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When simplifying expressions, it's crucial to follow the order of operations to avoid mistakes. The order of operations is a set of rules that dictates the correct sequence in which to evaluate a math expression. You might remember this order with the acronym PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In the given exercise, we focus on parentheses and subtraction. Recognizing and correctly calculating expressions within parentheses is vital before proceeding to other operations. Following the order of operations ensures that the expression is simplified systematically and correctly.

Negative numbers can seem tricky at first, but they become easier with practice. In the expression \(-8-(-2)\), we are dealing with subtracting a negative number. It's essential to understand that subtracting a negative number is the same as adding its positive counterpart. This means \(-8-(-2)\) becomes \(-8+2\). When working with negative numbers, remember:

• Subtracting a negative = Adding a positive
• Adding a negative = Simple addition in the direction opposite to the positive numbers
• Negative multiplied or divided by a negative = Positive
• Negative multiplied or divided by a positive = Negative

With these rules, manipulating negative numbers becomes more straightforward, helping avoid common pitfalls in arithmetic operations.

Arithmetic operations involve basic calculations such as addition, subtraction, multiplication, and division. In this exercise, we mainly look at subtraction and division. First, we convert subtraction of negative numbers into addition by removing the double negatives. This transforms \(-8-(-2)\) into \(-8+2\), which simplifies the expression.Then, when dividing negative numbers like in \(\frac{-6}{-1}\), remember that a negative number divided by another negative number yields a positive result. This transforms the expression into 6.These operations rely heavily on understanding both the arithmetic operations themselves and the properties of negative numbers. Each step ensures that overall computations proceed smoothly, eventually simplifying expressions to their simplest form effectively.