Which property states that multiplying a sum by a number results in the same answer as multiplying each addend by that number and then adding the products?

The property that indicates multiplying a sum by a number yields the same result as multiplying each individual addend by that number and summing the products is known as the Distributive Property.

This property can be illustrated using an example: if you have a sum like (a + b) and you multiply it by (c), the Distributive Property states that this is equivalent to (c \cdot (a + b) = c \cdot a + c \cdot b). This shows how multiplication distributes over addition.

Understanding this property is essential in algebra as it assists in simplifying expressions and solving equations, ensuring that operations are applied uniformly across all parts of an expression. The Distributive Property is foundational for expanding expressions and is often used in various mathematical contexts, making it a crucial concept to grasp.