How to Convert Mixed Numbers and Improper Fractions

By Tina Molly Lang; Updated April 24, 2017
Mixed numbers can be converted into improper fractions.

Fractions are expressed as two numbers separated by a line. The number above the line is the numerator. The number below the line is the denominator. If the numerator is less than the denominator, then the fraction is proper. Examples include 3/4, 4/5 and 7/9. If the numerator is greater than the denominator, then the fraction is improper. Examples include 4/3, 6/5 and 20/17. Mixed numbers consist of a whole number and a proper fraction, such as 4 1/2. Improper fractions can be converted into mixed numbers and vice versa.

Pick an example problem: 4 5/7.

Multiply the denominator, 7, by the whole number, 4. 7 x 4 = 28.

Take that product, 28, and add that to the numerator of the fraction, 5. 28 + 5 = 33.

Take that sum, 33, and place it over the denominator, 7. 33/7. 4 5/7 = 33/7.

Use the procedure in reverse to convert improper fractions into mixed numbers. Take an example problem: 33/7.

Divide the denominator, 7, into the numerator, 33. 7 goes into 33 four times. So 4 is the whole number.

Take the remainder and place it over the denominator, 7. 33 divided by 7 is 4. 4 x 7 = 28. 33 -28 = 5. The remainder is 5. The fraction is 5/7. 33/7 = 4 5/7.


You can always check your work by converting the improper fraction back into a mixed number and vice versa.

About the Author

Tina Molly Lang is a violinist, freelance writer, and Yale School of Music graduate. She is also a regular news writer for Associated Content, arts writer for the Examiner and has been published in other magazines including The American Thinker. She has been writing on a freelance basis since 2007.