Welcome to HP Prime Guide Algebra Fundamentals, HP Prime Innovation in Education Series.
There is no one road to the learning of mathematics. Different approaches for different learners are needed to take learners to where they want to go. The goal of this guide is to give you the flexibility of various approaches aided by the use of the HP Prime to reach your goals.
Manual explanations of math concepts in the guide are accompanied by HP Prime illustrations that can be used with the calculator, computer software, and iOS/ Android/ Windows app. Techniques, examples, and exercises can be done using any of the platforms.
The HP Prime Guide Algebra Fundamentals emphasis is its attention on math standards that work. Significant time is spent on learning math by using methods that have shown to be successful in the classroom. There is additional emphasis given to building blocks topics.
HP Prime Calculator, HP Prime/Pro, and HP Prime Free Revealed and Extended feature of the guide is used to show how the HP Prime Calculator, HP Prime/Pro, and HP Prime Free commands and functions can be used to work individual problems as well as how they can be extended to help us understand complex math concepts or create a set of tools that can help with problem solving.
Upon mastery of the manual techniques apply the HP Prime Calculator, HP Prime/Pro, and HP Prime Free solutions to increase your efficiency and problem solving power. Concentrate on the solution without being bogged down with traditional labor-intense steps. Embrace failure; use your additional time, to attempt more word and real world problems.
The HP Prime Guide Algebra Fundamentals is available in print and a digital learning eBook. In the digital eBook version, every example is followed by an interactive reinforcement exercise. Hyperlinks are used to references earlier discussions of a topic, future discussions of a topic, websites, Table of Contents entries, and Detailed Index entries. The hyperlinks are shown as underlined text in the print version. This enables us to see where the eBook’s links are. The solutions to the reinforcement exercises are in the back of the printed and eBook versions with eBook's solution linked back to the topic's explanation.
In addition to the print version, the guide is available on various eBook readers and eBook applications, be it a stand-alone reader, on a phone, tablet, pc, or through a web-browser. The content in the Guide uses mathematical notation, text, graphics, and HP Prime screenshots. The eBook version takes advantage of the resolution of the display. The real-time access, anytime, anyplace nature of the eBook version, allows a new way for you to gain the math knowledge and skills necessary to succeed in the classroom, at your job, and in your personal pursuit of learning. The print version gives you the option of using a traditional book.
An innovative approach is to use HP Prime Calculator, HP Prime/Pro, and HP Prime Free Computer Algebra Solutions (CAS) as an aide in moving forward. In lessons requiring a concept that you have not yet mastered, use the HP Prime Calculator, HP Prime/Pro, and HP Prime Free CAS solutions to assist with class assignments, allowing you to keep current. You keep moving forward with the new material, giving you additional time to master the concept causing problems.
About the Author
Table of Contents
Table of Contents
Welcome and What We’re All About. 9
Understanding the HP Prime Family of Graphing Calculator. 11
HP Family. 11
HP Prime Handheld Essentials. 12
HP Prime Virtual Computer Software Essentials. 12
HP Prime iOS/ Android/ Windows Apps Essentials. 12
Explanation 1.1 - Real Numbers. 15
Exponential Notation.. 15
Order of Operations. 20
The Set of Real Numbers. 22
Decimal Representation for the Real Numbers. 23
Representing Real Numbers on a Number Line. 26
Introduction to Absolute Value. 27
Absolute Value and Distance. 28
Programming Related Information.. 33
Gauss Anecdote. 46
Explanation 1.2 - Operations and Properties of Real Numbers. 51
Addition and Subtraction of Real Numbers. 51
Rules for Addition of Two Real Numbers. 52
Rule for Subtraction of Two Real Numbers. 52
Alternate Approach to Addition and Subtraction of Real Numbers. 54
Collecting Like Terms – Part 1.. 60
Basic Properties of Algebra. 60
Multiplication and Division of Real Numbers. 62
Additional Properties. 70
Collecting Like Terms – Part 2.. 77
Explanation 1.3 - Integer Exponents. 83
Integer Exponents. 83
Additional Exponential Properties. 95
Scientific Notation.. 98
Explanation 1.4 – Radicals and Rational Exponents. 113
Radicals and Their Properties. 113
Rational Exponents. 130
Reducing the Index. 137
Rationalizing Denominators. 141
Explanation 1.5 - Algebraic Expressions. 147
Adding and Subtracting Polynomials. 147
Multiplying Polynomials. 149
Special Product Formulas. 151
Explanation 1.6 - Factoring. 155
Common Factors. 157
Factoring Trinomials. 159
Factor by Grouping. 164
Special Factoring Formulas. 165
Explanation 1.7 – Rational Expressions. 169
Simplifying Rational Expressions. 174
Multiplying and Dividing Rational Expressions. 176
Adding and Subtracting Rational Expressions. 178
Compound Fractions. 182
Apartment Complex Revenue. 219
Solutions 1.1 - Real Numbers. 231
Solutions 1.2 - Operations and Properties of Real Numbers. 235
Solutions 1.3 Integer Exponents. 239
Solutions 1.4 – Radicals and Rational Exponents. 245
Solutions 1.5 – Algebraic Expressions. 251
Solutions 1.6 – Factoring. 255
Solutions 1.7 – Rational Expressions. 259
Detailed Index: HP Prime Techniques. 275
HP Prime Techniques. 275
Works Cited.. 283