6

CBSE

MATHEMATICS Kuber 

Full Marks Pvt Ltd (Progressive Educational Publishers)

New Delhi-110002

Published by:

9, Daryaganj, New Delhi-110002 Phone: 011- 40556600 (100 Lines) Website: www.fullmarks.org E-mail: [email protected] © Publishers All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages.

Branches: • Chennai • Guwahati Marketing Offices: • Ahmedabad • Bengaluru • Bhopal • Dehradun • Hyderabad • Jaipur • Jalandhar • Kochi • Kolkata • Lucknow • Mumbai • Patna • Ranchi

NEW EDITION

“This book is meant for educational and learning purposes. The author(s) of the book has/have taken all reasonable care to ensure that the contents of the book do not violate any existing copyright or other intellectual property rights of any person in any manner whatsoever. In the event the author(s) has/have been unable to track any source and if any copyright has been inadvertently infringed, please notify the publisher in writing for corrective action.”

Printed at:

Preface I

Mathematics-V is based on the latest curriculum guidelines specified by the CBSE. The book will certainly prove to be a torch-bearer for those who toil hard to achieve their goal. Salient Features of the Book: ●● The whole book is well designed to aim at total and easy learning. This will not only build up students’ morale but their confidence also. ●● Each chapter is designed in Topicwise manner where every topic is briefly explained with sufficient solved examples and exercise. ●● All topicwise exercises incorporate VSA, SA-I, SA-II and LA for indepth practice and learning. ●● Most important questions from NCERT Textbook and NCERT Exemplar are included. ●● HOTS and Value Based Questions have been given to assess students understanding beyond the text and its application in the real world. ●● Termwise Periodic Test Papers, Model Examination Papers and Chapterwise worksheets provided at the end of the book prepare the student from examination point of view. Suggestions for further improvement of the book, pointing out printing errors/mistakes which might have crept in, in spite of all efforts, will be thankfully received and incorporated in the next edition. CBSE Circular No.: Acad-14/2017 Dated: 21/03/2017 Scholastic Area: The assessment structure and examination for classes VI to VIII have been prepared in view of the provisions of RTE-Act 2009 and comprises of two terms i.e. Term-1 and 2 as explained below: Subjects Term-1 (100 marks) Term-2 (100 marks) (1st half of the session) (2nd half of the session) 20 marks Periodic Assessment + 80 20 marks Periodic Assessment + 80 marks for marks for Half Yearly Exam Half Yearly Exam Language - 1 Half Yearly PA 20 Marks PA 20 Marks Yearly Exam Exam • Periodic Test • Periodic Test • Written exam for 80 marks Language - 2 • Written exam 10 marks with 10 marks with with syllabus coverage as for 80 marks syllabus covered syllabus covered below: Language - 3 till announcement with syllabus till announcement Class VI: 10% of 1st term covered till of test dates by Mathematics of test dates by covering significant topics + announcement school school entire syllabus of 2nd term Science of Half Yearly • Note Book • Note Book Class VII: 20% of 1st term exam dates by Submission 5 Submission 5 covering significant topics + Social school marks at term marks at term end entire syllabus of 2nd term Science end • Sub Enrichment Class VIII: 30% of 1st term Any other • Sub Enrichment 5 marks at term covering significant topics + Subjects 5 marks at term end entire syllabus of 2nd term end

(iii)

CONTENTS 1. Knowing Our Numbers..................................................................................................5 2. Whole Numbers............................................................................................................16 3. Playing with Numbers..................................................................................................28 4. Basic Geometrical Ideas...............................................................................................44 5. Understanding Elementary Shapes...............................................................................62 6. Integers.........................................................................................................................86 7. Fractions.......................................................................................................................97 8. Decimals.....................................................................................................................115 9. Data Handling.............................................................................................................128 10. Mensuration................................................................................................................158 11. Algebra.......................................................................................................................174 12. Ratio and Proportion...................................................................................................191 13. Symmetry....................................................................................................................203 14. Practical Geometry.....................................................................................................213 • Term–I: Periodic Test Papers 1 & 2 ��������������������������������������������������������������������������������������233 • Term–I: Half-yearly Test Papers 1 & 2���������������������������������������������������������������������������������235 • Term–II: Periodic Test Papers 1 & 2������������������������������������������������������������������������������������� 239 • Term–II: Annual Test Papers 1 & 2��������������������������������������������������������������������������������������� 241 • Chapterwise Worksheets���������������������������������������������������������������������������������������������������������249 Answers to Test Papers and Chapterwise Worksheets��������������������������������������������������������� 277

(iv)

1

Knowing Our Numbers

Topics Covered 1.1 Comparing Numbers 1.3 Estimation and Use of Brackets

1.2 Large Numbers in Practice 1.4 Roman Numerals

Let’s Recall • Numbers help us to count concrete objects. • Numbers help us to arrange collection of objects and identify which is bigger or smaller. • Successor of a number is a number which comes just after the given number. For example, 20 is a successor of 19. • Predecessor of a number is a number which comes just before the given number. For example, 19 is a predecessor of 20.

1.1 Comparing Numbers • To compare two numbers, the number with more number of digits is the greater number. If number of digits is same then compare their leftmost digit. The number with greater leftmost digit is greater and if the leftmost digit of the numbers is the same then compare their next digit, and so on. • To form the greatest number from given digits we write the digits in descending order. For example, given digits are 5, 7, 2, 9, then the greatest number is 9752. • To form the smallest number from given digits, we write digits in ascending order (in case zero is not one of the digits), e.g., if given digits are 5, 7, 2, 9, then the smallest number is 2579. In case zero is one of the given digits, then leftmost digit is the second smallest digit, followed by zero and remaining digits are in ascending order, e.g., if 5, 0, 2, 9 are given digits then the smallest number is 2059. • The smallest number of three digits is 100, of four digits is 1000, of five digits is 10000, and so on. • The greatest number of three digits is 999, of four digits is 9999, of five digits is 99999, and so on. • To write a number in words, in the Indian System of Numeration, first we put commas in between the words. We start from right side and place first comma after the first three digits and next commas after every two digits. i.e., TC C, TL L, TTh Th, H T O. • To write a number in words in the International System of Numeration, we start from the right side and put comma after every three digits like HM TM M, HTh TTh Th, H T O Example. (a) Express six crore nine lakh nine thousand four hundred in figures. (b) Express in expanded notation 2,01,902. (c) Write place value of the digit given in bold in 610379. Solution. (a) 6,09,09,400 (b) 2,01,902 = 2 × 100000 + 1 × 1000 + 9 × 100 + 2 × 1 (c) 10,000

5

Exercise 1.1 I.  Very Short Answer Type Questions (1 Mark) A. Answer the following. 1. Which number is successor of the largest three-digit number? 2. Which number is predecessor of the smallest five-digit number? 3. What is place value of 1 in the smallest four-digit number? 4. What is face value of zero in 9074? 5. How many thousands make a million? 6. How many lakhs make one crore? 7. Write the name of 7653384 according to International System of Numeration. 8. Write the greatest number of 5 digits. B. Fill in the blanks. 1. With commas at appropriate places as in the Indian System of Numeration 6234570 will be written as .................. . 2. According to International System of Numeration the number 56643175 is written as .................. . 3. The numbers 6234, 6024, 5235, 8100 when arranged in ascending order, will be .................. . 4. Form the greatest and the smallest four-digit numbers using the given digits only once 6, 0, 2, 4, ................... , ................... . C. Say True or False 1. Expanded form of 6205 is 6  1000 + 2  100 + 5  1 2. Successor of the largest 6-digit number is 1 million. 3. The sum of the place value and the face value of 5 in 62578 is 1000.

II. Short Answer Type Questions–I (2 Marks)

1. Write the smallest number of 6 digits using 2, 0, 7. 2. Select the smallest number: 108912, 78905, 93210 3. In three consecutive years, number of girls born are 5,60,005; 5,40,720;  5,40,360. Arrange them in ascending order. Write a suitable slogan on saving the girl child. (VBQs)

III. Short Answer Type Questions–II (3 Marks)



6

1. Write the greatest 4-digit number using different digits with tens digit smallest natural number and unit digit is five times the tens digit. 2. Find 8 times the difference of place values of 5’s in 450253. 3. Kanu receives an e-mail every 15 minutes during the work day. How many e-mails would she receive between 9:00 am and noon? Write benefits of using technology; also write a drawback. (Multidisciplinary Question) 4. There are 380 eggs in a farm. If to fill 14 trays of equal size it was short of 1 dozen eggs then find how many eggs could be accommodated in each tray? (Life Skills Question)

Mathematics–6

IV. Long Answer Type Questions (4 Marks)



1. I am a multiple of 10 greater than 30,000 but less than 50,000. My tens digit and hundreds digit are same. Ten thousand digit is two times thousand digit. Sum of my digits is 8. Find what number am I? 2. Using digits 1 to 9, fill the squares such that sum of numbers of each row is same as sum of numbers of each column is same as sum of numbers of each diagonal. Read numbers as per arrows marked. Write the largest number and the smallest number also. (HOTS) 3. Following table enlists the world’s five largest deserts. Name of the Desert 1. Kalahari desert 2. Australian desert 3. Gobi desert 4. Arabian desert 5. Sahara desert



Country Africa Australia Asia Asia Africa

Area (in sq km) 5,80,000 1,250,000 1,300,000 8,50,000 8,800,000

(i) Write the area of each desert in the Indian system as well as in the International System of Numeration. (ii) Write the names of the deserts in ascending order of their areas. (iii) Write the name of the largest desert of the world. (iv) Write the 4th largest desert of the world. (Multidisciplinary Questions) 4. The prices of 4 cars on display in a showroom are `735710, `518959, `536718 and `775925. Arrange these prices in ascending order. Saumya wants to buy a car. What is the minimum amount she will spend?

Answers and Hints I. A. 1. 1000 2. 9999 3. Thousand 4. Zero 5. Thousand 6. Hundred 7. 7,653,384: seven million six hundred fiftythree thousand three hundred eighty-four 8. 99999 B. 1. 62,34,570 2. 56,643,175: Fifty-six million six hundred forty-three thousand one hundred seventy-five 3. 5235, 6024, 6234, 8100 4. 6420, 2046 C. 1. True. 2. True; Successor of 999999 = 999999 + 1 = 10,00,000 3. False; Place value of 5 is 500 and face value is 5. Sum is 505 and not 1000. II. 1. 200007 2. 78905 3. Ascending order is:

5,40,360;  5,40,720;  5,60,005 Slogan: ‘Saving a Girl Child is Like Saving Humanity. III. 1. 9815 2. 399600; 3. 12 e-mails, People can communicate very easily and very fast. Drawback is misuse of it like sending unnecessary posts to others. 4. 28 eggs IV. 1. 42110 2. 8

3 4

1 5

6 7

9

2

Numbers along rows are 816, 357, 492

Knowing Our Numbers 7



Numbers along columns are 834, 159, 672 Numbers along diagonals are 852, 654 Largest number is 852 Smallest number is 159 3. (i) Kalahari Desert Indian system: Five lakh eighty thousand sq km. International System: Five hundred eighty thousand sq km. Australian Desert Indian system: Twelve lakh fifty thousand sq km. International System: One million two hundred fifty thousand sq km. Gobi Desert Indian system: Thirteen lakh sq km. International System: One million three

hundred thousand sq km. Arabian Desert Indian system: Eight lakh fifty thousand sq km. International System: Eight hundred fifty thousand sq km. Sahara Desert Indian system: Eighty eight lakh sq km. International System: Eight million eight hundred thousand sq km. (ii) Kalahari Desert, Arabian Desert, Australian Desert, Gobi Desert, Sahara Desert. (iii) Sahara Desert (iv) Arabian Desert 4. `518959, `536718, `735710, `775925 Minimum amount what Saumya has to spend to buy a car is `518959.

  1.2. Large Numbers In Practice The metric measurement is used to measure length, mass and capacity in standard units which are metre (m), gram (g) and litre (l), respectively. The prefixes such as kilo, hecto deca, deci centi and mili are used with these units. The easy way to learn these prefixes are • King Henry Died Mother Didnot Cry Much

For example, 1 km = 1000 m (Leftmost is the greatest unit. To convert from the greatest unit to the smallest, we multiply the greatest unit and from the smallest to the greatest, we divide the smallest units). To change from kilometre to metre multiply by 1000 and to change from metre to kilometre divide by 1000, and so on. Example 1. The distance between two cities is 42 km 875 m. A bus makes 6 round trips every day. How much distance does it cover in the month of July? Solution. Distance between two cities = 42 km 875 m = 42 × 1000 m + 875 m = 42875 m Number of rounds per day = 6 Distance covered in 1 day = 42875 m × 6 = 257,250 m Month of July has 31 days. ∴  Distance covered in 31 days = 257250 × 31 = 7974750 m 7974750 ∏ 1000 = 7974 km 750 m Example 2. The population of a small town is 40,000. The number of women and children in the town were 19,587 and 6,703, respectively. Find the number of men in the town.

8

Mathematics–6

Solution. Number of men = 40,000 – (19, 587 + 6,703)             = 40,000 – 26,290 = 13,710. Example 3. There are 5 sections of class VI in a public school and there are 40 students in each of the sections. If the monthly bus charges for each student be `895, find the total collection of bus fees from class VI. 157600 Solution. Number of students in one section = 40 34 535840 Number of sections = 5 –34 Total number of students = 40 × 5 = 200 195 –170 Fees collected from 1 student = `895 258 Total fees collected = 895 × 200 = `1,79,000 –238 Example 4. The cost of 34 refrigerators is `5,35,840. 204 Determine the cost of one, if each costs the same. –204 Solution. Cost of 34 refrigerators = `5,35,840 0000 –000 So, cost of 1 refrigerator = 5,35,840 ∏ 34 = `15,760. 0

Exercise 1.2 I.  Very Short Answer Type Questions (1 Mark) A. Answer the following.

1. How many centimetres make a kilometre? 2. A snake is 625 cm long. Express it in metres. 3. Today in the morning I had one-fourth litre of milk. How much is it in mL? 4. How many milligram make one kilogram? 5. If a and b are whole numbers. Is a × b always a whole number.

B. Fill in the blanks.

1. King Henry Died ................... . 2. (i) 1 metre = ................... centimetres. (iii) 1 kilometre = ................... metres. 3. (i) 1 kilogram = ................... grams. (iii) 1 millilitre = ................... kilolitres.



4. Standard unit of capacity is ................... .

C. State True or False. 1. Standard unit for length is centimetre.

(ii) 1 millimetre = ................... centimetres. (ii) 1 litre = ................... millilitres.

2. 79 kg = 79000 g.

II. Short Answer Type Questions–I (2 Marks)

1. Every day I drink 200 mL of hot chocolate milk. Find total milk consumed in litres from January to April. 2. A carton containing tetra packs of mango juice weighs 780 g. If carton weighs 40 g, what is the weight of each tetra pack? 3. An oil tin contains 92 L of refined oil. How many bottles of capacity 250 mL can be filled? 4. Find the value of 745 – 275 ∏ 275. 5. Find the whole numbers which satisfy x × x = x.

Knowing Our Numbers 9

III. Short Answer Type Questions–II (3 Marks)



1. What must be added to the largest 4-digit number to get smallest number of five different digits formed by 1, 2, 0, 3, 4? 2. How much should be subtracted from smallest four-digit number having different digits to obtain largest three-digit number with unit digit 8? 3. Capacity of a tank is 500,000 cm3. The family used up 110 L of water in cooking, drinking and bathing. 100 L of water in washing car and 100 L of water in washing terrace. What is remaining quantity of water in the tank? What will you like to suggest to the family regarding use of water? 4. Soni made 25 Vandanvaar using cloth of length 150 cm each whereas Jyanti made same using paper. What was total length of paper or cloth used? What would you like to suggest to Jyanti and give reason? 5. Find the product of greatest number of three digits and the greatest number of two digits.

IV. Long Answer Type Questions (4 Marks)

1. Vijaya earns `155 an hour. If she works 38.5 hours in a week, how much will she earn for the week? 2. Vandana had 50 kg of oranges to sell in the morning. By noon time she could sell only 38 kg 750 gm. She notices 2 kg 500 gm was rotten so she planned to sell remaining by same day. What quantity is she left with to sell? 3. Radhika needs 1 m 15 cm cloth to stitch a frock. Out of 50 m cloth how many frocks can she stitch and how much cloth will be left unused? 4. If cloth required for 1 pair of pyjamas is 1 m 200  cm and if 50 cm of cloth is wasted while making one pair of pyjama then how many pairs can be stitched from 50 m cloth? 5. In the month of February of the year 2012, average rainfall was noted to be 3 cm. What was the total rainfall in the month of February? How much is it less than 1 m? 6. The distance between school and home of Neesha is 2 km 325 m. Every day she walks 750 m and then takes Rickshaw for remaining distance. (i) How much does she walk in 25 working days? (ii) How much will she pay to Rickshaw if it charges `2 per km? How is she contributing towards reducing pollution?

Answers and Hints I. A. 1. 1,00,000 2. 6 m 25 cm = 6.25 m 3. 250 mL 4. 10,00,000 mg 5. Yes, product of two whole numbers is always a whole number. B. 1. Mother Didnot Cry Much 2. (i) 100 (ii)

1 cm (iii) 1000 10

1

3. (i)  1000  (ii)  1000  (iii)  10 , 00 , 000 4. Litre

10

Mathematics–6

C. 1. False: Metre is the standard unit of length. 2. True: as 1 kg = 1000 g II. 1. 24 litres 2. 37 g 3. 368 bottles 4. 745 – 275 ∏ 275 = 745 – 1 = 744 5. 0 × 0 = 0 and 1 × 1 = 1 III. 1. 235 2. 25 3. 190 L; Suggestion to the family is instead of washing car, it could have been wiped off with wet cloth. Instead of washing terrace, it could be moped to save water.

4. Cloth used is 3750 cm, i.e., 3 m 750 cm. Jyanti used paper, if paper gets spoiled, it will be thrown, whereas if cloth is used, it can be washed and reused. 5. Greatest 3-digit number = 999 Greatest 2-digit number = 99

1.3. Estimation And Use

of

Product = 999 × 99 = 98,901 IV. 1. `5967.5 2. 8 kg 750 g 3. 43 frocks, 55 cm 4. 40 pairs of pyjamas 5. 87 cm; 13 cm 6. (i)  18 km 750 m,  (ii)  `78.75

Brackets

• In number of situations in daily life, we have to estimate the outcome of mathematical operations and this is done by rounding off the numbers involved and getting a quick rough idea. Example: I have `1295 in my pocket and the toy costs `575. What will be left with me after purchasing that toy? What will I do if I have approximately `1300 and toy is for around `600? I will be left with around `700 whereas actual answer is `720. • We use brackets to avoid confusion in the problems where we need to carry out two or more than two mathematical operations. Estimating to the nearest ten Example: Look at the number line given below. 30

31

32

33

34

35

36

37

38

39

40

The number 32 is between 30 and 40. Is the number 32 nearer to 40 than to 30?   No Is the number 32 nearer to 30 than to 40?   Yes   It is nearer to 30. ∴  We round 32 to 30. Similarly, as 38 is closer to 40, we round 38 to 40 and 35 is exactly between 30 and 40, so it is rounded to 40. Estimating (rounding) to the nearest hundred Consider the number line given below. 300 310 320 330 340 350 360 370 380 390 400

Is the number 340 nearer to 400 than 300?   No Is the number 340 nearer to 300 than 400?   Yes   340 is nearer to 300. ∴  We round 340 to 300. As 390 is nearer to 400 so it is rounded to 400. 350 is exactly in between so it is rounded to 500. Estimating (rounding) to the nearest thousand 350 2600 2700 2800 2900 3000 2000 2100 2200 2300 2400 2500

As number 2200 is closer to 2000, so it is rounded off to 2000. As number 2700 is closer to 3,000, so it is rounded to 3000. As number 2500 is exactly in between it is rounded up to 3000. Sometimes, brackets play a crucial role in calculation.

Knowing Our Numbers 11

Example: Suppose a toy costs `3813. Rajat sold 4 toys to Sahar and 6 toys to Neha. How much money did Rajat get? This can be done in the following two ways: (a) Find the cost of 4 toys and 6 toys separately and then add. `3813 × 4 + `3813 × 6 = `15252 + `22878 = `38130 (b) Add the number of toys and multiply by the cost of 1 toy. 4 + 6 = 10 and 10 × `3813 = `38130 ∴  Total `38130 Is 4 + 6 × `3813 = `38130? No. So, we put 4 + 6 within brackets, i.e., (4 + 6) and then multiply this sum by `3813 and get `38130, i.e., (4 + 6) × `3813 = 10 × `3813 = `38130

Exercise 1.3 I.  Very Short Answer Type Questions (1 Mark) A. Answer the following. 1. Round off 62578 to the nearest thousand. 2. Estimate 795 – 324 using general rule. 3. Round off 1625 to the nearest hundred. 4. Round off 2351 to the nearest thousand. 5. Round off 873 to the nearest thousand. B. Fill in the blanks. 1. Cost of a washing machine is `67824. Rounded off to the nearest thousand is ................... . 2. 2315 when rounded to the nearest ten is ................... . 3. 948 when rounded to the nearest hundred is ................... . 4. 580219 rounded to the nearest lakh is ................... . C. Say True or False. 1. Estimated sum of 3425 and 4688 rounded off to hundreds is 8000.

II. Short Answer Type Questions–I (2 Marks) 1. List all numbers which are rounded off to the nearest tens as 580. 2. Estimate the sum 4,250 + 17,480 by estimating the number to the nearest (i)  hundreds (ii)  thousands. 3. Find the estimated (i) quotient for 745  24 by rounding off to its greatest places, (ii) product for 898  785 by rounding off each factor to its greatest place. 4. Complete the table: Rounded to the nearest Number Thousand Ten Thousand Lakh 378259 378000 380000 _________ 459832 _________ 460000 _________

III. Short Answer Type Questions–II (3 Marks)

12

1. Using the digits 1, 2, 3, 5 form numbers which when rounded off to nearest hundreds give 5300.

Mathematics–6



2. In the month of February of the year 2012, average rainfall was noted to be 6 cm. What was the total rainfall in the month of February? How much is it more than 1 m? 3. Estimate and compare with the actual sum 730 + 998. 4. Give a rough estimate and also a closer estimate of (108734 – 47599).

IV. Long Answer Type Questions (4 Marks)

1. Rajat and Jacob play for 2 and 3 hours daily. How many hours do they play in a week? 2. Simplify: 12 + 3[5 + 3{(9 – 7) + 2]. 3. Simplify: 215 – [1320 ∏ (12 × 11) + 7 – {5 – 9 – 7}] 4. Simplify: 81 of [59 – {7 × 8 + (13 – 2 of 5)}].

Answers and Hints

I. A. 1. 63000 2. 500 3. 1600 4. 2000 5. 1000 B. 1. ` 68000 2. 2320 3. 900 4. 600000 C. 1. False: 3400 + 4700 = 8100 II. 1. 575, 576, 577, 578, 579, 581, 582, 583, 584 2. (i)  21700 (ii) 22000 3. (i)  35 (ii) 720000 4. 4,00,000;  4,60,000;  5,00,000 III. 1. 5312, 5321 2. 174 cm; 74 cm 3. We round off to the nearest hundred 730 is rounded to 700. 998 is rounded to 1000. Estimated sum = 700 + 1000 = 1700 Actual sum = 730 + 998 = 1728 Estimation is quite reasonable.

4. Rough estimate = 100000 – 50000 = 50000 For closer estimate we round off to the nearest ten thousand 108734 is rounded to 110000 47599 is rounded to 50000. Closer estimated difference = 60,000. IV. 1. (2 + 3) × 7 = 5 × 7 = 35 hours 2. 12 + 3[5 + 3{2 + 2}] = 12 + 3[5 + 3 × 4] = 12 + 3[5 + 12] = 12 + 3 × 17 = 12 + 51 = 63 3. 215 – [1320 ∏ (12 × 11) + 7 – {5 – 9 – 7}] = 215 – [1320 ∏ 132 + 7 – {5 – 2}] = 215 – 14 = 201 4. 81 of [59 – {7 × 8 + (13 – 10)}]

  1.4. Roman Numerals • In Roman System of Numeration, there are only 7 symbols–I, V, X, L, C, D, & M, where I stands for 1, V for 5, X for 10, L for 50, C for 100, D for 500 and M for 1000. Rules 1. When written to the left of V and X, I is subtracted, i.e., IV = 5 – 1 = 4 and IX = 10 – 1 = 9. 2. When written to the left of L and C, X is subtracted, i.e., XL = 50 – 10 = 40 and XC = 100 – 10 = 90. 3. When written to the right of a numeral, I is added, i.e., II = 1 + 1 = 2, VI = 5 + 1 = 6, XI = 10 + 1 = 11 LI = 50 + 1 = 51, CI = 100 + 1 = 101 4. When written to the right of a numeral greater than or equal to X, X is added, e.g., XX = 10 + 10 = 20, LX = 50 + 10 = 60.

Knowing Our Numbers 13

Remember: 1. V, L and D are never repeated. 2. I, C and X can be repeated at the most 3 times. 3. A smaller number can be subtracted from the bigger number at the most one time. Example 1: Write in roman numerals (a) 205  (b) 113  (c) 345  (d) 400  (e) 469 Solution: (a) 205 = 200 + 5 = CC + V = CCV (b) 113 = 100 + 13 = CXIII (c) 345 = CCCXLV (d) 400 = CD (e) 469 = CDLXIX Example 2: Write in Hindu-Arabic numerals (a) XCIV  (b) CXXV  (c) CXLII  (d) CCLIV  (e) CDXIX Solution: (a) XCIV = XC + IV = 90 + 4 = 94 (b) CXXV = C + XX + V = 100 + 20 + 5 = 125 (c) CXLII = C + XL + II = 100 + 40 + 2 = 142 (d) CCLIV = CC + L + IV = 200 + 50 + 4 = 254 (e) CDXIX = CD + X + IX = 400 + 10 + 9 = 419

Exercise 1.4 I.  Very Short Answer Type Questions (1 Mark) A. Answer the following. 1. Write correct numeral for 439. 2. At the most how many times a symbol can be repeated? 3. Write 173 in roman numbers. 4. Match the correct numbers (a) 135 (i) CDLIX (b) 361 (ii) CCLXXXIV (c) 284 (iii) CXXXV (d) 459 (iv) CCCLXI

Answers and Hints I. A. 1. CDXXXIX 2. 3 3. 173 = 100 + 70 + 3 = C + LXX + III = CLXXIII

14

Mathematics–6

4.

(a) Æ (b) Æ (c) Æ (d) Æ

(iii) (iv) (ii) (i)

Subject Enrichment Activities I. Crossword

Complete the following crossword using the given clues. Across 1. Number used for counting is called ............. 2. Arranging of numbers from greater to smaller is called ............. 3. A number comes just after the given number is called ............. Down 4. A judgment about the quantity of something is called.......... 5. A number comes just before the given number is callled ....... 6. Arranging of numbers from smaller to greater is ..........

2 3 1 6

5 4

II. Activity

Objective: To represent Roman Numerals using matchsticks / ice-cream sticks. Materials required: Matchbox, Water-colour (Red and Yellow). Steps: 1. Colour few matchsticks with red and some with yellow and let them dry. 2. Make the following Roman numerals for the following numbers 3, 50, 65, 110, 525, 1010. 3. Use yellow matchstick for horizontal lines and for vertical or diagonal lines use red match sticks. 1 50 110 500 1000 use red

use yellow

half matchstick (red)

yellow

yellow

red red

use little more than half matchstick (red)

red

yellow yellow

Numeral

Write as a Roman Numeral

3

III

Yellow

use red

Use Matchsticks use yellow colour

65 525 1010 Puzzle: After learning Roman Numerals Montu wrote the following: ‘One fifty O five E thousand Y thousand O thousand’. What did he write?

Answers I.  Down: 1. NATURAL 2. DESCENDING 3. SUCCESSOR

Across: 4. ESTIMATION 5. PREDECESSOR 6. ASCENDING

II.  I LOVE MY MOM.

qqq

Knowing Our Numbers 15

Buy Online at

FREE ONLINE SUPPORT AVAILABLE ON

Available on

www.fullmarks.org

Full Marks Pvt Ltd (Progressive Educational Publishers)

9, Daryaganj, New Delhi-110002 Phone: 011- 40556600 (100 Lines) Website: www.fullmarks.org E-mail: [email protected]