How can you represent −5⋅−12 with a model?(1 point) Responses −12+−12+−12+−12+−12 negative 12 plus negative 12 plus negative 12 plus negative 12 plus negative 12 12+12+12+12+12 12 plus 12 plus 12 plus 12 plus 12 −(−12+−12+−12+−12+−12) negative left parenthesis negative 12 plus negative 12 plus negative 12 plus negative 12 plus negative 12 right parenthesis −(12+12+12+12+12)

Question

GPT-4o mini · Answer

To represent $-5 \cdot -12$ with a model, you want to express the concept of multiplying negative numbers. When you multiply two negative numbers, the result is positive. Here is how the options relate: 1. **−12 + −12 + −12 + −12 + −12**: This represents $-5 \cdot -12$ incorrectly; it adds negative twelves together. 2. **12 + 12 + 12 + 12 + 12**: This correctly represents $5 \cdot 12$, which is equivalent to $-5 \cdot -12$ because both are equal to $60$. 3. **−(−12 + −12 + −12 + −12 + −12)**: This expression represents the negation of negative twelves added together, which simplifies to $5 \cdot 12$. 4. **−(12 + 12 + 12 + 12 + 12)**: This represents the negation of positive twelves, which does not correspond to the original multiplication. The most accurate models among the responses you provided are: - **12 + 12 + 12 + 12 + 12** - **−(−12 + −12 + −12 + −12 + −12)** Both correctly express the concept of $-5 \cdot -12$ as a positive result.

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pick one

GPT-4o mini · Answer

The best choice to represent $-5 \cdot -12$ is: **12 + 12 + 12 + 12 + 12** This accurately represents the multiplication as it results in a positive value, effectively showing that multiplying two negative numbers results in a positive product.

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How can you represent −2⋅9 with a model?(1 point) Responses 9+9 9 plus 9 −2+−2 negative 2 plus negative 2 −9+−9 negative 9 plus negative 9 −(9+9)

GPT-4o mini · Answer

To represent $-2 \cdot 9$ with a model, you want to express the multiplication of a negative number and a positive number. The product will be negative. Here’s a breakdown of the options: 1. **9 + 9**: This represents $2 \cdot 9$, which is not correct since we want $-2 \cdot 9$. 2. **−2 + −2**: This adds two negative twos together, which equals $-4$ and does not accurately represent $-2 \cdot 9$. 3. **−9 + −9**: This adds two negative nines together, which equals $-18$ and does not correspond directly to $-2 \cdot 9$. 4. **−(9 + 9)**: This represents the negation of $2 \cdot 9$, which equals $-18$. This is the most accurate representation of $-2 \cdot 9$. Therefore, the best choice to represent $-2 \cdot 9$ is: **−(9 + 9)**.

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I got a whole bunch WRONG

GPT-4o mini · Answer

I apologize for any confusion in my previous messages. Let's clarify the modeling of $-2 \cdot 9$ more clearly and ensure we identify the correct response.

To represent $-2 \cdot 9$, we want to show that you are taking 9 and adding it negatively (indicating the negative coefficient).

Given Options:

9 + 9: Represents $2 \cdot 9$, or $18$.
−2 + −2: Represents $-2$ added together, which equals $-4$ and does not correspond to $-2 \cdot 9$.
−9 + −9: Represents $-9 + -9$, which equals $-18$ and does not correctly represent $-2 \cdot 9$.
−(9 + 9): This represents the negation of $2 \cdot 9$, or $-18$, which is indeed the correct representation. This means you're modeling taking away two sets of 9.

The correct representation for $-2 \cdot 9$ is:

−(9 + 9)

If you have questions about specific items you got wrong or need further explanation, feel free to ask, and I'll be happy to clarify!