Question

Does the associative property always, sometimes, or never hold for subtraction. Explain your reasoning using examples and non-examples! please help!

Answer 1

Answer: You should remember that if the minus sign is before the parentheses, you need to distribute it, otherwise, you can always use it.

Step-by-step explanation:

The associative property says that:

A + (B + C) = (A + B) + C  

Where A, B, and C are real numbers.

Let's see if it does:

10 + (- 5 - 4) = 10 + (-9) = 1

(10 + -(5)) - 4 = 5 - 4 = 1

thiw seems to work, let's se other case:

10 - (5 - 4) = 10 - (1) = 9

now, apply the associative relation

(10 -5) + 4 = 9

Where the sign must change, because we actually have that -(5 - 4) = -1*(5 - 4) so we must distribute the minus sign in the parentheses.

Then, if you take this in mind, you always can use the associative property.

Answer 2

The associative property never works with subtraction.

For example:
2 - (7-8) ≠ (2-7) - 8
2-(-1)=3, but (-5)-8=-13