1. What is Ratio Simplification?

Ratio simplification is the process of reducing a ratio to its simplest form by dividing both terms 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 term of the ratio
• \( b \) — Second term of the ratio
• \( \gcd(a,b) \) — Greatest common divisor of a and b

Explanation: The calculator finds the GCD of both numbers and divides each term by this value to get the simplified ratio.

3. Importance of Simplified Ratios

Details: Simplified ratios are easier to work with in calculations, comparisons, and real-world applications. They represent the same proportional relationship in the most reduced form.

4. Using the Calculator

Tips: Enter two positive integers to get their ratio in simplest form. The calculator will automatically compute the GCD and simplify the ratio.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers have no common divisors?
A: If the GCD is 1, the ratio is already in its simplest form and will be returned unchanged.

Q2: Can I use decimal numbers?
A: This calculator works with integers only. For decimals, multiply by powers of 10 to convert to integers first.

Q3: What's the maximum number this calculator can handle?
A: It depends on your server's PHP configuration, but typically handles very large numbers (up to 2^63-1).

Q4: How is this different from simplifying fractions?
A: The mathematical process is identical, but ratios are often used to compare different quantities rather than represent parts of a whole.

Q5: Can I simplify more than two numbers?
A: This calculator handles two-number ratios only. For more numbers, you would need to find the GCD of all terms.