Problem 82 - Introductory Algebra for College Students

Question

State a commutative property and give an example.

Step-by-Step Solution

Answer

Commutative property states that the order in addition and multiplication does not affect the outcome. For example, \(2 + 3 = 3 + 2\) and \(4 \times 5 = 5 \times 4\).

Step 1: Define Commutative Property

The commutative law or commutative property states that the order or sequence of numbers does not change the outcome in addition and multiplication. Simply put, if you have two numbers, you can swap their places in addition or multiplication without affecting the result.

Step 2: Provide examples for Addition

For addition, here is an example. Suppose you have numbers 2 and 3. According to the commutative property, \(2 + 3 = 3 + 2\). This means you can switch the places of 2 and 3 in the addition, and you will still get the same outcome, 5 in both cases.

Step 3: Provide examples for Multiplication

For multiplication, consider numbers 4 and 5. The commutative property in multiplication states that \(4 \times 5 = 5 \times 4\). This means that whether you multiply \(4 \times 5\) or \(5 \times 4\), the result is the same - 20.