Converting Mixed Numbers to Fractions

Converting Mixed Numbers to FractionsExample 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.

Circle 2 halves RedCircle 2 halves RedCircle 2 halves RedCircle 1 half Red

Step 2:

mixed_fractions_example1_step2.gif

Solution:

mixed_fractions_example1_answer.gif

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: 9and1over2_equals.gif

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:

mixed_fractions_example2_analysis.gif

Step 1:

mixed_fractions_example2_step1.gif

Step 2:

mixed_fractions_example2_step2.gif

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:

mixed_fractions_example3_analysis.gif

Step 1:

mixed_fractions_example3_step1.gif

Step 2:

mixed_fractions_example3_step2.gif

Solution:

mixed_fractions_example3_solution.gif

Example 4: Write six and two-thirds as an improper fraction.

Analysis:

mixed_fractions_example4_analysis.gif

Step 1:

mixed_fractions_example4_step1.gif

Step 2:

mixed_fractions_example4_step2.gif

Solution:

mixed_fractions_example4_solution.gif

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
mixed_fractions_example1_summary.gif
mixed_fractions_example2_summary.gif
mixed_fractions_example3_summary.gif
mixed_fractions_example4_summary.gif

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.

Converting Mixed Numbers to Fractions

Recapping examples 1 to 4, we get:

Mixed Number Converted to an Improper Fraction
3and1over2.gif 3and1over2_converted.gif 7over2.gif
9and1over2.gif 9and1over2_converted.gif 19over2.gif
2and3over4.gif 2and3over4_converted.gif 11over4_0.gif
6and2over3.gif 6and2over3_converted.gif 20over3.gif

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:

mixed_fractions_example5.gif

Step 1:

mixed_fractions_example5_step1.gif

Solution:

mixed_fractions_example5_answer.gif

Example 6: Write fourteen and one-third as an improper fraction.

Analysis:

mixed_fractions_example6.gif

Step 1:

mixed_fractions_example6_step1.gif

Solution:

mixed_fractions_example6_answer.gif

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.
 
 
ANSWER BOX:   

RESULTS BOX: 

2.  Write four and one-fifth as an improper fraction.
 
 
ANSWER BOX:   

RESULTS BOX: 

3.  Write five and seven-eighths as an improper fraction.
 
 
ANSWER BOX:   

RESULTS BOX: 

4.  Write fifteen and two-thirds as an improper fraction.
 
 
ANSWER BOX:   

RESULTS BOX: 

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?
 
 
ANSWER BOX:  times   

RESULTS BOX: 

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