3 1/1×5 1/1÷4/4

Let's simplify the expression step by step.

1. **Convert mixed numbers to improper fractions**:
- \(3 \frac{1}{1} = 3\)
- \(5 \frac{1}{1} = 5\)

So the expression becomes:
\[
3 \times 5 \div \frac{4}{4}
\]

2. **Calculate \(4/4\)**:
- \(4/4 = 1\)

3. **Now rewrite the expression using this**:
\[
3 \times 5 \div 1
\]

4. **Perform the multiplication**:
- \(3 \times 5 = 15\)

5. **Now divide by 1**:
- \(15 \div 1 = 15\)

Thus, the final answer is:
\[
\boxed{15}
\]