Fraction Division – The Keep-Change-Flip Method
Dividing by a fraction might seem mysterious at first, but it follows one elegant rule that makes every division of fractions straightforward.
The Rule – Keep, Change, Flip (KCF)
Keep the first fraction unchanged. Change the ÷ to ×. Flip (take the reciprocal of) the second fraction.
a/b ÷ c/d → a/b × d/c
Why Does This Work?
Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of c/d is d/c.
Worked Examples
Easy: 3/4 ÷ 1/2
Keep 3/4. Change ÷ to ×. Flip 1/2 to 2/1.
3/4 × 2/1 = 6/4 = 1½
Medium: 5/6 ÷ 2/3
5/6 × 3/2 = 15/12 = 1¼
Dividing by a Whole Number: 3/5 ÷ 4
3/5 ÷ 4/1 → 3/5 × 1/4 = 3/20
Key Takeaways
- Keep the first fraction, change to multiplication, flip the second fraction.
- Dividing by a fraction always gives a result larger than the original (when both are positive proper fractions).
- Always simplify the result.
Practice Questions
- Calculate 2/3 ÷ 1/4.
- Calculate 7/8 ÷ 7/16.
- Calculate 4/5 ÷ 2.
- A ribbon 3/4 m long is cut into pieces of 1/8 m each. How many pieces?
- Calculate 5/6 ÷ 10/3.