Question

a. Evaluate: \(72 \cdot 23\) b. Evaluate: \(23 \cdot 72\) c. Are the answers to parts a and b the same? d. What property do the results of this exercise demonstrate?

Short answer

Answer: The Commutative Property of Multiplication is demonstrated in this exercise since \(72 \cdot 23 = 23 \cdot 72\).

Step-by-step solution

Evaluate the product of 72 and 23

To find the product of 72 and 23, we multiply these two numbers: \(72 \cdot 23\).

Compute the multiplication

Perform the multiplication \(72 \cdot 23\): \[72 \times 23 = 1656\]

Evaluate the product of 23 and 72

To find the product of 23 and 72, we multiply these two numbers: \(23 \cdot 72\).

Compute the multiplication

Perform the multiplication \(23 \cdot 72\): \[23 \times 72 = 1656\]

Compare the results of parts a and b

The results from part a and part b are both 1656.

Answer part c

Since the results of parts a and b are the same (1656), we can conclude that the answers to parts a and b are indeed the same.

Identify the mathematical property

The property demonstrated in this exercise is the Commutative Property of Multiplication, which states that for any real numbers a and b, we have a * b = b * a. In this case, we have \(72 \cdot 23 = 23 \cdot 72\).