
Converting Fractions
to
Mixed Numbers 

Unit 14 > Lesson 7 of 11 
You may recall the example below from a previous lesson.
Example 1 



In example 1, we used
circles to help us solve the problem. Now look at the next example.

Example 2: 
At a birthday party, there are 19 cupcakes to be shared
equally among 11 guests. What part of the cupcakes will each guest get? 

Analysis: 
We need to divide 19 cupcakes by 11 equal parts. It would be
timeconsuming to use circles or other shapes to help us solve this problem. Therefore, we
need an arithmetic method. 
Step 1: 
Look at the fraction nineteenelevenths below. Recall that the fraction bar means to divide
the numerator by the denominator. This is shown in step 2.

Step 2: 

Step 3: 

Solution: 

In example 2, the fraction nineteenelevenths was converted to the mixed number one
and eightelevenths. Recall that a mixed number consists of a wholenumber
part and a fractional part. Let's look at some more examples of converting
fractions to mixed numbers using the arithmetic method.

Example 3: 

Analysis: 
We need to divide 17 into 5 equal parts 
Step 1: 

Step 2: 

Answer: 

Example 4: 

Analysis: 
We need to divide 37 into 10 equal parts. 
Step 1: 

Step 2: 

Answer: 

Example 5: 

Analysis: 
We need to divide 37 into 13 equal parts. 
Step 1: 

Step 2: 

Answer: 

In each of the examples above, we converted a fraction to a mixed number through long division of
its numerator and denominator. Look at example 6 below. What is wrong with this problem?

Example 6: 

Analysis: 
In the fraction seveneighths, the numerator is less than
the denominator. Therefore, seveneighths is a proper fraction less than 1. We
know from a previous lesson that a mixed number is greater than 1. 
Answer: 
Seveneighths cannot be written as a mixed number because it is a proper
fraction.

Example 7: 
Can these fractions be written as mixed numbers? Explain
why or why not. 


Analysis: 
In each fraction above, the numerator is equal to the denominator.
Therefore, each of these fractions is an improper fraction equal
to 1. But a
mixed number is greater than 1. 
Answer: 
These fractions cannot be written as mixed numbers since
each is an improper fraction equal to 1.

After reading examples 6 and 7, you may be wondering: Which types of fractions
can be written as mixed
numbers? To
answer this question, let's review an important chart from a previous lesson.

Comparison of numerator and denominator 
Example 
Type of Fraction 
Write As 
If the numerator < denominator, then the fraction < 1. 

proper fraction 
proper fraction 
If the numerator = denominator, then the fraction = 1. 

improper fraction 
whole number 
If the numerator > denominator, then the fraction > 1. 

improper fraction 
mixed number 
The answer to the question is: Only an improper fraction greater than 1 can be
written to
a mixed number.

Summary: 
We can convert an improper fraction greater than one to a mixed number through long division of
its numerator and denominator. 
Exercises
In Exercises 1 through 5, click once
in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to
indicate whether your answer is correct or incorrect. To start over, click
CLEAR. Note: To write the mixed number four and twothirds, enter 4, a
space, and then 2/3 into the form.

1. 
Write elevenfifths as a mixed number.




2. 
Write elevenfourths as a mixed number.




3. 
Write thirteenninths as a mixed number.




4. 
On field day, there are 23 pies to share equally among 7 classes. What
part of the pies will each class get?




5. 
A teacher gives her class a spelling test worth 35 points. If there are 8
words graded equally, then how many points is each word worth?




This lesson is by Gisele Glosser. You can find me on Google.
