Answer :

- We are asked to find the sum of two numbers with opposite signs.
- We find the absolute values of both numbers and subtract the smaller from the larger: $356.1 - 258.6 = 97.5$.
- Since the number with the larger absolute value is negative, the result is negative.
- The final answer is $\boxed{{-97.5}}$.

### Explanation
1. Understanding the Problem
We need to calculate the sum of two real numbers: -356.1 and 258.6. This is a straightforward addition of two numbers with opposite signs.

2. Setting up the Calculation
To find the sum, we add the two numbers: $-356.1 + 258.6$. Since the numbers have opposite signs, we can think of this as finding the difference between their absolute values and using the sign of the number with the larger absolute value.

3. Calculating the Difference
The absolute value of -356.1 is 356.1, and the absolute value of 258.6 is 258.6. Since $|-356.1| > |258.6|$, the result will be negative. Now we calculate the difference: $356.1 - 258.6 = 97.5$.

4. Final Answer
Therefore, the sum of -356.1 and 258.6 is -97.5. So, $-356.1 + 258.6 = -97.5$.

### Examples
Understanding how to add numbers with different signs is crucial in managing finances. For instance, if you have a debt of $356.1 (represented as -356.1) and you deposit $258.6 into your account, the sum -356.1 + 258.6 = -97.5 tells you that you still owe $97.5. This concept is also used in physics to calculate net forces or net electric charges.

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