Which of the following properties is used in the preceding computation?
Distributive property of multiplication over addition.
The distributive property of multiplication over addition allows us to multiply a single term by each term within a parenthesis, effectively distributing the multiplication across the addition. This property is fundamental in simplifying expressions and performing calculations involving both multiplication and addition.
The commutative property of addition states that changing the order of addends does not change the sum (e.g., a + b = b + a). While this property is important in arithmetic, it does not apply to the computation at hand, which involves multiplication interacting with addition rather than solely rearranging addends.
The associative property of multiplication indicates that the grouping of factors does not affect the product (e.g., (a × b) × c = a × (b × c)). However, this property is not relevant to computations that involve distributing multiplication over addition, which is the focus of the question.
The commutative property of multiplication states that the order of factors does not affect the product (e.g., a × b = b × a). While this property influences multiplication, it does not address the interaction between multiplication and addition, which is essential for the computation being considered.
The distributive property is crucial when multiplying a number by a sum, as it allows one to multiply each addend separately and then sum the results (e.g., a × (b + c) = a × b + a × c). This property directly applies to the computations described, making it the correct choice.
In evaluating which property is used in the given computation, the distributive property of multiplication over addition is the appropriate choice. This property facilitates the multiplication of a number across terms in an addition scenario, proving essential for accurate calculations. The other properties, while significant in their contexts, do not apply to the specific operation being referenced in the question.
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