Topic: Introduction to Algebra

Subtopic: The Real Number System & Calculators

**Overview**

The graphing calculator is going to be an invaluable tool in this class. With this lesson we learn about the Real Number System as well as how to perform real number operations on a calculator. BTW, "Real numbers" are just all the numbers that you are used to dealing with -- decimals, fractions, the irrational number pi, etc. as opposed to "imaginary numbers" which we will learn about in Intermediate Algebra.

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 1.2.1 Identify rational vs. irrational numbers
- 1.2.2 Convert decimal fraction, repeating decimal fraction (by hand and on calc)
- 1.2.3 Find an opposite and a reciprocal of an expression
- 1.2.4 Simplify an absolute value (by hand and on calc)
- 1.2.5 Simplify exponents and roots (mostly on calc)
- 1.2.6 Simplify expressions according to order of operations (by hand and on calc)
- 1.2.7 Perform prime factorization (by hand)
- 1.2.8 Reduce algebraic fractions (by hand)
- 1.2.9 Calculator keys: ->FRAC, NEG, x
^{-1}, ABS, ^, SQRT, XthROOT

**Terminology**

Define: decimal, fraction (proper and improper), mixed number, repeating decimal, integer, rational number, irrational number, Real number, opposite (of a number; of an expression), reciprocal (of a number; of an expression), absolute value (of a number; of an expression), exponent, radical, root, order of operations, prime number, composite number, prime factorization, reduce, cancel, simplify.

**Supplementary Resources**

You must be able to use a scientific (or graphing) calculator (handheld or software) to perform basic operations including working with signs and fractions and finding powers, roots, and absolute values. If you have a handheld graphing calculator then these sites may help:

**Recommended!**For TI-84, TI-86, or TI-89 see:

Prof. Keely's Calculator Guide: Basics of Arithmetic

No matter what calculator or software you are using you are

encouraged to try the examples in this link using your own

technology to be sure you can get the right answers electronically.

- For TI-84 (TI=Texas Instruments) the first couple videos at

Prof. Milner's Graphing Calculator Tutorials may be helpful.

- For other models (or makes) try searching on one of the sites recommended here: FAQs - Graphing Calculator Tutorials

**Review Pre-Algebra:** Feeling like you need to spend a bit of time reviewing pre-algebra / arithmetic topics? I have links to lessons, videos, and some games covering the main topics from pre-algebra in my Just-In-Time Mathematics website.