Problem 15 - Algebra 1

Question

Evaluate the expression. $$|-103|$$

Step-by-Step Solution

Answer

The absolute value of |-103| is 103

Step 1: Understand absolute value

The absolute value of a number is its distance from 0 on a number line. It is always positive or zero.

Step 2: Evaluate the expression

The absolute value removes any negative sign, so the absolute value of \(-103\) is \(103\).

Key Concepts

Number Line

Imagine the number line as a long, straight line similar to a ruler. It's useful for visualizing and understanding numbers and their relationships. In the center of the number line is 0, which is the point of origin. To the right, numbers become larger and positive, like 1, 2, and 3. To the left, numbers become smaller and are negative, like -1, -2, and -3.
A number line helps in understanding the concept of distance. Distance is how far away one number is from another – and it’s always a positive quantity. When we talk about absolute value, we focus on distance, not direction. The absolute value of a number is simply how far that number is from 0 on the number line, without considering which side of 0 it is on. For instance, the number -103 is 103 units away from 0, and thus its absolute value is 103.

Evaluate Expression

Evaluating an expression means finding its numerical value. When it comes to absolute values, evaluating involves removing any negative signs to find the distance from 0. Consider the expression \(|-103|\). Here, the vertical bars around -103 denote "absolute value." To evaluate this, simply remove the negative sign from -103.
Doing this results in 103. The reason is simple: absolute value focuses on distance, disregarding any negative or positive sign. This is why the absolute value of \(-103\) evaluates to \(103\). In summary, to evaluate an absolute value expression:

• Ignore the negative sign, if any.
• Read off the positive value.

Positive Numbers

Positive numbers are all the numbers greater than zero. They are found to the right of zero on the number line. These numbers include 1, 2, 3, and so on. Unlike negative numbers, positive numbers have no negative sign.
In mathematics, positive numbers often represent quantities such as counts, measurements, or distances. Because the absolute value of a number is always positive, it transforms any negative number into its positive counterpart.
To clarify:

• Positive numbers themselves remain unchanged in absolute value expressions since they are already positive.
• Negative numbers, when taking their absolute value, become positive as they reflect distance from zero.

Therefore, while evaluating expressions involving absolute values, each result will always be a positive number or, in some cases, zero.