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How to Simplify a Ratio (and Scale It Up or Down)
Learn how to reduce a ratio to its simplest form using the greatest common divisor, turn it into a fraction or percentage split, and scale it while keeping the proportion.
Updated 19 October 2026 · 2 min read
A ratio compares two quantities — two parts of paint, the width and height of a screen, flour to water in a dough. Written as A : B, it reads "A to B". A ratio like 16 : 12 says the same thing as 4 : 3, just in larger numbers, and simplifying means finding that smallest equivalent form so the relationship is easy to read.
Simplify by dividing out the common factor
To reduce a ratio, divide both parts by their greatest common divisor (GCD) — the largest number that divides into each of them exactly. Whatever you do to one side you must do to the other, because that keeps the proportion unchanged.
- Find the GCD of the two numbers (the biggest number that divides both without a remainder).
- Divide the first part by the GCD.
- Divide the second part by the GCD.
- Write the two results as the simplified ratio.
If the two numbers share no factor larger than 1 — like 7 : 5 — the ratio is already in its simplest form and nothing changes.
A worked example
Say a recipe uses 200 g of sugar to 250 g of butter. The GCD of 200 and 250 is 50. Dividing both gives 4 : 5. That's far easier to remember and to scale than the original figures, and it tells you at a glance there's slightly more butter than sugar.
Ratios as fractions and percentages
A ratio is closely related to a fraction and a percentage split, which is often the clearest way to read it:
- As a fraction: A : B means A ÷ B. The ratio 4 : 5 is the fraction 4/5, or 0.8.
- As a percentage split: add the parts for the total, then divide each by it. For 4 : 5 the total is 9, so the split is about 44% : 56%.
- As parts of a whole: 4 : 5 shares something into 9 equal parts — 4 go one way, 5 the other.
Scaling a ratio
Scaling means changing the actual amounts while keeping the proportion. If a 4 : 3 mix needs to grow so the first part is 32, multiply both by the same factor: 32 ÷ 4 = 8, so the second part becomes 3 × 8 = 24, giving 32 : 24. The ratio calculator does the simplifying, the decimal and percentage split, and this scaling step for you — enter a new first part and it works out the matching second part.
Ratios and percentages are two views of the same idea, so if percentage splits are what you're really after, see percentages made simple, and for sharing a quantity into unequal parts the percentage calculator handles the final step.
Frequently asked questions
- How do I simplify a ratio to its lowest terms?
- Divide both parts by their greatest common divisor — the largest number that divides into each exactly. For 16 : 12 that number is 4, giving 4 : 3. If no number larger than 1 divides both, the ratio is already simplified.
- Can a ratio contain decimals?
- Yes. When the parts aren't whole numbers it's usually clearest to normalise the ratio to the form 1 : x by dividing both sides by the first part. That way you can compare it directly with other ratios.
- What's the difference between a ratio and a fraction?
- A fraction compares a part to the whole, while a ratio compares two parts to each other. The ratio 4 : 5 can be written as the fraction 4/5, but it also implies a whole of 9 parts split 4 and 5.