Understanding the Problem
To find the product of -17 and -29, we can utilize the properties of multiplication, particularly focusing on the rules concerning negative numbers.
Properties of Multiplication
- Negative Times Negative: When you multiply two negative numbers, the result is positive.
- Order of Operations: Multiplication can be performed in any order without affecting the result (commutative property).
Step-by-Step Solution
1. Identify the Numbers: We have -17 and -29.
2. Apply the Negative Times Negative Rule:
- Since both numbers are negative, we can write:
- (-17) × (-29) = 17 × 29
3. Calculate the Positive Product:
- Now, we only need to find the product of 17 and 29.
- To do this, we can break it down:
- 17 × 29 can be calculated by breaking it into smaller parts:
- 17 × 20 + 17 × 9
- 340 + 153 = 493
4. Conclude:
- Therefore, -17 × -29 = 493.
Final Answer
The final answer to the multiplication of -17 and -29 is 493. By understanding and applying the properties of multiplication, we see how negative signs impact the result, leading us to a positive outcome.