Question

Evaluate the expression. $$|-4.5|$$

Short answer

The absolute value of -4.5 is 4.5

Step-by-step solution

Understand Absolute Value Concept

An absolute value, represented as \(|x|\), of a number refers to its distance from zero on the number line. Regardless of whether the number is positive or negative, the absolute value is always positive.

Evaluate the Absolute Value

Looking at the problem, evaluate the absolute value of -4.5 to be 4.5.

Key concepts

Evaluate Expressions

The skill of evaluating expressions involves working out the value of a mathematical phrase using various operations such as addition, subtraction, multiplication, division, or as in this case, finding the absolute value. To evaluate the expression \(|-4.5|\), a student simply needs to determine the value of the expression inside the absolute value bars without considering its sign.

Understanding how to handle negative numbers is crucial here. Students must remember that the absolute value symbol transforms any negative number within it to its positive counterpart. The procedure can be likened to asking how far the number is from zero, and in this instance, \(|-4.5| = 4.5\) because -4.5 is 4.5 units away from zero on the number line. By practicing evaluating expressions with absolute values, students become more proficient in dealing with complex algebraic expressions later on.

Number Line

A number line is a visual representation of numbers arranged in order from smallest to largest, left to right. It is an essential tool in understanding the concept of absolute value as it clearly shows the distance of a number from zero. The number line stretches infinitely in both directions, with positive numbers placed to the right of the zero and negative numbers to the left.

In the given exercise, plotting -4.5 on the number line would show that it is 4.5 units to the left of zero. By visualizing the number's position, it becomes easier to comprehend that the absolute value of -4.5 is indeed 4.5 because no matter which side of zero the number lies on, the distance remains the same.

Positive and Negative Numbers

The concept of positive and negative numbers is foundational in mathematics. Positive numbers are those greater than zero and are often used to represent quantities of objects or distances in the forward direction. Negative numbers, which are less than zero, can represent the opposite, such as debt or movement in the reverse direction.

When working with absolute values, the sign of a number is disregarded, as it is the magnitude that is of interest. This is exemplified by the exercise \(|-4.5|\), where -4.5, though negative, has an absolute value of 4.5. It is important to note that while the absolute value deals with magnitude only, in other contexts, the sign of a number carries significant meaning related to the direction or nature of the value it represents.