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When faced with a mathematical expression involving multiple operations, it is crucial to follow the "Order of Operations." This concept helps us determine which operations to perform first to obtain the correct result. The standard sequence to follow is represented by the acronym PEMDAS. Here's a simple breakdown:

• Parentheses: Solve anything inside parentheses first.
• Exponents: Next, calculate any exponents or powers.
• Multiplication and Division: Perform these operations from left to right.
• Addition and Subtraction: Finally, perform these, also from left to right.

In the given problem, we see that only subtraction and multiplication are involved, with subtraction wrapped inside parentheses. According to the order of operations, we must first handle the parentheses before moving on to multiplication. Ignoring this order might lead to incorrect answers. Always remember to solve expressions in the correct sequence.

Parentheses in a mathematical expression indicate which operations should be conducted first. They help in grouping numbers and operations, clarifying the intended order of calculations. Let's break this down further with the expression from the given exercise:

The expression inside the parentheses is \(6 - 1\). Operations inside the parentheses take precedence before doing anything else in the equation. Thus, we first calculate \(6 - 1\), which results in \(5\). By tackling the parentheses early on, we ensure that all components of the expression are processed correctly.

Understanding the role and the correct evaluation of parentheses is crucial in achieving the right solution in complex and simpler expressions alike.

After evaluating expressions within parentheses, as outlined by the order of operations, we must often execute multiplication, particularly when dealing with integers. Integer multiplication can involve positive and negative numbers, as seen in the exercise above.

Let's revisit the expression: after computing \(6 - 1 = 5\), we are left to handle \(-1 imes 5\). Integer multiplication follows these rules:

• The product of two positive numbers is positive.
• The product of two negative numbers is also positive.
• The product of a positive number and a negative number is negative.

In our exercise, multiplying \(-1\) and \(5\) gives us \(-5\), since we combine a negative integer with a positive one. Understanding how signs interact during multiplication is essential for finding the right answer. This not only aids in simple arithmetic but also forms the foundation for solving more complex algebraic equations.