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Chapter 3—Fractions

3-9 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 3/51/5 because they have the same denominator.
  • Example: You cannot directly subtract 1/21/4 until you adjust them to have the same denominator.

Subtracting Fractions That Have a Common Denominator

Procedure

fig040301.gif (2325 bytes)To subtract fractions that have a common denominator:

  1. Subtract the numerators to get the numerator of the difference.
  2. Assign the common denominator to the difference.
  3. Reduce or simplify the result as necessary.

Example 1-1

Problem

3/102/10 = _____

Procedure
  1. Subtract the numerators to get the numerator for the difference.

3/102/101/?

  1. Assign the common denominator to the difference.

3/102/10 =   1/10

Solution

3/102/10 = 1/10

Example 1-2

Problem

3/41/4 = _____

Procedure
  1. Subtract the numerators to get the numerator for the difference.

3/41/42/?

  1. Assign the common denominator to the difference.

3/41/4 =   2/4

  1. Reduce or simplify the result as necessary.

3/4 = 1/2

Solution

3/41/4 = 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:

  1. Find a suitable common denominator for the fractions
  2. Expand the fractions to have the common denominator
  3. Subtract the fractions

Example

Problem

3/81/4 = _____

Procedure
  1. Find the LCD for the fractions

The LCD is 8.

  1. Expand the fractions to have the common denominator

3/8 = 3/8 and 1/4 = 2/8

3/82/8 =   ? 

  1. Subtract the numerators to get the numerator for the difference.

3/82/81/?

  1. Assign the common denominator to the difference.

3/82/8 =   1/8

Solution

3/81/4  = 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:

  1. Convert the mixed fractions to improper fractions.
  2. Subtract the resulting fractions.

Example

4 3/4 – 1 1/4 =   ? 

Problem

4 3/4 – 1 1/4 = _____

Procedure
  1. Convert the mixed fractions to improper fractions.

4 3/4 – 1 1/4 = 19/4 – 5/4

  1. Subtract the numerators to get the numerator for the difference.

19/45/414/?

  1. Assign the common denominator to the difference.

19/45/4 =  14/4

  1. 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.

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015