Multiplying and Dividing Fractions

 

Resource Overview  Quantile® Measure: 

870Q 

Skill or Concept: 

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  1150 65th Street, Emeryville, CA 94608  www.keypress.com  © Key Curriculum Press    

 

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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, 1150 65th Street, Emeryville, CA 94608 ISBN 978-0-913684-92-4 28 27 26 25 14 13 12 11 10