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:

1. Write the whole-number part as an improper fraction, using the denominator from the fractional part.
2. 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:

Mixed Number Converted to an Improper Fraction

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.