Pengi Editor's Note: This article was originally published by Think Academy. We're sharing it here for educational value. Think Academy is a leading K-12 math education provider.
How to Divide Fractions in 3 Simple Steps
Dividing fractions is one of the most frequently misunderstood operations in middle school math — but once you understand the "keep, change, flip" method, it becomes straightforward.
The Rule: Keep, Change, Flip (KCF)
To divide by a fraction:
- Keep the first fraction as-is
- Change the division sign (÷) to multiplication (×)
- Flip the second fraction (take the reciprocal)
Then multiply normally.
Why Does This Work?
Dividing by a number is the same as multiplying by its reciprocal.
$$6 ÷ 2 = 6 × \frac{1}{2} = 3$$
The same logic applies to fractions. Dividing by ¾ is the same as multiplying by 4/3.
Example 1: Basic Fraction Division
$$\frac{2}{3} ÷ \frac{4}{5}$$
Step 1: Keep ²⁄₃
Step 2: Change ÷ to ×
Step 3: Flip ⁴⁄₅ → ⁵⁄₄
$$= \frac{2}{3} × \frac{5}{4}$$
$$= \frac{2 × 5}{3 × 4} = \frac{10}{12} = \frac{5}{6}$$
Answer: 5/6
Example 2: Dividing by a Whole Number
$$\frac{3}{4} ÷ 6$$
Rewrite 6 as ⁶⁄₁:
$$\frac{3}{4} ÷ \frac{6}{1}$$
Keep: ³⁄₄
Change: ÷ → ×
Flip: ⁶⁄₁ → ¹⁄₆
$$= \frac{3}{4} × \frac{1}{6} = \frac{3}{24} = \frac{1}{8}$$
Answer: 1/8
Example 3: Dividing a Whole Number by a Fraction
$$4 ÷ \frac{2}{3}$$
Rewrite 4 as ⁴⁄₁:
$$\frac{4}{1} ÷ \frac{2}{3}$$
Keep: ⁴⁄₁
Change: ÷ → ×
Flip: ²⁄₃ → ³⁄₂
$$= \frac{4}{1} × \frac{3}{2} = \frac{12}{2} = 6$$
Answer: 6
Example 4: Dividing Mixed Numbers
$$2\frac{1}{2} ÷ 1\frac{1}{4}$$
First: Convert to improper fractions:
2½ = 5/2
1¼ = 5/4
Then apply KCF:
$$\frac{5}{2} ÷ \frac{5}{4}$$
$$= \frac{5}{2} × \frac{4}{5} = \frac{20}{10} = 2$$
Answer: 2
Simplifying Before Multiplying (Cross-Cancellation)
You can simplify diagonally before multiplying to keep numbers smaller.
$$\frac{3}{4} × \frac{8}{9}$$
Cross-cancel: 3 and 9 share a factor of 3; 4 and 8 share a factor of 4:
$$\frac{1}{1} × \frac{2}{3} = \frac{2}{3}$$
This works because you're simplifying before the final multiplication step.
Common Mistakes to Avoid
- Flipping the wrong fraction: Always flip the second fraction (the divisor), not the first.
- Forgetting to convert mixed numbers: Always convert mixed numbers to improper fractions first.
- Not simplifying the final answer: Check if the answer can be reduced.
Practice Problems
- ½ ÷ ¼ = ?
- ⅔ ÷ ⅘ = ?
- 5 ÷ ½ = ?
- 3¾ ÷ 1½ = ?
Want more printable practice?
Explore the K–12 Worksheets Hub
Try Pengi AI — Smarter Math Practice for Students
Pengi AI supports K–12 learners with personalized math practice, guided explanations, and feedback designed to help them build confidence and improve steadily.
