Ratio Calculator: Simplify Ratios and Scale Both Terms
Simplify and scale
a ÷ GCF : b ÷ GCF
First term · Second term · Scale factor
Start with the two nonnegative whole-number terms.
a ÷ GCF : b ÷ GCF
An arithmetic walkthrough keeps large integer ratios exact; the labelled pairs are not a count of drawn objects, and long labels are abbreviated here while full integers appear below.
Worked example you can change
Reduced ratio = first ÷ GCF : second ÷ GCF
- Reduced ratio = (12 ÷ 6) : (18 ÷ 6)
- Reduced ratio = 2:3
- Scale the original ratio by 1: 12:18
Calculator
Enter nonnegative whole-number terms and a positive whole-number scale factor, each up to 100 digits; 0:0 is undefined.
- Reduced first term
- 2
- Reduced second term
- 3
- Scaled original first term
- 12
- Scaled original second term
- 18
Formula variants
| Shape or method | Formula | Meaning |
|---|---|---|
| Reduce a ratio | (a/g) : (b/g), where g = GCF(a,b) | Divide both terms by their greatest common factor. |
| Scale the original ratio | (a × k) : (b × k) | The factor multiplies both original terms, rather than the reduced terms. |
| Zero second term | a:0 → 1:0 for a > 0 | A valid pair has no finite quotient when its second term is zero. |
Questions
How do I simplify a ratio?
Divide both whole-number terms by their greatest common factor. For 12:18 the factor is 6, giving 2:3.
Does scaling use the original terms?
Yes. Scaling 12:18 by 2 gives 24:36, while its simplified ratio remains 2:3.
Can a ratio contain zero?
One term may be zero, but 0:0 is rejected. A zero second term has no finite quotient.
Sources and method
Simplify whole-number ratios exactly and scale both original terms by a positive whole-number factor. Follow the common-factor steps and edit the example.
We use exact integer arithmetic and retain every digit of supported integer results. Diagrams are labelled explanations and are not measurement drawings.
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