What a ratio tells you
A ratio tells you how big things are compared with each other, with the actual amounts stripped out. A class with 12 girls and 18 boys and a club with 2 girls and 3 boys have the same ratio, 2:3. That's why you can simplify a ratio and scale it without changing what it says.
Both jobs come down to one rule: whatever you do to one part, do to every part. Divide them all by the same number to simplify. Multiply them all by the same number to scale.
Simplifying whole-number ratios
Find the greatest common factor (GCF) of all the parts and divide each one by it. For 12:18:30, the factors of 12 are 1, 2, 3, 4, 6 and 12. The biggest one that also divides 18 and 30 is 6. Divide through and you get 2:3:5.
If you can't see the GCF straight away, divide by any common factor and repeat. 1920:1080 divides by 10 to give 192:108, then by 4 to give 48:27, then by 3 to give 16:9. That's the familiar widescreen ratio. You're done when no number above 1 divides every part.
- 24:36 = 2:3 (GCF 12)
- 45:60:75 = 3:4:5 (GCF 15)
- 1920:1080 = 16:9 (GCF 120)
Ratios with decimals or fractions
Get rid of the decimals or fractions first, then simplify. For decimals, multiply every part by 10, 100 or 1,000, enough to clear the longest decimal. 0.4:1.2 times 10 is 4:12, which simplifies to 1:3.
For fractions, multiply every part by the least common multiple of the denominators. In 1/2:3/4, the denominators are 2 and 4, so multiply by 4 to get 2:3. Mixed types work too. 1/2:0.75:1.25 is 1/2:3/4:5/4, and multiplying by 4 gives 2:3:5.
Scaling a ratio to real amounts
Scaling starts with one known amount. Say a dressing is oil, vinegar and mustard in the ratio 6:2:1, and you have 150 ml of vinegar. Vinegar is 2 parts, so one part is 150 / 2 = 75 ml. Oil is 6 x 75 = 450 ml and mustard is 75 ml.
Splitting a total works the other way round. If you want 270 ml of dressing in total, the parts add to 9, so one part is 270 / 9 = 30 ml. That gives 180 ml of oil, 60 ml of vinegar and 30 ml of mustard. Both are the same idea: find the value of one part, then multiply.
Check scaled amounts by dividing each one by its ratio part. You should get the same number every time. Here 450 / 6, 150 / 2 and 75 / 1 all give 75, so the recipe kept its balance.
Formula notes
Value of one part = known amount / its ratio part, or total / sum of parts
Common mistakes
Most ratio errors come from treating the parts unequally or mixing up what's being compared. Run through this list when an answer looks off. If you'd rather check with a tool, our ratio calculator shows the common factor, each share and the scale factor it used.
- Simplifying only some of the parts. 6:9:12 becomes 2:3:4, and stopping at 2:3:12 changes the ratio.
- Adding instead of multiplying to scale. Adding 2 to each part of 1:2 gives 3:4, which isn't the same ratio.
- Mixing units. 50 cm to 2 m is 50:200, which is 1:4, not 25:1.
- Confusing part-to-part with part-to-whole. In 2:3 the first part is 2/5 of the total, not 2/3.
- Swapping the order. 3:2 and 2:3 say opposite things.
Frequently asked questions
How do you know when a ratio is fully simplified?
When the only number that divides every part evenly is 1. 2:3:5 is done. 4:6:10 isn't, because all three divide by 2.
Can a simplified ratio contain decimals?
Usually not. Simplest form normally means whole numbers with no shared factor, so 1.5:2 becomes 3:4.
How do you scale a ratio by a fraction?
Multiply every part by the fraction. Scaling 6:2:1 by 1/2 gives 3:1:0.5, which is the same ratio with half the amounts.
Do you simplify a ratio before scaling it?
It isn't required, but it helps. The numbers stay small and the value of one part is easier to see.
References
These sources support the method or guidance used for Ratio Calculator. Verify time-sensitive rules at the source.
Try the calculator
Open Ratio Calculator, enter your scenario, and compare its supporting rows with this guide's method and checks.