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Chapter 1: Problem 82

Find each absolute value. SEE EXAMPLE 7. (OBJECTIVE 4). $$|12-4|$$

Short Answer

Expert verified
The absolute value of \(12-4\) is 8.

Step by step solution

01

Perform the Subtraction

The priority within the absolute value brackets is to subtract 4 from 12 which gives 8.
02

Calculate the Absolute Value

The absolute value of any positive number remains the same. Therefore, the absolute value of 8 is 8.

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Key Concepts

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

Subtraction in Absolute Value
Understanding subtraction within the context of absolute value is crucial for solving these kinds of problems accurately. When faced with an expression like \(| 12 - 4 |\), your first step should be to perform the subtraction inside the absolute value bars.
This is because the absolute value function fundamentally depends on evaluating the expression within it first, before considering its magnitude.
  • Identify the numbers that are being subtracted: in this case 12 and 4.
  • Perform the subtraction: calculate 12 minus 4, which equals 8.
After successfully subtracting, you move to interpret the result in terms of absolute value. This method simplifies the process and avoids confusion, ensuring you handle these types of numbers correctly every time.
Understanding Positive Numbers
Positive numbers are the values greater than zero on a number line. In the context of absolute value, these numbers have a consistently simple and predictable absolute value.
The absolute value of a positive number is essentially the same as the number itself. Let's continue with our example \(| 12 - 4 | = | 8 |\). Here鈥檚 how positive numbers work in this situation:
  • Once the subtraction is performed, the result is positive: 8.
  • The absolute value of 8 is simply 8, because it's a positive number.
This is a straightforward property of positive numbers and is one of the reasons they are often easy to work with in mathematics. This consistency makes a strong foundation for learning more advanced math concepts later on.
Mathematics Education and Absolute Value
When learning mathematics, especially at foundational levels, tackling absolute values can often be an important step. Understanding the absolute value concept enhances problem-solving skills in a wide range of mathematical contexts.
Here鈥檚 how focusing on mathematical education activities like absolute values can be beneficial:
  • Helps clarify the notion of distance and magnitude, enhancing spatial reasoning.
  • Supports arithmetic skills, especially in operations such as subtraction.
  • Prepares students for algebraic manipulation, giving them confidence to deal with more complex expressions.
For students, the journey from basic subtraction to grasping the absolute values is key to understanding mathematics more deeply. Teachers and educational materials prioritize this understanding because of its broad applications across all math-related disciplines.

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