How can I convert a percentage into a fraction in simplest form?
Quick answer
Write the percentage as a fraction with 100 as the denominator, then divide the numerator and denominator by the same shared factor until they cannot both be reduced further. For example, 42% becomes 42/100; dividing both numbers by 2 gives 21/50. The fraction represents the same proportion as the percentage. [S1]
The question, the details, the next step.
What does a percentage have to do with a fraction? I can remember the percent sign, but I’m not sure how to start converting one.
“Percent” means a count out of 100. Remove the percent sign and put the number over 100: 42% becomes 42/100. That fraction represents the same proportion as 42%; it is just written in a different form. The basic method is to write the percentage over 100, then simplify if possible. [S1]
You do not need to change the number into a decimal first. Starting with the fraction makes it clear what you will reduce.
How do I simplify 42/100? I’m worried I might change the value by dividing.
Divide the top and bottom by the same number. For 42/100, both numbers are even, so divide each by 2:
42/100 = (42 ÷ 2)/(100 ÷ 2) = 21/50
That is simplest form: 21 and 50 have no common whole-number factor greater than 1. Dividing both parts by the same factor keeps the fraction equivalent. As a check, multiply 21/50’s numerator and denominator by 2 to get back to 42/100. This follows the write-over-100-and-simplify method. [S1]
What if the percentage is 60%? And how can the fraction help me compare it with another percentage?
For 60%, start with 60/100. Divide both numbers by 10 to get 6/10, then divide both by 2 to get 3/5. So 60% = 60/100 = 6/10 = 3/5. OpenStax gives this same conversion as an example. [S1]
A fraction can make a comparison convenient when the fractions are easy to compare. For instance, 60% is 3/5 and 50% is 1/2. Give them the same denominator: 3/5 = 6/10, while 1/2 = 5/10, so 3/5 is larger. This shows one way to compare these values; fractions are not always the easiest form to use. [S1]
Can you give me a quick routine to use on a percentage I haven’t seen before?
Use this routine:
- Put the percentage number over 100.
- Find a number that divides both the numerator and denominator evenly.
- Divide both by that number.
- Repeat until no shared factor greater than 1 remains.
- Check that the final numerator and denominator have no shared factor greater than 1.
For example, with 18%, write 18/100, then divide both numbers by 2 to get 9/50. Since 9 and 50 have no shared factor greater than 1, 9/50 is in simplest form. [S1]
This routine converts the percentage to an equivalent fraction. To compare it with another value, you still need to compare the resulting values.
A practical checklist
Write the percentage number as the numerator and 100 as the denominator.
Choose a factor that divides both numerator and denominator evenly.
Divide both parts by the same factor; repeat if they can still be reduced.
Check that the final numerator and denominator have no shared factor greater than 1.
To compare values, use a clear method, such as equivalent denominators.
A few more useful answers
Do I have to reduce a fraction all at once?
No. You can divide the numerator and denominator by a shared factor in several steps, as with 60/100 → 6/10 → 3/5. Divide both by the same factor each time.
How do I know when the fraction is in simplest form?
It is in simplest form when the numerator and denominator have no shared whole-number factor greater than 1. For example, 21/50 cannot be reduced further.
Is a fraction always better than a percentage for comparing amounts?
Not always. Fractions can be convenient for some comparisons, but choose a form or method that makes the values easy to compare. Converting alone does not establish a universal comparison rule.
Sources
References used for this guide.
- [S1] OpenStax Prealgebra 2e: Understand Percent openstax.org · Checked