Dividing Improper Fractions & Mixed Numbers

Master division with improper fractions and mixed numbers through step-by-step examples and practice!

Working with Improper Fractions and Mixed Numbers

Two-Step Process for Mixed Numbers

Step 1: Convert mixed numbers to improper fractions

$$a\frac{b}{c} \div d\frac{e}{f} = \frac{ac + b}{c} \div \frac{df + e}{f} $$

Step 2: Apply KCF (Keep, Change, Flip)

$$ = \frac{ac + b}{c} \times \frac{f}{df + e}$$

💡 Converting Mixed to Improper: For $a\frac{b}{c}$, multiply the whole number by the denominator, add the numerator: $\frac{a \times c + b}{c}$

📚 Step-by-Step Examples

Example 1: Simple Improper Fractions

Problem: $\frac{5}{3} \div \frac{2}{3}$

Step 1: Keep the first fraction: $\frac{5}{3}$
Step 2: Change ÷ to × and flip: $\frac{5}{3} \times \frac{3}{2}$
Step 3: Multiply: $\frac{15}{6}$
Step 4: Simplify: $\frac{5}{2}$
Step 5: Convert to mixed: $2\frac{1}{2}$
✅ Answer: $\frac{5}{2}$ or $2\frac{1}{2}$
Example 2: Mixed Number Division

Problem: $2\frac{1}{3} \div 1\frac{1}{2}$

Step 1: Convert to improper: $\frac{7}{3} \div \frac{3}{2}$
Step 2: Flip and multiply: $\frac{7}{3} \times \frac{2}{3}$
Step 3: Multiply: $\frac{14}{9}$
Step 4: Convert to mixed: $1\frac{5}{9}$
✅ Answer: $\frac{14}{9}$ or $1\frac{5}{9}$
Example 3: Mixed ÷ Proper Fraction

Problem: $3\frac{1}{4} \div \frac{1}{2}$

Step 1: Convert mixed to improper: $\frac{13}{4} \div \frac{1}{2}$
Step 2: Flip and multiply: $\frac{13}{4} \times \frac{2}{1}$
Step 3: Multiply: $\frac{26}{4}$
Step 4: Simplify: $\frac{13}{2}$
Step 5: Convert to mixed: $6\frac{1}{2}$
✅ Answer: $6\frac{1}{2}$
Example 4: Large Improper Fractions

Problem: $\frac{9}{4} \div \frac{3}{8}$

Step 1: Flip and multiply: $\frac{9}{4} \times \frac{8}{3}$
Step 2: Cancel common factors: $\frac{3}{1} \times \frac{2}{1}$
Step 3: Multiply: $6$
✅ Answer: $6$
Example 5: Whole Number ÷ Mixed

Problem: $5 \div 1\frac{1}{4}$

Step 1: Convert to improper: $\frac{5}{1} \div \frac{5}{4}$
Step 2: Flip and multiply: $\frac{5}{1} \times \frac{4}{5}$
Step 3: Cancel 5s: $\frac{1}{1} \times \frac{4}{1}$
Step 4: Result: $4$
✅ Answer: $4$
Example 6: Complex Mixed Numbers

Problem: $4\frac{2}{3} \div 2\frac{1}{3}$

Step 1: Convert to improper: $\frac{14}{3} \div \frac{7}{3}$
Step 2: Flip and multiply: $\frac{14}{3} \times \frac{3}{7}$
Step 3: Cancel: $\frac{2}{1} \times \frac{1}{1}$
Step 4: Result: $2$
✅ Answer: $2$

🧮 Interactive Calculators

Practice dividing improper fractions and mixed numbers!

Improper Fraction Division

Mixed Number Division

📊 Test Your Skills!

1. Calculate: $\frac{7}{4} \div \frac{1}{2}$
A) $\frac{7}{8}$
B) $\frac{14}{4}$
C) $\frac{7}{2}$
D) $\frac{1}{2}$
2. Calculate: $2\frac{1}{2} \div 1\frac{1}{4}$
A) $2$
B) $\frac{5}{4}$
C) $3\frac{1}{8}$
D) $1\frac{1}{2}$
3. Calculate: $\frac{9}{5} \div \frac{3}{10}$
A) $6$
B) $\frac{27}{50}$
C) $\frac{3}{2}$
D) $\frac{90}{15}$
4. Calculate: $3\frac{1}{3} \div 2$
A) $6\frac{2}{3}$
B) $1\frac{1}{3}$
C) $\frac{10}{6}$
D) $\frac{5}{3}$
5. Calculate: $4\frac{1}{2} \div \frac{3}{4}$
A) $3\frac{3}{8}$
B) $6$
C) $\frac{27}{8}$
D) $5\frac{1}{4}$