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Negative numbers can often be confusing, especially when they're involved in subtraction. However, grasping their fundamental properties is crucial. A negative number is any number less than zero. It's often represented with a minus sign (-). When subtracting a negative number, an interesting rule comes into play: subtracting a negative is the same as adding a positive.

Here's why it works. Imagine you're at sea level, and you want to go up. Moving up three steps (adding 3) is the opposite of moving down three steps (subtracting 3). So, when you see something like '-(-13)', you're essentially being asked to do the opposite of moving down, which means moving up. In other words:

• '-(-x)' becomes '+x'

Understanding this rule can help simplify expressions efficiently without getting tangled up in multiple negative signs.

Addition is one of the fundamental arithmetic operations. It's simply about putting numbers together to calculate a total. In this context, after we convert the negative signs to plus signs, we're left with straightforward addition.

For instance, once we changed the expression from '7 - (-13) - (-1)' to '7 + 13 + 1', it's nothing more than basic adding. Here are some basic tips:

• Add numbers sequentially to simplify the operation.
• Start with smaller groups if dealing with more than two numbers to avoid errors.
• Visualize adding on a number line if needed.

Using these strategies, you can efficiently manage addition in any given situation.

Arithmetic calculations encompass a variety of mathematical operations, but the main four are addition, subtraction, multiplication, and division. In this exercise, we primarily focus on the first two because the problem deals with simplifying an expression combining these operations.

In arithmetic, follow basic operational rules to simplify expressions: processes like removing parentheses correctly and following the order of operations (BODMAS/BIDMAS). Imagine your expression is like a puzzle. Each piece (whether it's a number or an operation) fits together to give you the final answer. When we solved the problem:

• We turned subtractions of negatives into additions to make the puzzles fit together logically.
• Calculated each addition step-by-step to ensure accuracy.

Remember, the goal is not just to reach the answer but to understand how and why each step works. This understanding builds towards more complex arithmetic calculations in the future.