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The Distributive Property is a fundamental tool in algebra that helps to simplify expressions, particularly when dealing with parentheses. It states that for any numbers a, b, and c, the expression \(a(b + c)\) is the same as \(ab + ac\).
In our exercise, we used the Distributive Property to handle \( -5(-3)\). Here's a step-by-step breakdown:
- We took the multiplication \(-5(-3)\).
- According to the Distributive Property, when multiplying two negative numbers, the result is positive. Thus, \(-5(-3) = 15\).
This step helps eliminate the complexity of dealing with parentheses and prepares the equation for further simplification. Applying the Distributive Property correctly makes it easier to solve equations and understand algebraic expressions.

The Order of Operations is a rule to ensure that expressions are simplified in a consistent manner. This rule is often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In our exercise, we followed these steps:
- First, handled the multiplication inside the parentheses \(-5(-3) = 15\).
- After that, we replaced the multiplication result back into the original expression, which gave us \(19 + 15 + 3\).
- Then, we sequentially added the remaining numbers. First, adding \(19 + 15 = 34\), and finally \(34 + 3 = 37\).
Following the Order of Operations helps to avoid confusion and ensures everyone gets the same result for the same expression.

Basic Arithmetic is the foundation of all math. It involves operations like addition, subtraction, multiplication, and division. In the given problem, we used basic arithmetic to simplify the expression step by step.
After applying the Distributive Property and the Order of Operations, we are left with a simple addition problem: \(19 + 15 + 3\).
Here are the steps we followed:
- First, we added \(19 + 15\) to get \(34\).
- Then, added \(34 + 3\) to get \(37\).
This demonstrates how basic arithmetic operations play a crucial role in more complex algebraic processes. Understanding these basic operations is essential for tackling higher-level math problems efficiently.