Video: The Associative Property of Addition and Multiplication

Which of the following illustrates the associative property of addition? [A] 𝑧 + 41 = 41 + 𝑧 [B] (41 + 𝑧) + 4 = 41 + (𝑧 + 4) [C] (41 + 𝑧) + 4 = (41 + 4) + (𝑧 + 4) [D] (41 Γ— 𝑧) Γ— 4 = 41 Γ— (𝑧 Γ— 4) [E] (41 + 𝑧) Γ— 4 = (41 Γ— 4) + (𝑧 Γ— 4)

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Video Transcript

Which of the following illustrates the associative property of addition? Is it (A) 𝑧 plus 41 is equal to 41 plus 𝑧? (B) 41 plus 𝑧 plus four is equal to 41 plus 𝑧 plus four? (C) 41 plus 𝑧 plus four is equal to 41 plus four plus 𝑧 plus four? (D) 41 multiplied by 𝑧 multiplied by four is equal to 41 multiplied by 𝑧 multiplied by four? Or (E) 41 plus 𝑧 multiplied by four is equal to 41 multiplied by four plus 𝑧 multiplied by four?

The associative property of addition states that when three or more numbers are added, that sum is the same regardless of the grouping. For example, two plus three in parentheses plus four is the same as two plus three plus four in parentheses. It doesn’t matter which order we add our numbers. The correct answer is, therefore, option (B). When adding 41, 𝑧, and four, we can add 41 and 𝑧 first or 𝑧 and four first. We could also have added 41 and four first.

Option (A) demonstrates the commutative property of addition. This states that when two numbers are added, the sum is the same regardless of the order.

Option (D) looks similar to the correct answer of option (B). This demonstrates the associative property of multiplication. As with addition, when three or more numbers are multiplied, the product is the same regardless of the grouping.

Option (E) demonstrates the distributive property of multiplication. The sum of two numbers multiplied by a third is equal to the sum of each number inside the parentheses multiplied by the third number. In this case, we can multiply 41 by four and 𝑧 by four. We then add these values.

Option (C) is actually an incorrect equation. 41 plus 𝑧 plus four is not equal to 41 plus four plus 𝑧 plus four.

The correct answer, as previously stated, is option (B). 41 plus 𝑧 plus four is equal to 41 plus 𝑧 plus four illustrates the associative property of addition.

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