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Understanding the order of operations is crucial when simplifying algebraic expressions. It is an essential set of rules that dictates which calculations to perform first to arrive at the correct answer. The acronym PEMDAS is a common way to remember this order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In the given exercise, the order of operations instructs us to deal with the multiplication inside the parentheses first. This approach prevents mistakes that could lead to incorrect results. By applying the correct order, we ensure that all multiplication operations, even those involving negative numbers, are completed before the addition operation.

Multiplying negative numbers may seem tricky, but there's a simple rule to follow. When you multiply two negative numbers, the result is positive. This happens because a negative number is essentially the opposite of a positive number. Therefore, when you're finding the product of two 'opposites,' they cancel each other out, resulting in a positive number.

In our example, \( -1 \times 2 \times -3 \), we first multiply \( -1 \times 2 \) to get \( -2 \). Then we multiply \( -2 \times -3 \), and because both numbers are negative, the result is a positive \( 6 \). By keeping this rule in mind, you'll find working with negative numbers much less intimidating.

Arithmetic operations are the building blocks of math, including addition, subtraction, multiplication, and division. When simplifying expressions, it's important to perform these operations accurately and in the correct order.

After applying the multiplication of negative numbers in our exercise, we're left with a simpler arithmetic operation—addition. We add the two positive numbers to arrive at the final solution, demonstrating that even complex expressions can be broken down into basic arithmetic steps. By mastering each of these operations and applying them in the right sequence, you'll be able to simplify a wide range of algebraic expressions with confidence.