Mathematics HOLY FAITH INTERNATIONAL (P) LTD. Preetika Sawhney. M.Sc., M.Ed.

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2 Mathematics 5 Preetika Sawhney M.Sc., M.Ed. HOLY FAITH INTERNATIONAL (P) LTD.

3 New Delhi: MBD House, Gulab Bhawan, 6, Bahadur Shah Zafar Marg Ph , , Mumbai: A-683, T.T.C. Industrial Area, M.I.D.C. Off. Thane-Belapur Road, Navi Mumbai Ph , , Chennai: No. 26 B/2 SIDCO Estate, North Phase, Pataravakkam Ambattur Industrial Estate, Ambattur Chennai: Plot No. 3018, Old Y Block, 3rd Street, 12th Main Road, Anna Nagar West, HOLY FAITH INTERNATIONAL We are committed to serve students with best of our knowledge and resources. We have taken utmost care and paid much attention while editing and printing this book but we would beg to state that authors and publishers should not be held responsible for unintentional mistakes that might have crept in. However, errors brought to our notice shall be gratefully acknowledged and attended to. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior written permission of the publisher. Any breach will entail legal action and prosecution without further notice. Published by : MANIK JUNEJA HOLY FAITH INTERNATIONAL (P) LTD. MBD House, Gulab Bhawan, 6, Bahadur Shah Zafar Marg, New Delhi Printed at : MBD PRINTOGRAPHICS (P) LTD. Industrial Area Ram Nagar, Gagret. Tehsil Amb, Distt Una (H.P.) Kolkata: Satyam Building, 46-D, Rafi Ahmed Kidwai Marg Jalandhar City: MBD House, Railway Road Bengaluru: 124/31, 1st Main, Industrial Town (Near Chowdeshwari Kalyan Mantap), West of Chord Road, Rajajinagar Hyderabad: , Varun Towers, Barkatpura Ernakulam: Surabhi Building, South Janatha Road, Palarivattom Ph , Pune: Survey No. 44, Behind Matoshree Garden, Kondhwa - Khadi Machine - Pisoli Road, At. Post-Pisoli Nagpur: Near N.I.T. Swimming Pool, North Ambazari Road, Ambazari Layout Ph , , , Ahmedabad: Godown No.10, Vedant Prabha Estate, Opp. ONGC Pumping Station, Sarkhej Sanand Road, Sarkhej Cuttack: Badam Bari, Link Road Guwahati: Chancellor Commercial, Hem Baruah Road, Paan Bazar Ph , Lucknow: 173/15, Dr. B. N. Verma Road, Old 30 Kutchery Road Ph , Patna: Ist Floor, Annapurna Complex, Naya Tola Bhopal: Plot No. 137, 138, 139, Sector-I, Special Industrial Area,Govindpura Ph , Jabalpur: 840, Palash Chamber, Malviya Chowk Goa: H. No. 932, Plot No. 66, Kranti Nagar (Behind Azad Bhawan), Alto Porvorim, Bardez Jaipur: C-66A, In front of Malpani Hospital, Road No.1, V.K. Industrial Area, Sikar Road Raipur: Behind Kailash Provision Store, Ravi Nagar Karnal: Plot No. 203, Sector-3, HSIDC, Near Namaste Chowk, Opp. New World Shimla (H.P.): C-89, Sector-I, New Shimla-9 Jammu (J&K): MBD Office, 48 Gujjar Colony, C/o Gurjar Desh Charitable Trust, N.H. Bye Pass Road Ranchi (Jharkhand): Shivani Complex, 2nd Floor, Jyoti Sangam Lane, Upper Bazar Sahibabad (U.P.): B-9 & 10, Site IV, Industrial Area Dehradun (Uttarakhand): GMS Road DELHI LOCAL OFFICES: Delhi (Shakarpur): MB 161, Street No. 4 Delhi (Daryaganj): MBD House, 4587/15, Opp. Times of India Delhi (Patparganj): Plot No. 225, Industrial Area

4 Preface The Hummingbird series of Primary Books from I to V are based on National Curriculum Framework (NCF) 2005 and the new Syllabi for classes at the Elementary Level. In the guidelines some of the objectives of teaching the different subjects at primary stage are: to train children to locate and comprehend relationships between the natural, social and cultural environment; to nurture the curiosity and creativity of the child particularly in relation to the natural environment; to develop an awareness about environmental issues; to engage the child in exploratory and hands-on activities. The Hummingbird series focuses on themes that allow for a connected and interrelated understanding to develop and trigger the child s thinking in new directions. They connect knowledge to the child s life outside the classroom and also provide an overall development of children. The series comprises of textbooks on: MATHEMATICS Children need to develop a positive attitude towards and a liking for Mathematics at the primary stage, along with the cognitive skills and concepts that they acquire. The content includes Mathematical games, puzzles and stories that help in making connections between Mathematics and everyday thinking. ENGLISH An integrated approach to the teaching of language is of particular relevance at the primary level. The books address different skills of language, namely listening, speaking, reading and writing, which focus on across the curriculum approach through a variety of genres poems, stories, role-plays and drama to develop the language skills creatively. SCIENCE Science education should develop competence and encourage inventiveness and creativity. The textbooks incorporate activities, observation, experimentation and encourage an active approach to science, connecting it to the world around the child, rather than information based learning. SOCIAL SCIENCE The textbooks provide the social, cultural and analytical skills required to adjust to an increasingly interdependent world. The focus of the books is on a conceptual understanding rather than lining up facts to be memorized. ENVIRONMENTAL STUDIES Environmental Studies is a subject dealing with Man s relation to his whole environment, viz. his surroundings, his home, his neighbourhood, his city or town, extending ever outward. The books contextualize the relevance of the subject and bring it to life. The textbooks present the subjects in a clear, concise, logical and chronological manner. It is expected that this new series will inspire the children to analyse, demonstrate and transform their world view.

5 CONTENTS Numbers upto Ten Crores 1 22 Roman Numerals Operations on Large Numbers Simplification Factors and Multiples Fractions Decimals Average and Percentage Ratio and Proportion Measurement of Length, Mass and Capacity Time and Temperature Money Perimeter and Area Lines and Angles Volume Triangles Circle Spatial Geometry Patterns Data Handling ANSWERS

6 Learning Objectives Eight-digit numbers Nine-digit numbers Indian place value chart Expanded form Writing the numeral Successor and predecessor Skip counting Comparison of numbers The largest and smallest numbers using given digits Rounding off numbers International system Comparison of International and Indian numeral systems You have learnt in class IV that The places ones, tens and hundreds together are called the ones period. The places thousands and ten thousands together are called the thousands period. The places lakhs and ten lakhs together are called lakhs period. The periods are separated by commas. Greatest Number Smallest Number T.L L T.Th Th H T O (4-digits) (5-digits) (5-digits) (6-digits) (6-digits) (7-digits) can be written as. 2. The numeral for : 4 lakhs, 3 ten thousands, 4 thousands, 3 hundreds, 6 tens and 3 ones is can be written in expanded form as. 4. The numeral for : is. 1 NUMBERS UPTO TEN CRORES

7 5. The number name for is. 6. The numeral for seven lakh fifty-six thousand nine hundred thirty-four is. 7. Place value of 9 in is. 8. The number with 2 at ones place, 8 at tens place, 8 at hundreds place, 7 at thousands place, 5 at ten thousands place and 9 at lakhs place is. 9. The successor of is. 10. The predecessor of is. 11. Write the next three numbers that come just after :. 12. Write the three numbers that come just before :. 13. Two numbers which come in between and are. 14. Encircle the greater number : , Encircle the smaller number : , Arrange , , in increasing order. 17. Arrange , , in decreasing order. 18. Make the largest and the smallest numbers of 6 digits using each digit only once. Digits Largest number Smallest number 4, 5, 7, 2, 8, Make the largest and the smallest numbers of 5-digits using the given digits. You may repeat the digits. Digits Largest number Smallest number 6, 4, 3, 7, rounded to the nearest tens is rounded to the nearest hundreds is rounded to the nearest thousands is rounded to the nearest ten thousands is rounded to the nearest lakh is. MATHEMATICS-5 2

8 EIGHT-DIGIT NUMBERS Now let us learn numbers bigger than 7-digits. We know that the largest 7-digit number is Let us find its successor. To do this we add 1 to T.L L T.Th Th H T O digit number begins in the crores place. We get a new place value. We will call it the crores place. We write C for it is read as one crore. It is the smallest 8-digit number. Thus, 7-digits : = (8-digits) Thus, 8-digit number means we have one place further to the left in the place value chart. NINE-DIGIT NUMBERS Now let us learn numbers bigger than 8-digits. We know that the largest 8-digit number is Let us find its successor. To do this we add 1 to C T.L L T.Th Th H T O We get a new place value. We will call it the ten crores place. We write TC for it is read as ten crore. It is the smallest nine digit number. The largest nine digit number is Thus, 8-digit : = (9-digits) Thus, 9-digit number means we have one place further to the left in the place value chart. Crores and ten-crores together are crores period. 1 hundred lakhs is also called one crore. 100 thousand make one lakh 100 lakhs make one crore How many 7-digits numbers are there? [Hints ] 3 NUMBERS UPTO TEN CRORES

9 INDIAN PLACE VALUE CHART Indian System Place Value Chart Periods CRORES LAKHS THOUSANDS ONES Places Ten Crores One Crores Ten Lakhs One Lakhs Ten Thousands One Thousands 1000 Hundreds 100 Tens 10 Ones Ones period has three places Ones, tens, hundreds Thousands period has two places One thousands, ten thousands Lakhs period has two places One lakhs, ten lakhs Crores period has two places One crores, ten crores Reading a numeral : All the digits in the same period are read together and the name of the period (except ones) is read along with them. Thus, we read as Twenty-six crore sixtyseven lakh eighty-two thousand four hundred ninety-four. Example 1 : Write the number name of the numeral Solution : T.C C T.L L T.Th Th H T O We read it as Twenty-three crore ninety lakh eleven thousand two hundred thirty-seven. We read as Sixteen crore thirty-eight lakh seven thousand five hundred twenty. Finding the place value of a digit in a numeral Find the place value of the digit underlined in each numeral. (a) is in the lakhs place. So its place value is 8 lakhs or ten lakhs = crore To write the place value of a digit in a number, write the digit and write 0 for all other digits to its right. Place value of 2 in is MATHEMATICS-5 4

10 (b) crores or (c) ten crores or 30 crores or (d) hundreds or 300 Example 2 : Write the numeral seventeen crores eighty-two lakh six thousand nine hundred three. Solution : The number represents 1 ten crore 7 crores, 8 ten lakhs 2 lakhs, 6 thousands, 9 hundreds 3 ones. Arrange these digits in the place value chart. Place Value Chart (Indian System) REMEMBER Lakhs has 2 places, thousands has 2 places and ones has 3 places. Mark the periods using commas (,) for convenience. Periods CRORES LAKHS THOUSANDS ONES Places 10 Crores Crores 10 Lakhs Lakhs 10 Thousands Thousands Hundreds Tens Ones We find that places 10 thousands and tens are vacant. So, we put 0 to complete the numeral. Thus, the numeral is EXPANDED FORM A number when expressed as a sum of the place values of its digits is said to be in expanded form. T.C C T.L L T.Th Th H T O Place value of 8 is 8 Place value of 7 is 70 Place value of 1 is 100 Place value of 2 is 2000 Place value of 4 is Place value of 2 is Place value of 3 is Place value of 4 is Place value of 6 is NUMBERS UPTO TEN CRORES

11 Expanded form of = T.C C T.L L T.Th Th H T O Place value of 8 is 8 Place value of 2 is 20 Place value of 1 is 100 Place value of 7 is 7000 Place value of 6 is Place value of 5 is Place value of 3 is Place value of 9 is Place value of 4 is Expanded form of = Example 3 : Write the following numbers in expanded form : (a) (b) Solution : (a) = (b) = WRITING THE NUMERAL To write the numeral for any number given in words, draw the place value chart and fill in the numbers according to the periods and places. If there are any vacant places, fill them with zeros. Example 4 : Write the numeral for six crore fifty-three thousand one. Solution : Arrange the digits in the place value chart as : C T.L L T.Th TH H T O MATHEMATICS-5 6

12 Fill in the vacant places with zeros C T.L L T.Th TH H T O So, the numeral for the given number is Example 5 : Write the numeral for the following : (a) (b) Solution : (a) = (b) = LET US PRACTISE Write the place value of each digit of the following numbers : (a) (b) (c) (d) Write the following numbers in the place value chart : (a) (b) (c) (d) Write the number name for each of the following (in Indian system) : (a) (b) (c) (d) Write the numeral for each of the following (in Indian system) : (a) Six crore four lakh thirty-two thousand eight hundred sixty-nine. (b) Seventy crore eight lakh seventy-nine thousand nine hundred seven. (c) Six crore thirty-two lakh forty-nine thousand seven hundred fifteen. (d) Seventy-two crore twenty-four lakh fifty- two thousand nine hundred twenty-nine. 5. Write the following in expanded form : (a) (b) (c) (d) Write the numeral for each of these : (a) (b) (c) (d) (e) Write the period, place and place value of the underlined digits : (a) (b) (c) (d) (e) NUMBERS UPTO TEN CRORES

13 SUCCESSOR AND PREDECESSOR The number that comes just after a given number is called its SUCCESSOR comes just after So, is the successor of is the next to So, is the successor of We can obtain the successor of a number by adding 1 to it. Successor of is = Successor of is = We can add 1 to any number, so every number has a successor. The number that comes just before a given number is called its PREDECESSOR comes just before So, is the predecessor of is just before So, is the predecessor of We can obtain the predecessor of a number by subtracting 1 from it. Predecessor of is = Predecessor of is = The number after another number can be obtained by adding 1. The number before another number can be obtained by subtracting 1. Example 6 : (a) Write the successor of (b) Write the predecessor of (c) Write two numbers just after (d) Write two numbers just before Solution : (a) Successor of = = (b) Predecessor of = = (c) Successor of = = Successor of = = Required numbers are and (d) Predecessor of = = Predecessor of = = Required numbers are and MATHEMATICS-5 8

14 SKIP COUNTING In skip counting we start with a given number and write more numbers with a fixed gap between the successive numbers. Counting by twos : Gap of two between every two successive numbers. Suppose we start with Then counting by twos we get : , , , and so on. Counting by tens : Gap of ten between every two successive numbers. Suppose we start with Then counting by tens we get : , , , and so on. Counting by hundreds : Gap of hundred between every two successive numbers. Suppose we start with Then counting by hundreds we get : , , , and so on. Example 7 : Counting by fours write four numerals from Solution : = ; = ; = ; = The numerals are: , , and Example 8 : Counting by two hundreds write four numerals from Solution : The numerals are : , , , Example 9 : Counting by thousands write four numerals from Solution : The numerals are : , , and Example 10 : Counting by ten thousands write four numerals from Solution : The numerals are : , , and Example 11 : Counting by lakhs write four numerals from Solution : The numerals are : , , and Example 12 : Counting by ten lakhs write four numerals from Solution : The numerals are : , , and LET US PRACTISE Write the successor of each of the following : (a) (b) (c) (d) Write the predecessor of each of the following : (a) (b) (c) (d) NUMBERS UPTO TEN CRORES

15 3. Write the next two numbers for each of the following : (a) (b) (c) (d) Write the two numbers that come just before each of the following : (a) (b) (c) (d) Write the next three numbers for each of the following : (a) (b) (c) (d) Write three numbers that come just before each of the following : (a) (b) (c) (d) Write two numbers which come in between : (a) and (b) and (c) and (d) and Write three numbers that come in between : (a) and (b) and (c) and (d) and Find : (a) Counting by threes write four numerals from (b) Counting by seven hundreds write four numerals from (c) Counting by five thousands write four numerals from (d) Counting by three lakhs write four numerals from (e) Counting by ten lakhs write four numerals from The signs of comparison COMPARISON OF NUMBERS The 'equal to' ( = ) sign shows that numbers on both sides have the same value = , = etc. The 'greater than' ( > ) sign shows that the number on the left side has a greater value than that of right > , > etc. The 'less than' ( < ) sign shows that the number on the left side has a smaller value than that of right < , < etc. MATHEMATICS-5 10

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