Final answer:
Garry's use of the Associative Property for subtraction is incorrect because this property does not apply to subtraction. Subtraction should be done directly without re-associating the numbers. The correct procedure would be to subtract both 6,145 and 2,145 from 17,422 to find the final answer.
Step-by-step explanation:
Garry's reasoning to solve a subtraction problem by first using the Associative Property to group 6,145 and 2,145 together is incorrect because the Associative Property applies to addition and multiplication, not subtraction. Garry should directly subtract these numbers from 17,422 without rearranging them. The correct method is to perform a straightforward subtraction: 17,422 - 6,145 - 2,145 = 9,132.
To understand why Garry's method is incorrect, let's review the basic principles of addition and subtraction. The Associative Property states that when adding or multiplying, the grouping of numbers does not affect the result, such as (a + b) + c = a + (b + c). However, this property does not hold true for subtraction, as changing the grouping of numbers can lead to a different result.
Additionally, when working with whole numbers, it is important to pay attention to the signs of the numbers involved. For subtraction, changing the sign of the subtracted number to its opposite and then adding according to the rules of addition is critical. Specifically, subtracting a positive number is equivalent to adding its negative counterpart, as exemplified by 5 - 3 = 5 + (-3) = 2.
Therefore, Garry should have subtracted both 6,145 and 2,145 directly from 17,422, then added the results together to find the final answer. By attempting to use the Associative Property, Garry may unintentionally alter the problem's original meaning and arrive at an incorrect solution.