Elementary Mathematics - .:: e-Book

1 Prescribed by National Curriculum and Textbook Board as a Textbook (Bangla version) for Class Five from 2006, English version of the book from academic year Mathematics book Five Written by Dr. Munibur Rahman Chowdhury A. M. M. Ahsan Ullah Hamida Banu Begum Md. Rafiqul Islam Edited by Khodadad Khan Translated by Ahsan Ullah Arjumand AraNATIONAL CURRICULUM & TEXTBOOK BOARD, DHAKAP ublished by National Curriculum and Textbook Board69-70, Motijheel Commercial Area, Dhaka-1000.

2 [All rights reserved by the publisher]Is permitted to print and sell 500 (Five hundred)Copies of the book for the year 2009 Date: 15/12/08 Allotment Letter No. 717/08/09 Date : 23/02/09 Rahmania Offest Press, Banglabazer, Dhaka- 1100 First Print (Bangla version) : September 2005 First Print (English Version) : February 2007 2nd Print (English version) : March 2008 Reprint (English Version) : April 2009 Computer GraphicLaser Scan Limited15/2, Topkhana Road, BMA & Illustrations:Domion Neoton PinaruPicture Coloured byAhmed UllahPrinting Supervision Ferial AzadDesignNational Curriculum and Textbook BoardWebsite version developed by Mars Solutions Limited PrefaceFor improving the existing quality of Primary Education in Bangladesh, National Curriculum and Textbook Board (NCTB) in collaboration with PEDP-II initiated an extensive program for development of curriculum and teaching learning materials in 2002.

3 In the light of this program the curriculum, textbooks and other teaching learning materials of Primary levels have been prepared, revised and textbook entitled, ' Elementary Mathematics ' has been prepared on the basis of attainable competencies for the students of Class Five. The subject matter of the textbook is derived from the basic elements of Mathematics following the attainable learning outcomes as depicted in the curriculum. This will facilitate our young learners to know how they can make best use of this contents of the book are analyzed and explained in such a manner with practical examples, illustrations and system of planned activities, that students are inspired to study the subject with a keen book is originally published in Bangla.

4 From this year NCTB is publishing the English version of the textbook. English is the language of choice in today's globalized world. To facilitate the verbal and written communication skills of our future citizens and suitably prepare them for international competition, we decided to translate the original Bangla textbooks into English. It's pleasant to note that the number of English medium schools in Bangladesh is increasing very fast. In this context NCTB decided to publish all the textbooks of Primary level in English. This was a big endeavour for us. Despite our all efforts the first edition may not be totally error free. However, in the future editions we shall try to remove all errors and , I would like to express my heartfelt thanks and gratitude to those who have made their valuable contributions in writing, editing, evaluating and translating this book .

5 I sincerely hope that the book will be useful to those for whom it has been prepared. Prof. Md. Mostafa Kamaluddin Chairman National Curriculum and Textbook Board DhakaContentsChapter Subject PageOne Addition and Subtraction 1 - 9 Two Multiplication and Division 10 - 19 Three Problems Involving the First Four Rules 20 - 23 Four The Unitary Method 24 - 31 Five Simplification 32 - 35 Six Average 36 - 40 Seven and 41 - 50 Eight Mathematical Symbols and Sentences 51 - 57 Nine Common

6 Fractions 58 - 100 Ten The Decimal Fraction 101 - 115 Eleven Percentage 116 - 127 Twelve Measurement 128 - 148 Thirteen Time 149 - 164 Forteen Income, Expenditure and Cash Memo 165 - 171 Fifteen The Arrangement of Data 172 - 175 Sixteen Graph 176 - 180 Seventeen Geometry 181 - 192 Eighteen The Usage of Calculator 193 - 197 Nineteen Population 198 - 203 Answer 204 - 215 Addition and Subtraction Example 1. Add : 23041, 10532, 31210, 22000, 2104 and 102. Solution : 2 3 0 4 1 Ajuts Thousands Hundreds Tens Ones 1 0 5 3 2 2 3 0 4 1 3 1 2 1 0 1 0 5 3 2 2 2 0 0 0 3 1 2 1 0 2 1 0 4 2 2 0 0 0 1 0 2 2 1 0 4 8 8 9 8 9 1 0 2 8 8 9 8 9 Answer : 88989.

7 Example 2. Add : 312024, 103001, 150310, 201200, 131141 and 102203. Solution : 3 1 2 0 2 4 L Aj Th H T O 1 0 3 0 0 1 3 1 2 0 2 4 1 5 0 3 1 0 1 0 3 0 0 1 2 0 1 2 0 0 1 5 0 3 1 0 1 3 1 1 4 1 2 0 1 2 0 0 1 0 2 2 0 3 1 3 1 1 4 1 9 9 9 8 7 9 1 0 2 2 0 3 9 9 9 8 7 9 Answer : 999879. The numbers are placed as ones under ones, tens under tens, hundreds under hundreds. Addition is started from the place of ones. The sum of each place is written below in absence of carrying number. Chapter - 12 Addition and SubtractionExample 3.

8 Add : 572104, 650489, 948531, 886350, 95448 and 749065. Solution :Ni L Aj Th H T O 3 4 5 6 9 8 7 3 7 5 4 8 9 4 1 2 0 8 6 5 9 2 1 4 5 3 4 0 2 0 8 3 5 4 6 4 9 1 0 8 5 Answer : 5 7 2 1 0 4 6 5 0 4 8 9 9 4 8 5 3 1 8 8 6 3 5 0 9 5 4 4 8 7 4 9 0 6 5 3 9 0 1 9 8 7 3901987. 3 9 0 1 9 8 7 The numbers are arranged in the table. The sum of the digits of ones is 27. 27 is 2 tens and 7 ones, so7 of 27 is placed under the line in the ones place and 2 of 27 is written within a circle on the top of tens place. In the same way, adding the digits of tens place, the carrying number 2 is written on the top of the hundreds place. Similarly, the digits of the hundreds place, thousands place, ajuts place and lacs place are added.

9 Adding the digits of lacs place, the carrying number is written on the top of nijuts place within a circle. As there is no other digit in the nijuts place, the digit is written as sum in nijuts place, within the circle. Example 4. Add the numbers writing them side by side. (a) 31420, 50261, 47523, 9431, 23084 and 62100. (b) 425731, 653802, 749243, 86010, 72301 and 930211. 3 Elementary MathematicsSolution : (a) 31420 + 50261 + 47523 + 9431 + 23084 + 62100 = 223819 Answer : 223819. (b) 425731 + 653802 + 749243 + 86010 +72301 + 930211 = 2917298 Answer : 2917298. The numbers are written side by side putting plus sign (+) in between them. The result of the addition is written on the line below putting equal sign (=).

10 Before adding the digits of ones, tens, hundreds, thousands, ..places successively the digits are marked with ( ). The carrying digits are added to the digit on the left side. Remarks : It is convenient to mark on the digits of the same place with ( ) at the time of adding. Add (One is worked out) : (a) 6 3 2 0 5 4 (b) 4 6 8 5 3 (c) 5 3 2 8 6 1 (d) 7 3 2 8 4 6 2 8 4 7 1 8 7 2 0 4 1 7 0 4 1 0 5 8 5 3 9 2 4 0 5 6 5 3 5 3 9 0 5 2 9 5 0 3 1 9 0 8 7 0 5 5 2 0 8 9 0 2 0 7 1 4 3 2 0 5 2 4 6 2 4 1 5 7 7 4 1 5 0 6 1 6 3 0 0 8 1 3 0 1 6 5 7 0 2 3 4 8 1 3 2 3 2 8 1 4 6 7 9 0 6 3 3 3 9 8 0 5 3 Fill in the boxes : (a) 645317 + 8297 + 53086 + 264309 + 708321 = (b) 526394 + 230087 + 630801 + 319500 + 460009 + 809625 = 4 Addition and SubtractionExample 5.