Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

0. Review of College Algebra

Solving Linear Equations

Trigonometry

0. Review of College Algebra

Solving Linear Equations

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1:08 minutes

Problem 55

Textbook Question

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

Verified step by step guidance

Identify the expression given: \(|\frac{3}{2}|\).

Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative.

Since \(\frac{3}{2}\) is a positive number, its absolute value is simply \(\frac{3}{2}\).

Write the expression as \(\frac{3}{2}\) because the absolute value of a positive number is the number itself.

Conclude that the absolute value operation does not change the value of \(\frac{3}{2}\) since it is already positive.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.