Question

Simplify. $$|-2004|$$

Short answer

Answer: The absolute value of -2004 is 2004.

Step-by-step solution

Understanding absolute value

The absolute value of a number is the numerical value without considering its sign. In other words, if the number is negative, we simply change its sign to positive.

Find the absolute value of -2004

Since -2004 is a negative number, to find its absolute value, we change its sign to positive. Therefore, the absolute value of -2004 is: $$|-2004| = 2004$$

Key concepts

Simplifying Numerical Expressions

When we come across numerical expressions, it's important to know how to simplify them to make them easier to work with. Simplifying can involve various operations like addition, subtraction, multiplication, division, and finding the absolute value of numbers. Specifically, the process of simplifying can help us find the most basic form of the expression, which is essential in mathematics for solving problems accurately and efficiently.

In the context of the given exercise, simplifying means finding the absolute value of a given number. It's a straightforward process because it involves only one step: removing the sign of the number to make it a positive value if it's not already, which aligns with the definition of absolute value. Thus, simplifying the expression \(|-2004|\) results in 2004, which is the number's absolute value.

Numerical Value

Understanding the concept of numerical value is fundamental in mathematics. It refers to the actual quantity represented by a figure, irrespective of the sign attached to it. This concept becomes particularly important when dealing with absolute values, as it requires us to focus on the magnitude of a number and not its direction (positive or negative).

For instance, whether you have \(-2004\) or \(2004\), the numerical value is 2004. The absolute value symbol, denoted as \(|\text{ }|\text{ }|\text{ }|\), is a way to extract this numerical value. Whenever you come across this symbol, remember that you are looking for how large the number is without regard to its sign. Therefore, an expression like \(|-2004|\) simplifies to 2004 because we are only concerned with the number's size.

Positive and Negative Numbers

The rules of positive and negative numbers are vital for understanding the number line, operations, and the concept of absolute value. A positive number is any number greater than zero, without any sign or with a plus sign in front of it. Conversely, a negative number is any number less than zero, indicated by a minus sign in front of it.

Positive numbers represent quantities or values that we can consider being 'added' to something, such as money earned or temperature going above zero. Negative numbers, on the other hand, often represent a loss, debt, or a decrease in quantity, like money spent or temperature below zero.

When simplifying numerical expressions involving absolute values, understanding that the absolute value of both positive and negative numbers is positive is essential. For example, both \(|-2004|\) and \(|2004|\) result in 2004 since the absolute value function only measures the 'distance' of the number from zero, disregarding its direction on the number line.