of a ratio, which is useful in mathematics, engineering, cooking recipes, and various proportional calculations.

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 simplify the ratio.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand and work with, especially when scaling up or down proportions in recipes, construction, or chemical mixtures.

4. Using the Calculator

Tips: Enter two positive integers to find 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 automatically converts inputs to integers. For decimal ratios, multiply both numbers by 10 until they become integers.

Q2: Can this calculator handle zero values?
A: No, both numbers must be positive integers (greater than zero).

Q3: What's the maximum number this calculator can handle?
A: It depends on your server's PHP configuration, but typically up to 2 billion.

Q4: How is this different from a fraction calculator?
A: While similar, ratio calculators maintain the colon (:) notation and are often used in different contexts than fractions.

Q5: Can I simplify more than two numbers?
A: This calculator is designed for two numbers only. For more numbers, you would need a different tool.