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Chapter 3—Fractions
39 Subtracting Fractions and Mixed Numbers
When you complete the work for this section, you should be able to:  Demonstrate your ability to subtract fractions that have common denominators.
 Demonstrate your ability to subtract fractions that do not have common denominators.
 Demonstrate your ability to subtract fractions and mixed numbers.

Just as you can only add fractions that have the same denominator, you can only subtract fractions that have the same denominator.
 Example: You can directly subtract ^{3}/_{5} – ^{1}/_{5} because they have the same denominator.
 Example: You cannot directly subtract ^{1}/_{2} – ^{1}/_{4} until you adjust them to have the same denominator.
Subtracting Fractions That Have a Common Denominator
Procedure To subtract fractions that have a common denominator:  Subtract the numerators to get the numerator of the difference.
 Assign the common denominator to the difference.
 Reduce or simplify the result as necessary.
 
Example 11
Problem ^{3}/_{10} – ^{2}/_{10} = _____  
Procedure  
 Subtract the numerators to get the numerator for the difference.
 ^{3}/_{10} – ^{2}/_{10} = ^{1}/? 
 Assign the common denominator to the difference.
 ^{3}/_{10} – ^{2}/_{10} = ^{1}/_{10} 
Solution ^{3}/_{10} – ^{2}/_{10} = ^{1}/_{10}  
Example 12
Problem ^{3}/_{4} – ^{1}/_{4} = _____  
Procedure  
 Subtract the numerators to get the numerator for the difference.
 ^{3}/_{4} – ^{1}/_{4} = ^{2}/? 
 Assign the common denominator to the difference.
 ^{3}/_{4} – ^{1}/_{4} = ^{2}/_{4} 
 Reduce or simplify the result as necessary.
 _{3/4 = 1/2 } 
Solution ^{3}/_{4} – ^{1}/_{4} = ^{1}/_{2}  
Examples and Exercises
Subtracting Fractions Having a Common Denominator Subtract, then reduce or simplify as necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills.  
Subtracting Fractions That Do Not Have a Common Denominator
Fractions can be added or subtracted only when they have the same denominator. When they do not, you must adjust them so that the denominators are the same.
Procedure To subtract fractions that do not have a common denominator:  Find a suitable common denominator for the fractions
 Expand the fractions to have the common denominator
 Subtract the fractions
 
Example
Problem ^{3}/_{8} – ^{1}/_{4} = _____  
Procedure  
 Find the LCD for the fractions
 The LCD is 8. 
 Expand the fractions to have the common denominator
 ^{3}/_{8} = ^{3}/_{8} and ^{1}/_{4} = ^{2}/_{8} ^{3}/_{8} – ^{2}/_{8} = ? 
 Subtract the numerators to get the numerator for the difference.
 ^{3}/_{8} – ^{2}/_{8} = ^{1}/? 
 Assign the common denominator to the difference.
 ^{3}/_{8} – ^{2}/_{8} = ^{1}/_{8} 
Solution ^{3}/_{8} – ^{1}/_{4} = ^{1}/_{8}  
Examples and Exercises
Subtracting Fractions That Do Not Have a Common Denominator Subtract, then reduce or simplify as necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills.  
Subtracting Mixed Fractions
The procedure for subtracting fractions and mixed numbers is essentially the same as for adding fractions and mixed numbers.
Procedure To subtract mixed fractions:  Convert the mixed fractions to improper fractions.
 Subtract the resulting fractions.

Example
4 ^{3}/_{4} – 1 ^{1}/_{4} = ?
Problem 4 ^{3}/_{4} – 1 ^{1}/_{4} = _____  
Procedure  
 Convert the mixed fractions to improper fractions.
 4 ^{3}/_{4} – 1 ^{1}/_{4} = ^{19}/_{4} – ^{5}/_{4} 
 Subtract the numerators to get the numerator for the difference.
 ^{19}/_{4} – ^{5}/_{4} = ^{14}/? 
 Assign the common denominator to the difference.
 ^{19}/_{4} – ^{5}/_{4} = ^{14}/_{4} 
 Reduce or simplify the result as necessary.
 ^{14}/_{4} = 3 ^{2}/_{4} = 3 ^{1}/_{2} 
Solution 4 ^{3}/_{4} – 1 ^{1}/_{4} = 3 ^{1}/_{2}  
Examples and Exercises
Subtracting Mixed Fractions Subtract, then reduce or simplify as necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills.  