Converting Mixed Numbers to Fractions Lesson
Example 1: A school bell rings every halfhour. If it just rang, then how many times will it ring in in the next three and onehalf hours?
Analysis: This problem is asking: How many halves are in three and onehalf?
Step 1: Let’s use shapes to represent the mixed number three and onehalf.
Step 2:
Solution:
In example 1, we used shapes to help us solve the problem. Let’s look at example 2.
Example 2: A school bell rings every halfhour. If it just rang, then how many times will it ring in in the next nine and onehalf hours?
Analysis: Using shapes to solve this problem would not be practical. We need to find another method.
Recall that a mixed number consists of a wholenumber part and a fractional part. For example:
Procedure: To write a mixed number as an improper fraction:
 Write the wholenumber part as an improper fraction, using the denominator from the fractional part.
 Add the result from step 1 to the fractional part of the mixed number.
Let’s use the procedure above to solve the problem from example 2.
Example 2: A school bell rings every halfhour. If it just rang, then how many times will it ring in in the next nine and onehalf hours?
Analysis:
Step 1:
Step 2:
Solution: The school bell will ring 19 times in the next nine and onehalf hours.
Let’s look at some more examples of writing a mixed number as an improper fraction.
Example 3: Write two and threefourths as an improper fraction.
Analysis:
Step 1:
Step 2:
Solution:
Example 4: Write six and twothirds as an improper fraction.
Analysis:
Step 1:
Step 2:
Solution:
Here is a summary of examples 1 to 4. Do you see a pattern? Do you see an easier way to write a mixed number as an improper fraction?
Examples 1 to 4 
There is a shortcut we can take for writing a mixed number as an improper fraction: If you multiply the denominator by the wholenumber part, then add the numerator, the result gives you the numerator of the improper fraction. This is shown below for the mixed number two and threefourths.
Recapping examples 1 to 4, we get:

Let’s look at some more examples of writing a mixed number as an improper fraction using this shortcut.
Example 5: Write eleven and threefifths as an improper fraction.
Analysis:
Step 1:
Solution:
Example 6: Write fourteen and onethird as an improper fraction.
Analysis:
Step 1:
Solution:
This shortcut uses only one step, and makes it easier to convert large mixed numbers into improper fractions.
Summary: There are several methods for converting a mixed number into an improper fraction. Use the one that is appropriate for the given problem.
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 improper fraction fivethirds, enter 5/3 into the form.
1.  Write one and threefourths as an improper fraction. 
2.  Write four and onefifth as an improper fraction. 
3.  Write five and seveneighths as an improper fraction. 
4.  Write fifteen and twothirds as an improper fraction. 
5.  A recipe calls for two and threefourths cups of milk. If the measuring cup holds only onefourth cup, then how many times will you have to fill it? 