Question

Ten 40-count packages of hot dogs are purchased. a. Determine the total number of hot dogs by calculating \(10 \cdot 40\). b. Calculate: \(40 \cdot 10\) c. What property of multiplication is demonstrated by the fact that the answers to parts a and b should be the same?

Short answer

Answer: The Commutative Property of multiplication is demonstrated in this case.

Step-by-step solution

Calculate the product of 10 and 40

To determine the total number of hot dogs, multiply the number of packages (10) by the number of hot dogs in each package (40). So, \(10 \cdot 40 = 400\).

Calculate the product of 40 and 10

Now, we need to calculate the product of 40 and 10. So, \(40 \cdot 10 = 400\).

Identify the property

Since the answers to parts a and b are the same, the property of multiplication being demonstrated is the Commutative Property. The Commutative Property states that for any two numbers a and b, \(a \cdot b = b \cdot a\). In our case, we have shown that \(10 \cdot 40 = 40 \cdot 10\).