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Contributor: Katie Schnabel. Lesson ID: 14190
You rocked your test and even got the extra credit questions correct! But what percentage did you receive? Explore how to convert mixed numbers into percentages to find out!
Imagine you’re sitting in class, your heart racing a bit as you prepare to take the history test you’ve been preparing for.
You’ve poured your energy into studying—reading every chapter, crafting flashcards, and mastering the study guide. You feel ready, like a superhero about to tackle a big mission.
As you breeze through the test, you spot some extra credit questions at the end. You take a deep breath and confidently answer them.
When your teacher hands back your test, your eyes widen in disbelief. You scored more than 100%! Your teacher says you got 1 and 1/4 points extra on top of a perfect score.
Dive in and uncover the magic of converting mixed numbers into percentages greater than 100%.
Remember, fractions are like pieces of a pie. They show you part of a whole.
Because all fractions are less than 1, they are all less than 100% of the whole.
Since one whole equals 100%, anything greater than one is more than 100%.
Exactly! 200%.
Mixed numbers have a whole number and a fraction, just like your test score of 1 1/4. The whole number tells you your score is over 100%.
Whenever you see a mixed number, remember to just multiply the whole number by 100. That gives you a head start on your answer.
Break it down! Start with your whole number, which is 1. That's 100%. Now, add the fraction 1/4.
To turn a fraction into a percent, first divide the numerator by the denominator.
| 0 | . | 2 | 5 | |||
| 4 | 1 | . | 0 | 0 | ||
| - | 8 | |||||
| 2 | 0 | |||||
| - | 2 | 0 | ||||
| 0 |
Yes! You get 0.25.
To turn that into a percent, multiply by 100. You can do this easily by moving the decimal two places to the right.
Correct! 25, giving you 25%.
Add the 25% to the whole number you know is 100%.
Now, add that 25% to your 100% from the whole number.
Awesome! You scored 125% on your test! Well done!
Tackle another one. Check out this mixed number.
| 7 | 1 | |
| 3 |
You have 7 wholes, which is 700%, and one-third of a whole. You can divide the numerator by the denominator and multiply the answer by 100 to turn 1/3 into a percentage.
| 0 | . | 3 | 3 | ... | x | 100 | = | 33% | |||
| 3 | 1 | . | 0 | 0 | |||||||
| - | 9 | ||||||||||
| 1 | 0 | ||||||||||
| - | 0 | 9 | |||||||||
| 1 | |||||||||||
Because you can continue the division process indefinitely, round the answer to the nearest hundredths, 0.33. When you multiply that by 100, you get 33.
1/3 equals 33%!
So 7 1/3 equals 733%.
Another way to convert a mixed number into a percent is by changing it into an improper fraction. An improper fraction is when the numerator is greater than the denominator.
First, multiply the whole number by the denominator.
Yes! It is 21. Now, add your answer of 21 to the numerator.
Correct, it's 22.
Now, write 22 as the numerator and keep the original denominator of 3. Your improper fraction is 22/3.
To express this as a percent, multiply your improper fraction by 100 (or 100/1).
| 22 | x | 100 | = | 2200 | |
| 3 | 1 | 3 |
Now, set it up for division.
| 0 | 7 | 3 | 3 | . | 3 | 3 | ... | ||
| 3 | 2 | 2 | 0 | 0 | . | 0 | 0 | ||
| - | 2 | 1 | |||||||
| 1 | 0 | ||||||||
| - | 9 | ||||||||
| 1 | 0 | ||||||||
| - | 9 | ||||||||
| 1 | . | 0 | |||||||
| - | 9 | ||||||||
| 1 | 0 | ||||||||
| - | 9 | ||||||||
| 1 |
After you complete the division, round to the nearest hundredths to find the percentage: 733%. Whoa!
Now, you have not one but two methods for turning mixed numbers into percentages.
Head to the Got It? section for fun practice problems and interactive games!
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