1. What is a Ratio Calculator for Two Numbers?

Definition: This calculator simplifies 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 proportional calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — First number (unitless)
• \( b \) — Second number (unitless)
• \( \gcd(a,b) \) — 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 recipes, mixing solutions, or creating scale models.

4. Using the Calculator

Tips: Enter two positive integers. The calculator will show both the GCD and the simplified ratio.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers have decimals?
A: Multiply both numbers by 10, 100, etc. to make them integers before calculating, then simplify.

Q2: What does it mean if the GCD is 1?
A: The numbers are coprime (no common divisors other than 1), and the ratio is already in simplest form.

Q3: Can I use this for more than two numbers?
A: This calculator is for two numbers only. For more numbers, you'd need to find the GCD of all numbers.

Q4: What's the practical use of ratio simplification?
A: Used in scaling recipes, mixing chemicals, creating scale models, aspect ratios in design, and more.

Q5: How is the GCD calculated?
A: Using the Euclidean algorithm which efficiently finds the GCD through repeated division.