Problem 76 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. \(-|6.8|\)

Step-by-Step Solution

Answer

\(-|6.8| = -6.8\)

Step 1: Evaluate the absolute value

The absolute value of any number whether it is positive or negative is a positive number. So, the absolute value of 6.8 is \(|6.8| = 6.8\).

Step 2: Apply the negation

The original problem is to evaluate \(-|6.8|\), and we found in step 1 that \(|6.8| = 6.8\). Substituting this value into the expression gives us \(-6.8\).

Key Concepts

Understanding Negative Numbers

Negative numbers are an important concept in math, representing values below zero.
They are often represented with a minus sign (e.g., \(-3\)) to distinguish them from positive numbers.
A negative number can be thought of as the opposite of a positive number.
In mathematics, negative numbers are used to describe a loss, decrease, or deficit.
For example, if you owe someone money, you can represent that debt as a negative number.
Here are some quick points about negative numbers:

• They are used in temperatures, sea levels, finance, and more.
• When combined with positive numbers, they can represent a change in amount.
• Subtracting a negative number is the same as adding its positive value.

Steps to Evaluate an Expression

Evaluating an expression in math involves simplifying it to find its value.
This process requires understanding each component of the expression, such as operations and numbers.
For example, in the expression \(-|6.8|\) the goal is to reduce it to a single number:
- **Step 1**: Look for any absolute value bars.
Absolute value is the distance of a number from zero, and it is always positive.
Hence, in this example, \(|6.8| = 6.8\).
- **Step 2**: Apply any other operations like negation.
In this case, we put a negative sign in front of the absolute value, resulting in \(-6.8\).
By following these steps, we simplify expressions and solve math problems effectively.

Effective Math Problem Solving Techniques

Solving math problems requires a mix of logic, arithmetic skills, and sometimes a bit of creativity.
Here are some strategies to enhance your problem-solving skills:

• **Understand the problem**: Take time to fully read and interpret what the problem is asking.
  Identify important information and what you need to find.
• **Break it down**: Divide the problem into smaller, more manageable parts.
  Address each part step-by-step.
• **Check your work**: After solving, reassess your steps and ensure your final answer makes sense.
  Look for possible errors and correct them.

By improving your ability to solve math problems, you build confidence and increase your mathematical understanding.
Practice is crucial, so regularly work on various problems to strengthen your skills.