Fractions, Decimals & Percents (Mastery) • Topic 2 of 3

Dividing Fractions

The "Keep-Change-Flip" Rule

Dividing fractions is easy with this trick:

Keep the first fraction

Change ÷ to ×

Flip the second fraction (reciprocal)

Rule: (a)/(b) ÷ (c)/(d) = (a)/(b) × (d)/(c) = (a × d)/(b × c)

Examples:

  • ⅔ ÷ ⅘ = ⅔ × 5/4 = 10/12 = (5)/(6)
  • ⅚ ÷ ⅓ = ⅚ × 3/1 = 15/6 = 5/2 = 2½

Dividing Mixed Numbers:

  1. Convert mixed numbers to improper fractions
  2. Use Keep-Change-Flip
  3. Simplify
KEEP-CHANGE-FLIP VISUAL:

    2   ÷   4    =    2   ×   5
    3       5         3       4
    
    KEEP    CHANGE    FLIP
    2/3      ×        5/4
    
    Multiply: 2×5=10, 3×4=12, 10/12 = 5/6


VISUAL REPRESENTATION: ½ ÷ ¼

    "How many ¼ are in ½?"
    
    ½ of a whole:    
    ┌─────────────────┐
    │░░░░░░░░░░░░░░░░░│
    └─────────────────┘
    
    ¼ of a whole:     
    ┌─────────┐
    │░░░░░░░░░│
    └─────────┘
    
    Count how many ¼ fit into ½:
    
    ┌─────────┬─────────┐
    │░░░░░░░░░│░░░░░░░░░│
    └─────────┴─────────┘
        ¼        ¼
    
    Answer: 2 (½ ÷ ¼ = 2)


DIVIDING MIXED NUMBERS:

    2⅓ ÷ 1½ = ?
    
    Step 1: Convert to improper fractions
    2⅓ = 7/3, 1½ = 3/2
    
    Step 2: Keep-Change-Flip
    7/3 ÷ 3/2 = 7/3 × 2/3
    
    Step 3: Multiply
    7×2=14, 3×3=9, 14/9 = 1⁵⁄₉
Solved Examples
1
Worked Example

Divide ⅔ ÷ ⅘

Solution
  • Keep: ⅔
  • Change: ×
  • Flip: ⅘ → 5/4
  • Multiply: ⅔ × 5/4 = (2×5)/(3×4) = 10/12 = (5)/(6)
2
Worked Example

Divide ⅚ ÷ ⅓

Solution
  • Keep: ⅚
  • Change: ×
  • Flip: ⅓ → 3/1
  • Multiply: ⅚ × 3/1 = (5×3)/(6×1) = 15/6 = 5/2 = 2½
3
Worked Example

Divide 2⅓ ÷ 1½

Solution
  • Convert: 2⅓ = (7)/(3), 1½ = (3)/(2)
  • Keep-Change-Flip: (7)/(3) × (2)/(3)
  • Multiply: (7×2)/(3×3) = 14/9 = 1⁵⁄₉
4
Worked Example

Divide ¾ ÷ 2

Solution
  • Write 2 as 2/1
  • Keep-Change-Flip: ¾ × ½ = (3)/(8)
  • Answer: (3)/(8)

Key Points

  • Keep-Change-Flip: Keep 1st, Change ÷ to ×, Flip 2nd
  • Reciprocal = flipped fraction (a/b → b/a)
  • Convert mixed numbers before starting
  • Whole numbers = number over 1
  • Always simplify final answer
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.To divide by a fraction, multiply by its:
Explanation: Reciprocal.
Q2.The reciprocal of $\tfrac34$ is:
Explanation: $\tfrac43$.
Q3.$\tfrac12\div\tfrac14=$
Explanation: $\tfrac12\times4=2$.
Q4.Dividing by $\tfrac12$ is the same as multiplying by:
Explanation: $2$.
Practice more MCQs → 📝 Assignment · 35 marks