Question

Simplify. $$|12|$$

Short answer

Solution: The absolute value of 12 is denoted as |12|. Since 12 is a positive number, its absolute value is the number itself. Therefore, |12| = 12.

Step-by-step solution

Identify the Number Inside the Absolute Value Sign

In this exercise, the number inside the absolute value sign is 12.

Determine if the Number is Positive, Negative, or Zero

The number 12 is a positive number, as it is greater than 0.

Calculate the Absolute Value

Since 12 is a positive number, its absolute value is the number itself. Therefore, the absolute value of 12 is: $$|12| = 12$$

Key concepts

Solving Absolute Value

Understanding the concept of absolute value is foundational to grasping key prealgebra concepts. The absolute value of a number is the distance of that number from zero on a number line, regardless of direction. So it is always a positive value or zero. To solve an absolute value problem, like \( |12| \), the first step is to look at the number inside the absolute value sign.

For instance, with \( |12| \), we see that the number inside is 12. Then, determine if this number is positive, negative, or zero. Since 12 is a positive number, the absolute value is simply the number itself, which in this case is 12. The general rule is: if the number is positive or zero, the absolute value is the same number; if it’s negative, the absolute value is the number without the negative sign.

Positive Numbers

Positive numbers are those that are greater than zero. They can be found to the right of zero on the number line and signify quantities that exist or are gained. In the context of absolute values, if the number inside the absolute value sign is positive, it remains unchanged because it’s already a distance from zero. A number’s positivity is associated with concepts like profit, height above sea level, and deposits in a bank account in real-world applications. For example, in our exercise \( |12| \), the number 12 is positive. Therefore, its absolute value does not change and remains 12.

Prealgebra Concepts

Grasping prealgebra concepts is essential for building a solid foundation in mathematics. Prealgebra introduces students to basic algebraic thinking, often starting with understanding numbers, their properties, and operations that can be performed on them, including the concept of absolute value. This preparatory stage involves working with variables, simple equations, and inequalities. It also involves understanding how to evaluate expressions with absolute values - an understanding that simplifies more complex algebraic expressions. Apart from solving for absolute value, other prealgebra concepts include operations with integers, fractions, decimals, and the use of mathematical properties to simplify expressions. Recognizing and building upon these skills are vital for success in more advanced mathematics courses.