Operations with Fractions (Unlike Denominators) • Topic 3 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)

Example: ¾ ÷ 2 = ¾ ÷ 2/1 = ¾ × ½ = (3)/(8)

Dividing Mixed Numbers:

Convert mixed numbers to improper fractions
Use Keep-Change-Flip
Simplify

VISUAL EXPLANATION: 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)


KEEP-CHANGE-FLIP STEPS:

    ¾ ÷ ⅚
    
    KEEP     CHANGE    FLIP
    ¾    →    ×    →   ⁶⁄₅
    
    = ¾ × ⁶⁄₅ = ¹⁸⁄₂₀ = ⁹⁄₁₀

Solved Examples

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)

Worked Example

Divide ⅚ ÷ 3

Solution

Write 3 as 3/1
Keep: ⅚
Change: ×
Flip: 3/1 → (1)/(3)
Multiply: ⅚ × ⅓ = 5/18

Worked Example

Divide 2⅓ ÷ 1½

Solution

Convert: 2⅓ = (7)/(3), 1½ = (3)/(2)
Keep: (7)/(3)
Change: ×
Flip: (3)/(2) → (2)/(3)
Multiply: (7)/(3) × (2)/(3) = 14/9 = 1⁵⁄₉

Key Points

Keep-Change-Flip: Keep 1st, Change ÷ to ×, Flip 2nd
Reciprocal of a fraction = flip numerator and denominator
Whole number = number over 1
Convert mixed numbers before starting
Simplify your 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