Evaluate each expression. See Example 5.|3⁄2|

Verified step by step guidance

1. Identify the expression given: \(|\frac{3}{2}|\).
2. Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative.
3. Since \(\frac{3}{2}\) is a positive number, its absolute value is simply \(\frac{3}{2}\).
4. Write the expression as \(\frac{3}{2}\) because the absolute value of a positive number is the number itself.
5. Conclude that the absolute value operation does not change the value of \(\frac{3}{2}\) since it is already positive.

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |3| = 3 and |-3| = 3, indicating that both 3 and -3 are three units away from zero.

Evaluating Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify it to a single numerical value. In this case, evaluating |3/2| means determining the absolute value of the fraction, which remains 3/2 since it is already positive.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. The fraction 3/2 is a rational number, representing a value greater than 1. Understanding rational numbers is essential for evaluating expressions involving fractions and their properties.