Converting Between Improper Fractions and Mixed Numbers
Learning Outcomes
 Convert mixed numbers to improper fractions
 Convert improper fractions to mixed numbers
$\frac{11}{6}$
to the mixed number $1\frac{5}{6}$
using fraction circles. We did this by grouping six sixths together to make a whole; then we looked to see how many of the $11$
pieces were left. We saw that $\frac{11}{6}$
made one whole group of six sixths plus five more sixths, showing that $\frac{11}{6}=1\frac{5}{6}$
.The division expression
$\frac{11}{6}$
(which can also be written as $6\overline{)11}$
) tells us to find how many groups of $6$
are in $11$
. To convert an improper fraction to a mixed number without fraction circles, we divide.Example
Convert$\frac{11}{6}$
to a mixed number.Solution:
$\frac{11}{6}$ 

Divide the denominator into the numerator.  Remember $\frac{11}{6}$ means $11\div 6$ . 
Identify the quotient, remainder and divisor.  
Write the mixed number as $\text{quotient}\frac{\text{remainder}}{\text{divisor}}$ . 
$1\frac{5}{6}$ 
So, $\frac{11}{6}=1\frac{5}{6}$ 
Try it
#145979
Convert an improper fraction to a mixed number.
 Divide the denominator into the numerator.
 Identify the quotient, remainder, and divisor.
 Write the mixed number as quotient $\frac{\text{remainder}}{\text{divisor}}$.
Example
Convert the improper fraction$\frac{33}{8}$
to a mixed number.Show Solution
Solution:
$\frac{33}{8}$ 

Divide the denominator into the numerator.  Remember, $\frac{33}{8}$ means $8\overline{)33}$ . 
Identify the quotient, remainder, and divisor.  
Write the mixed number as quotient $\frac{\text{remainder}}{\text{divisor}}$ . 
$4\frac{1}{8}$ 
So, $\frac{33}{8}=4\frac{1}{8}$ 
try it
#145979
In an earlier example, we changed
$1\frac{4}{5}$
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.$\frac{5}{5}+\frac{4}{5}=\frac{9}{5}$
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$4\frac{2}{3}$
to an improper fraction.Show Solution
Solution:
$4\frac{2}{3}$ 

Multiply the whole number by the denominator.  
The whole number is 4 and the denominator is 3.  
Simplify.  
Add the numerator to the product.  
The numerator of the mixed number is 2.  
Simplify.  
Write the final sum over the original denominator.  
The denominator is 3.  $\frac{14}{3}$ 
try it
#145980
Convert a mixed number to an improper fraction.
 Multiply the whole number by the denominator.
 Add the numerator to the product found in Step 1.
 Write the final sum over the original denominator.
Example
Convert the mixed number$10\frac{2}{7}$
to an improper fraction.Show Solution
Solution:
$10\frac{2}{7}$ 

Multiply the whole number by the denominator.  
The whole number is 10 and the denominator is 7.  
Simplify.  
Add the numerator to the product.  
The numerator of the mixed number is 2.  
Simplify.  
Write the final sum over the original denominator.  
The denominator is 7.  $\frac{72}{7}$ 
Try it
#145980
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