Problem 94 - Prealgebra and Introductory Algebra

Question

Evaluate. -|-81|

Step-by-Step Solution

Answer

The result is 81.

Step 1: Determine the Absolute Value of -81

Firstly, determine the absolute value of -81. By the definition, it's the distance from 0 on the number line, which is simply 81. So, |-81| = 81.

Step 2: Take the Absolute Value of the Result

Next, since there is another absolute value sign remaining, take the absolute value of 81. As |81| = 81.

Key Concepts

Understanding the Number Line

The number line is a visual tool used to help us understand numbers and their relationships. Imagine a horizontal line marked with numbers at equal distances. Zero is at the center, positive numbers extend to the right, and negative numbers stretch to the left.

• Zero divides positive and negative numbers.
• Each step to the right increases the value, while each step to the left decreases it.

Visualizing numbers on a number line can make it easier for you to grasp concepts like absolute value and integer operations.

Exploring Distance From Zero

Distance from zero is another way to think about absolute value. This concept involves measuring how far a number is from zero on the number line.

• For a positive number, the distance from zero is simply the number itself.
• For a negative number, it's the positive counterpart of that number.

For instance, the absolute value of -81 is 81. It's 81 steps away from zero, regardless of direction.

Evaluating Expressions with Absolute Values

When evaluating expressions, absolute values act as a mathematical tool to measure distance. An absolute value \(|x|\) represents the non-negative value of \(-x\) or \(+x\).
When you see an expression like \(|-81|\), it means you're measuring 81 units away from zero. Absolute value bars can appear multiple times, and solving them step-by-step is crucial.
Always replace the expression inside the absolute value with its non-negative equivalent.

Mastering Integer Operations

Integer operations are the basic arithmetic activities involving whole numbers, including addition, subtraction, multiplication, and division.

• Addition and subtraction involve moving left or right on the number line.
• Multiplication and division deal with scaling numbers.

In problems like evaluating \(|-81|\), understanding how integers relate to each other simplifies the task. Remember that absolute values transform any negative integer into its positive form.