Converting Between Improper Fractions and Mixed Numbers

Learning Outcomes

  • Convert mixed numbers to improper fractions
  • Convert improper fractions to mixed numbers


In an earlier example, we converted the improper fraction
116\frac{11}{6}
to the mixed number
1561\frac{5}{6}
using fraction circles. We did this by grouping six sixths together to make a whole; then we looked to see how many of the
1111
pieces were left. We saw that
116\frac{11}{6}
made one whole group of six sixths plus five more sixths, showing that
116=156\frac{11}{6}=1\frac{5}{6}
.

The division expression
116\frac{11}{6}
(which can also be written as
6)116\overline{)11}
) tells us to find how many groups of
66
are in
1111
. To convert an improper fraction to a mixed number without fraction circles, we divide.

Example

Convert
116\frac{11}{6}
to a mixed number.

Solution:

116\frac{11}{6}
Divide the denominator into the numerator. Remember
116\frac{11}{6}
means
11÷611\div 6
.
.
Identify the quotient, remainder and divisor.
Write the mixed number as
quotientremainderdivisor\text{quotient}\frac{\text{remainder}}{\text{divisor}}
.
1561\frac{5}{6}
So,
116=156\frac{11}{6}=1\frac{5}{6}
 

Try it

 

#145979



 

Convert an improper fraction to a mixed number.

  1. Divide the denominator into the numerator.
  2. Identify the quotient, remainder, and divisor.
  3. Write the mixed number as quotient
    remainderdivisor\frac{\text{remainder}}{\text{divisor}}
    .


Example

Convert the improper fraction
338\frac{33}{8}
to a mixed number.





 

try it

 

#145979



Now you can watch worked examples of how to convert an improper fraction to a mixed number in the following video.



In an earlier example, we changed
1451\frac{4}{5}
to an improper fraction by first seeing that the whole is a set of five fifths. So we had five fifths and four more fifths.

55+45=95\frac{5}{5}+\frac{4}{5}=\frac{9}{5}


Where did the nine come from? There are nine fifths—one whole (five fifths) plus four fifths. Let us use this idea to see how to convert a mixed number to an improper fraction.

Example

Convert the mixed number
4234\frac{2}{3}
to an improper fraction.





 

try it

 

#145980



 

Convert a mixed number to an improper fraction.

  1. Multiply the whole number by the denominator.
  2. Add the numerator to the product found in Step 1.
  3. Write the final sum over the original denominator.


Example

Convert the mixed number
102710\frac{2}{7}
to an improper fraction.





 

Try it

 

#145980



In the following video we show more example of how to convert a mixed number to an improper fraction.



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