Which mathematical property describes the operation of multiplying each addend by a number and then adding the products?

The operation of multiplying each addend by a number and then adding the products is described by the Distributive Property. This property shows how multiplication interacts with addition, stating that when you multiply a number by a sum, you can distribute the multiplication over each addend. For example, if you have a number ( a ) and an expression ( b + c ), the Distributive Property allows you to write this as ( a(b + c) = ab + ac ).

This property is fundamental in algebra, as it provides a systematic way to simplify expressions and equations. It is particularly useful when expanding expressions or solving equations where you need to distribute a factor across a sum. Recognizing this property helps students understand how to manipulate and combine terms in mathematical expressions effectively.