How to convert a ratio to a percentage
Add the parts, divide each by the total, multiply by 100. Plus the reverse trip and a common trap.
3 min read →What simplifying a ratio means
Simplifying a ratio means rewriting it with the smallest whole numbers that still describe the same relationship. The ratio 24:36 says "for every 24 of one thing there are 36 of the other". Divide both sides by 12 and you get 2:3, which says exactly the same thing in plainer terms.
It works for the same reason you can simplify a fraction. Dividing every part of a ratio by the same number never changes what the ratio means, so you are free to keep dividing until nothing more divides evenly.
The method in three steps
- Make every number whole. If there are decimals, multiply all the numbers by 10, 100 or 1000 first.
- Find the greatest common divisor (GCD). This is the largest number that divides every part with no remainder.
- Divide every part by the GCD. The result is the simplest form.
Example 1: a simple two-part ratio
Simplify 24 : 36.
The factors of 24 include 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36. The biggest one they share is 12.
The factors of 24 include 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36. The biggest one they share is 12.
24 : 36 = 2412 : 3612 = 2 : 3
Example 2: three or more parts
The same idea works with any number of parts. You need one number that divides all of them.
Simplify 12 : 18 : 30.
The GCD of 12, 18 and 30 is 6.
The GCD of 12, 18 and 30 is 6.
12 : 18 : 30 = 126 : 186 : 306 = 2 : 3 : 5
Example 3: ratios with decimals
A ratio is not simplest while it still contains decimals. Clear them first by multiplying every number by the same power of 10.
Simplify 0.75 : 1.5.
Multiply both by 100 to get 75 : 150. The GCD of 75 and 150 is 75.
Multiply both by 100 to get 75 : 150. The GCD of 75 and 150 is 75.
75 : 150 = 7575 : 15075 = 1 : 2
Example 4: different units
Both sides of a ratio must be in the same unit before you simplify. Comparing 2 metres to 50 centimetres as 2 : 50 would be wrong.
Simplify 2 m : 50 cm.
Convert to centimetres first: 200 cm : 50 cm. The GCD is 50.
Convert to centimetres first: 200 cm : 50 cm. The GCD is 50.
200 : 50 = 20050 : 5050 = 4 : 1
A quick way to find the GCD: Euclid's method
For big numbers, listing factors is slow. Euclid's method is faster. Divide the larger number by the smaller, keep the remainder, and repeat with the smaller number and that remainder. The last non-zero remainder is the GCD.
Find the GCD of 48 and 18.
48 = 2 × 18 + 12
18 = 1 × 12 + 6
12 = 2 × 6 + 0
The last non-zero remainder is 6, so the GCD is 6 and 48 : 18 simplifies to 8 : 3.
48 = 2 × 18 + 12
18 = 1 × 12 + 6
12 = 2 × 6 + 0
The last non-zero remainder is 6, so the GCD is 6 and 48 : 18 simplifies to 8 : 3.
If you do not want to do this by hand, the simplify calculator shows every Euclid step for you.
Mistakes to avoid
- Dividing the parts by different numbers. Every part must be divided by the same number.
- Stopping too early. 6 : 9 divided by 3 is 2 : 3, but 6 : 9 divided by 1.5 is 4 : 6, which is not the simplest form. Always check that nothing else divides both numbers.
- Forgetting to match units or to clear decimals before simplifying.
- Treating 1 as a problem. A ratio like 5 : 1 is already as simple as it gets.
Check your own ratio
Open the simplify calculatorType up to four numbers and see every step, including the Euclid working, in plain words and in maths form.
Frequently asked questions
Is 1 : 1 the simplest form of a ratio?
Yes. When both parts are equal the ratio simplifies to 1 : 1, and it cannot be reduced any further.
Does simplifying change the value of a ratio?
No. 24 : 36 and 2 : 3 describe exactly the same relationship. Simplifying only rewrites it with smaller numbers.
What if the two numbers have no common factor?
Then the greatest common divisor is 1 and the ratio is already in its simplest form. For example, 7 : 5 cannot be reduced.