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In math, parentheses are used to group parts of an expression that should be dealt with first. They help determine the order of operations, which is crucial for simplification. When you see an equation like \[ (2-7) \cdot (6-19) \]understanding how to handle the parentheses is essential. Here is a quick overview:

• Perform Operations Inside Parentheses First: Always simplify the expression inside each parenthesis before performing any other operations. This is part of what mathematicians refer to as the ‘Order of Operations’ or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our exercise, you first calculate \(2-7\) and \(6-19\).
• Sub-problems Simplification: Each set of parentheses could be seen as a sub-section to solve, often being simplified down to a single number or variable.

Applying these operations not only makes the problem easier to digest but also prevents mistakes that stem from a misunderstanding of math hierarchy.

Multiplying with negative numbers might initially seem tricky, but there's a simple rule that applies:

• Positive Times Negative: The result is negative.
• Negative Times Negative: The result is positive.

In the solution, we encountered \( (-5) \cdot (-13) \). Here both numbers are negative. According to the rule, multiplying two negatives yields a positive result, so the answer is \(65\). Understanding these rules ensures accurate multiplication outcomes and minimizes errors during problem-solving.

Solving math problems step-by-step is an invaluable skill. It allows you to break down complex problems into manageable parts. Let's revisit the original example:- **Simplify Each Parenthesis**: Start by simplifying individual parts, as with \(2-7\) becoming \(-5\).- **Perform Operations Carefully**: With each step, ensure accuracy. After simplifying the parentheses to \(-5\) and \(-13\), the next step was multiplying these two numbers.- **Check Each Step**: It's always good practice to review each step. This ensures that no errors were made, especially in arithmetic.Following these logical steps helps build confidence and strengthen problem-solving capabilities. It lets you focus on one piece at a time, allowing for careful and correct calculation.