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Chapter 2: Problem 37

Simplify. $$ |-55| $$

Short Answer

Expert verified
The simplified expression is 55.

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.
02

Identify the Number Inside the Absolute Value

The expression given is \(|-55|\). The number inside the absolute value is -55.
03

Apply Absolute Value Definition

Since absolute value measures distance from zero, the absolute value of -55 is 55, because it is 55 units away from zero.
04

Simplify the Expression

Based on the previous steps, \(|-55|\) simplifies directly to 55.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions
Simplifying expressions is one of the fundamental processes in algebra that helps us rewrite expressions in a more manageable or comprehensible form. When simplifying, the goal is to reduce the number of operations, making the equation easier to work with. This often involves applying basic arithmetic principles and understanding specific functions, like absolute value.
  • Consider the operations involved: Here, we want to simplify \(|-55|\).
  • Apply properties of operations: Understanding that absolute value strips away any negative sign influences how we resolve expressions like \(|-55|\).
By simplifying expressions accurately, we increase our efficiency in problem-solving, making complicated problems digestible and solvable.
Number Line
A number line is a visual representation of numbers - arranged in order on a straight line. This tool is remarkably useful when demonstrating arithmetic concepts like addition, subtraction, or identifying the absolute value of a number.
  • Starts from any number, but typically it begins at zero.
  • Numbers to the right are positive; numbers to the left are negative.
When we talk about absolute value, we refer to how far a specific number is from zero, regardless of direction. Visualizing this on a number line clarifies concepts by providing an immediate, concrete image of the distance being calculated. This makes understanding absolute value both intuitive and straightforward.
Distance from Zero
Distance from zero is at the heart of understanding absolute value. Absolute value, represented by vertical bars as in \(|-55|\), measures just how far a number lies from zero, disregarding its direction on a number line.
  • The distance is always non-negative.
  • For \(-55\), you consider the distance without the minus sign; hence, the distance is \55\.
This concept reinforces why the absolute value of any real number is never negative. It's purely about measuring space or separation from zero, which is an inherently positive quantity. Understanding this principle allows us to simplify problems that involve absolute value easily and confidently.

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