State the name of the property illustrated. 6+(2+7)=(6+2)+7

Verified step by step guidance

1. Identify the expression given: \$6 + (2 + 7) = (6 + 2) + 7$.
2. Notice that the numbers and the operation (addition) remain the same on both sides of the equation; only the grouping of the numbers changes.
3. Recall that the property which allows you to change the grouping of numbers in addition without changing the result is called the Associative Property of Addition.
4. The Associative Property of Addition states that for any numbers \(a\), \(b\), and \(c\), the equation \(a + (b + c) = (a + b) + c\) holds true.
5. Therefore, the given equation illustrates the Associative Property of Addition.

Key Concepts

Associative Property of Addition

The associative property of addition states that when adding three or more numbers, the way in which the numbers are grouped does not affect the sum. For example, (a + b) + c = a + (b + c). This property allows us to change the grouping of addends without changing the result.

Addition Operation

Addition is a fundamental arithmetic operation that combines two or more numbers to get their total or sum. Understanding how addition works is essential to grasp properties like associativity, as it involves manipulating sums without altering their values.

Mathematical Properties in Algebra

Mathematical properties, such as associative, commutative, and distributive properties, describe consistent rules that apply to operations like addition and multiplication. Recognizing these properties helps simplify expressions and solve algebraic problems efficiently.