Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Elementary Algebra
Topic: Introduction to Algebra
Subtopic: The Real Number System & Calculators

Overview

A scientific 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 Recognize Real number vs. non-Real number
• 1.2.7 Place Real number on a number line
• 1.2.8 Order set of Real numbers from smallest to largest
• 1.2.9 Simplify expressions according to order of operations (by hand and on calc)
• 1.2.10 Perform prime factorization (by hand)
• 1.2.11 Reduce algebraic fractions (by hand)
• 1.2.12 Use common calculator tools sech as ->FRAC, NEG, x-1, ABS, ^, SQRT, XthROOT

Terminology

Terms you should be able to 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, number line, order of operations, prime number, composite number, prime factorization, reduce, cancel, simplify.

Supplementary Resources (recommended)

You must be able to use a scientific (or graphing) calculator (app, software, or physical handheld) to perform basic operations including working with signs and fractions and finding powers, roots, and absolute values.

I recommend using a free online calculator or app. One of the most complete is DESMOS.com/calculator, click the keyboard icon at the bottom left of the screen, then click "functions" and explore the tabs. DESMOS also has free apps for mobile devices.

If instead you have a handheld graphing calculator then these sites may help:

Supplementary Resources (optional)

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 and MathIsPower4U.com provides large database of videos at Arthmetic Videos.

rev. 2021-03-31