Ratio Simplifier
Reduce a pair of signed whole-number ratio terms by their greatest common divisor.
How to use Ratio Simplifier
1. Enter First Ratio Value, Second Ratio Value in the stated order. 2. Follow nonzero denominator and whole-number requirements where they apply. Keep corresponding quantities on the same unit scale. 3. Select Calculate or press Enter to see simplified ratio. 4. Copy result copies the output; Reset clears the inputs and answer.
Why use this tool?
Express a part-to-part ratio with the smallest corresponding integer terms.
How the calculation works
Divide each integer term by the greatest common divisor of their magnitudes. Preserve the signs and term order; reject 0:0. Integer fraction outputs and decimal-ratio comparisons use exact integer arithmetic; numeric input components are bounded as stated. Numeric input magnitudes, including each fraction or ratio component, must not exceed 9,007,199,254,740,991. Mathematical references: https://openstax.org/books/prealgebra-2e/pages/4-key-concepts and https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications.
Example
First Ratio Value = 18 and Second Ratio Value = 24 give 3:4. The part-to-part notation 5:0 reduces to 1:0.
Practical tip
A zero second term can describe part-to-part notation, but its quotient is undefined and cannot be used in Ratio Comparison Calculator.
Frequently asked questions
Can one ratio term be zero?
Yes, if the other is nonzero. For example, 0:5 becomes 0:1. Both zero is undefined and rejected.
Can the exact result be larger than the input limit?
Yes. Exact integer fractions can have larger output numerators or denominators after multiplication. Their text remains exact. Floating-point numeric outputs on other maths pages are limited to the supported numeric range.
Does the tool choose units or round my input first?
Enter corresponding measurements in matching units; the maths forms do not convert units automatically. Exact fraction and ratio text is kept for integer arithmetic. Other numeric operations use browser floating-point values and the display precision stated above.