Ratios & Proportions
Simplifying with the greatest common divisor
Dividing the numerator and denominator by their greatest common divisor gives the equivalent fraction in lowest terms.
The Formula
a/b = (a / g) / (b / g) where g = gcd(a, b)
Dividing the numerator and denominator by their greatest common divisor gives the equivalent fraction in lowest terms.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a | Numerator | count | The count above the line. |
| b | Denominator | count | How many parts make a whole. |
| g | Greatest common divisor | count | The largest number dividing both a and b. |
What Each Symbol Means
acount
Numerator
The count above the line.
bcount
Denominator
How many parts make a whole.
gcount
Greatest common divisor
The largest number dividing both a and b.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate fractions 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 Fractions, filed under Math. Every number the guide produces comes from substituting into this one line.