Converting Mixed Numbers to Fractions Lesson
Example 1: A school bell rings every half-hour. If it just rang, then how many times will it ring in in the next three and one-half hours?
Analysis: This problem is asking: How many halves are in three and one-half?
Step 1: Let’s use shapes to represent the mixed number three and one-half.
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 half-hour. If it just rang, then how many times will it ring in in the next nine and one-half 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 whole-number part and a fractional part. For example:
Procedure: To write a mixed number as an improper fraction:
- Write the whole-number 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 half-hour. If it just rang, then how many times will it ring in in the next nine and one-half hours?
Analysis:
Step 1:
Step 2:
Solution: The school bell will ring 19 times in the next nine and one-half hours.
Let’s look at some more examples of writing a mixed number as an improper fraction.
Example 3: Write two and three-fourths as an improper fraction.
Analysis:
Step 1:
Step 2:
Solution:
Example 4: Write six and two-thirds 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 whole-number 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 three-fourths.
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 three-fifths as an improper fraction.
Analysis:
Step 1:
Solution:
Example 6: Write fourteen and one-third 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 five-thirds, enter 5/3 into the form.
1. | Write one and three-fourths as an improper fraction. |
2. | Write four and one-fifth as an improper fraction. |
3. | Write five and seven-eighths as an improper fraction. |
4. | Write fifteen and two-thirds as an improper fraction. |
5. | A recipe calls for two and three-fourths cups of milk. If the measuring cup holds only one-fourth cup, then how many times will you have to fill it? |