What does the associative property tell us about addition and multiplication?

What does the associative property tell us about addition and multiplication?

• A. Grouping does not matter
• B. Order does not matter
• C. Numbers must be rearranged
• D. Distributive property is needed

Answer: (D)

The associative property tells us we can regroup numbers when adding or multiplying and still get the same result. For addition, (a + b) + c equals a + (b + c); for multiplication, (a × b) × c equals a × (b × c). The order of the numbers isn’t in question here—that’s a different idea called the commutative property, where a + b equals b + a. The idea about having to rearrange numbers isn’t what associative is about, and the distributive property (multiplication over addition) is a separate rule, not about regrouping. So the key point is that grouping or parenthesizing can change without changing the outcome for both addition and multiplication.

The associative property tells us we can regroup numbers when adding or multiplying and still get the same result. For addition, (a + b) + c equals a + (b + c); for multiplication, (a × b) × c equals a × (b × c). The order of the numbers isn’t in question here—that’s a different idea called the commutative property, where a + b equals b + a. The idea about having to rearrange numbers isn’t what associative is about, and the distributive property (multiplication over addition) is a separate rule, not about regrouping. So the key point is that grouping or parenthesizing can change without changing the outcome for both addition and multiplication.