How to Simplify a Ratio to Its Lowest Terms
Simplifying a ratio means dividing every part by the same number until no common factor is left. The Ratio Simplifier does it, and finding the right divisor in one step is the only real skill involved.
Divide by the greatest common divisor
The number you want is the greatest common divisor of all the parts - the largest number that divides every one of them exactly.
For 18:24, the GCD is 6, so dividing both gives 3:4. You could get there by halving twice and then dividing by three, but dividing by the GCD does it in one move, and the LCM and GCD Calculator finds it for any set of numbers.
A ratio is in its lowest terms when the GCD of its parts is 1. For 3:4 it is, so that is as far as it goes.
For three or more parts, the principle is identical - find the GCD of all of them. 12:18:30 has a GCD of 6, giving 2:3:5.
Decimals and fractions
Multiply rather than divide. For 2.5:4, multiply both by 10 to get 25:40, then simplify by 5 to get 5:8.
For fractions, multiply every part by the lowest common denominator first, which clears them into whole numbers, and then simplify as usual. The Fraction Calculator handles that step.
Units have to match, and this is where it goes wrong
A ratio compares like with like, so the parts must be in the same unit before you simplify.
30 minutes to 2 hours is not 30:2 and does not simplify to 15:1. Convert first: 30 minutes to 120 minutes is 30:120, which simplifies to 1:4. The difference between 15:1 and 1:4 is not a rounding error.
Once converted, a ratio has no units at all - it is a pure comparison, which is what makes it portable between contexts.
Ratio, proportion and fraction
Three related things worth keeping apart.
2:3 is a ratio - two parts to three parts. As a fraction of the whole, the first part is 2/5, not 2/3, because the whole is five parts. That confusion is the commonest error in using a ratio after simplifying it.
And a ratio stays the same when scaled, which is what makes it useful for recipes, scale models and mixing. A 1:4 concentrate is 1:4 whether you are making a cup or a bucket - a property the Cooking Measurement Converter relies on.
Common questions
Should a ratio have a 1 in it?
A unit ratio - 1:4, or 2.5:1 - is easiest to use mentally, and it is not always a whole-number simplification. Divide both parts by the smaller to get it.
Can a ratio have more than two parts?
Yes, and the method is the same: the GCD of all the parts.
How do I compare two ratios?
Convert both to the same first term, or to fractions of the whole, and then compare directly.
What about an aspect ratio like 16:9?
Already in lowest terms, which is why it is written that way rather than as 1920:1080.
Got a ratio to tidy up?