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Identify Structure When simplifying -7(3)(-10) + (-4), can you multiply 3 and -10 first and get the same result as multiplying - 7 and 3 first? Choose the correct answer and explanation.

• A) no; The Commutative Property of Multiplication states the order in which numbers are group does change the product.

B) yes; The Distributive Property states that the order in which numbers are grouped does not change the product.

O C) yes; The Associative Property of Multiplication states that the order in which numbers are grouped does not change the product.

• D) no; The Inverse Property of Multiplication states the order in which numbers are group does change the product.

1 answer

The correct answer is:

C) yes; The Associative Property of Multiplication states that the order in which numbers are grouped does not change the product.

Explanation:

You can multiply different pairs of numbers first without changing the final result because of the Associative Property of Multiplication. This property states that when you multiply three or more numbers together, the way you group them does not affect the product.

For example, in the expression -7(3)(-10) + (-4):

  1. You can group and multiply 3 and -10 first: \[ -7(3)(-10) = -7(30) = -210 \]

  2. Or, you can multiply -7 and 3 first: \[ (-7)(3) = -21 \] Then multiply by -10: \[ (-21)(-10) = 210. \]

Therefore, in both cases, the overall multiplication will yield the same product, demonstrating the Associative Property.