2. 4.4 Adding and Subtracting Signed Fractions
Chapter 4 Rational Numbers: Positive and
Negative Fractions

3. 4.4 Adding and Subtracting Signed Fractions
Objectives
Add and subtract like fractions.
Find the lowest common denominator for unlike fractions.
Add and subtract unlike fractions.
Add and subtract unlike fractions that contain variables.
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4. Objective 1: Add and subtract like fractions.
When fractions have the same denominator, we say that they have common denominator, which makes them like fractions.
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5. Objective 1: Add and subtract like fractions.
When fractions have different denominators, they are called unlike fractions.
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6. Objective 1: Add and subtract like fractions.
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7. Objective 1: Add and subtract like fractions.
Example
Find the sum
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8. Objective 1: Add and subtract like fractions.
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9. Objective 1: Add and subtract like fractions.
Example
Find the difference
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10. Objective 1: Add and subtract like fractions.
Example
Find the difference
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11. Objective 2: Find the lowest common denominator for unlike fractions.
Notice that 12 is also a common denominator for and because 2 and 3 both go into 12 evenly.
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12. Objective 2: Find the lowest common denominator for unlike fractions.
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13. Objective 2: Find the lowest common denominator for unlike fractions.
Example
Find the LCD for and by inspection.
Check to see if 9 (the larger denominator) will work as the LCD.
Is 9 divisible by 3 (the other denominator)?
Yes, so 9 is the LCD for and .
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14. Objective 2: Find the lowest common denominator for unlike fractions.
Example
Find the LCD for and by inspection.
Check to see if 8 (the larger denominator) will work as the LCD.
Is 8 divisible by 6 (the other denominator)?
No, 8 is not divisible by 6. Check numbers that are multiples of 8, that is, 16, 24, and 32.
Notice that 24 will work because it is divisible by 8 and by 6. The LCD for and is 24.
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15. Objective 2: Find the lowest common denominator for unlike fractions.
Example
What is the LCD for and ?
Write 12 and 18 as the product of prime factors. Then use prime factors in the LCD that “cover” both 12 and 18.
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16. Objective 2: Find the lowest common denominator for unlike fractions.
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17. Objective 2: Find the lowest common denominator for unlike fractions.
Example
What is the LCD for and ?
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18. Objective 3: Add and subtract unlike fractions.
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19. Objective 3: Add and subtract unlike fractions.
Example
Find the difference
Step 1 The LCD is 12.
Step 2
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20. Objective 3: Add and subtract unlike fractions.
Example
(continued)
Step 3
Step is in lowest terms.
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21. Objective 3: Add and subtract unlike fractions.
Example
Find the sum
Step 1 Use prime factorization to find the LCD.
Step 2
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22. Objective 3: Add and subtract unlike fractions.
Example
(continued)
Step 3
Step is in lowest terms.
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23. Objective 3: Add and subtract unlike fractions.
Example
Find the difference
Step 1 Think of 4 as . The LCD for and is 3.
Step 2
already has the LCD.
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24. Objective 3: Add and subtract unlike fractions.
Example
(continued)
Step 3
Step is in lowest terms.
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25. Objective 4: Add and subtract unlike fractions that contain variables.
Example
Find the sum
Step 1 The LCD is 20.
Step 2
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26. Objective 3: Add and subtract unlike fractions that contain variables.
Example
(continued)
Step 3
Step is in lowest terms.
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27. Objective 4: Add and subtract unlike fractions that contain variables.
Example
Find the difference
Step 1 The LCD is 3 • x, or 3x.
Step 2
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28. Objective 3: Add and subtract unlike fractions that contain variables.
Example
(continued)
Step 3
Step is in lowest terms.
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