Problem 12 - Elementary Algebra

Question

Simplify. $$ (-23) 2 $$

Step-by-Step Solution

Answer

The simplified form is -46.

Step 1: Understand the operation

In this exercise, we are asked to multiply two numbers, (-23) and 2. Multiplication involves adding a number multiple times based on the other number. Here, we'll add -23 two times.

Step 2: Multiply the numbers

Multiply -23 by 2 directly:\[(-23) \times 2 = -46\]

Step 3: Verify the sign of the result

When multiplying a negative number with a positive number, the result is negative. Since -23 is negative and 2 is positive, the result is correctly negative.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. They are usually found to the left of zero on a number line. These numbers are used to represent situations like debts, temperatures below zero, or any kind of deficit.

When dealing with operations involving negative numbers, it’s crucial to keep track of their signs:

• A negative number times a positive number always results in a negative number.
• Negative numbers multiplied together, such as (-2) imes (-3), result in a positive number because the negatives cancel each other out.
• Adding and subtracting negative numbers require careful attention to their values and signs.

Understanding these rules helps in problem-solving and simplifies algebraic expressions.

Integer Operations Made Easy

Integer operations include addition, subtraction, multiplication, and division of whole numbers. These operations extend to both positive and negative numbers.

When multiplying integers like (-23) and 2:

• Determine the product of the absolute values: 23 times 2 equals 46.
• Consider the rules of signs: A negative number times a positive gives a negative result, so (-23) imes 2 = -46.

This understanding is also crucial for division and other complex mathematical processes, ensuring accurate results through consistent application of integer rules.

Algebra Basics: Multiplication Involving Signs

In algebra, multiplication with signs (positive or negative) plays a foundational role. It is important to follow the rules of signs to ensure consistency and accuracy.

When performing multiplication in algebra:

• A positive times a positive yields a positive product.
• A negative times a negative also yields a positive product.
• A positive and a negative together result in a negative product.

By mastering these basics, algebra students can simplify expressions, solve equations, and tackle more advanced topics with confidence. This knowledge forms the groundwork for exploring deeper algebra concepts and solving problems across various mathematical domains.