1. What is a Ratio Calculator?

Definition: This calculator simplifies ratios by dividing both terms by their greatest common divisor (GCD).

Purpose: It helps find the simplest form of a ratio, which is useful in mathematics, cooking, mixing solutions, and various proportional calculations.

2. How Does the Ratio Calculator Work?

The calculator uses the 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 GCD is found using the Euclidean algorithm, then both terms are divided by this value to get the simplified ratio.

3. Importance of Ratio Simplification

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

4. Using the Calculator

Tips: Enter both values of your ratio (a and b). The calculator will find the GCD and display the simplified ratio. Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What if my ratio has more than two numbers?
A: This calculator handles two-number ratios. For more complex ratios, you would need to find the GCD of all numbers.

Q2: Can I use decimal numbers?
A: Yes, the calculator accepts decimal inputs, though ratios are often expressed with whole numbers.

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

Q4: How is this different from a fraction calculator?
A: While similar, ratio calculators maintain the proportional relationship rather than converting to a single fractional value.

Q5: Why would I need to simplify a ratio?
A: Simplified ratios are easier to work with when scaling recipes, mixing solutions, or comparing proportions.