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Chapter 3—Fractions

3-8 Adding Fractions and Mixed Numbers

 When you complete the work for this section, you should be able to: Demonstrate the multiplication method for determining the lowest common denominator for two or more fractions. Demonstrate the division methods for determining the lowest common denominator for two or more fractions. Demonstrate your ability to add fractions that have common denominators. Demonstrate your ability to add fractions that do not have common denominators. Demonstrate your ability to add fractions and mixed numbers.

 Very Important You can add  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.

Adding Proper Fractions that Have a Common Denominator

 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.

Example 1-1

 Problem 1/8 + 2/8 = _____ Procedure Add the numerators to get the numerator for the sum 1/8 + 2/8 =  3/? Assign the common denominator to the sum 1/8 + 2/8 =  3/8 Solution 1/8 + 2/8 =  3/8

Example 1-2

 Problem 3/10 + 2/10 = _____ Procedure Add the numerators to get the numerator for the sum 3/10 + 2/10 =  5/? Assign the common denominator to the sum 3/10 + 2/10 =  5/10 Reduce or simplify the result as necessary. 3/10 + 2/10 = 5/10 = 1/2 Solution 3/10 + 2/10 = 1/2

Examples and Exercises

 Adding Fractions Having Common Denominators Add, then reduce or simplify as necessary.

Adding Proper Fractions That Do Not Have a Common Denominator

Fractions can be added only when they have the same denominator. When they do not, you must adjust them so that the denominators are the same.

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

Example 2-1

 Problem 1/5 + 3/4 = _____ Procedure Find the LCD for the fractions LCD = 20 Expand the fractions to have the common denominator 1/5 = ?/20 = 4/20 3/4 = ?/20 = 15/20 Add the fractions 4/20 + 15/20 = 19/20 Solution 1/5 + 3/4 = 19/20

Example 2-2

 The Problem 7/8 + 5/16 =   _____ Procedure Find the LCD for the fractions LCD = 16 Expand the fractions to have the common denominator 7/8 = ?/16 = 14/16 5/16 = ?/16 = 5/16 Add the fractions 14/16 + 5/16 = 19/16 Simplify 19/16 = 1 3/16 The Solution 7/8 + 5/16 = 1 3/16

Examples and Exercises

 Adding Fractions That Do Not Have a Common Denominator Use these interactive examples and exercises to strengthen your understanding and build your skills. Add, then reduce or simplify as necessary.

 Procedure To add mixed fractions: Convert the mixed fractions to improper fractions. Add the resulting fractions.

Example 3-1

 Problem 2 3/4 + 1/4 = _____ Procedure Convert the mixed fractions to improper fractions. 2 3/4 + 1/4 = 11/4 + 1/4 Add the numerators to get the numerator for the sum 11/4 + 1/4 =  12/? Assign the common denominator to the sum 11/4 + 1/4 =  12/4 Reduce or simplify the result as necessary. 11/4 +  1/4 =  12/4 = 3 Solution 2 3/4 + 1/4 = 3

Example 3-2

 Problem 2 3/8  + 8 1/4 = _____ Procedure Convert the mixed fractions to improper fractions. 23/8  +  8 1/4 = 19/8+  33/4 Adjust for common denominators 19/8 +  33/4 = 19/8  +  66/8 Add the fractions 19/8  +  66/8   =  85/8 Reduce or simplify the result as necessary. 85/8= 10 5/8 Solution 2 3/8  + 8 1/4 = 10 5/8

Examples and Exercises

 Adding Mixed Fractions Use these interactive examples and exercises to strengthen your understanding and build your skills. Add, then reduce or simplify as necessary.

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