Final answer:
The equation 3(6+5) = 18+15 illustrates the Distributive Property, where multiplication is distributed over addition. This property is essential for simplifying expressions and solving algebraic equations.
Step-by-step explanation:
The equation 3(6+5) = 18+15 demonstrates the use of the Distributive Property. This property states that when a number is multiplied by a sum, it can be distributed to each addend in the sum, and the result is the same as multiplying the number by each addend separately and then adding the products together. In this case, multiplying 3 by the sum of 6 and 5 gives the same result as multiplying 3 by 6 and 3 by 5 separately, and then adding the results to get 18 + 15.
The Distributive Property is a crucial concept in algebra and helps simplify expressions and solve equations by breaking them into smaller, more manageable parts. It is often used to remove parentheses in expressions and can be applied in various mathematical scenarios including working with variables. For example, A(B+C) = AB + AC. Another important property mentioned is the Commutative Property of Addition, which affirms A+B = B+A, indicating that the order in which two numbers are added does not affect the sum. This property applies to ordinary number addition such as 2+3 = 3+2.