Ratio Calculator
This calculator helps you simplify ratios and compare numbers in ratio form quickly and easily.
Understanding Ratios
A ratio expresses the relative size of two numbers.
Formula to simplify a ratio:
Ratio = A : B → divide both numbers by their greatest common divisor (GCD)
Example: Ratio 12:18 → GCD(12,18) = 6 → Simplified ratio = 2:3
How the Calculator Works
The calculator automatically:
Step 1: Takes input numbers A and B
Step 2: Calculates the greatest common divisor (GCD)
Step 3: Simplifies the ratio by dividing both numbers by the GCD
Step 4: Displays the simplified ratio instantly
Examples
1. 8 : 12 → GCD = 4 → Simplified = 2 : 3
2. 45 : 60 → GCD = 15 → Simplified = 3 : 4
3. 7 : 14 → GCD = 7 → Simplified = 1 : 2
4. 36 : 48 → GCD = 12 → Simplified = 3 : 4
Why Ratios Matter
Ratios are widely used in cooking, finance, map reading, probability, and comparing quantities in real life.
Common Mistakes to Avoid
- Forgetting to simplify using GCD
- Swapping the order of numbers
- Misinterpreting the ratio as division result
Important: Always simplify by dividing both terms by their GCD.
Correct: The order of numbers matters: A:B is different from B:A.
Frequently Asked Questions
Can the numbers be decimals?
Yes. Decimals can be converted to fractions first and simplified as a ratio.
Can a ratio be greater than 1?
Yes. Ratios can be any positive numbers; for example, 5:2 is valid.
What if one number is zero?
If A = 0 → ratio = 0:B, if B = 0 → ratio = A:0. Cannot both be zero.
Conclusion
This ratio calculator is a simple tool to simplify and compare numbers in ratio form, making it easier for students and professionals to solve real-life problems.