Final answer:
The commutative property of addition states that numbers can be added in any order with the same result. While working with whole numbers, attention must be paid to the signs, because they determine the result's sign. This property helps in simplifying and verifying addition problems.
Step-by-step explanation:
The commutative property of addition states that you can add numbers in any order and still get the same result. For example, both 2 + 3 and 3 + 2 will give you the result of 5. This basic principle holds true for both whole numbers and vectors, meaning that whether you're adding scalars or vectors, the commutative property applies.
When working with whole numbers, it's essential to pay attention to the signs of the numbers to determine the outcome. Following these rules:
- Two positive numbers added together result in a positive sum.
- Two negative numbers added together result in a negative sum.
- When adding numbers with opposite signs, subtract the smaller number from the larger and take the sign of the larger number.
- In subtraction, the operation can be approached by changing the sign of the subtracted number and then adding it to the other number.
When checking an addition problem, the commutative property can be used to rearrange the terms and potentially simplify the problem or verify the result by calculating it in a different order.