Operations with Fractions (Unlike Denominators) • Topic 2 of 3

Multiplying Fractions

Multiplying Fractions is EASY!

Unlike addition, you DON'T need common denominators. Just multiply straight across!

Rule: (a/b) × (c/d) = (a×c)/(b×d)

Steps:

  1. Multiply the numerators
  2. Multiply the denominators
  3. Simplify if needed

Example: ⅔ × ⅘ = (2×4)/(3×5) = 8/15

Multiplying Mixed Numbers:

  1. Convert mixed numbers to improper fractions
  2. Multiply straight across
  3. Convert back to mixed number
VISUAL REPRESENTATION: ⅔ × ¾
    
    Step 1: Start with ⅔ of a whole
    ┌───┬───┐
    │░░░│░░░│░░░  (2 of 3 columns)
    └───┴───┘
    
    Step 2: Take ¾ of that shaded part
    ┌───┬───┐
    │░░░│░░░│░░░
    │░░░│░░░│░░░
    └───┴───┘
    
    Result: 6 out of 12 squares = 6/12 = ½


AREA MODEL: ⅔ × ¾

    Total rectangle = 3 × 4 = 12 equal parts
    
    ┌─────┬─────┬─────┬─────┐
    │     │     │     │     │
    │░░░░░│░░░░░│░░░░░│     │ Row 1 (¾)
    ├─────┼─────┼─────┼─────┤
    │░░░░░│░░░░░│░░░░░│     │ Row 2 (¾)
    ├─────┼─────┼─────┼─────┤
    │     │     │     │     │ Row 3
    └─────┴─────┴─────┴─────┘
     Col1   Col2   Col3   Col4
     (⅔ of columns)
     
    Overlap = 6 squares = 6/12 = ½
Solved Examples
1
Worked Example

Multiply ⅖ × ⅗

Solution
  • Multiply numerators: 2 × 3 = 6
  • Multiply denominators: 5 × 7 = 35
  • Answer: 6/35 (already simplified)
2
Worked Example

Multiply 1½ × 2⅓

Solution
  • Convert: 1½ = (3)/(2), 2⅓ = (7)/(3)
  • Multiply: (3)/(2) × (7)/(3) = 21/6
  • Simplify: 21/6 = (7)/(2) = 3½
3
Worked Example

Multiply ⅚ × 9

Solution
  • Write 9 as 9/1
  • Multiply: (5×9)/(6×1) = 45/6
  • Simplify: 45/6 = 15/2 = 7½

Key Points

  • Multiply numerators, multiply denominators
  • No common denominator needed!
  • Simplify before multiplying (cross-cancel) to make easier
  • Convert mixed numbers to improper fractions first
  • Any whole number = that number over 1
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.To multiply fractions, multiply the numerators and the:
Explanation: Multiply denominators too.
Q2.$\tfrac23\times\tfrac34=$
Explanation: $\tfrac{6}{12}=\tfrac12$.
Q3.In fractions, "of" usually means:
Explanation: Multiply.
Q4.$\tfrac12$ of $10$ is:
Explanation: $5$.
Practice more MCQs → 📝 Assignment · 35 marks