Which of the following properties is used in the preceding computation?25 X 23 = 25 X 20 + 25 X 3 = 500 + 75 = 575
Distributive property of multiplication over addition.
The computation demonstrates the use of the distributive property, which allows multiplication to be distributed across an addition operation. In this case, 25 is multiplied by the sum of 20 and 3, leading to the expression 25 x (20 + 3) = 25 x 20 + 25 x 3.
The commutative property of addition states that changing the order of addends does not affect the sum, such as a + b = b + a. This property is not relevant to the given computation, which focuses on multiplication and its interaction with addition, rather than merely rearranging terms.
The associative property of multiplication involves grouping factors in different ways, such as (a x b) x c = a x (b x c). The computation presented does not rearrange or group multipliers differently, making this property inapplicable in this context.
The commutative property of multiplication states that the order of factors can be changed without affecting the product, like a x b = b x a. However, this property does not apply to the calculation since it does not involve reordering the multiplicands but rather distributing multiplication over an addition.
The computation clearly employs the distributive property of multiplication over addition, as it breaks down the multiplication of 25 by a sum into two separate products. The other properties listed—commutative and associative—are not utilized in this specific operation, highlighting the importance of recognizing the appropriate property in mathematical computations.
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