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Chapter 1: Problem 80

Find each absolute value. SEE EXAMPLE 7. (OBJECTIVE 4). $$|18-12|$$

Short Answer

Expert verified
The absolute value of \(|18-12|\) is 6

Step by step solution

01

Understanding Absolute Value

The absolute value |x| of a number x is its distance from 0 on the number line. It is defined as x if x is greater than or equal to 0, and -x if x is less than 0.
02

Perform Subtraction

Calculate the value inside the absolute function. In this case, \(18-12 = 6\).
03

Calculate Absolute Value

Next, find the absolute value of 6, which is just 6, because 6 is a positive number.

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Key Concepts

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

Subtraction
Subtraction is the mathematical operation of finding the difference between two numbers. Imagine you have 18 apples, and you give 12 away, you are left with 6 apples. This is how subtraction works in a nutshell. For the exercise, \(18 - 12\) means you start at 18 on the number line and move 12 steps down. You're essentially counting backwards. Subtraction can often help you find differences or compare how much larger one number is than another.
  • The first number (minuend) is what you start with, in this case, 18.
  • The second number (subtrahend) is what you are taking away, here it's 12.
  • The result of subtraction is called the difference, and it is 6 in this example.
When you perform subtraction, it's all about finding what remains after taking something away. Remember, if you reverse the order of subtraction (like 12 - 18), you could end up with a negative number.
Number Line
A number line is a straight line with numbers placed at equal intervals along its length. It's an essential tool for visualizing math operations, especially addition and subtraction. When you work with subtraction or absolute value, using a number line can make things clearer.
Imagine the number line as a ruler stretched out with 0 in the middle. Positive numbers go to the right, while negative numbers extend to the left.
  • If you start from 18 and move 12 steps towards the left, you land on 6.
  • This visual process aids in understanding how subtracting results in a smaller number further left on the line.
Using a number line helps make abstract math concepts more concrete, turning numbers into visual moves that you can follow step by step.
When needing to find an absolute value, it's about focusing on how far a number is from zero on this line.
Distance from Zero
"Distance from zero" is a way to understand absolute value. It's the idea of measuring how far away a number is from zero on the number line, regardless of direction. Absolute value removes any negative sign, because distance can't be negative.
  • For example, both 6 and -6 have an absolute value of 6 because both are 6 units away from zero.
  • Absolute value is represented with two vertical bars like this: \(|x|\).
When calculating \(|18-12|\), first solve the expression inside the bars: 18 minus 12 equals 6. Then, consider the distance of 6 from zero, which is simply 6.
This means distance from zero focuses purely on how many steps away from zero a number is without considering direction (positive or negative). Thus, absolute value can be thought of as the 'positive side' of any number when measuring its proximity to zero.

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