Adding and Subtracting Fractions

Basic Addition of Two Fractions

• Example: 3/5 + 4/7
  • Find common denominator: 5 * 7 = 35
  • Convert fractions:
    • 3 * 7 = 21
    • 4 * 5 = 20
  • Sum the numerators: 21 + 20 = 41
  • Final answer: 41/35*

Basic Subtraction of Two Fractions

• Example: 7/8 - 2/9
  • Find common denominator: 8 * 9 = 72
  • Convert fractions:
    • 7 * 9 = 63
    • 2 * 8 = 16
  • Subtract the numerators: 63 - 16 = 47
  • Final answer: 47/72 (not reducible)*

Adding/Subtracting Three Fractions

• Example: 3/4 + 5/3 - 7/2
  • Find least common denominator (LCD):
    • Multiples of 2: 2, 4, 6, 8, 10, 12...
    • Multiples of 3: 3, 6, 9, 12, 15, 18...
    • Multiples of 4: 4, 8, 12, 16, 20...
  • LCD is 12 (common to all)
  • Convert each fraction:
    • 3/4 -> (3 * 3)/(4 * 3) = 9/12
    • 5/3 -> (5 * 4)/(3 * 4) = 20/12
    • 7/2 -> (7 * 6)/(2 * 6) = 42/12
  • Combine numerators: 9 + 20 - 42 = -13
  • Final answer: -13/12

Adding/Subtracting Mixed Fractions Example

• Example: 8/5 - 2/3 + 9/4
  • Find common denominator: 5 * 3 * 4 = 60
  • Convert fractions:
    • 8/5 = (8 * 12)/(5 * 12) = 96/60
    • 2/3 = (2 * 20)/(3 * 20) = 40/60
    • 9/4 = (9 * 15)/(4 * 15) = 135/60
  • Calculate: 96 - 40 + 135 = 191
  • Final answer: 191/60

Multiplying Fractions

• Example: (3/5) * (7/2)
  • Multiply across: 3 * 7 = 21, 5 * 2 = 10
  • Final answer: 21/10*

Multiplying Larger Numbers

• Break down large numbers for cancellation:
  • Example: (24/30) * (45/27)
  • Factor numbers:
    • 24 = 6 * 4, 30 = 6 * 5, 45 = 9 * 5, 27 = 9 * 3
  • Cancel common factors to simplify calculations.*

Dividing Fractions

• Example: (8/5) ÷ (12/7)
  • Use the "Keep, Change, Flip" method
    • Keep: (8/5)
    • Change: ÷ to *
    • Flip: (12/7) to (7/12)
  • Result: (8 * 7)/(5 * 12)
  • Simplify as needed*

Example of Dividing Larger Fractions

• Example: (36/54) ÷ (64/48)
  • Rewrite: (36/54) ÷ (64/48) = (36/54) * (48/64)
  • Use "Keep, Change, Flip"
  • Simplify and reduce where possible.*