Problem 12 - Algebra 1

Question

Evaluate the expression. $$|-12|$$

Step-by-Step Solution

Answer

The absolute value of -12 is 12.

Step 1: Understand the concept of Absolute Value

The absolute value of a number is its distance from 0 on the number line. It is denoted as \( |a| \), where 'a' is a real number. The absolute value is always positive or zero, even if 'a' is negative.

Step 2: Apply the Absolute Value

Applying the absolute value to \( |-12| \), the '-' (minus) sign is removed, and the result is positive 12.

Key Concepts

Number Line

The number line is a visual representation of numbers laid out in a straight line. Think of it as a ruler, but instead of inches or centimeters, it marks numbers. Every point on the line corresponds to a real number, with zero typically at the center.

• Numbers to the right of zero are positive.
• Numbers to the left are negative.

The number line helps us understand numerical concepts like absolute value by providing a clear picture of the distance and direction between numbers.

Real Numbers

Real numbers include all the numbers that you can think of on the number line. From extreme negative numbers to extreme positives, including zero, decimals, fractions, and even irrational numbers like π. Real numbers are incredibly vital in mathematics, as they form the building blocks for more complex concepts.

• They are infinite in both positive and negative directions.
• Real numbers encompass rational and irrational numbers.

Understanding real numbers helps in grasping the concept of absolute value, which is defined for any real number.

Positive Number

A positive number is any number greater than zero. It's located to the right of zero on the number line. Positive numbers represent quantities like height, money, or time that are more than nothing.

• They don't carry a negative sign.
• Examples include 1, 2.5, and 100.

When we take the absolute value of a number, the result is always a positive number, representing the magnitudes or sizes of values without considering direction.

Distance from Zero

Distance from zero measures how far a number is from the central point of zero on the number line. This concept is crucial in understanding absolute value.

• The absolute value of a number is its distance from zero.
• This distance is always expressed as a non-negative number.

For example, the absolute value of -12 is 12, because 12 is the distance between -12 and 0 on the number line.