To divide mixed numbers, we first convert them to improper fractions.

Step 1: Convert to improper fractions

• $3 \frac{3}{5}$ becomes: $3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}$

• $2 \frac{1}{4}$ becomes: $2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$

Step 2: Divide the fractions

Now, we divide $\frac{18}{5}$ by $\frac{9}{4}$. When dividing fractions, multiply by the reciprocal of the second fraction:

$\frac{18}{5} \div \frac{9}{4} = \frac{18}{5} \times \frac{4}{9}$

Step 3: Multiply the fractions

Multiply the numerators and denominators:

$\frac{18 \times 4}{5 \times 9} = \frac{72}{45}$

Step 4: Simplify the fraction

To simplify $\frac{72}{45}$, divide both the numerator and the denominator by their greatest common divisor (GCD), which is 9:

$\frac{72 \div 9}{45 \div 9} = \frac{8}{5}$

Step 5: Convert back to a mixed number

Finally, convert $\frac{8}{5}$ back to a mixed number:

$\frac{8}{5} = 1 \frac{3}{5}$

Final Answer:

$3 \frac{3}{5} \div 2 \frac{1}{4} = 1 \frac{3}{5}$

Would you like further details or explanations?

Here are some related questions you can explore:

1. How do you simplify fractions?
2. How do you add or subtract mixed numbers?
3. What is the process for multiplying mixed numbers?
4. How do you convert an improper fraction back to a mixed number?
5. How can you check if your fraction simplification is correct?

Tip: Always check if the numerator and denominator have a common factor before simplifying a fraction!