Mathematics · Algebra
Ratio Calculator and Simplifier
Simplify a two-number whole-number ratio and calculate its decimal relationship.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Greatest common divisor of 18 and 24 is 6.
- Divide both terms by 6.
- Simplified ratio = 3:4.
Definition and formula
Dividing both terms by their greatest common divisor preserves the relationship while producing the smallest equivalent whole-number ratio.
Simplified ratio = a ÷ gcd(a,b) : b ÷ gcd(a,b)
Worked example
The ratio 18:24 simplifies to 3:4 because the greatest common divisor is 6.
Common mistake
Both ratio terms must be divided by the same nonzero factor.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Ratio simplifier do?
Simplify a two-number whole-number ratio and calculate its decimal relationship.
How does the Ratio simplifier work?
The calculator applies Simplified ratio = a ÷ gcd(a,b) : b ÷ gcd(a,b). Dividing both terms by their greatest common divisor preserves the relationship while producing the smallest equivalent whole-number ratio.
What can I learn from the Ratio simplifier?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.