Problem 65 - Prealgebra

Question

Simplify each of the following. $$-(-8)$$

Step-by-Step Solution

Answer

The simplified expression of \(-(-8)\) is 8.

Step 1: Identify the Expression

The expression given is \(-(-8)\).It involves a double negative sign.

Step 2: Simplify the Double Negative

When you have a negative sign directly acting on another negative sign, it results in a positive. Simplify \(-(-8)\) by removing both negatives: \(-(-8) = 8\).

Key Concepts

Understanding Double Negatives

A double negative is a mathematical concept where two negative signs appear in succession. In mathematics, a negative sign can be thought of as undoing or reversing the direction of a number on the number line. So, what happens when we have two negative signs?

• The first negative sign flips the number to its opposite.
• The second negative sign flips it back.

In the expression \(-(-8)\), the first negative flips the number 8, making it negative: -8. The second negative sign placed in front flips it back to positive: 8. This is analogous to turning your socks inside out and then right side out again; you're left with the original condition.

By understanding double negatives, you become more comfortable with simplifying expressions that might initially seem confusing but are, in fact, straightforward.

Basics of Number Operations

Number operations form the foundation of mathematics and include addition, subtraction, multiplication, and division. Handling these efficiently is crucial for tackling any mathematical problem, especially in topics like prealgebra.

• Addition: This operation combines numbers, often visualized as moving right on the number line.
• Subtraction: This is like addition's opposite, moving left on the number line.
• Multiplication: Think of it as repeated addition. It's a faster way to add a number to itself many times.
• Division: This breaks a number into a specified number of equal parts, the opposite of multiplication.

Simplifying expressions often involves one or more of these basic operations. In our example, by identifying the double negative, we used the understanding of subtraction to simplify \(-(-8)\) to 8, employing a mental operation similar to two subtractions effectively becoming an addition.

Understanding Prealgebra Concepts

Prealgebra is the stepping stone from arithmetic into algebra. It involves understanding properties and operations that prepare students for solving equations and working with variables. Key concepts include:

• Understanding Expressions: An expression is a combination of numbers and operations without an equality sign.
• Properties of Numbers: This includes concepts like even and odd numbers, prime numbers, and understanding integers (positive and negative whole numbers).
• Simplification Strategies: Learning how to simplify expressions, such as identifying and resolving double negatives or combining like terms.

Prealgebra introduces these concepts to foster mathematical thinking by teaching students how to see the relationships between numbers and how they can be transformed through different operations. This skill is crucial as it leads to solving equations, manipulating variables, and understanding functions in more advanced mathematics.