Here is Marco's method for calculating \( 38 \cdot 60 \) : Four times 6 is 24 , so 40 times 60 is 2400 . Then 2 times 6 is 12 , so it's \( 2400-120 \), which is 2280 . Write equations that incorporate Marco's method and that also show why his method is valid. Write your equations in the following form: \[ \begin{aligned} 38 \cdot 60 & =\text { some expression } \\ & =\text { some expression } \\ & =\text { \$ } \\ & =2280\end{aligned} \] \( \begin{aligned} \text { Which properties of arithmetic did Marco use } \\ \text { (knowingly or not), and where? }\end{aligned} \)

Marco's method for calculating \( 38 \cdot 60 \) can be expressed in a series of equations that demonstrate the validity of his approach. Here’s how we can break it down: \[ \begin{aligned} 38 \cdot 60 & = (40 - 2) \cdot 60 \\ & = 40 \cdot 60 - 2 \cdot 60 \quad \text{(Distributive Property)} \\ & = 2400 - 120 \quad \text{(Calculating each term)} \\ & = 2280 \end{aligned} \] ### Explanation of the Properties of Arithmetic Used: 1. **Distributive Property**: Marco used the distributive property when he expressed \( 38 \) as \( 40 - 2 \) and then distributed \( 60 \) across both terms: \[ (40 - 2) \cdot 60 = 40 \cdot 60 - 2 \cdot 60 \] 2. **Multiplication**: Marco calculated \( 40 \cdot 60 \) and \( 2 \cdot 60 \) separately, which is a straightforward application of multiplication. 3. **Subtraction**: Finally, he performed the subtraction \( 2400 - 120 \) to arrive at the final answer, which is a basic arithmetic operation. By using these properties, Marco was able to simplify the calculation of \( 38 \cdot 60 \) into more manageable parts, leading him to the correct answer of \( 2280 \).