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}.

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4 Responses

  1. October 16, 2013

    […] the previous post, we have learned how to convert improper fractions to mixed number . Now, try the following exercises. All the answers must also be reduced to lowest terms. Good […]

  2. November 6, 2013

    […] have already learned how to convert improper fractions to mixed fractions.  In this post, we are going to learn how to convert mixed fractions to improper fractions.  In […]

  3. March 8, 2014

    […] is, or in mixed fraction or in […]

  4. October 12, 2015

    […] can convert the improper fraction to mixed form which is equal […]

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