Dividing Fractions – Keep, Change, Flip
Dividing fractions uses the Keep, Change, Flip method (KCF). It turns division into multiplication.
The KCF Rule
a/b divided by c/d = a/b times d/c. Keep the first fraction. Change division to multiplication. Flip the second fraction.
Why It Works
Dividing by c/d is the same as multiplying by d/c because (c/d) times (d/c) = 1. You multiply by the reciprocal.
Examples
3/4 divided by 2/5
Keep 3/4. Change to multiply. Flip 2/5 to 5/2. 3/4 times 5/2 = 15/8 = 1 and 7/8.
5/6 divided by 10/3
5/6 times 3/10 = 15/60 = 1/4.
Dividing by a Whole Number
3/5 divided by 6
Write 6 as 6/1. 3/5 times 1/6 = 3/30 = 1/10.
Dividing Mixed Numbers
2 and 1/2 divided by 1 and 1/3
5/2 divided by 4/3 = 5/2 times 3/4 = 15/8 = 1 and 7/8.
3 and 3/4 divided by 2 and 1/2
15/4 divided by 5/2 = 15/4 times 2/5 = 30/20 = 3/2 = 1 and 1/2.
Real-Life Example
A 3/4 m ribbon is cut into 1/8 m pieces. How many pieces? 3/4 divided by 1/8 = 3/4 times 8 = 24/4 = 6 pieces.
Key Takeaways
- Keep the first fraction, change to multiply, flip the second.
- Always convert mixed numbers to improper fractions before dividing.
- The reciprocal of a/b is b/a.
- Never divide with a common denominator - that is for addition only.
Practice Questions
- 2/3 divided by 4/9
- 7/8 divided by 7/4
- 4 divided by 2/3
- 3 and 1/2 divided by 1 and 3/4
- A journey of 4 and 1/2 km is split into stages of 3/4 km each. How many stages?