What does the distributive property state regarding multiplication over addition?

The distributive property is a fundamental principle in mathematics that describes how multiplication interacts with addition. The correct statement representing this property is that when a number is multiplied by a sum, it can be distributed to each addend within the parentheses. Specifically, if you have a quantity 'a' being multiplied by the sum of 'b' and 'c', this can be expressed as 'a(b + c)'. According to the distributive property, this is equivalent to multiplying 'a' by 'b' and then adding that to the product of 'a' and 'c', which results in the expression 'ab + ac'. This illustrates how the operation of multiplication distributes over addition, allowing for simplification and reorganization of terms when performing calculations.

The other choices involve similar concepts but do not directly state the core definition of the distributive property in the standard form. They illustrate applications of the distributive property in different contexts but do not provide the most straightforward representation of the property itself. For instance, while the second choice shows an analogous distribution, it alters the original structure which can lead to confusion regarding its relationship to the original property definition.