How to Convert Improper Fractions to Mixed Forms

In Introduction to Functions, we have learned about proper and improper fractions. A fraction whose numerator (the number above the fraction bar) is less than its denominator (the number below the fraction bar) is called a proper fraction. Therefore, \frac{1}{3}, \frac{2}{5} and \frac{11}{20} are proper fractions.

On the other hand,  a fraction whose numerator is greater than its denominator is called an improper fraction. Therefore the fractions \frac{21}{7}, \frac{8}{3} and \frac{67}{5} are improper fractions.

In the Civil Service Examinations, some fractions need to be converted from one form to another. For example, in answering a number series test, you might need to convert an improper fraction to mixed form in order to compare it to other fractions in mixed form. In this post, we learn this method: how to convert an improper fraction to mixed form.

In converting improper fractions to mixed form you will just have to divide the fraction, find its quotient and its remainder. Remember that the fraction \frac{34}{5} also means 34 divided by 5.

mixed formWhen we divide 34 by 5, we call 5 the divisor.  The quotient to this division  is 6 with a remainder of 4. From the method, we can observe the following:

  • The quotient 6 is the whole number on the mixed fraction.
  • The divisor 5 is the denominator of the mixed fraction.
  • The remainder 4 goes to the numerator of the mixed fraction.

Now, for the second example, let us convert \frac{28}{3} into mixed fraction. If we divide 28 by 3, the divisor is 3, the quotient is 9 and the remainder is 1. Therefore, the equivalent of the improper fraction \frac{28}{3} is

9 \displaystyle\frac{1}{3}.

One Comments

  • Fraction Calc

    June 26, 2019

    In my elementary years, I was taught to divide the numerator to the denominator. The quotient would be the whole number while the remainder will be the new numerator and the denominator remained the same. That is the way to convert improper fraction to mixed number. This rule has has been implanted in my mind even though I am 37 now.


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