How this instrument works
A ratio compares two quantities, written a:b, and simplifying it means dividing both numbers by their greatest common divisor (GCD) — the largest whole number that fits evenly into both. Doing so always produces the smallest possible whole-number pair that still represents the exact same proportional relationship, since dividing both sides of a ratio by the same number never changes what that ratio actually means.
This is the identical technique used to reduce a fraction to lowest terms, since a ratio and a fraction share the same underlying structure — a:b and the fraction a⁄b simplify by exactly the same division. A ratio already in lowest terms, where the two numbers share no common factor beyond 1, cannot be simplified any further.
Simplified ratios are easier to read, compare, and communicate — a mixing ratio of 48:18 conveys the identical proportion as 8:3, but the second is far easier to recognize, remember, and scale up or down by hand, which is exactly why recipes, concrete mixes, and aspect ratios are almost always quoted in their simplest form.
- Enter the first number of the ratio into the First number field.
- Enter the second number into the Second number field.
- Read Simplified a and Simplified b: the sheet divides both original numbers by their greatest common divisor.
Worked example — simplifying 48:18
The ratio 48:18 has a greatest common divisor of 6, so dividing both numbers by 6 gives 8:3 — the simplest whole-number form of the identical proportional relationship, easier to read and scale than the original.
The ratio 8:4 simplifies to 2:1, dividing both by their GCD of 4. And the ratio 7:5 is already in lowest terms, since 7 and 5 share no common factor beyond 1 — their GCD is 1, so dividing by it changes nothing at all.
Questions
How do you simplify a ratio?
Find the greatest common divisor of the two numbers, then divide both by it. The result is the smallest possible whole-number pair still representing the same proportional relationship as the original ratio.
Is simplifying a ratio the same as simplifying a fraction?
Yes — a ratio a:b and a fraction a⁄b share the identical structure and simplify through exactly the same technique: dividing both numbers by their greatest common divisor.
How do I know when a ratio is already fully simplified?
When the two numbers share no common factor beyond 1 — their greatest common divisor is exactly 1, meaning dividing by it leaves the ratio completely unchanged from its original form.
Why simplify a ratio instead of leaving it as-is?
Simplified ratios are far easier to read, remember, and scale up or down by hand. A recipe, concrete mix, or aspect ratio quoted as 8:3 is immediately clearer than the equivalent but unsimplified 48:18, even though both describe the identical proportion.
Can this method handle any two positive whole numbers?
Yes — the greatest common divisor is well-defined for any two positive whole numbers, so this simplification always works, whether the numbers are small and closely related or large with a less obvious shared factor.