1. What is a Ratio Calculator?

Definition: This calculator simplifies or computes the ratio between two numbers 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, and various other fields.

2. How Does the Ratio 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 the GCD to simplify the ratio.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand and work with, especially in recipes, construction plans, and financial calculations.

4. Using the Calculator

Tips: Enter any two positive numbers to see their GCD and simplified ratio. The calculator works with whole numbers and decimals.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers have decimals?
A: The calculator works with decimal numbers. The GCD will be calculated for the decimal values.

Q2: Can I calculate ratios with more than two numbers?
A: This calculator handles two numbers. For more numbers, you would need to find the GCD of all numbers.

Q3: What's the GCD of prime numbers?
A: The GCD of two prime numbers is always 1, so their ratio is the numbers themselves.

Q4: Can I use negative numbers?
A: This calculator only accepts positive numbers as ratios are typically expressed with positive values.

Q5: How is this different from a fraction calculator?
A: While similar, ratio calculators maintain the ratio format (a:b) rather than converting to fractional form (a/b).