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Chapter 3: Problem 378

In the following exercises, simplify. $$ -|-75| $$

Short Answer

Expert verified
-75

Step by step solution

01

Identify the Absolute Value

The absolute value of a number is the distance from zero without considering direction. Here, we need to find the absolute value of -75.
02

Calculate the Absolute Value

The absolute value of -75 is 75. So, \[ |-75| = 75 \]
03

Apply the Negative Sign

After calculating the absolute value, apply the negative sign as required by the problem statement. Thus, \[ -|-75| = -75 \]

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Key Concepts

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

absolute value
The absolute value of a number represents its distance from zero on the number line, regardless of the direction. It is denoted by two vertical bars around the number, like \(|-75|\). For any number, whether positive or negative, the absolute value is always non-negative.
For example:
  • The absolute value of 75 is 75, written as \(|75| = 75|\).
  • The absolute value of -75 is also 75, written as \(|-75| = 75|\).
Understanding absolute value is crucial because it transforms negative numbers into positive ones. Therefore, in our problem, \(|-75| = 75|\). This step is essential before applying any additional operations or negative signs associated with the problem.
negative sign
In mathematics, the negative sign indicates a value less than zero. It is represented by a minus sign (-) in front of a number. Incorporating negative signs correctly in calculations is key to mastering mathematical operations.
For example:
  • -5 is negative five, indicating a position five units to the left of zero on the number line.
  • In expressions, -|...| signifies that the result of the absolute value function should retain its negative sign.
In our problem, after simplifying the absolute value of -75 to 75, the negative sign outside the absolute value bars then makes it -75. This shows the importance of sequence and attention to detail in math operations.
prealgebra
Prealgebra lays the foundation for understanding algebra by dealing with basic arithmetic like addition, subtraction, multiplication, and division. It introduces students to more complex concepts such as absolute values and negative numbers.
Key topics in prealgebra include:
  • Understanding integers and their operations, including positive and negative values.
  • Order of operations to determine the correct sequence of calculations.
  • Basic properties of numbers, such as the distributive property.
Simplifying expressions like \(-|-75|\) helps students strengthen their comprehension of these foundational concepts. Here, students learn to methodically approach problems by first resolving the absolute value and then applying the negative sign to reach the final simplified expression.

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