Key Curriculum Press th Street, Emeryville, CA

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1 Resource Overview Quantile Measure: Skill or Concept: 870Q Multiply two fractions or a fraction and a whole number. (QT N 224) Divide two fractions or a fraction and a whole number. (QT N 230) Identify additive inverses (opposites) and multiplicative inverses (reciprocals, including zero). (QT N 623) Excerpted from: Key Curriculum Press th Street, Emeryville, CA Key Curriculum Press This resource may be available in other Quantile utilities. For full access to these free utilities, visit The Quantile Framework for Mathematics, developed by educational measurement and research organization MetaMetrics, comprises more than 500 skills and concepts (called QTaxons) taught from kindergarten through high school. The Quantile Framework depicts the developmental nature of mathematics and the connections between mathematics content across the strands. By matching a student s Quantile measure with the Quantile measure of a mathematical skill or concept, you can determine if the student is ready to learn that skill, needs to learn supporting concepts first, or has already learned it. For more information and to use free Quantile utilities, visit Park Forty Plaza Drive, Suite 120, Durham, North Carolina METAMETRICS, the METAMETRICS logo and tagline, QUANTILE, QUANTILE FRAMEWORK and the QUANTILE logo are trademarks of MetaMetrics, Inc., and are registered in the United States and abroad. The names of other companies and products mentioned herein may be the trademarks of their respective owners.

2 KeyTo_Fractions_SW2_Cpyrt.pdf 8/6/10 3:12:39 PM Key to Fractions 1 Simplest Form 2 Factors and Products Table 3 Factors 4 Common Factors 6 Greatest Common Factor 8 Finding the Greatest Common Factor 11 Simplifying Fractions 12 Simplifying Fractions with Large Numbers 18 Multiplying Fractions 19 Multiplying and Simplifying 22 Word Problems 23 Simplifying and Multiplying 25 Reciprocals 30 Dividing Fractions 31 Multiplying and Dividing 34 Vocabulary Review 35 Practice Test 36 AND DIVIDING 2 Student Workbook About the Cover TABLE OF CONTENTS Equal Fractions Review MULTIPLYING Greek mathematicians are famous for their geometry. They did not excel in arithemetic. The number system of the early Greeks was based entirely on whole numbers and it made no provision for breaking a unit into fractions. To the early Greeks one half was not a number but was simply the relationship between the whole numbers one and two. Later Greek mathematicians introduced fractions into their number system. Although they invented ways to represent fractions, they never developed easy ways to work with them. Greek astronomers turned to the Babylonian method of dividing a unit into 60 equal parts. They divided a circle into 360 degrees (360 = 6 x 60), a degree into 60 minutes and a minute into 60 seconds. Our own way of dividing an hour can be traced to this Babylonian system of fractions. Other Greek mathematicians followed the Egyptian example and used only unit fractions. The Romans needed fractions for their commerce to exchange money or to weigh and measure goods. Not known as great mathematicians, the Romans limited their calculations to four types of fractions: twelfths, twenty-fourths, forty-eighths, and seventy-seconds. They simply ignored other fractions. On the cover of this book a Roman merchant is working out a problem involving fractions on an abacus. The abacus was the calculator of Roman times. The last two sets of grooves on the bronze plate are used for the four types of Roman fractions. If you were a student in a Roman arithmetic class, you would spend most of your time learning how to handle fractions on an abacus. Cover Art by James Dyekman IMPORTANT NOTICE: This book is sold as a student workbook and is not to be used as a duplicating master. No part of this book may be reproduced in any form without the prior written permission of the publisher. Copyright infringement is a violation of Federal Law. Copyright 1980 by Steve Rasmussen. All rights reserved. Key to Fractions, Key to Decimals, Key to Percents, Key to Algebra, Key to Geometry, Key to Measurement, and Key to Metric Measurement are registered trademarks of Key Curriculum Press. Published by Key Curriculum Press, th Street, Emeryville, CA ISBN

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