To solve the problem \( 17 \mod 5 \), we need to understand what the modulus operation means. The modulus operation finds the remainder when one number is divided by another. In this case, we are dividing 17 by 5 and looking for the remainder. ### Step-by-Step Explanation: 1. **Division**: First, we divide 17 by 5. - When we perform the division, we can see how many times 5 fits into 17. - \( 5 \times 3 = 15 \) is the largest multiple of 5 that is less than or equal to 17. - So, 5 fits into 17 a total of 3 times. 2. **Multiplication**: Next, we multiply the quotient (3) by the divisor (5) to find the largest multiple of 5 that is less than or equal to 17. - \( 3 \times 5 = 15 \) 3. **Subtraction**: Now, we subtract this product from the original number (17) to find the remainder. - \( 17 - 15 = 2 \) 4. **Conclusion**: The remainder, which is the result of \( 17 \mod 5 \), is 2. Thus, the correct answer is **A. 2**. ### Explanation of Other Options: - **Option B (3)**: This option is incorrect because it suggests that the remainder when dividing 17 by 5 is 3. However, as we calculated, the remainder is actually 2, not 3. - **Option C (4)**: This option is also incorrect. If the remainder were 4, it would imply that \( 17 - 4 = 13 \) is a multiple of 5, which it is not. The closest multiple of 5 to 17 is 15, leading to a remainder of 2. - **Option D (1)**: This option is incorrect as well. A remainder of 1 would suggest that \( 17 - 1 = 16 \) is a multiple of 5, which it is not. The correct calculation shows that the remainder is 2. ### Common Pitfalls: - **Misunderstanding Modulus**: Some students confuse the modulus operation with simple division. Remember, modulus gives the remainder, not the quotient. - **Rounding Errors**: When dividing, ensure you are considering only whole numbers for the quotient. The remainder must always be less than the divisor. - **Skipping Steps**: It’s important to show all steps in your calculations to avoid mistakes. Always check your work by verifying that the remainder plus the largest multiple of the divisor equals the original number. ### Revision Summary: - The modulus operation finds the remainder of a division. - To calculate \( 17 \mod 5 \), divide 17 by 5, find the largest multiple of 5 less than 17, and subtract it from 17. - The correct answer is **A. 2**. - Always check your calculations to avoid common pitfalls in modulus problems.