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When you encounter complex mathematical expressions, it's essential to follow the proper order of operations to get the correct result. This order is often remembered by the acronym PEMDAS, which stands for:

• P - Parentheses
• E - Exponents (or indices)
• M - Multiplication
• D - Division
• A - Addition
• S - Subtraction

This means you first perform any operations inside parentheses. Next, you resolve any exponents. Then, you carry out multiplication and division from left to right. Finally, you do addition and subtraction, also from left to right. In the given exercise, \(8 - 2 \cdot 5\), we need to follow PEMDAS to solve it correctly. Note that multiplication is prioritized over subtraction, so you handle \(2 \cdot 5\) first before addressing the subtraction.

Arithmetic operations refer to the basic functions you perform with numbers: addition, subtraction, multiplication, and division. When simplifying expressions, you need to follow initial rules, especially the order mentioned in PEMDAS. In our example, \(8 - 2 \cdot 5\), we must first identify which operations are present and then apply them in the correct sequence. Multiplication comes before subtraction in PEMDAS rules.

So we first multiply \(2 \cdot 5\) to get 10, simplifying our expression to \(8 - 10\). Only after handling this multiplication do we proceed to the subtraction.

This is how you can break complex expressions into manageable steps. Each step follows the logical rules to eventually solve them accurately.

Subtracting integers can sometimes trip up students, especially when the result is a negative number. In the given problem, after performing the multiplication, we are left with the expression \(8 - 10\).

Here, we're subtracting a larger number from a smaller one. When you subtract an integer and end up with a negative result, it helps to think of it in terms of owing. For instance, if you have 8 dollars but need to pay 10 dollars, you would owe 2 dollars, represented as \(-2\).

So, \(8 - 10\) simplifies to \(-2\).

Understanding this concept of subtracting integers helps in grasping more intricate mathematical ideas later on. It ensures you have a strong foundation in handling both positive and negative numbers.