Identify which of three conceptual models of division (repeated subtraction, partition, missing-factor) best corresponds to the problem. Do not solve the problem. A student arranges to pay off a loan with monthly payments. If the loan is for $$ \$ 2,925 $$ and the monthly payment is $$ \$ 225 $$, how many months will it take to pay off the loan? A. Partition B. Missing-factor C. Repeated subtraction

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To identify which conceptual model of division best corresponds to the problem, let's analyze the situation:

The problem involves a loan amount of $$ \$ 2,925 $$ and a monthly payment of $$ \$ 225 $$. The question asks how many months it will take to pay off the loan, which essentially involves determining how many times the monthly payment fits into the total loan amount.

1. **Partition Model**: This model involves dividing a whole into equal parts. In this case, we are looking to find out how many equal parts (monthly payments) can be made from the total amount (loan).

2. **Missing-factor Model**: This model is used when one factor in a multiplication equation is unknown. It typically involves finding a missing number that, when multiplied by another known number, gives a specific product. This model does not directly apply here since we are not looking for a missing factor in a multiplication context.

3. **Repeated Subtraction Model**: This model involves subtracting the divisor repeatedly from the dividend until reaching zero. While this could conceptually apply, it is less efficient and not the primary way to think about this problem.

Given the context of the problem, the best fit is the **Partition Model** (A), as we are essentially partitioning the total loan amount into equal monthly payments to find out how many payments are needed.

Thus, the answer is:
**A. Partition**
The best conceptual model is **Partition** (A).

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