Adding and subtracting like fractions (fractions with the same denominator) is straightforward: simply add or subtract the numerators and keep the same denominator.
Here's a breakdown of the process:
Steps to Add or Subtract Like Fractions:
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Verify the Denominators: Ensure the fractions you are adding or subtracting have the same denominator. If they don't, you'll need to find a common denominator first (covered in another topic).
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Add or Subtract the Numerators: Perform the addition or subtraction operation on the numerators (the top numbers) of the fractions.
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Keep the Denominator: The denominator (the bottom number) remains the same.
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Simplify (if possible): Reduce the resulting fraction to its simplest form by dividing both the numerator and denominator by their greatest common factor (GCF).
Examples:
Addition:
- Problem: 2/5 + 1/5
- Solution: (2 + 1) / 5 = 3/5
Subtraction:
- Problem: 7/8 - 3/8
- Solution: (7 - 3) / 8 = 4/8
- Simplify: 4/8 = 1/2 (dividing both numerator and denominator by 4)
Important Considerations:
- Simplifying is Key: Always simplify your final answer to its lowest terms. This makes the fraction easier to understand and work with in future calculations.
- Improper Fractions: If the numerator is larger than the denominator (an improper fraction), you may need to convert it to a mixed number (e.g., 5/3 = 1 2/3).
- Negative Fractions: The rules apply similarly to negative fractions. Be mindful of the signs when adding or subtracting.
In essence, when dealing with like fractions, the denominator acts as a common unit. You're simply combining or removing a certain number of these units (represented by the numerators).
