To turn a percentage into a fraction, write it over 100 and simplify. So 55% becomes 55/100, which simplifies to 11/20, and 22.5% becomes 22.5/100, then 225/1000, which simplifies to 9/40.
To go the other way, divide the top number of the fraction by the bottom number and multiply by 100. So 11/20 is 11 ÷ 20 = 0.55, which is 55%.
Both directions come up in numerical reasoning tests and in conversion questions generally, almost always without a calculator, so it is worth being able to run the method on paper.
A step-by-step guide to converting percentages into fractions
The four steps below work through a question that comes up often: express 22.5% as a fraction in its simplest form. Keep blank paper to hand during an assessment so you can jot down your workings at each stage.
Once the steps are familiar, most conversions take a few seconds, and the common ones can be recognised on sight.
Step 1: Express the percentage as a fraction
Take the percentage you have been given and write it as a fraction over 100. Per cent means per hundred, so this step is just writing the words out as numbers.
For example: 45% becomes 45/100.
So, for the question Express 22.5% as a fraction, you would start with 22.5/100.
Note that the top value of a fraction is known as the numerator, and the bottom value is called the denominator.
Step 2: Write the numerator as a whole number
If the numerator is not a whole number, multiply the value by 10 for every digit to the right of the decimal place. Then, do the same to the denominator.
For example: If after step 1 you have 22.5/100, multiply 22.5 x 10 and then 100 x 10.
This will give you 225/1000
You now have what is known as a decimal fraction.
If the numerator is already a whole number, you can skip this stage.
Step 3: Simplify the fractions
Next, reduce the fraction to its lowest terms, which simply means expressing it as simply as possible.
You do this by dividing the numerator and the denominator by the same number. That number has to divide into both of them exactly, with nothing left over.
Start by seeing if both values divide by 2. If not, try 3, then 5, then 7, then 11 and so on.
There is no point checking 4, because anything that divides exactly by 4 also divides by 2. The same goes for 6, 8 and other multiples, so stick to prime numbers.
For example: 225/1000 doesn’t divide exactly by 2 or by 3, as you’ll end up with a decimal point.
Both values do, however, divide by 5.
225 ÷ 5 = 45
1000 ÷ 5 = 200
So, 45/200
These values can also be divided by 5.
45 ÷ 5 = 9
200 ÷ 5 = 40
We now have a fraction of 9/40, and 9 and 40 share no further common factor, so it is fully simplified.
Alternatively, if you are good with your multiplication tables, you can go straight to identifying the greatest common factor of the numerator and denominator. Which, in this case, is 25.
225 ÷ 25 = 9
1000 ÷ 25 = 40
= 9/40
So, to answer our question, 22.5% expressed as a fraction is 9/40.
Step 4: If the fraction is improper, convert it to a mixed number
If you are left with an improper fraction, meaning the numerator is larger than the denominator, you’ll need to convert it to a mixed number. To do this, see how many whole times the denominator fits into the numerator, then write whatever is left over as the fractional part.
For example, 250% is 250/100, which simplifies to 5/2. Two fits into 5 twice with 1 left over, so 5/2 becomes 2 1/2.
You can tell in advance whether you will need a mixed number: any percentage above 100 will give a numerator larger than the denominator at the end of the first step.
Worked examples: percentage to fraction
To see the method applied in different circumstances, here are three more worked examples.
Convert 32% to a fraction
Step 1: Write the percentage over 100. So, 32/100.
Step 2: 32 is already a whole number (there aren’t any digits after a decimal point), so Step 2 is not required.
Step 3: Identify the greatest common factor. In this case, it’s 4.
32 ÷ 4 = 8
100 ÷ 4 = 25
Therefore, the fraction, when reduced to its simplest form, is 8/25.
There’s no need for Step 4, as 8/25 is not an improper fraction.
Answer: 32% expressed as a fraction is 8/25.
Express 55% as a fraction
Step 1: Write the percentage over 100. So, 55/100.
Step 2: 55 is already a whole number, so Step 2 is not required.
Step 3: Identify the greatest common factor. In this case, it’s 5.
55 ÷ 5 = 11
100 ÷ 5 = 20
Therefore, the fraction, when reduced to its simplest form, is 11/20.
There’s no need for Step 4, as 11/20 is not an improper fraction.
Answer: 55% expressed as a fraction is 11/20.
Express 22.5% as a fraction in its simplest form
Step 1: Write the percentage over 100. So, 22.5/100.
Step 2: There is one digit after the decimal point, so multiply both the numerator and the denominator by 10. That gives 225/1000.
Step 3: Identify the greatest common factor of 225 and 1000. In this case, it’s 25.
225 ÷ 25 = 9
1000 ÷ 25 = 40
Answer: 22.5% expressed as a fraction in its simplest form is 9/40.
Going the other way: fractions to percentages
Assessment questions run in both directions, so it is worth being equally quick at turning a fraction into a percentage.
There are two reliable methods. Either divide the numerator by the denominator and multiply the result by 100, or, if the denominator divides neatly into 100, scale the fraction up so the denominator becomes 100 and read the numerator as the percentage.
What is 11/20 as a percentage?
Twenty goes into 100 five times, so multiply the numerator and the denominator by 5:
11 x 5 = 55
20 x 5 = 100
That gives 55/100. So 11/20 as a percentage is 55%.
The division method agrees: 11 ÷ 20 = 0.55, and 0.55 x 100 = 55.
What is 22 out of 40 as a percentage?
Simplify first. Both numbers divide by 2, so 22/40 becomes 11/20, which we have just shown is 55%.
Dividing straight through gives the same result: 22 ÷ 40 = 0.55, so 22 out of 40 is 55%.
What is 9/40 as a percentage?
This one checks our earlier answer. 9 ÷ 40 = 0.225, and 0.225 x 100 = 22.5, so 9/40 as a percentage is 22.5%, which is exactly the percentage we converted in the step-by-step example.
What is 22 as a percentage of 100?
Anything expressed out of 100 is already a percentage, because per cent means per hundred. So 22 as a percentage of 100 is 22%. As a fraction that is 22/100, and both values divide by 2, giving 11/50 in its simplest form.
Conversions worth memorising
Recognising the common conversions on sight saves time in a timed assessment, because you can write the answer down without working it through.
- 10% = 1/10
- 12.5% = 1/8
- 20% = 1/5
- 22.5% = 9/40
- 25% = 1/4
- 32% = 8/25
- 50% = 1/2
- 55% = 11/20
- 60% = 3/5
- 75% = 3/4
- 80% = 4/5
Practice conversion questions
Conversions between percentages, fractions and decimals appear throughout numerical reasoning tests, usually buried inside a longer question rather than asked directly. If you want to drill the arithmetic on its own first, basic numeracy tests are the closer match.
Working through timed questions is what makes the method fast enough to be useful under exam conditions, so try a set of free aptitude tests to see where you currently stand.
