Problem 83 - Introductory Algebra for College Students

Question

State an associative property and give an example.

Step-by-Step Solution

Answer

The associative property states that the way numbers are grouped in an operation (specifically multiplication or addition) does not change the result. For example, in addition, (3 + 4) + 5 equals 3 + (4 + 5), both of which yield 12. In multiplication, (2 * 3) * 4 equals 2 * (3 * 4), both of which yield 24.

Step 1: Define the Associative Property

The 'associative property' refers to the rule in mathematics which states that the way numbers are grouped in an operation does not change the result. This property holds true for addition and multiplication, but not for subtraction and division.

Step 2: State the Associative Property for Addition

The associative property of addition can be stated as: for all real numbers a, b, and c, the equation (a + b) + c equals a + (b + c). This means that if you are adding three (or more) numbers together, it does not matter how the numbers are grouped, you will always get the same result.

Step 3: Provide an Example for Associative Property of Addition

For instance, consider the numbers 3, 4 and 5. Using the associative property for addition, (3 + 4) + 5 equals 3 + (4 + 5). Both will yield the same result, which is 12.

Step 4: State the Associative Property for Multiplication

The associative property of multiplication can be stated as: for all real numbers a, b, and c, the equation (a * b) * c equals a * (b * c). Similarly, it means that if you are multiplying three (or more) numbers together, it does not matter how the numbers are grouped, you will always get the same result.

Step 5: Provide an Example for Associative Property of Multiplication

For instance, consider the numbers 2, 3, and 4. Using the associative property for multiplication, (2 * 3) * 4 equals 2 * (3 * 4). Both will yield the same result, which is 24.