- Simplified ratio
- 2 : 3
How it works
Adding equally does not preserve proportion
The ratio 12:18 simplifies to 2:3, but adding 2 to each side gives 14:20, which simplifies to 7:10. Preserve a ratio by multiplying both parts by the same factor, not by adding equal amounts.
Keeping the order of a ratio consistent
A 2:3 mixture contains 5 parts in total. To make 20 units of mixture, each part is 20 ÷ 5 = 4 units, so the two ingredients need 8 and 12 units. The first ingredient is 2/5 of the total, not 2/3: 2/3 compares the ingredients with each other. Keep their order consistent when scaling or solving a proportion, and convert measurements to compatible units before comparing them.
Simplify ratio: formula and assumptions
a:b reduces to (a/gcd):(b/gcd).
Whole-number ratios use the greatest common divisor.
Solve a proportion: formula and assumptions
A/B = C/D, so D = B × C / A.
A must be nonzero.
Solve any proportion term: formula and assumptions
A/B=C/D, so AD=BC.
The unknown is omitted. Zero denominators and underdetermined equations are rejected.
Scale a ratio: formula and assumptions
Multiply both terms by the scale factor to enlarge; divide to shrink.
Scaling changes both quantities in the same proportion.
Worked example
Using the Simplify ratio example:
- First quantity
- 12
- Second quantity
- 18
a:b reduces to (a/gcd):(b/gcd).
Example result
Simplified ratio: 2 : 3
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Does scaling a ratio change the relationship between its parts?
No. Multiplying or dividing both parts by the same nonzero factor preserves their proportion.
Why can some proportions not be solved uniquely?
A zero denominator is invalid, and some combinations reduce to an identity with infinitely many possible values rather than one answer.
Prepared by Finflo. See our methodology and editorial policy.