top

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:fig040201.gif (2370 bytes)

  1. Add the numerators to get the numerator for the sum.
  2. Assign the common denominator to the sum.
  3. Reduce or simplify the result as necessary.

Example 1-1

Problem

1/8 + 2/8 = _____

Procedure
  1. Add the numerators to get the numerator for the sum

1/8 + 2/83/?

  1. Assign the common denominator to the sum

1/8 + 2/83/8

Solution

1/8 + 2/83/8

Example 1-2

Problem

3/10 + 2/10 = _____

Procedure
  1. Add the numerators to get the numerator for the sum

3/10 + 2/105/?

  1. Assign the common denominator to the sum

3/10 + 2/105/10

  1. 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:

  1. Find a suitable common denominator for the fractions.
  2. Expand the fractions to have the common denominator
  3. Add the fractions
  4. Reduce or simplify as necessary

Example 2-1

Problem

1/5 + 3/4 = _____

Procedure
  1. Find the LCD for the fractions
LCD = 20
  1. Expand the fractions to have the common denominator
1/5 = ?/20 = 4/20
3/4 = ?/20 = 15/20
  1. 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
  1. Find the LCD for the fractions
LCD = 16
  1. Expand the fractions to have the common denominator
7/8 = ?/16 = 14/16
5/16 = ?/16 = 5/16
  1. Add the fractions
14/16 + 5/16 = 19/16
  1. 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.

Adding Mixed Fractions

 

Procedure

To add mixed fractions:

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

Example 3-1

Problem

2 3/4 + 1/4 = _____

Procedure
  1. Convert the mixed fractions to improper fractions.

2 3/4 + 1/4 = 11/4 + 1/4

  1. Add the numerators to get the numerator for the sum

11/4 + 1/412/?

  1. Assign the common denominator to the sum

11/4 + 1/412/4

  1. Reduce or simplify the result as necessary.

11/41/412/4 = 3

Solution

2 3/4 + 1/4 = 3

Example 3-2

Problem

2 3/8  + 8 1/4 = _____

Procedure
  1. Convert the mixed fractions to improper fractions.

23/8  +  8 1/4 = 19/833/4

  1. Adjust for common denominators

19/833/419/8  +  66/8

  1. Add the fractions

19/8  +  66/8   =  85/8

  1. 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.

David L. Heiserman, Editor

Copyright   SweetHaven Publishing Services
All Rights Reserved

Revised: June 06, 2015