MTH-4110-1 C1 10/5/11 12:01 PM Page 1 MTH-4110-1 he Four Operations on AlgebraicT Fractions MTH-4110-1 THE FOUR OPERATIONS ON ALGEBRAIC FRACTIONS Author: Suzie Asselin Content revision: Daniel Gélineau Jean-Paul Groleau Mireille Moisan-Sanscartier Nicole Perreault Adult Education Consultants: Les Productions C.G.L. enr. Coordinator for the DDFD: Jean-Paul Groleau Coordinator for the DFGA: Ronald Côté Word processing: Francine Lessard Photocomposition and layout: Multitexte Plus English version: Direction du développement pédagogique en langue anglaise Translation: Elizabeth Dundas Linguistic revision: William Gore Translation of updated sections: Claudia de Fulviis Reprint: 2004 © Société de formation à distance des commissions scolaires du Québec All rights for translation and adaptation, in whole or in part, reserved for all countries. Any reproduction by mechanical or electronic means, including micro-reproduction, is forbidden without the written permission of a duly authorized representative of the Société de formation à distance des commissions scolaires du Québec (SOFAD). Legal Deposit — 2004 Bibliothèque et Archives nationales du Québec Bibliothèque et Archives Canada ISBN 2-89493-288-9 MTH-4110-1 The Four Operations on Algebraic Fractions TABLE OF CONTENTS Introduction to the Program Flowchart ................................................... 0.4 The Program Flowchart ............................................................................ 0.5 How to Use This Guide ............................................................................. 0.6 General Introduction................................................................................. 0.9 Intermediate and Terminal Objectives of the Module ............................ 0.11 Diagnostic Test on the Prerequisites ....................................................... 0.13 Answer Key for the Diagnostic Test on the Prerequisites ...................... 0.17 Analysis of Diagnostic Test Results ......................................................... 0.19 Information for Distance Education Students......................................... 0.21 UNITS 1. Simplifying Algebraic Fractions ............................................................... 1.1 2. Product and Quotient of Algebraic Fractions .......................................... 2.1 3. Multiplying and Dividing Algebraic Fractions ........................................ 3.1 4. Adding and Subtracting Algebraic Fractions .......................................... 4.1 5. Order of Operations Involving Algebraic Fractions ................................ 5.1 Final Summary.......................................................................................... 6.1 Answer Key for the Final Summary ........................................................ 6.5 Terminal Objective .................................................................................... 6.6 Self-Evaluation Test.................................................................................. 6.7 Answer Key for the Self-Evaluation Test ................................................ 6.13 Analysis of the Self-Evaluation Test Results .......................................... 6.17 Final Evaluation........................................................................................ 6.18 Answer Key for the Exercises ................................................................... 6.19 Glossary ..................................................................................................... 6.41 List of Symbols .......................................................................................... 6.45 Bibliography .............................................................................................. 6.46 Review Activities ....................................................................................... 7.1 © SOFAD 0.3 MTH-4110-1 The Four Operations on Algebraic Fractions INTRODUCTION TO THE PROGRAM FLOWCHART Welcome to the World of Mathematics! This mathematics program has been developed for the adult students of the Adult Education Services of school boards and distance education. The learning activities have been designed for individualized learning. If you encounter difficulties, do not hesitate to consult your teacher or to telephone the resource person assigned to you. The following flowchart shows where this module fits into the overall program. It allows you to see how far you have progressed and how much you still have to do to achieve your vocational goal. There are several possible paths you can take, depending on your chosen goal. The first path consists of modules MTH-3003-2 (MTH-314) and MTH-4104-2 (MTH-416), and leads to a Diploma of Vocational Studies (DVS). The second path consists of modules MTH-4109-1 (MTH-426), MTH-4111-2 (MTH-436) and MTH-5104-1 (MTH-514), and leads to a Secondary School Diploma (SSD), which allows you to enroll in certain Gegep-level programs that do not call for a knowledge of advanced mathematics. The third path consists of modules MTH-5109-1 (MTH-526) and MTH-5111-2 (MTH-536), and leads to Cegep programs that call for a solid knowledge of mathematics in addition to other abiliies. If this is your first contact with this mathematics program, consult the flowchart on the next page and then read the section “How to Use This Guide.” Otherwise, go directly to the section entitled “General Introduction.” Enjoy your work! 0.4 © SOFAD MTH-4110-1 The Four Operations on Algebraic Fractions THE PROGRAM FLOWCHART CEGEP MTH-5112-1 Logic MTH-5111-2 Complement and Synthesis II MTH-536 MTH-5110-1 Introduction to Vectors MTH-5109-1 Geometry IV MTH-5108-1 Trigonometric Functions and Equations MTH-526 Exponential and Logarithmic Functions MTH-5107-1 and Equations MTH-5104-1 Optimization II MTH-5106-1 Real Functions and Equations MTH-514 MTH-5103-1 Probability II MTH-5105-1 Conics MTH-5102-1 Statistics III MTH-5101-1 Optimization I MTH-4111-2 Complement and Synthesis I MTH-436 Trades The Four Operations on MTH-4110-1 You ar e here DVS Algebraic Fractions MTH-4109-1 Sets, Relations and Functions MTH-4108-1 Quadratic Functions MTH-426 MTH-4107-1 Straight Lines II MTH-4106-1 Factoring and Algebraic Functions MTH-4105-1 Exponents and Radicals MTH-4104-2 Statistics II MTH-4103-1 Trigonometry I MTH-416 MTH-4102-1 Geometry III MTH-4101-2 Equations and Inequalities II MTH-3003-2 Straight Lines I MTH-314 MTH-3002-2 Geometry II MTH-3001-2 The Four Operations on Polynomials MAT-2008-2 Statistics and Probabilities I MTH-216 MTH-2007-2 Geometry I MTH-2006-2 Equations and Inequalities I MTH-1007-2 Decimals and Percent MTH-1006-2 The Four Operations on Fractions MTH-116 MTH-1005-2 The Four Operations on Integers 25 hours = 1 credit 50 hours = 2 credits © SOFAD 0.5 MTH-4110-1 The Four Operations on Algebraic Fractions HOW TO USE THIS GUIDE Hi! My name is Monica and I have been You’ll see that with this method, math is I’m Andy. asked to tell you about this math module. a real breeze! What’s your name? My results on the test Whether you are ... you have probably taken a placement test which tells you indicate that I should begin registered at an with this module. adult education exactly which module you center or at should start with. Formation à distance, ... Now, the module you have in your ... the entry activity, which By carefully correcting this test using the hand is divided into three contains the test on the corresponding answer key, and record- sections. The first section is... prerequisites. ing your results on the analysis sheet ... 0.6 © SOFAD MTH-4110-1 The Four Operations on Algebraic Fractions ... you can tell if you’re well enough And if I’m not, if I need a little In that case, before you start the prepared to do all the activities in the activities in the module, the results review before moving on, what analysis chart refers you to a review module. happens then? activity near the end of the module. I see! In this way, I can be sure I have all the prerequisites START for starting. The starting line shows where the Exactly! The second section contains the learning activities. It’s learning activities the main part of the module. begin. The little white question mark indicates the questions ? for which answers are given in the text. The target precedes the objective to be met. The memo pad signals a brief reminder of concepts which you have already studied. The boldface question mark indicates practice exercices which allow you to try out what ? you have just learned. Look closely at the box to the right. It explains the symbols used to identify the various activities. The calculator symbol reminds you that you will need to use your calculator. The sheaf of wheat indicates a review designed to ? reinforce what you have just learned. A row of sheaves near the end of the module indicates the final review, which helps you to interrelate all the learning activities in the module. FINISH Lastly, the finish line indicates that it is time to go on to the self-evaluation test to verify how well you have understood the learning activities. © SOFAD 0.7 MTH-4110-1 The Four Operations on Algebraic Fractions There are also many fun things in this module. For example, A “Did you know that...”? Must I memorize what the sage says? when you see the drawing of a sage, it introduces a “Did you know that...” Yes, for example, short tidbits No, it’s not part of the learn- on the history of mathematics ing activity. It’s just there to and fun puzzles. They are in- give you a breather. teresting and relieve