1. What is Ratio of Integers?

The ratio of integers represents the proportional relationship between two numbers. Simplifying a ratio to its lowest terms makes it easier to understand and compare relationships between quantities.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

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

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

3. Importance of Ratio Simplification

Details: Simplified ratios are essential in mathematics, engineering, and everyday life for comparing quantities, mixing solutions, creating scale models, and solving proportion problems.

4. Using the Calculator

Tips: Enter two positive integers. The calculator will display the simplified ratio and the GCD used to simplify it. Both numbers must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What is a ratio?
A: A ratio compares two quantities by division, showing how many times one value contains or is contained within the other.

Q2: Why simplify ratios?
A: Simplified ratios are easier to understand and work with, especially when comparing different ratios or using them in calculations.

Q3: What is the GCD?
A: The greatest common divisor is the largest positive integer that divides both numbers without leaving a remainder.

Q4: Can this calculator handle decimal numbers?
A: No, this calculator works only with positive integers. For decimal numbers, multiply by powers of 10 to convert to integers first.

Q5: What's the difference between ratio and fraction?
A: A ratio compares two quantities, while a fraction represents a part of a whole. However, ratios can often be expressed as fractions.