1. What is a Ratio?

A ratio compares two quantities showing the relative sizes of two values. It shows how much of one thing there is compared to another thing. Ratios can be simplified to their smallest whole number equivalents.

2. How Does the Ratio Calculator Work?

The calculator uses the ratio formula:

Where:

• \( a \) — First integer value
• \( b \) — Second integer value
• \( \gcd(a,b) \) — Greatest common divisor of a and b

Explanation: The calculator finds the greatest common divisor (GCD) of the two numbers, then divides both numbers by the GCD to get the simplified ratio.

3. Importance of Ratio Calculation

Details: Simplified ratios are essential in mathematics, engineering, cooking, financial analysis, and many other fields where proportional relationships need to be clearly expressed.

4. Using the Calculator

Tips: Enter two positive integers. The calculator will automatically compute their GCD and display the simplified ratio in its smallest whole number form.

5. Frequently Asked Questions (FAQ)

Q1: What is a ratio used for?
A: Ratios are used to compare quantities in recipes, financial statements, maps, scale models, and many other applications.

Q2: Can ratios have decimals?
A: While ratios can technically have decimal values, they are typically expressed as whole numbers for simplicity and clarity.

Q3: What if my numbers have a GCD of 1?
A: If the GCD is 1, the ratio is already in its simplest form and cannot be reduced further.

Q4: Can I calculate ratios for more than 2 numbers?
A: Yes, the same principle applies - find the GCD of all numbers and divide each by the GCD.

Q5: What's the difference between ratio and fraction?
A: A ratio compares parts to parts, while a fraction compares a part to the whole. Both can be simplified similarly.