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Understanding mathematical operations is crucial for solving various math problems. These operations include addition (+), subtraction (−), multiplication (×), and division (÷). When facing a combination of these operations in a single problem, the order in which we perform them is essential. This order is remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In the given exercise, \(2+(-1)(-3)\), we follow this principle by addressing the multiplication first. The reason we tackle multiplication before addition is because it ranks higher in the hierarchy of operations. Thus, ensuring accurate and mistake-free solutions even in more complex problems. Applying this process consistently helps in enhancing problem-solving skills in basic algebra and beyond.

Negative numbers are numbers less than zero and are often represented with a minus sign (−) in front of them. In the context of mathematical operations, their behavior can lead to results that may initially seem counterintuitive. For instance, when multiplying two negative numbers, the result is positive. This concept is demonstrated in the exercise with the multiplication \( (-1)\times(-3) \), which equals 3.

The rule of thumb is that a negative times a negative gives a positive, while a negative times a positive gives a negative. Understanding how to work with negative numbers is essential in various real-world contexts and is a foundational aspect of basic algebra that enables students to solve equations and inequalities where negative values are involved.

Basic algebra is a segment of mathematics that deals with symbols and the rules for manipulating these symbols. It’s a language that allows us to describe patterns and relationships among quantities. A key to algebra is understanding that letters (often x, y, or z) can be used to represent numbers, and operations can be performed on them just like with numbers.

When solving algebraic expressions, like in our example, the same order of operations is followed. First addressing the multiplication inside the parentheses \( (-1)\times(-3) \) and then moving on to the addition \( 2 + 3 \), is a demonstration of algebraic principles being applied to numerical values. As students advance in algebra, they'll encounter more complex expressions and equations, but the foundation built through understanding simple mathematical operations becomes invaluable.