Lesson 8Adding Fractions and Mixed Numbers

 Very Important You can add or subtract  fractions only when they have the same denominator. Example: You can directly add 1/5 + 3/5 because they have the same denominator. Example: You cannot directly add 1/2 + 1/4 until you adjust them to have the same denominator.

The fact that you can add and subtract fractions when they have a common denominator explains why these operations are often more complicated than multiplying and dividing fractions—there is that additional step of reworking the fractions so they have the same denominators.

• Example: You can directly add 1/5 + 3/5 because they have the same denominator.
• Example: You cannot directly add 1/2 + 1/4 until you adjust them to 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.

The fact that you can add and subtract fractions only when they have a common denominator explains why these operations are often more complicated than multiplying and dividing fractions—there is that additional step of reworking the fractions so they have the same denominators.

Topic 1
Adding and Subtracting Fractions: Common Denominators

 Procedure To add fractions that have a common, or same, denominator: Add the numerators to get the numerator for the sum. Assign the common denominator to the sum. Reduce or simplify the result as necessary,

Use these interactive examples and exercises to test and strengthen your understanding and build your skills.

 Procedure To subtract fractions that have a common, or same, 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.

Use these interactive examples and exercises to test and strengthen your understanding and build your skills.

 If you are having any trouble understanding the content of this lesson, you will benefit from a more detailed tutorial on the subject.

Topic 2
Adding and Subtracting Fractions Having Unlike Denominators

 Procedure To add fractions that do not have a common denominator: Find a common denominator for the fractions. Expand the fractions to have the common denominator Add the fractions Reduce or simplify as necessary

Use these interactive examples and exercises to test and strengthen your understanding and build your skills.

 If you are having any trouble understanding how to add fractions that have unlike denominators, you will benefit from a more detailed tutorial on the subject.

 Procedure To subtract fractions that do not have a common denominator: Find a common denominator for the fractions. Expand the fractions to have the common denominator Subtract the fractions Reduce or simplify as necessary

Use these interactive examples and exercises to test and strengthen your understanding and build your skills.

 If you are having any trouble understanding how to add fractions that have unlike denominators, you will benefit from a more detailed tutorial on the subject.