How to simplify a ratio
A ratio compares two quantities in a fixed proportion: flour to butter in a crumble, sand to cement in mortar, width to height on a screen. A ratio is in its simplest form when no whole number bigger than 1 divides into both sides. To get there, divide both parts by their highest common factor (HCF).
Take 18 : 24. The HCF of 18 and 24 is 6, so dividing both sides gives 3 : 4. The two ratios are equivalent, meaning they describe exactly the same proportion, but 3 : 4 is far easier to work with. If either side has decimals, multiply both by 10 until they are whole numbers first: 2.5 : 1.5 becomes 25 : 15, which simplifies to 5 : 3. The calculator does the whole routine for you and also shows the ratio in the form 1 : n, which is handy for dilution ratios and map scales.
Worked examples
Finding a missing value
Two ratios are equivalent when one is a scaled-up or scaled-down copy of the other. That is exactly what recipe scaling is: if a recipe pairs 2 parts rice with 3 parts water and you are cooking 5 cups of rice, you need to find x in 2 : 3 = 5 : x. The reliable method is cross multiplication.
Here x = 3 × 5 ÷ 2 = 7.5 cups of water. The logic is that you scaled the first side up by 5 ÷ 2 = 2.5 times, so the second side must scale by the same factor: 3 × 2.5 = 7.5. The same sum sorts out paint mixing, squash dilution (a 1 : 4 squash needs 4 parts water for every 1 part concentrate) and map reading, where a 1 : 25,000 scale means every centimetre on the map is 25,000 cm, or 250 metres, on the ground.
Sharing an amount in a ratio
A related job, and a GCSE favourite, is splitting an amount in a given ratio. Add the parts together to find how many equal shares there are, divide the amount by that total, then multiply by each part. Splitting £120 between two people in the ratio 2 : 3 gives 2 + 3 = 5 parts, each worth £120 ÷ 5 = £24. One person gets 2 × £24 = £48 and the other gets 3 × £24 = £72. A quick sense check: the two shares should always add back to the original amount, and £48 + £72 = £120.
Simplifying first makes sharing easier too. Asked to split a bill in the ratio 18 : 24, reduce it to 3 : 4 before you start; the answer is identical and the arithmetic is friendlier. If you want the proportion as a percentage instead, our percentage calculator will convert either share in one step.
Frequently asked questions
How do I simplify a ratio?
Divide both sides by their highest common factor (HCF), the largest whole number that divides into both. For 18 : 24 the HCF is 6, so the ratio simplifies to 3 : 4. When no whole number bigger than 1 divides both sides, the ratio is already in its simplest form.
How do I find a missing value in a ratio?
Use cross multiplication. If A : B = C : x, then x = B multiplied by C, divided by A. For example, if 2 : 3 = 5 : x, then x = 3 multiplied by 5 divided by 2, which is 7.5.
Can a ratio include decimals?
Yes, but the convention is to clear them before simplifying. Multiply both sides by 10 until both are whole numbers, then divide by the HCF as usual. So 2.5 : 1.5 becomes 25 : 15, which simplifies to 5 : 3. This calculator handles that step for you.
What does 16 : 9 mean on a screen?
It is the aspect ratio, the width compared with the height. A full HD screen is 1920 by 1080 pixels, and 1920 : 1080 simplifies to 16 : 9 because both numbers divide by 120. Most modern TVs, laptops and YouTube videos use this shape.
How do I split an amount in a given ratio?
Add the parts of the ratio together, divide the amount by that total, then multiply by each part. To split 120 pounds in the ratio 2 : 3, add 2 and 3 to get 5 parts, so each part is worth 24 pounds. The shares are 48 pounds and 72 pounds.