A worked example: 8:12
The ratio 8:12 simplifies to 2:3 — dividing both numbers by their greatest common factor, 4. As a decimal, that's 0.66666667 (2 ÷ 3), useful for comparing against a percentage or another ratio.
The formula: divide both values by their GCF
The greatest common factor of 8 and 12 is 4 (the largest number dividing both evenly) — dividing each side by 4 gives 2 and 3, which share no common factor greater than 1, confirming the ratio is fully reduced.
Simplifying a decimal ratio: 2.5:5
A ratio with decimal values, like 2.5:5, is first scaled up to whole numbers based on how many decimal places are involved — 2.5:5 scales to 25:50 — then simplified the normal way, reducing to 1:2.
Why simplifying a ratio doesn't change what it represents
2:3 and 8:12 describe the exact same proportional relationship — for every 2 units of one quantity, there are 3 of the other, regardless of which equivalent numbers are used to express it. Simplifying just finds the smallest whole numbers that preserve that same relationship.
Where a simplified ratio gets used next
A simplified ratio is often the starting point for a proportion — scaling that same relationship up or down to a specific real-world quantity, like recipe scaling or map distances.