Which property states that multiplying a sum by a number results in the same product as multiplying each addend by that number?

The property that states multiplying a sum by a number results in the same product as multiplying each addend by that number is known as the Distributive Property. This property can be expressed mathematically as ( a(b + c) = ab + ac ), where ( a ) is the number that multiplies the sum ( (b + c) ).

This illustrates that regardless of how the numbers are grouped in addition, the multiplication distributes over the addition. For example, if you have ( 2(3 + 5) ), you can either first add the numbers in parentheses to get ( 2 \times 8 = 16 ) or distribute the ( 2 ) to each term to get ( 2 \times 3 + 2 \times 5 = 6 + 10 = 16 ), leading to the same result.

Understanding the Distributive Property is fundamental in simplifying expressions and solving equations, making it a vital concept in mathematics overall.