Problem 38 - Fundamentals of Mathematics

Question

Determine each value. $$ |16| $$

Step-by-Step Solution

Answer

The absolute value of 16 is 16.

Step 1: Understanding Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Step 2: Apply Absolute Value Definition

Apply the definition of absolute value to the number 16. Since 16 is already a positive number, its absolute value is simply 16.

Key Concepts

Number Line

The number line is a visual representation of numbers placed on a straight line. Think of it like a ruler that stretches infinitely in both directions. The numbers increase to the right and decrease to the left. - Zero sits in the middle, creating a natural division between the positive numbers on the right and the negative numbers on the left. - Each point on this line represents a number, and this helps in visualizing concepts like absolute values and distances. Using the number line is a powerful way to understand numbers and their relationships with one another. You can see where numbers are located in relation to zero, which is key when talking about absolute values.

Non-Negative

The term 'non-negative' refers to any number that is either zero or greater. Simply put, all positive numbers and zero fall under this category. Here are some things to keep in mind:

• Zero itself is non-negative.
• All positive numbers are non-negative, as they are greater than zero.
• Non-negative numbers are crucial in absolute value calculations because absolute values can never be negative.

Remembering this will help to simplify many math problems, especially those involving distances and magnitudes.

Positive Number

A positive number is any number that is greater than zero. These numbers are found to the right of zero on the number line. When you think about positive numbers, consider these characteristics:

• Positive numbers do not include zero—only numbers greater than zero qualify.
• They represent quantities that are more, greater, or higher.
• In problems involving absolute value, if a number is positive, its absolute value is the number itself.

Positive numbers are everywhere and are essential in assessing quantities, distances, and calculations.

Distance from Zero

One of the key concepts in understanding absolute value is the measure of 'distance from zero.' Absolute value tells us how far a number is from zero on the number line. Some important points include:

• Distance is always non-negative, meaning it cannot be less than zero.
• For any number, whether positive or negative, its distance from zero is shown as a positive figure.
• Absolute values, hence the term 'distance from zero,' is essential in mathematical calculations as they provide clarity on magnitude regardless of direction.

Calculating distance from zero helps us in real-life scenarios, where knowing the magnitude is essential, not the direction.