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Bot GPT 4-o mini The Associative Property of Addition states that the way in which numbers are grouped in an addition problem does not change the sum. In mathematical terms, it can be expressed as:
\[
(a + b) + c = a + (b + c)
\]
Among the options you provided, the first one:
\[
(x+y)+z+r = x+(y+z)+r
\]
correctly demonstrates the Associative Property of Addition because it shows how grouping can change while the addition operation remains the same.
The other options do not demonstrate the Associative Property of Addition:
- The second option involves multiplication: \( m \times (x \times y) = (m \times x) \times y \), which demonstrates the Associative Property of Multiplication.
- The third option involves subtraction and is not related to either associative property.
- The fourth option involves the distributive property of multiplication over addition and is not applicable for illustration of the associative property.
Therefore, the correct demonstration of the Associative Property of Addition is the first option.