To determine how many months Mira's bill covers, you need to first account for the activation fee and then see how much of the bill is left to cover the monthly costs.
- Identify the total charges: The total bill is $412 and includes a $100 activation fee.
- Subtract the activation fee from the total bill: \[ \text{Remaining amount} = \text{Total bill} - \text{Activation fee} = 412 - 100 = 312 \]
- Determine the monthly cost: The monthly cost is $52.
- Divide the remaining amount by the monthly cost to find the number of months covered: \[ \text{Number of months} = \frac{\text{Remaining amount}}{\text{Monthly cost}} = \frac{312}{52} = 6 \]
The operations needed to solve this problem are subtraction and division.
Therefore, the correct answer is: subtraction and division.