Problem 14 - Elementary Algebra

Question

Simplify the following problems. $$ (-5)(2) $$

Step-by-Step Solution

Answer

Question: Simplify the expression \((-5)(2)\). Answer: -10

Step 1: Identify the numbers to be multiplied

We are given the expression \((-5)(2)\). The two numbers to be multiplied are -5 and 2.

Step 2: Multiply the numbers

Now we will multiply the two numbers together: \((-5)(2) = -10\). Since a negative number multiplied by a positive number results in a negative number, the answer is -10.

Step 3: Write the final answer

The simplified expression for \((-5)(2)\) is -10.

Key Concepts

Understanding Negative Numbers

Negative numbers are those less than zero, often represented with a minus sign in front. They are crucial when dealing with a variety of mathematical concepts, especially in operations like multiplication.

When multiplying negative numbers, remember these simple rules:

• A negative number multiplied by a positive number results in a negative product.
• A negative number multiplied by another negative number results in a positive product.
• A negative number multiplied by zero results in zero.

These rules help maintain consistency in value when performing algebraic operations. In the exercise \((-5)(2)\), we multiplied a negative number with a positive, resulting in \(-10\). Hence, understanding these rules is key to simplifying expressions correctly.

Simplification Process

Simplification in mathematics involves making an expression as straightforward as possible. For multiplication, it means breaking down the problem to its most basic terms and arriving swiftly at the answer.

Here's how simplification works in this context:

• Identify the numbers or variables involved in the operation.
• Understand their relationships (e.g., negative and positive interactions).
• Apply the simple arithmetic operations: multiplication rules, addition, etc., while respecting algebraic principles.

When we were tasked to solve \((-5)(2)\), we simplified it to \(-10\). We kept it simple by applying the rule that a negative times a positive yields a negative result.

Algebra and Its Fundamentals

Algebra forms the backbone of many complicated mathematical computations. Understanding basic algebraic principles is crucial for solving problems like the one provided. It involves using symbols (usually letters) to represent numbers in equations and expressions.

With algebra:

• We use variables to symbolize unknown values or numbers.
• You can formulate expressions that represent real-world problems.
• Rules such as the order of operations ensure we simplify expressions correctly.

In the case of multiplying \((-5)(2)\), even though it does not explicitly involve variables, the operation still relies on algebraic principles to simplify the expression. Mastering these fundamentals will aid you in seamlessly dealing with more complex algebraic expressions.