Arithmetic
Simplifying a ratio
Divide both terms by their greatest common divisor to get the smallest whole-number form.
The Formula
a : b = (a / g) : (b / g), where g = gcd(a, b)
Divide both terms by their greatest common divisor to get the smallest whole-number form.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| g | Common divisor | none | The largest number dividing both terms exactly. |
| a | First term | none | The original first term. |
| b | Second term | none | The original second term. |
What Each Symbol Means
gnone
Common divisor
The largest number dividing both terms exactly.
anone
First term
The original first term.
bnone
Second term
The original second term.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a ratio page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Ratio, filed under Math. Every number the guide produces comes from substituting into this one line.