Final answer:
The associative property of addition is illustrated in option a. (u + 7) + 13 = u + (7 + 13), as it shows how the sum remains the same regardless of how the numbers are grouped.
Step-by-step explanation:
The question asks us to identify which statement demonstrates the associative property of addition. This property states that when three or more numbers are added, the sum is the same regardless of the grouping of the addends. The associative property of addition can be expressed as (A + B) + C = A + (B + C).
Given the four options in the question:
• Option a. (u + 7) + 13 = u + (7 + 13) is the correct representation of the associative property of addition. In this equation, the grouping of numbers changes, but the sum remains the same.
• Option b. 21 + 2y = 2y + 21 shows the commutative property of addition, which allows us to change the order of the numbers we are adding.
• Option c. 3⋅(5⋅x)=(3⋅5)⋅x demonstrates the associative property of multiplication.
• Option d. If m + 3 = 18, then 18 = m + 3, shows that equality is maintained when both sides of the equation are reversed, illustrating the symmetric property.
Therefore, the answer that shows the associative property of addition is option a. (u + 7) + 13 = u + (7 + 13).