1. **State the problem:** Multiply 47 by -25. 2. **Formula and rules:** Multiplication of integers follows the rule that a positive number times a negative number results in a negative number. So, $a \times (-b) = -(a \times b)$. 3. **Calculate the product:** $$47 \times (-25) = -(47 \times 25)$$ 4. **Multiply the absolute values:** $$47 \times 25 = 1175$$ 5. **Apply the negative sign:** $$-(1175) = -1175$$ **Final answer:** $$47 \times (-25) = -1175$$