Explanation:

Let's evaluate the equation and options to find out which signs should be swapped.

- Original equation: $15+15÷15-15\times 15=15$

1. Option 1: + and ×

Swap + and ×:

$15\times 15÷15+15-15=15$

Simplified: $15+15-15=15$

This is correct.

2. Option 2: ÷ and +

Swap ÷ and +:

$15÷15+15-15\times 15=15$

Simplified: $1+15-225=15$

This is incorrect.

3. Option 3: + and -

Swap + and -:

$15-15÷15+15\times 15=15$

Simplified: $15-1+225=15$

This is incorrect.

4. Option 4: ÷ and ×

Swap ÷ and ×:

$15+15\times 15÷15-15=15$

Simplified: $15+15-15=15$

This is correct.

Correct Answer: Option 1