A fraction and a ratio are two ways of writing the same relationship between two numbers. The fraction 8/12 and the ratio 8:12 both compare 8 of something to 12 of something else, and both simplify the same way — by dividing out their greatest common divisor.
How to Convert a Fraction to a Ratio (step by step)
Step One: Find the greatest common divisor (GCD) of the numerator and denominator
gcd(8, 12) = 4
Step Two: Divide both numbers by the GCD
8 ÷ 4 = 2
12 ÷ 4 = 3
Step Three: Write the result as a ratio
8/12 = 2:3
With the calculator’s default values, 8/12 simplifies to the ratio 2:3 — meaning for every 2 parts of one quantity, there are 3 parts of the other.
What your results mean
The first term and second term together form your simplified ratio, written as first:second. Like a simplified fraction, this is the smallest pair of whole numbers that still represents the exact same relationship as your original numerator and denominator.
If the GCD of your numbers is 1, the ratio is already in simplest form and will match your original numerator and denominator exactly.
Common fractions and their ratios
| Fraction | GCD | Ratio |
|---|---|---|
| 4/6 | 2 | 2:3 |
| 6/9 | 3 | 2:3 |
| 10/15 | 5 | 2:3 |
| 3/9 | 3 | 1:3 |
| 12/16 | 4 | 3:4 |
Notice the first three rows all simplify to the same 2:3 ratio — like equivalent fractions, different starting numbers can describe the same underlying relationship.
Where this comes up
Ratios show up anywhere two quantities are being compared directly rather than one being described as a share of a whole: mixing ratios for paint or concrete, aspect ratios for screens, and scale ratios on maps and models. If you actually need the fraction reduced to lowest terms rather than rewritten as a ratio, use the fraction simplifier instead — the math is identical, just the notation differs.