State the name of the property illustrated: (3 • 7) + (4 • 7) = (4 • 7) + (3 •7)

Verified step by step guidance

1. Observe the given expression: \( (3 \cdot 7) + (4 \cdot 7) = (4 \cdot 7) + (3 \cdot 7) \). Notice that the two products are being added together on both sides.
2. Identify that the terms on the left side are \$3 \cdot 7\( and \)4 \cdot 7\(, and on the right side, the same terms appear but in reversed order: \)4 \cdot 7\( and \)3 \cdot 7$.
3. Recall the Commutative Property of Addition, which states that changing the order of addends does not change the sum. In symbolic form, this is \(a + b = b + a\).
4. Since the expression shows the sum of two products with their order switched but the sum remains the same, this illustrates the Commutative Property of Addition.
5. Therefore, the property illustrated by the equation is the Commutative Property of Addition.

Key Concepts

Commutative Property of Addition

The commutative property of addition states that changing the order of addends does not change the sum. For example, a + b = b + a. In the given expression, the sums on both sides have the same terms added in different orders, illustrating this property.

Distributive Property

The distributive property connects multiplication and addition, stating that a(b + c) = ab + ac. Although the given expression resembles terms from distribution, it primarily shows rearrangement of terms rather than distribution itself.

Multiplication of Real Numbers

Multiplication of real numbers is commutative, meaning a × b = b × a. This allows factors to be reordered without changing the product, which is essential in understanding why (3 • 7) and (7 • 3) are equivalent in the expression.