| Chapter 4 Fractions, Part 2 4-3 Subtracting Fractions and Mixed Numbers Very Important You can subtract fractions only when they have the same denominator. - Example: You can directly subtract 3/5 – 1/5 because they have the same denominator.
- Example: You cannot directly subtract 1/2 – 1/4 until you adjust them to have the same denominator.
| Subtracting Fractions That Have a Common Denominator Procedure To subtract fractions that have a common denominator: - Subtract the numerators to get the numerator of the difference.
- Assign the common denominator to the difference.
- Reduce or simplfy the result as necessary.
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Subtracting proper fractions that have a common denominator.
| Example 3/10 – 2/10 = ? | Problem | | 3/10 – 2/10 = ? | - Subtract the numerators to get the numerator for the difference.
| 3/10 – 2/10 = 1/? | | - Assign the common denominator to the difference.
| 3/10 – 2/10 = 1/10 | | | Solution | | 3/10 – 2/10 = 1/10 | 3/4 – 1/4 = ? | Problem | | 3/4 – 1/4 = ? | - Subtract the numerators to get the numerator for the difference.
| 3/4 – 1/4 = 2/? | | - Assign the common denominator to the difference.
| 3/4 – 1/4 = 2/4 | | - Reduce or simplfy the result as necessary.
| 3/4 = 1/2 | | | Solution | | 3/4 – 1/4 = 1/2 | Exercises Click the ? symbol to see the correct answer. | 1. 5/7 –- 3/7 = ? | 2. 7/11 – 4/11 = ? | | 3. 5/6 – 3/6 = ? | 4. 7/8 – 3/8 = ? | | 5. 5/16 – 1/16 = ? | Subtracting Fractions That Do Not Have a Common Denominator Procedure To subtract fractions that do not have a common denominator: - Find a suitable common denominator for the fractions
- Expand the fractions to have the common denominator
- Subtract the fractions
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Subtracting fractions that do not have a common denominator.
| Example 3/8 – 1/4 = ? | Problem | | 3/8 – 1/4 = ? | - Find the LCD for the fractions
| The LCD is 8. | | - Expand the fractions to have the common denominator
| 3/8 = 3/8 and 1/4 = 2/8 3/8 – 2/8 = ? | | - Subtract the numerators to get the numerator for the difference.
| 3/8 – 2/8 = 1/? | | - Assign the common denominator to the difference.
| 3/8 – 2/8 = 1/8 | | | Solution | | 3/8 – 1/4 = 1/8 | Exercises Click the ? symbol to see the correct answer. | 1. 2/3 – 4/9 = ? | 2. 1/2 –- 3/7 = ? | | 3. 4/5 – 2/3 = ? | 4. 2/5 – 3/8 = ? | | 5. 5/6 – 5/7 = ? | Subtracting Mixed Fractions Procedure To subtract mixed fractions: - Convert the mixed fractions to improper fractions.
- Subtract the resulting fractions.
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Subtracting mixed fractions.
| Example 4 3/4 – 1 1/4 = ? | Problem | | 4 3/4 – 1 1/4 = ? | - Convert the mixed fractions to improper fractions.
| 4 3/4 – 1 1/4 = 15/4 – 5/4 | | - Subtract the numerators to get the numerator for the difference.
| 19/4 – 5/4 = 14/? | | - Assign the common denominator to the difference.
| 19/4 – 5/4 = 14/4 | | - Reduce or simplfy the result as necessary.
| 14/4 = 3 2/4 = 3 1/2 | | | Solution | | 4 3/4 – 1 1/4 = 3 1/2 | Exercises Click the ? symbol to see the correct answer. | 1. 2 – 11/2 = ? | 2. 10 5/9 – 1 8/9 = ? | | 3. 6 4/7 – 4 3/7 = ? | 4. 9 5/7 – 8 1/5 = ? | | 5. 8 7/11 – 4 1/2 = ? | |
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