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Chapter 4 Fractions, Part 2 4-2 Adding 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 simplfy the result as necessary.
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Adding proper fractions that have a common denominator.
| Example 1/8 + 2/8 = ? | Problem | | 1/8 + 2/8 = ? | - 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 3/10 + 2/10 = ? | Problem | | 3/10 + 2/10 = ? | 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 simplfy the result as necessary. | 3/10 + 2/10 = 5/10 = 1/2 | | | Solution | | 3/10 + 2/10 = 1/2 | Examples and Exercises Use these interactive examples and exercises to strengthen your understanding and build your skills. Add, then reduce or simplify as necessary. | | Adding Proper Fractions That Do Not Have a Common Denominator 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: 1/5 + 3/4 = ? | The Problem | | 1/5 + 3/4 = ? | 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 | | | The Solution | | 1/5 + 3/4 = 19/20 | Example: 7/8 + 5/16 = ? | The Problem | | 7/8 + 5/16 = ? | 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 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: - Convert the mixed fractions to improper fractions.
- Add the resulting fractions.
| Example 2 3/4 + 1/4 = ? | Problem | | 2 3/4 + 1/4 = ? | - 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 simplfy 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 simplfy the result as necessary.
| 85/8= 10 5/8 | Solution 2 3/8 + 8 1/4 = 10 5/8 | | Examples and Exercises 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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