Final answer:
Option C, (3 + 51) - (2 - 1), is the most likely candidate for yielding the difference 1 + 4/?, which simplifies to 4 + 51. This relies on the rules of changing the sign in subtraction and the outcome of adding numbers with similar or different signs.
Step-by-step explanation:
The student is asking which subtraction expression results in the difference 1 + 4/? To find this out, we need to evaluate the provided expressions and determine which one yields the mentioned difference. Let's look at each option:
- A. (-2 + 61) - (1 - 21): Here, subtracting the second parenthesis from the first will not give us a result that has a division operator (4/?).
- B. (-2 + 61) - (-1 - 21): This expression involves subtracting a negative, which is the same as adding the positive equivalent, but again it does not give us a division operator as part of the answer.
- C. (3 + 51) - (2 - 1): This expression looks promising because after simplifying the parentheses and subtracting, we might end up with a fraction which could resemble the requested form of 1 + 4/?.
- D. (3 + 51) - (2 + 1): Like options A and B, subtracting these parentheses will not result in a fraction of the form 4/?.
Thus, the most likely candidate for yielding the difference 1 + 4/? would be option C. To verify this, let's simplify option C step by step:
(3 + 51) - (2 - 1) = (3 + 51) - 2 + 1 = 3 + 51 + 1 - 2 = 4 + 51
As we can see, the expression (3 + 51) - (2 - 1) simplifies to 4 + 51, which matches the form of the difference 1 + 4/? assuming the ? in the original expression could stand for '51'.
The answer to this question is based on the principles that in subtraction, we change the sign of the subtracted number before operating, and that when two numbers add, the resulting sign depends on the signs of the original numbers.