Improper and Mixed Fraction Conversion

As has already been stated, improper and mixed fractions represent the same type of number. (A number that is one or greater than one). Since this is true, you can convert improper fractions to mixed fractions and back again. This is useful as it is easier to add, subtract, multiply and divide improper fractions than mixed fractions.

Converting a Mixed Fraction to an Improper Fraction

Take a look at the following mixed fraction:

To change this to an improper fraction, follow these two steps:

1. Multiply the denominator of the fraction by the whole number (in this case, 5 x 3 = 15) and remember this result.
2. Add the result of step 1 to the numerator of the fraction (15 + 2 = 17) and put this number over the old denominator (5) to get the following improper fraction:

Converting an Improper Fraction to a Mixed Fraction

For this example, we will reverse the process above. Examine the improper fraction that we got as an answer:

To convert this to a mixed fraction, follow these two steps:

1. Divide 17 by 5 and ignore the remainder for now. 5 goes into 17 3 times. Remember the number 3. (That will be the whole number part of our mixed fraction.)
2. Examine your remainder when 5 is divided into 17. 5 x 3 = 15, so there is a remainder of 2. This remainder is your new numerator. This gives you an answer of:

You can now head back to the fractions main page, or try some sample conversion questions.