Which property allows you to multiply a number by a sum and distribute it across the addends?

The correct answer is the Distributive property, which states that when you multiply a number by a sum, you can distribute the multiplication across each addend within the parentheses. This property can be expressed mathematically as ( a \times (b + c) = a \times b + a \times c ). For example, if you have ( 3 \times (4 + 5) ), using the Distributive property means you can calculate it as ( 3 \times 4 + 3 \times 5 ), which results in ( 12 + 15 = 27 ). This property is essential in simplifying expressions and solving equations.

The other properties mentioned do not address the distribution of multiplication over addition. The Associative property pertains to how numbers are grouped in addition or multiplication; the Commutative property deals with the order of numbers in addition or multiplication; while the Inverse property describes how a number combined with its reciprocal results in one. Each of these properties serves a different function in mathematics, but the Distributive property specifically focuses on multiplication across a sum.