Ratio Simplifier is designed for the exact search intent behind “ratio simplifier”. Simplify a ratio by reducing its terms to an equivalent ratio with the smallest whole-number values. For integer ratios, this is done by dividing all terms by their greatest common divisor. Reduce a ratio to an equivalent ratio in lowest whole-number terms. How to simplify a ratio For a two-part whole-number ratio A:B, find g = GCD(A,B) . Then divide both terms by g: Simplified ratio = (A ÷ g):(B ÷ g) If the greatest common divisor is 1, the ratio is already in lowest terms. Why the ratio stays equivalent Dividing every term by the same nonzero factor changes the size of the numbers but not their proportion. That is why 20:45 and 4:9 describe the same relationship. Decimals and fractions When a ratio contains decimals or fractions, they are commonly converted to proportional whole numbers first, then reduced by their common factor. The exact accepted input format depends on the tool. Worked example: The greatest common divisor of 20 and 45 is 5. Divide both terms by 5: 20÷5 : 45÷5 = 4:9. Common practical uses include Reduce recipe or mixing proportions; Simplify scale and dimension ratios; Check ratio homework; Express comparison data in lowest terms. Important limitations: The supported format for decimal, fractional, negative or multi-part ratios depends on the implementation. Ratios containing zero require interpretation in context; division by a zero common factor is never valid. Key questions this page should answer include: How do I simplify a ratio? Find the greatest common divisor of the terms and divide every term by it. What is 20:45 in simplest form? 4:9, because the greatest common divisor of 20 and 45 is 5. Is simplifying a ratio the same as simplifying a fraction? For a two-part ratio, the reduction process is essentially the same: divide numerator-like and denominator-like terms by a common factor. Can you simplify a ratio with decimals? Yes. A common method is to multiply all terms by a power of ten that clears the decimals, then reduce the resulting whole-number ratio. How do I know a ratio is fully simplified? For whole-number terms, it is in lowest terms when their greatest common divisor is 1. The page should stay focused on this differentiator: Fast reduction + GCD method + equivalent-ratio explanation.
How to use this tool
How to simplify a ratio
For a two-part whole-number ratio A:B, find g = GCD(A,B). Then divide both terms by g:
Simplified ratio = (A ÷ g):(B ÷ g)
If the greatest common divisor is 1, the ratio is already in lowest terms.
Why the ratio stays equivalent
Dividing every term by the same nonzero factor changes the size of the numbers but not their proportion. That is why 20:45 and 4:9 describe the same relationship.
Decimals and fractions
When a ratio contains decimals or fractions, they are commonly converted to proportional whole numbers first, then reduced by their common factor. The exact accepted input format depends on the tool.
Examples
Simplify 20:45
The greatest common divisor of 20 and 45 is 5. Divide both terms by 5: 20÷5 : 45÷5 = 4:9.
Common use cases
- Reduce recipe or mixing proportions
- Simplify scale and dimension ratios
- Check ratio homework
- Express comparison data in lowest terms
Frequently asked questions
How do I simplify a ratio?
Find the greatest common divisor of the terms and divide every term by it.
What is 20:45 in simplest form?
4:9, because the greatest common divisor of 20 and 45 is 5.
Is simplifying a ratio the same as simplifying a fraction?
For a two-part ratio, the reduction process is essentially the same: divide numerator-like and denominator-like terms by a common factor.
Can you simplify a ratio with decimals?
Yes. A common method is to multiply all terms by a power of ten that clears the decimals, then reduce the resulting whole-number ratio.
How do I know a ratio is fully simplified?
For whole-number terms, it is in lowest terms when their greatest common divisor is 1.