Problem 48 - Prealgebra

Question

Find each of the following absolute values. $$|9|$$

Step-by-Step Solution

Answer

|9| = 9

Step 1: Understand Absolute Value

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

Step 2: Apply Absolute Value to Positive Number

Since the given number is 9, which is positive, the absolute value of 9 is simply 9 itself, because it is already a non-negative number.

Step 3: Conclusion

The absolute value of 9 is the same as the number itself because it is positive and these values are never negative.

Key Concepts

number line

The number line is a visual representation of numbers laid out in order on a straight line. Imagine it as a ruler where each point corresponds to a number. Zero is typically at the center.
Numbers to the right of zero are positive, and numbers to the left are negative. This layout helps us understand absolute value, which refers to how far a number is from zero on this line, without considering its direction.
Using a number line, you can visually see that the distance from zero is always a non-negative number.

• Zero sits at the center, representing a starting point for both directions.
• Each step to the right increases the value by 1.
• Each step to the left decreases the value by 1.

This straight line helps in easy comprehension of concepts such as distance and magnitude of numbers.

non-negative numbers

Non-negative numbers include all positive numbers and zero. These numbers are essential when discussing absolute value, which is always non-negative. Absolute value is essentially a measure of distance on the number line from zero.
For any given number on the number line, its absolute value is how far away it is from zero, ensuring a non-negative result.

• Zero is considered non-negative since it is neither positive nor negative.
• Any number that is positive or zero falls into this non-negative category.

Understanding non-negative numbers prepares you to grasp the concept of absolute values effectively, seeing them as simply the numeral's magnitude.

positive numbers

Positive numbers are all numbers greater than zero. On the number line, they appear to the right of zero, representing values that increase as they move farther from zero. This knowledge is crucial for calculating absolute values.
When a number is positive, like the given number 9, its absolute value remains the same, as the absolute value measures only the distance from zero.

• They are always greater than zero.
• These numbers are often encountered first when learning about the number line and distances.

Comprehending positive numbers as a foundational aspect aids in identifying other types of numbers and further comprehending how the number line operates, especially when calculating the absolute value.