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Understanding multiplication is crucial when we are dealing with numbers in mathematics. It is one of the basic operations and involves combining equal groups of items to find the total number of items. When we say that we are multiplying 10 by -3 (written as 10 x -3 or \(10(-3)\)), we are essentially adding -3 to itself 10 times.This operation may seem straightforward, but when negative numbers are involved, it can cause some confusion. However, the rules remain consistent. For example, if you have a positive number multiplied by a negative number, the result will always be negative, which helps explain why \(10(-3)= -30\). It's essential to understand this fundamental operation, as multiplication is a building block for more complex concepts in mathematics, including algebra.

Algebraic properties are the rules that apply to numbers and operations, allowing us to manipulate expressions and equations consistently. One such property is the Commutative Property of Multiplication, which we are focusing on in our exercise.

Commutative Property of Multiplication

This property states that changing the order of the numbers we are multiplying does not change the product. In other words, \(a * b = b * a\). This property can be extremely useful when simplifying algebraic expressions or solving equations, as it allows for flexibility in how we approach a problem. There are other algebraic properties such as the Associative Property and the Distributive Property, and understanding these properties will enhance your ability to work with and understand algebraic expressions and equations.

When solving mathematical expressions, it is important to follow the Order of Operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This set of rules tells us the sequence in which we should solve parts of an expression to obtain the correct answer.In the context of our problem involving \(10(-3)\), we focus particularly on the multiplication aspect. However, if this multiplication were part of a larger expression, we would need to determine where it fits into the Order of Operations to solve the expression correctly. The Order of Operations is fundamental in ensuring that everyone can arrive at the same correct answer when solving the same mathematical problem.