Adding and Subtracting Fractions

Key Points

• Common Denominator: Ensure the denominators (bottom numbers) of the fractions are the same.
• Add/Subtract Numerators Only: Perform the operations on the numerators (top numbers) only.

Finding a Common Denominator

1. Find the Lowest Common Multiple (LCM):
   • Example: To add 3/4 and 1/3, find LCM of 4 and 3, which is 12.
2. Rewrite Fractions with Common Denominator:
   • Convert each fraction to have this common denominator.
   • Example: Change 3/4 to 9/12 and 1/3 to 4/12.

Changing Numerators

• Multiply the numerators by the same factor used to change the denominators.
  • Example:
    • 3/4 becomes 9/12 (multiplied numerator by 3).
    • 1/3 becomes 4/12 (multiplied numerator by 4).

Adding Fractions

• Example: 9/12 + 4/12 = 13/12 (cannot simplify further, final answer).

Subtracting Fractions

• Find common denominator by LCM.
• Example: Subtracting 2/5 from 5/3:
  • LCM of 3 and 5 is 15.
  • Convert: 5/3 to 25/15, 2/5 to 6/15.
  • Subtract: 25/15 - 6/15 = 19/15 (cannot simplify further, final answer).

Handling Improper Fractions

• An improper fraction has a numerator larger than the denominator.
• Treat them like regular fractions when adding or subtracting.
• Example: Convert mixed numbers to improper fractions for calculations.

Example Problems

Problem 1: Adding Mixed Numbers and Fractions

• Convert mixed number to improper fraction:
  • Example: 2 3/4 to 11/4 (Multiply 2 by 4, add 3).
• Find LCM to rewrite with common denominator:
  • Example: LCM of 4 and 12 is 12. Convert 11/4 to 33/12.
• Add fractions: 33/12 + 5/12 = 38/12 (simplified to 19/6).

Problem 2: Subtracting Fractions

• Find LCM of 6 and 15, which is 30.
• Convert fractions:
  • Example: 5/6 to 25/30, 4/15 to 8/30.
• Subtract: 25/30 - 8/30 = 17/30 (final answer).

Conclusion

• Always convert to common denominators and simplify if possible.
• If any questions or feedback, leave comments.