Tài liệu hay dành cho giáo viên toán và học sinh tham khảo . Nội dung sách giới thiệu về phép chia với những góc độ tiếp cận hay, nhẹ nhàng giúp học sinh hứng thú và học toán một cách tự nhiên. Từ phần giới thiệu, đặt vấn đề về phép chia đến những ví dụ minh hoạ đều gần gũi với cuộc song hàng ngày. Hình vẽ, màu sắc bắt mắt,... Tài liệu giúp giáo viên toán có thêm nguồn tham khảo để hoàn thiện phương pháp giảng dạy, bên cạnh đó cũng giúp giáo viên phát triển vốn tiếng anh, rèn luyện kỹ năng dạy toán song ngữ cho học sinh.
Rebecca Wingard-Nelson Illustrated by Tom LaBaff This page intentionally left blank Division Made Easy Rebecca Wingard-Nelson Enslow Elementary, an imprint of Enslow Publishers, Inc Enslow Elementary® is a registered trademark of Enslow Publishers, Inc Copyright © 2005 by Enslow Publishers, Inc All rights reserved No part of this book may be reproduced by any means without the written permission of the publisher Library of Congress Cataloging-in-Publication Data Wingard-Nelson, Rebecca Division made easy / Rebecca Wingard-Nelson p cm — (Making math easy) Includes index ISBN 0-7660-2511-X (hardcover) Division—Juvenile literature I Title QA115.W76 2005 513.2'14—dc22 2004021660 Printed in the United States of America 10 To Our Readers: We have done our best to make sure all Internet Addresses in this book were active and appropriate when we went to press However, the author and the publisher have no control over and assume no liability for the material available on those Internet sites or on other Web sites they may link to Any comments or suggestions can be sent by e-mail to comments@enslow.com or to the address on the back cover Illustration credits: Tom LaBaff Cover illustration: Tom LaBaff Contents Introduction What Is Division? Why Divide? Division Terms Division and Multiplication Division Facts Zero and One Long Division Dividing Greater Numbers What Are Remainders? The Largest Remainder Dividing by Greater Numbers Powers of Ten Multiples of Ten Division and Estimation Properties and Division Checking Your Answer Division Key Words Word Problems Understanding the Remainder Word Problems and Remainders Further Reading Internet Addresses Index 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 47 48 Introduction M ath is all around, and an important part of your life You use math when you are playing games, cooking food, spending money, telling time, reading music, and doing any other activity that uses numbers Even finding a television station uses math! Division Is Everywhere You use division in everyday life When you split a bag of candy or a box of cookies with a friend, you are dividing When you decide how many rows of seats your class will need during an assembly, you are dividing Any time you have a group of things and need to separate them into smaller equal groups, you are dividing Using This Book This book can be used to learn or review division at your own speed It can be used on your own or with a friend, tutor, or parent Get ready to discover math made easy! What Is D ivision is a way to break something into equal parts You have 20 king cobras A basket holds cobras How many baskets you need to hold all of your king cobras? There are two ways to find the answer You can find the number of baskets by subtracting cobras at a time from the total 20 Ϫ ϭ 15 basket 15 Ϫ ϭ 10 baskets 10 Ϫ ϭ baskets 5Ϫ5ϭ0 baskets You need baskets to hold all 20 king cobras Division? You can divide Division is just another way to subtract over and over again 20 divided by is Division is repeated subtr action 20 king cobras, divided into baskets of snakes each, will fill baskets Why S uppose you know a total number of items You also know the number of groups you want to equally put them into You can divide to find how many items will be in each group Three friends bought a pizza The pizza had six slices If three friends shared the pizza equally, how many slices did each friend eat? Six slices of pizza, divided equally among three friends, gave each friend two slices Six divided by three is two 6Ϭ3=2 Properties A re the same properties true for division that are true for multiplication? Let’s check When you multiply, you can change the order of the numbers and the answer will not change Is this true for division? 9Ϭ3 3Ϭ9 How many groups of can you make from 9? 9Ϭ3ϭ3 How many groups of can you make from 3? None! The number is bigger than You cannot change the order of the numbers in a division problem 34 and Division When you multiply more than two numbers, you can group the numbers in any way to multiply them Is this true for division? (60 Ϭ 6) Ϭ 60 Ϭ (6 Ϭ 2) Divide inside (60 Ϭ 6) Ϭ parentheses first (10) Ϭ Divide again 10 Ϭ ϭ (60 Ϭ 6) Ϭ ϭ 60 Ϭ (6 Ϭ 2) 60 Ϭ (3) 60 Ϭ ϭ 20 60 Ϭ (6 Ϭ 2) ϭ 20 You cannot group the numbers any way you choose in a division problem 35 Checking B ecause multiplication and division are opposite operations, you can use multiplication to check the answer to a division problem On page 19, we found that 42 Ϭ ϭ 14 If 42 Ϭ ϭ 14 is correct, then 14 ϫ ϭ 42 14 ϫ Multiply ones ϫ ϭ 12 Regroup 14 ϫ 42 Multiply tens ϫ ϭ Add ϩ ϭ 14 ϫ ϭ 42, so 42 Ϭ ϭ 14 36 Your Answer When the answer to a division problem r emainder—Th e has a remainder, first use multiplication, number left then add the remainder over in a division proble On page 23, we found that m 30 Ϭ = R3 divisor Multiply the divisor and the part of the answer that is not the remainder ϫ ϭ 27 remainder Add the remainder to the number you just found 27 ϩ ϭ 30 The result (30) is the same as the number you divided, so the answer is correct 30 Ϭ = R3 37 Division O wen is half as old as his sister Lauren Lauren is 14 How old is Owen? The word half tells you that you should divide by to find Owen’s age 14 years Ϭ ϭ years Owen is years old Words that help you know how to solve problems are called key words Some key words for division problems are listed in the table below Division Key Words average cut divided divisor each 38 equal parts evenly every half out of per quotient separate shared split Key Words Some division problems will ask you to change a value for more than one item to a value for one item If you know the: and you need to find the: Price of more than one Price of one Size of more than one Size of one Length of more than one Length of one A package of three computer games sells for $51 What is the cost per game? Since you know the cost of three (more than one) games, you can find the cost of one game by dividing First write the problem in words cost of three games divided by three is the cost per game $51 Ϭ ϭ $17 The cost is $17 per game 39 Word W ord problems can be solved by following four steps Your club bought 168 flowers to give to 12 teachers Each teacher will get the same number of flowers How many flowers will each teacher get? 40 Problems Understand the problem Find what you know Find what you want to know There are 168 flowers and 12 teachers The number of flowers each teacher will get Plan how to solve the problem You are looking for the equal number of flowers each teacher will get You know the total number of flowers and the number of teachers This is a division problem Solve the problem Divide the number of flowers by the number of teachers 168 flowers Ϭ 12 teachers ϭ 14 flowers per teacher Check your work Check division by multiplying 14 flowers per teacher ϫ 12 teachers ϭ 168 flowers 41 Understanding W hen a quotient has a remainder, you must decide what the remainder means Let’s look at some problems that use the same facts, but ask different questions A coin collection book displays four coins on each page You have collected 51 coins How many pages will you use if you put all of the coins in the book? You are being asked to divide your 51 coins into groups of 51 Ϭ ϭ 12 R3 The question asks how many pages will you use Twelve pages will be full; another page will be needed for the remaining coins Since 12 ϩ ϭ 13, you will use 13 pages 42 the Remainder A coin collection book displays four coins on each page You have collected 51 coins How many pages can you fill completely? In this problem, only the full pages are counted You will have 12 full pages A coin collection book displays four coins on each page You have collected 51 coins How many coins will be on the last page? In this problem, the question asks how many coins will be on the last page, which is the remainder There will be coins on the last page 43 Word Problems L et’s use the steps from pages 40 and 41 to solve a word problem that uses a remainder There are 2,153 chocolate candies in a bag You get to eat what is left after the candies are divided equally into 20 bags How many candies are you allowed to eat? Understand the problem Find what you know There are 2,153 candies to go equally into 20 bags Find what you want to know The number of candies left over 44 and Remainders Plan how to solve the problem A large group of candies is being divided equally into smaller groups This is a division problem Solve the problem Divide the number of candies by the number of bags 2,153 Ϭ 20 ϭ 107 R13 The question asks how many candies you get to eat Since you get what is left over, or what remains, the remainder is the answer You get to eat 13 candies Check your work When division problems have a remainder, first multiply (107 ϫ 20 ϭ 2,140), then add the remainder (2,140 ϩ 13 ϭ 2,153) You are back to the original number you divided, so your answer is correct 45 Further Reading Long, Lynette Dazzling Division Indianapolis: John Wiley & Sons, 2000 Moore, Jo E Manipulative Math: Multiplication and Division Monterey, Calif.: Evan-Moor Educational Publishers, 1996 Rainbow Bridge Publishing Deep Space Division Fission Salt Lake City: Rainbow Bridge Publishing, 2004 46 Internet Addresses Aplusmath “Division Flashcards.” © 1998–2004 Minori, Carla “Division Facts.” © 1998–2004 The Math Forum “Ask Dr Math.” © 1994–2004 47 Index C K checking your answer, 36–37 key words, 38–39 D long division, 18–19 symbol, 11 dividend, 10–11 division, 6–7, 8–9 facts, 14–15 by greater numbers, 26–27 of greater numbers, 20–21 by multiples of ten, 30–31 by powers of ten, 28–29 division symbol, 11 divisor, 10–11 E estimation, 32–33 F factor, 14 fraction bar, 11 H L M multiplication, 12–13 facts, 14–15 O one, 17 P properties, 34–35 Q quotient, 10–11 R remainders, 22–23, 37 largest, 24–25 understanding, 42–43 S subtraction, 6–7 W half, 38 word problems, 40–41, 42–43, 44–45 I Z inverse operations, 12, 36 48 zero, 16 ... Cataloging-in-Publication Data Wingard-Nelson, Rebecca Division made easy / Rebecca Wingard-Nelson p cm — (Making math easy) Includes index ISBN 0-7660-2511-X (hardcover) Division Juvenile literature I Title QA115.W76... illustration: Tom LaBaff Contents Introduction What Is Division? Why Divide? Division Terms Division and Multiplication Division Facts Zero and One Long Division Dividing Greater Numbers What Are Remainders?...This page intentionally left blank Division Made Easy Rebecca Wingard-Nelson Enslow Elementary, an imprint of Enslow Publishers, Inc Enslow