Question

Simplify. $$|97|$$

Short answer

Answer: The absolute value of 97 is 97.

Step-by-step solution

Definition of Absolute Value

The absolute value of a number is the non-negative value of the number without regard to its sign. It is denoted by two vertical bars surrounding the number, like |x|. Mathematically, the absolute value function can be defined as: |x| = { x, if x ≥ 0 -x, if x < 0 } Now let's apply this definition to the given exercise.

Absolute Value of 97

To find the absolute value of 97, we will follow the rules from the definition we provided above: Since 97 is a positive number (97 > 0), we don't need to change its sign. Therefore, |97| = 97. This completes the exercise and gives the final result: |97| = 97

Key concepts

Prealgebra and Its Basics

Prealgebra is a fundamental part of mathematics that lays the groundwork for algebra. It helps students understand the basic arithmetic concepts and prepares them for more complex subjects. In prealgebra, students learn about integers, fractions, decimals, and properties of numbers like the absolute value.

• Prealgebra emphasizes the importance of arithmetic operations such as addition, subtraction, multiplication, and division.
• It introduces the concept of variables, which are symbols that stand for unknown values.
• Understanding the properties of numbers, including the absolute value, is crucial in building a strong prealgebra foundation.

Grasping these concepts ensures students are better equipped to tackle algebraic problems with confidence.

Understanding the Number Line

The number line is a visual representation of numbers in a straight line, where each point corresponds to a real number. It is an essential tool in prealgebra to understand the position and order of numbers.

• A number line is infinite in both directions. To the right are positive numbers, and to the left are negative numbers.
• The number zero is the central point on the number line; it separates positive numbers from negative numbers.
• Using a number line helps students visualize mathematical concepts such as addition, subtraction, and absolute values.
  For instance, the distance a number is from zero on the number line is its absolute value.

Thus, the number line aids in understanding positional relationships and distances among numbers.

Exploring Positive Numbers

Positive numbers are numbers greater than zero and are fundamental in prealgebra. They are situated to the right of zero on the number line and do not have a negative sign.

• Positive numbers include natural numbers such as 1, 2, 3, etc.
• They are often used to denote quantities, distances, and growths.
• In absolute value terms, a number is naturally kept as is, if it is positive. For example, the absolute value of 97, as seen in the exercise, stays 97 because it is already positive.

Understanding positive numbers is key in prealgebra, as they form the basis for arithmetic operations and help solve real-world problems.