How to Reduce Mixed Numbers & Improper Fractions to the Lowest Terms

By Suzanne Akerman
Add & Subtract Radical Expressions With Fractions
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Reducing a fraction refers to getting the numerator and denominator as small as possible, while retaining a fraction equivalent to the one you started with. When a fraction has reached this form, it is called “lowest terms” or sometimes “simplest terms.” An improper fraction is a fraction with a numerator higher than its denominator, which means the fraction is greater than one, such as 3/2 or 100/50. A mixed number is a whole number and a fraction of a number together, such as 7 and 1/2 or 2 and 23/25.

Reducing Improper Fractions

Step 1

Find a factor that the numerator and denominator have in common. If you have 24/18, the number 2 is a factor for both.

Step 2

Divide the numerator by 2 and put the quotient in the numerator position of your answer. Divide the denominator by 2 and put the quotient in the denominator position of your answer. For this example, we have 24 divided by 2, which is 12, and 18 divided by 2, which is 9, giving us 12/9.

Step 3

Find another factor that the new numerator and denominator share. If we continue with our example, we have 12 and 9, which share 3 as a common factor. Divide the numerator by 3 and put the quotient in the numerator position of your answer. Divide the denominator by 3 and put the quotient in the denominator position. Twelve divided by 3 is 4; 9 divided by 3 is 3, so now we have 4/3.

Step 4

Find common factors until the numerator and denominator no longer have any factors in common. Then the fraction is in lowest terms. Because the numerator is larger than the denominator, the fraction is still improper, but it is in its simplest form. Get to the simplest form faster by choosing the largest common denominator when you divide the very first time, rather than choosing just any common denominator.

Converting Mixed Numbers to Simplest Terms

Step 1

Multiply the whole number of the mixed number by the denominator of the fraction. For example, if you have 7 1/2, multiply 7 by 2, which is 14. Add this number to the original numerator; in our example this is 1, so the sum is 15. Write this number in the numerator position of your answer.

Step 2

Write the same denominator that you started with in the denominator position of your answer. In our example, we have 2 as the denominator in the fraction at the beginning, so we will put 2 in the denominator of the answer. Now we have 15/2.

Step 3

Check that your numerator is larger than your denominator, which will always be true of a mixed number once it has been converted into simplest terms. If you attempt to reduce the improper fraction further, you will find that it is already in lowest terms; if you can reduce it farther, you have made an error, so go back and check your work.

About the Author

Suzanne Akerman began writing in 2000. She has worked as a consultant at Pacific Lutheran University's Writing Center and her works have been published in the creative arts journal "Saxifrage." Akerman holds a Bachelor of Arts in English and a Master of Arts in education from Pacific Lutheran University.