math4

hs PV3\".9*9

tcAs ldentifyyour strongest skills, ilackyear on year pedormance See clearlywhere you need to improve Measure your true capabilities on a global scale In 2017the most comprehenslve, annual, g oba benchmarkof rad Fg p og es5 /r' rlbo a ir'f6d 11Ld a rACo<<6<sF<rre high€r-orderthinkingsk sthat!nderpinsuccess n Methematics, Sclence, English [C]2-12)and Digta Technolog es,lC 3 101. Find out more at www.macmillanoducation.in/icas S uNswctooal ,Vl macmillan educat on CAS is3 produ.t ol UNSW 6 oba,a wholly owned ente.priseol UNSWAustra a (The UnNorsrty 01 New South WalesJ Ltisdislributed erclls vey ln .d a by Macm lan Edlcat oi

(Ytd}4\\\\j( ruoro,r)fr Dr Revothy Poromesworon Usho Vorodorojon Vice Principal, PS. Senior Secondary School Former Vice Principal & HOD l\\.4athematics Mylapore, Chennai PS. Senior Secondary School Mylapore, Chennai Y,/tv',tft-^ L| e.a\\rhert f|ir Ut.ffe '0\"',J:i.;ioi161;;ou,,,o eoucalon

A MACMILLAN A ntuchillM Ptblishers Indid Ptitate Ltd, 2013, 2017 All rights resened under the coplright act..No pan of this publicatioD day be Eproduced. transcribed, lransmitted, srored in a retrievat system or trdslated into any ldguage or cornpurq lmguage, iD ey form or by any means, electronic, mecfieical, magnelic, op.ical, cheinical, mdual, photocopy or oth€trhe without the prior lemission of the coplriehr owDer Any pe6on who does any uauthdised act in relation to this publication may be liable 10 criminal proseculion and civil claims for damages. Reprinled 20Il Qhrice),2015 (wiceI 20t 6 MACMILLAN PUBLISHERS INDIA PRIVATE LIMITED Dehi Bengaluru Ch€mai Kolkara Mumbai Ahmedabad Bhopal Chandigdh Coimbatore Cuttack Guwahali Hyderabad Jaipur Lucknow Madlrai Nagpu Paha Pune Thinrvananthapw Visathapahd ISBNr 978-9352-52165-4 Published by Macrnilld Publishers tndia Private Ltd, ,?1, P6tullos Road, Chennai 600002, India Printcd di Krili, New Delhi ll0 020 \"Tlis book is meanl for educational and l€mhg pul?oses. The author(s) ofthe book has/have raken all reasonable care ro eDsE lhal the contents ofrhe book do not violire any co!'right or orher intellectuat property righrs ofany lqson in 0y manner whar- so€ver. In the evot the author(s) has/have been unabl€ io rack any souJce and if any coplright has been inadvenently infi.inged, please notify the publisher in writing for any coEective adion.',

,.irr'ri for Classes 1 to 8 has been developed by practising teachers and maths experts. Based on the latest pedagogical approaches to teaching mathematics, the series provides a strong mathematical focus and plenty of opportunities for Continuous and Comprehensive Evaluation. The series is based on the premise that all students can become powerful mathematical learners. r,'-i:1 .,::tt:,tt ::l Let's Recall recapitulates previous knowledge of concepts Maths Around Us helps students apply mathematical. concepts in real life situations HOTS/Target Otympiad/Problem Solving empowers students to think out-of-the-box Speed Maths/Mental Maths prepares students to carry out quick calculations Take Care helps students avoid common errors Maths Lab Activity and Project connect maths with real-life situations Fun With Maths and Maths Game reinforce the concepts taught in a fun way Enrich Yourself provides deeper insight into the concept under study Revision Station helps students in assessing their understanding of the concepts learnt Worksheet helps in reinforcing the concepts learnt Glossary serves as a ready reference Practice Sheets aid in comprehensive evaluation Maths Engine includes tasks that foster creative thinking and problem solving skills among students

[eEsem Strueilure Let's Reca ll Recapitulates previous knowledge of concepts. .fs.\"\" u,-*3 ivl;i:l:-' :..1 . l,ct: 'i:/ a'ir :::.Oi1cr Connect maths with real-life situations.

rr rougr rr I I Helps students in assessing their understanding of the concepts learnt. )? Helps in reinforcing the concepts learnt. Serves as a ready reference. 3 . . .--\"--'l. ,i,'1,

Dlglilol Reeources : 0 $lopdlot Multipl€s

Oge-qppropriote digitol resources to enricb leorning experieDce

-._-.\"_-__- Conrcnts 1. Large Numbers t9 2. Addition and Subtraction 3. Multiplication 36 51 4. Division 65 5. Factors and Multiples 79 5. Fractions 1.O2 7. The World of Shapes 1.1,4 8. Patterns and Symmetry 9. Metric Measures t24 r40 10. Perimeter and Area 1L. Time 1.52 12. Money 163 13. Data Handling 175 14. Problem Solving Skills L82 186 Practice Sheets 190 192 G lossary * n*i Answers to Selected euestions FFFW

Place Value of a digit is the value of the place occupied by that digit in a number. Face Value of a digit is the digit itself. trtrllrLet us see how the place value of any digit, say 5, changes in different numbers. €5 Place value of 5 is 5 ones, i.e., 5 €5 3 Place value of 5 is 5 tens, i.e.,50 56 €z Place value of 5 is 5 hundreds, i.e., 500 598 €3 Place value of 5 is 5 thousands, i.e., 5000 Expanded form of 5983 is 5 thousands (5000) + t hundreds (900)+ 8 tens (80)+ a ones (3). 1. Look at the picture given below and answerthe following questions. 378 m ..S764 m Playground Anu's home rlFrtl

T- ij a. l--_-lFind the distance from Anu,s home to the playground through the school. \\_-______J !i,. jitj b. ,Find the distance from the school to the temple th rough the plavsround. l-__-.') ji t__J ri ! c. , hom,. e.Find the distance from the school to the temple through Anut l--_-) ii ii d. aL__lJiwhich distance is greater-the distance from Anut home to the praveround i .i-..--.--:-----.---.-.--:.---..---.-.1 temple? t-Jthrough the school or through the i .----.------\"--.-.--.---..-------.-------''.i S-digit Numbers Do you know that Sachin Tendulkar has scored more than L7955 runs in One Day International cricket matches? Here, 17955 is a s-digit number. In previous class, we have learnt that the largest 4-digit number is 9999. Let us add 1to it and see what we get. We get the smallest s-digit number, that is, 1OOOO. 100 00 It is read as ten thousand. l.! r' 17955 is read as seventeen thousand nine hundred fifty-five. L Place Value Chart The place value chart is divided into the groups of places called periods. For S_digit numbers, we have two periods, that is, the ones period and the thousands period as shown below. These periods are separated bV a comma. Ten thousands Thousands Hurn---d--r--e--d---s-il-T---e--n---s------Ones So, L7955 will be written as i.7,955. The place values of the digits in 17,955 are as follows: 5x10=50 9x100=900 7x1000=7000 1x10,000=10,000

Representing a s-digit Number on an Abacus Represent 98,765 on an abacus. 98,765 is also the largest 5-digit number with different digits. 5-digit Numbers The cost of a car is 7 262354. Here, 252354 is a 6-digit number. We know that the largest 5-digit number is 99,999. lf we add 1 to 99,999, we get 100000. TdETEE It is the smallest 6-digit number. lt is read as 1 lakh. 99 L TEETETWe write 262354 in the place value table as shown. L00 000 262354 262354 is read as two lakh sixtv-two thousand three hundred fifty-four. Place Value Chart For 6-digit numbers, the place value chart is divided into three periods, that is, the ones period, the thousands period and the lakhs period. Lakhs Ten thousands Thousands H und reds Tens Ones So, 262354 will be written as2,62,354. EThe place values of the digits in 4,51,328 are as follows: Place value ) 8x1=8 2x70=20 3x100=300 1x1000=1000 5x10,000=50,000 4x1,00,000=4,00,000

Representing a 6-digit Number on an Abacus Represent 2,62,354 on an abacus. The place value of the first 2 in 2,62,354 is 2,OO,OOO. The place value of 6 in 2,62,354 is The place value of 3 in 2,62,354 is Expanded Form The expanded form of 65,432 is +5000+400+30+2. +The expanded form of 2,62,354 is 2.0U,0C[] + 2000 +:300 +:itj + 4. Write 7,15,0L3 in the place value table and also write its expanded form. Short Form E|rffir 0 0 00 0 To write 3,00,000 + 60,000 + 7,OOO + 5OO + 10 + 9 in short form, arrange the numbers In columns. 6 0 00 0 Then add all the numbers. 7 00 0 The sum, 367519, is the short form of 50 0 3,00,000 + 60,000 + 7,OOO + 5OO + 10 + 9. 70 +9 3575 L9 Write in short form. Then place the numbers in r ErEr the place value table. 1,. 1. 400,000 + 20,000 + 599.. 19 + 3: 2. 60,000 + 4000 + 5OO + 30 + 7: 3. 3. 8,00,000 + 3000 + 9OO + L0:

Moths Around Us Arjun is very fascinated by the plants around him. He wants to know about the different kinds of plants that exist in India. His teacher explained him that India has a wide variety of plant species. There are more than 47000 plant species that exist in India. Out of these species, more than 18000 are flowering plants whereas more than 3500 are non-flowering plants. Also, there are around 3000 plant species which have great medicinal values. Other plant species are more than 25000 in number. Arjun was amazed to learn this fact. But at the same time, he wanted to know and understand more about such large numbers. Seeing this, his teacher asked him to draw a place value table and write allthese numbers in that, in order to understand them in a better wav. 1. Write down the numbers represented on the abacus. B. ffiro ffiro Th H T o a. Write down the new number, if 3 more beads are added to the hundreds column in A. Write down the new number, if 4 more beads are added to the thousands column in 'B'. Write down the new number, if one bead is removed from the ten thousands column in 'C'.

Write in figures. One has been done for you. 21,562 a. Twenty-one thousand five hundred sixty_two b. Forty-four thousand ten Sixty-three thousand two hundred fifty-seven d. One lakh sixty-eight thousand Three lakh ninety-nine thousand 3. Write the number names of the given numbers. One has been done for Vou. a. 64,247 Sixty-four thousand two hundred fony_seven b. 78,081 c. 2,22,712 d. 4,56,20L e. 8,99,005 f. 3,08,196 4. Write ln short form. One has been done for you. a. 2,00,000 + 30,000 + 5OO + 6 b. 60,000 + 5000 + 200 + 80 + 1 c. 5,00,000 + 1_000 + 60 + 3 d. 70,000 + 6000 + 5OO +8 e. 1,00,000 + 20,000 + 5 5. What is the place value of 5 in each of the following numbers? One has been done for vou. 8750 5 tens or 50 b. 9560 c. 25,300 d. 57,276 e. 5,O0,290 98,105

6. Write the place value of 4 in each of the following numbers. One has been done for you. 4723 4000 or 4 thousands o. 42,380 994 o. 4,00,000 13,46s 23,L47 7. Write a number that has a. 4 hundreds, 5 tens, l ten thousand, 4 ones and 6 thousands: o. 1lakh,5 ten thousands,6 ones,2 hundreds and 3 thousands: 5 lakhs, 3 ten thousands, 7 ones, 8 hundreds, 3 thousands and 4 tens: Solve. a. Count in tens and fill in the blanks. 45,620 45,630 b. Count in hundreds and fill in the blanks. 43,100 43,200 c. Count in thousands and fill in the blanks. 7t,260 72,260 d. Count in ten thousands and fill in the blanks. 15,290 25,290 9. Put the missing commas and write in words. a. 7895 b. 34952 c. 14236 d. 144325 e. MIZIZ Comparing Numbers : :,- .. The library in a school has 10,000 books and the library in another school has 9999 books. . --,i!cei,Which librarv has lesser number of books? When the numbers to be compared have different number of digits, the number with more number of digits is greater. Here, 9999 has lesser number of digits than 10,000. Hence, 9999 < 10,000. . When the numbers to be compared have same number of digits, start comparing from the digit with the highest place value till you reach a column with different digits.

Example: The average weight of an Indian elephant is 1240 kg while that of an African elephant is 1280 kg. Which elephant is heavier? In this case, the first two digits are same for both the numbers. ETETil so, we compare the digits in the tens column for comparing the 40 two numbers. L2 80 Since, 4 < 8 t--J t Thus, 1.240 < 1\"280. Same Different Hence, the African elephant is heavier. Also remember that 1240 comes before L280 in forward counting. Ascending Order When the numbers are arranged in the order of the smallest to the largest, we say the numbers are in ascending order. The prices of four items in a shop are I 3980, { 3896, 3980 { 3698 and { 3869. Let us arrange these numbers in the order of the smallest to the largest. The ascending order is 3698; 3869; 3896; 3980. Arrange 52,800; 58,200; 50,820 and 50,280 in ascending order. ))) Descending Order When the numbers are arranged in the order of the largest to the smallest, we say the numbers are in 59,370 descendins order. The costs of five different brands of TV are I 56,390, { 59,370, 58,700 { 58,700, { 59,730 and { 57,800. Let us arrange these numbers in the order of the largest to the smallest. The descending order is 59,730; 59,37O; 58,70O;57,800; 55,390. Arra nge 58,945; 77 ,99q 88,869 and 66,698 in descending order. )))

Forming Numbers EEEEEFive different digits are given below. To form the greatest 5-digit number using all the digits, arrange the digits in decreasing order. The greatest number formed is 87532. To form the smallest 5-digit number using all the digits, arrange the digits in increasing order. The smallest number formed is 23578. Example: Write the greatest and the smallest 5-digit numbers using the digits 1.,0,5,9,6. To form the smallest number using the given digits, begin the number with L and not with zero as otherwise, it will be a 4-digit number. Hence, 10,569 is the smallest 5-digit number. To form the greatest number, arrange the digits in descending order. Hence, the greatest number is 96,510. 1. Match the following. One has been done for you. . x9r( 1 less than ) '\"t@ Z--'-\\--'w'----r \\( Greatest 6-diCit ) numberr---l

2. Fill in the boxes with <, > or = b. 2,sr,72sa)L!,734 d. s,32,s70--l s,32,s70 a. es,6sof__l2,oo,ooo c. z,tslzof-)z,rs,ttg 3. Write the number that coiles just before the given numbers. 7r,986 b. _4,68,250 c. 98,987 86,999 o. t,43,899 e. _ 5,00,000 t. 4. Write the number that comes just after the given numbers. a. 84,499 b. s,68,323 c. 75,296 d.4,99,579 A 7q qqa .f L7,378 5. Circle the smallest number in each row. 17,7LO a. 4278 L1,t7O 7t,OI7 4872 18,0t2 b. 18,L02 t8,207 L2,807 L2,tO8 6. Circle the greatest number in each row. L5,080 7,04,8tO a. L5,008 15,800 18,500 81,005 b. 1,48,010 1,84010 1,48,100 I,94,LOO 7. Arrange the numbers in ascending order. a. 95,264t 7 5,462; 96,524; 7 6,452; 94,6521 b. 4,L9,887 ; 4,a9,78Lt 4,98,87 L; 4,91,887 : 8. Arrange the numbers in descending order. a. 86,465; 84665; 86,654; 84,566; 86,5461 b. t,I5,79L; t,5I,97L; L,5I,79t; L,15,797: 9. Write the greatest and the smallest numbers using the given digits. Digits Greatest Number Smallest Number a. 8,2,3,4,9 b.4,o,3,7,5 c. 0,t,5,8,4 d. L,5,7,2,0,3

Form a 6-digit number such that every digit is the sum of the previous two digits. (Hint: The first two digits have to be chosen by you.) How many such numbers in all do you think you can form? 1. Write the largest s-digit number. 2. Write the number that comes iust after 89.499. 3. What is the number that has 1 ten thousand. 2 hundreds and 7 ones? 4. Find the number which is 1000 more than 9,LI,27O. 5. The place value of 8 in 5,68,100 is 6. The place value of 2in 2,51,799 is 7. The face value of 9 in 9532 is 8. Which is smaller: 23,499 or 24,399? 9. The sum of the place values of 3 and 5 in the number 14365 is 10. The difference between the place values of 2 and 4 in 32140 is Rounding Numbers Sometimes we round off a number to the nearest 10, 100 or 1000 to guess the answer of a given problem. It is an approximate value and not the actual value, Very often we use 'about' or 'approximately' to represent a rounded off number. My expenditure for a month is approximately { 10,000. The number of people who watched the World Cup cricket finals is about 95,000.

Rules for Rounding Numbers 1. Find the rounding digit. lf we have to round off a number to the nearest 10, the rounding digit is the digit at tens place. Similarly, if we have to round off a number to the nearest 100, the rounding digit is the digit at hundreds place. 2. lf the digit just to the right of the rounding digit is O, L,2,9 or 4, keep the rounding digit as it is and change all the digits to the right of the rounding digit ro zero. Example: 33 rounded off to the nearest ten is 30. 3. lf the digit just to the right of the rounding digit is 5,6,7,8 ot g, add 1 to the rounding digit and change all the digits to the right of the rounding digit to zero. Example: 270 rounded off to the nearest hundred is 3OO. Rounding to the Nearest 10 lf we have to round off a number to the nearest ten, Number I Round to nearest lO we round the given number to the closest multiple of 10. 42 40 67 83 is rounded to 80, while 87 is rounded to 90 as it is 75 closer to 90 than 80. 39 97 A number at the midpoint is always rounded off to the next large multiple. See the numbers given in the table. Round them to the nearest ten. Rounding to the Nearest 100 Number JRound to nearest 1OO lf we have to round off a number to the nearest 350 400 hundred, we round the given number to the closest 286 multiple of 100. 312 442 232 is rounded to 200, while 270 is rounded to 3OO. 250 is rounded to 300. Round the numbers given in the table to the nearest 100. Rounding to the Nearest 1000 505 lf we have to round off a number to the nearest 1000, we round the given number to the closest multiple of I_OOO. llFt .Gl12

Look at 3462 and 3780. Number I Round to nearest 1OOO 3462 is rounded to 3000, while 3780 is rounded to tt1? 4000. L600 2500 Round the numbers given in the table to the 3250 nearest 1000. 5100 t. Round off the given numbers to the nearest 10. a. 87i b.792: c. 1295i f. 7634i d. 4838: e. 3013: 2. Round off the given numbers to the nearest 100. a. 8326: b. 7316: c. 749: d. 4838: e. 3150: 5482: 3. Round off the given numbers to the nearest 1000. a. 4398: b. 1.823: c. 13,598: f. 74,874: d. 27,L97: a q, qqe. A See the pictures given below, and answer the questions that follow. Van Motorbike < 4I7L40 { 310430 < 278280 a. Write the rounded off price ofeach vehicle to the nearest 1.00. b. Findthetotal priceofallthethreevehiclesand round itoff tothe nearest LoO. ls there any difference between the actual price and the rourrded off price?

,.F Vplf tn 2OL5,72,525 families went to Singapore for a holiday. ln 2076,3,448 more |,- families had travelled to Singapore as compared to the previous year. How many families had travelled to Singapore in 2016? Round off the number of families who travelled to Singapore in 2016 to the nearest a. ten b. hundred c. thousand Aayush and his family were planning a trip during his summer vacation. Aayush's father suggested to visit Singapore. Aayush requested his father to choose a place in India as India has a rich culture and heritage. What value does Aayush depict? Write two things you love about India. Find a pair of numbers from the list given below, which add up to 1500 approximately. s99, 640,723, 862,857 :{# I am a 4-digit number. The digit in my tens place is 2 times the digit in my ones place. The digit in the hundreds place is 2 times the digit in the tens place. The digit in the thousands place is 2 times the digit in the hundreds place. lam Roman Numerals 0,1-,2, 3, 4,5, 6, 7, 8 and 9 were first used to represent numbers by the Hindus and then bV the Arabs. Thus, these numerals are called Hindu-Arabic numerals. Roman numerals originated in ancient Rome. These numerals are written using combinations of seven svmbols. Roman Number I X LCDM Hindu-Arabic Number t 5 10 50 100 500 1000 There are no zeros in Roman numerals. Roman numerals are made up by adding or subtracting these symbols. For example, 11 in Roman numeral is written as Xl.

Rules to Form Roman Numerals Rule l.: Repetition of a Roman numeral means addition. Examples: | = 1, + != 2, t = 1 + 1 + 1 = 3, XX= 10+ 10= 20 Remember Only l, X, C and M can be repeated. V L and D cannot be repeated. l, X, C and M can be repeated up to a maximum of three times onlv Rule 2: A smaller numeral written to the right of a greater numeral is always added to the greater numeral. Examples: Vl =5+1=6 XXV=10+10+5=25 3:Rule A smaller numeral written to the Ieft of a greater numeral is always subtracted from the greater numeral. Examples: lV=5-1=4 lX=L0-1=9 Rule 4: When a smaller numeral is placed between two greater numerals, then it is always subtracted from the greater numeraljust after it. Examples: XIV = 10 + (5 - 1) = 14 XX|X=10+L0+(10-1) =29 1. Write the Roman numerals for each of the following Hindu-Arabic numoers. a. 7 b. L2 c. 15 d. 20 e. 26 f. 29 h. 32 i. 35 c. 30 i?q 2. Write the Hindu-Arabic numbers corresponding to each of the following Roman numerals. a. Vlll b. XL c. XV d. XVI XXVII f. XXXVIII c. XXXIV h. XX i. XVII j. XIX

Worcs@ Who am l? Take the digits L,2,3 and 4. Write them in every possible order to give a 4-digit number. I am the sum of all of them. I am Target Olympiod Write as many 4-digit numbers with O, I,2 and 3 as possible. How many of them have 0 in the hundreds place? Number Systems There are many ancient numeration systems. Quipu-lnca Empire The lnca lndians of south America used a Svstem of Knots to . represent numbers. A special arrangement of knots on a string was used to reoresent a number. DIASES, A-uttrlr objective: To strengthen the understanding of the place values of the digits in a 6-digit number. Materials required: Abacus and beads in 6 colours Method: Ask the students to illustrate 5,62,L32 on an abacus 5b using different-coloured beads for each digit in a spike and then read the number. Make them speak out aloud the place values of different digits together. The students can also compare the numbers such as 2,98,597 and 2,97,598 by putting beads in the abacus.



1. The heights of some mountain peaks are given below. Mount Everest 29,O29 K2 2?4?L Lhotse 27,940 Annapurna 26,545 a. Arrange the heights of mountain peaks from the smallest to the greatest. b. Round offthe heights to the nearest hundred. c. The difference between the place value of 8 in the height of K2 and the place value of 9 in the height of Lhotse is d. The place value of 6 in the height of Annapurna peak is The number of thousands in the height of Lhotse is f. Find the total height of all the mountain peaks together. What is the sum of the place values of 7, G and 5 in that number? 2. Pick the numbers from the circle to make three different 5_digit numbers. Write the three numbers on the left of the circle. Arrange them from the smallest to the greatest on the right of the circte.

) ii Addition li . The numbers that are added in an addition problem are called addends. The result called the sum. 500 + 400 900 44 4 Addend Addend Sum Change in the order of the addends does not change the sum. 225+L36=36!; 736+225=367; 900+800=800+900 When zero is added to any number, the sum is the number itsell For example, 0 +458 = 458 + 0 = 458 Subtraction . In subtraction, the greater number is called the minuend and the number which is subtracted from the minuend is called the subtrahend. The result is called the difference. 456-323=133 ;' 440 Subtrahend Difference Minuend When a number is subtracted from itselt the result is 0. Forexample,2TS-278=O When zero is subtracted from a number, the result is the number itsell Forexample,456-0=456

We can use addition to check the difference. 435 To check: + z3b <-- Subtrahend 100 -z5b 9 Add difference and <- Difference +Jf, <- Minuend 19 subtrahend to get \"'4 8 2 the minuend tl tlL 6 Fitl in the blank boxes. o.g E tl 6n8 8 2476 -3 4 5 5 2204 s 2Es E[ NE Addition 5- and 6-digit Numbers Without LRegrou ping Addition oft5- or 6-digit numbers is the same as the addition of 4-disgiit numbers. Example 1: , Add 23,425 and L2,463. EIilTET 23425 -Step 1: Add the ones. 5 + 3 = 8 +12463 Step 2: Add the tens. 2 + 6 = 8 Step 3: Add the hundreds.4 + 4 = 8 558 88 Step 4: Add the thousands.3 + 2 = 5 Step 5: Add the ten thousands. 2 + l_ = 3 rhus, 23,425 + 12,463 = 35,888 Example 2: Add 3,25,128 and 2,52,640. TEETEEShort Form Expanded Form 325128 +300000 + 20000 + 5000 + 100 + 20 + 8 +252640 -->200000 + 50000 + 2000 + 600 + 40 + O 7 7 7 o 8 500000 + 70000 + 7000 + 700 + 60 + 8 = 577768 Thus, 3,25,128 + 2,52,640 = 5,77,768 .-$t s- _.. -

trEENEli4l Complete and solve the addition sum such that each digit from 0 to 9 is used only once. EENT]+ t____J With Regrouping Add the digits in each column, starting with the ones column. lf the sum in any column is more than nine, regroup with the next column on the left. Example 1: Add 63,785 and 98,876. o @o @g @7 o^6 5 98 7 6 45,006 + 83,688 = 74,535 + 91,035 = t6 66 t In subtroction, Thus, 63,785 + 98,876 = L,62,66L chonge in the order of .EEIIEtrExample 2: Find the sum of the following numbers. minuend ond subtrohend. chonges the difference z@s@s@s 4 6 42356 32412 983 02 'EThus, 23,534 + 42,356 + 32,4t2 = 98,302 o- o- o- o- 5 +38 05 654 3 L Thus, 2,65,375 + 3,89,056 = 6,54,43t

Word Problems Example 1: In a book fair, there are 3,42,568 books in English language and 1,52,343 book in languages other than English. Find the total number of books in the fair. trtrEEEtr 3 4 z@s@o 8 Number of books in English language 152343Number of books in languages other than English + Total number of books 4949 L Thus, there are 4,94,911 books in the book fair. 2:Example In a city, there are 53,418 men, 51,325 women and 22,426 children. How many people in all live in the city? 53,41a + 51,?25 + 22,426 = ? tortsr@tratcr@Er 88 51325 +22426 1 7L 9 Thus, 1,27,L69 people live in the city. Add the following: r o-L o. r 3 0 35 07 5438 9 +44 +2585

Ec. E 5 4329 4 8537 5894 7463 EEEET 5092L 47210 34167 10546 +3042 +124t ,EEETET - EEEITEE 4 7 5 ,4 0 9 302480 +68745 +274325 r@ErEtt EEr|ET 548265 300937 753180 +4645 153294 +85392 2. Mohan bought a study table for { 1.2,530 and a bookshelf for { 23,450. Find the total money spent by him in buying the two items. 3. An LED ry set costs { 92,425 and a digital camera costs < 79,946. Find the total cost of both the items. 4. ln a coaching centre, LL,230 students enrolled in the first yea\\ 27,220 in the second year and 31,012 in the third year. Find the total number of students who have enrolled at the coaching centre in the three years.

11,243 people enrolled for yoga classes last year 32,435 more people enrolled for the classes this year compared to last year. How many people in all enrolled for the yoga classes in the two years? Write two advantages of doing yoga every day. Properties of Addition Order property of addition: If we change the order of the addends, there is no change in the sum. Example: 32,L45 + 2000 = 34,145 an d 2000 + 32,f45 = 34,!45 Thus, 32,145 + 2000 = 2OOO + 32,L45 = 34,145 Grouping of addends: When three or more numbers are added, the sum remains the same regardless of the way addends are grouped. Example: (38,677 + 47,958) + 28,975 = 86,635 + 28,975 = !,f5,61O 38,677 + (47,958 + 28,975) = 38,677 +75,933 = rJ5,6IO Thus, (38,677 + 47,958) + 28,975 = 38 ,677 + (47 ,958 + 2A,9751 = 1,15,519 Property of zero: The sum of any number and 0 is the number itself. Example: 58,743 +0=58,743 and 0 + 58,743 = 58,743 Thus, 58,743 + 0 = 0 + 58,743 = 58,743 Property of one: The sum of any number and 1 is always the successor of the number. Example: 3,24,357 + I= 7 + 3,24,357 =3,24,358 1. Fill in the blanks. L,32,423 + 2,35,347 = 2,35,347 + b. 3,73,543 + O = c. 3,42,627 + 3,42,627 o. ) 4\", L\\L + = 2,33,455 e. 5,62,456 + 1s6,234 + 3,4s,2361 = (s,62,456 + | + 3,45,236 2. -=Using the properties of addition, add the following and compare the sums. a. b.22,457 + 27 ,456;27,456 + 22,457 4,25,693 + 3,72,877;3,72,8f7 + 4,25,693 c. 12,60,357 + 2,48,4861 + 2,20,567;2,60,357 + (2,48,486 + 2,20,567, d. 15,34,527 + 4,25,2761+ 4,25,267;5,34,527 + (4,25,276 + 4,25,267\\

{#orcxm@ Add:87+45+33+25=? Group the numbers smartly ! 87+45+33+25=(87+33) + (45 + 25],= 720 + 70 = L90 Solve the following using the same method. 7.2OI+92+18+4 2. 70'1, + 73 + 27 201+86+14 305+82+45+128 4. 105+12+25+38 5.7O7+12+79+78 (------l1.. 2,49,634 + 34,625 = A+,e ZS + 2. Find the sum of L and the largest s-digit number. 3. what is 2000L + 153? 4. 4+40+400+4000+ Estimating the Sum Estimating the sum is a way to get an approximate sum of the given numbers. lt does not give the exact sum. For calculating the estimated sum, we find the sum ofthe rounded offvalue of each ofthe addends. Example 1: Estimate the sum ot 43,525,53,626 and 73,558 by rounding offthe numbers to the nearest 100. 43525 rounded off to the nearest 100 is 43500. 53626 rounded off to the nearest 100 is 53500. 73658 rounded off to the nearest 100 is 73700. 43500 + 53600 + 73700 = 170800 Thus, the estimated sum of 43,525, 53,626 and 73,658 to the nearest 100 is 1,70,800. Example2: Estimate the sum of 32,425 and 53,525 by rounding off the numbers to the nearest 1000. 32425 rounded off to the nearest 1000 is 32000. 53525 rounded off to the nearest 1000 is 54000. 32000+54000=86000 Thus, the estimated sum of 32,425 and 53,525 to the nearest L000 is 86,000.

Estimate the sum ofthe following by rounding offthe numbers to the nearest l'00. Also find the actual sum. a. 2,64,576 + 3,67,634 b. 4,64,574 + 26,376 c. 5,63,476 + 4,53,623 d. 42,352 + 45,237 + 62,378 2. Estimate the sum ofthe following by rounding offthe numbers to the nearest 1000. Also find the actual sum. a. 32,425 + 53,436 b. a3,452 + 76,347 c. 5,63,468 + 2,35,623 d. 32,356 + 45,234 + 56,237 Subtraction 5- and 6-digit Numbers Without Regrouping Example 1: subtract 3,22,015 froms,44,278. [ffitrtrEtr Step 1: Subtract the ones. 8 - 5 = 3 Step 2: Subtract the tens. 7 - l. = 6 78 Step 3: Subtractthe hundreds. 2-0 = 2 Step 4: Subtract the thousands. 4- 2 = 2 Step 5: Subtract the ten thousands. 4 - 2 = 2 1 2 2 2 6 J Step 6: Subtractthe lakhs. 5 - 3 = 2 Thus,5,44,278 - 3,22,015 = 2,22,263 with Regrouping Example 1: Solve:. 5,62,562 - 23,425 Example 2: Solvei 6,37,382- 2,33,465 EMEtrEE trtrtrtrEtr ,@B@z s@B@z 6 3 @v @z @u'z 5 3 9 1, 5 7 A0 9T 7 rhus, 5,62,562 - 23,425 = 5,39,737 rhus, 6,37,382 - 2,33,465 = 4,O3,9I7 .Fr

Example 3: There are 78,453 milk booths in a city. 29,876 belong to Brand A. Find the number of booths of other brands. 78,45t-29,a76=! tYrtYrtHr'EBytr -2 9 8 7 6 485 7 Thus, there are 48,577 milk booths of other brands. Example 4: There are 6,2L,985 teak and lemon trees in a Dark. lf 2,11,089 of the trees are teak, how manv of them are lemon trees? trtr8trEtr Total number of trees I s@ 9 @5 Number of teak trees L9 Number of lemon trees 4 108 9o Thus, there are 4,10,896 lemon trees in the park. 1. Find the difference. D. @rrEEl 29847 \" EETET -lJzo 52894 -21342 EETilET 62376 trilETET -L238 54529 -72t6

\" EEETET TEETET 376954 3/564r -82341 -q?q7( E. 6,52,t75 - 6,5L,2Oa = h. 8,34,562 - 5,97,24O = There are 52,L78 apartments in a township. 21,256 apartments are already occupied. How many apartments are still vacant? 7,12,956 people comprising men and women watched the cricket match between India and South Africa. lf there were 2,65,567 women, how many men watched the cricket match? 4. Out of 5,26,438 people who visited Goa last year, 12,560 were Indian visitors. How many were foreign tourists? +,sa,ozz oeople voted in the state elections. The winning party got 'l-yEl 2,43,534 votes. How many votes did the other parties get? According to you, why is it important for us to vote? Properties of Subtraction Property of zero: lf 0 is subtracted from a number, the difference is the number itseli Example: 75,633-0 = 75,633 Property of one: lf 1 is subtracted from a number, the difference is the predecessor of the grven number. Example: 64,577- L= 64,576 Subtraction of a number from itself; tf a number is subtracted from itself, the difference is zero. Example: 83,762 - 83,762 = O 1. Fill in the blanks. b. 7,25,1,26 - I = = 45,623 a. 65,432-O = -45,623 c. 22,567 - 22,567 =

8. 98,045 - 98,045 = h. 99,999-1= 2. Subtract the following using the properties of subtraction. a. 56,234 - 0 = b. 4,25,693 - 4,2s,693 = [----___-l c. 83,735-1= d. s,se,zaz - [------__l = e Checking Subtraction Using Addition We can check subtraction with the help of addition. lf the sum of the subtrahend and the difference gives the minuend, then the subtraction is done correctly. Example: Subtract 24,354 from 73,634 and check the answer. trEtrEtr trtrtrEtr @-Minuend ------------> @- @5 @z 4 02 80 24Subtrahend -----+- 35 X-4 24 EA 6 34 Difference -----+ A 9 8 0 73,634-24,354=49,280 49,280+24,354=73,634 Here, Subtrahend + Difference = Minuend. Thus, the answer obtained in the subtraction is correct. \" IilEE1. Find the difference and check your answer. b. tilErEr 54764 t5z02 -31451 -41055 rilErEr 86350 OTEETET _ZJI5 864453 -853071

\" EMETE r 'rmErEr 91424 9995 -5ZLa 3 -t545 82 2. subtract and check your answer. c. 4,52,727 -2,53,764 a. 13,253-2,323 b. 24,364 - 1,4,336 Estimating the Difference Estimating the difference is a way to 8et an approximate difference of the given numbers. For calculating the estimated difference, we find the difference of the rounded off values of the minuend and the subtrahend. Examole 1: Estimate the difference between 43,526 and 23,354 by tounding off the numbers to the nearest 100. 43526 rounded off to the nearest 1OO is 43500. 23354 rounded off to the nearest 100 is 23400. Difference between 43500 and 23400 is 20100. Thus, the estimated difference between 43,526 an d 23,354 is 20,1OO. Example 2: Estimate the difference between 32,546 and 12,260 by rounding offthe numbers to the nearest 1000. 32546 rounded off to the nearest 1000 is 33000. 12260 rounded off to the nearest 1OOO is 12OOO. Difference between 33000 and 12000 is 21000. Thus, the estimated difference between 32,546 and 72,260 is 2l'ooo. 1. Estimate the difference by rounding off the numbers to the nearest 100. Also find the actual difference. a. 23,355 -'J.4,235 = b. 43,627 -13,42s = [-----__l I c. 2,42,353 - 7,32,435 = d. 7 ,36,342 - 4,35,637 = 2. Estimate the difference by rounding off the numbers to the nearest 1000. Also find the actual difference. 24,353 - L3,244 = b. 3L,526 - 16,252 = c. 7 ,26 ,245 - 5 ,34,232 = d. a,27 ,256 - r,52,437 =

3. Estimate the difference by rounding off the numbers to the nearest 1OOO. a. 79,456 - 32,954 = b.59,730-24,OO5= c.6,34,970-39,720= d. a-8,83,880 - 6,33,gSS = 4. There are 24,356 people comprising men and women in an auditorium. 73,245 arc men. Estimate the number of women in the auditorium to the nearest 1OOO. 5. There are 34,254 red and blue ribbons. 13,245 ribbons are blue in colour. Estimate the number of red ribbons to the nearest 1OOO. Addition and Subtractissl :,:r:.,:84f4+r, . lf in a sum, both addition and subtraction are involved, solve the addition first and then subtract the remaining number from the sum. Example: Solve 42 ,536 - 73,245 + 63,534. rmErEr rroErErStep 1: Add 42,536 and 63,534. Step2; Subtract L3,245 frcm L,O6,O7O. +z)50 106070 + ()5)54 -r'a+) 1060 70 928 2q Thus, the answer is 92.825. Moths Around Us Students of JoV International School decided to help children in an NGO, who were in need of course books. Students from all the classes donated used and new books. Teachers also took part in this campaign. The volunteers found that the total number of books collected from all the students is 10,456, while the total books coilected from all the teachers are 2,347. But, the NGO required only 11,346 books in all. The volunteers, who are students of Class 4, wanted to know the total number of books which would be left over, so that it can be given to the school librarv. So, their maths teacher guided them to first add the total number of books collected, i.e.,1-0456 + 2347 = 12803. From this sum, they are asked to subtract the number of books required by the NGO, i.e., L28O3 - t1346 = L457. So, 1457 books were given to the school library.

1. Solve the following: b. 23,354 - 73,243 + t4,253 d. 5,34,632 - 4,36,367 + 13,253 a. t3,243 + 13,243 - t4235 c. 34,252 - L4,353 + 73,243 f. 7 ,32,624 + L,63,534 - 3,43,434 e. 6,35,243 + 1,42,547 - 34,345 @o@@ subtract smartlv in 2 steps. Subtract l from both the numbers. SteP 1 SteP 2 40000 , (4ooo0 - 1) 39999 - rs61,2 - (1s612 - 1) - 15611 24388 \" EETETUsing the above method, find the difference. O EETET 300 00 500 00 356 25 1L 95 O EEEIilET 9000 00 735 97 1. circle the numbers in green whose sum is the number in the box. a. 236 53 92 80 L--:i;];T----)J b. r32 25 13 56 [ 1s7 I c. 396 243 t30 L24 t !91J d. 79 103 345 579 t jg.-J 2. Circle the numbers in violet whose difference is the number in the box. a. 436 592 L24 1.39 t ?q7 l b. 629 424 333 L27 lq1 I c. 249 3OZ 535 662 t 4!9J

Dtsrgs IlAts A-It!!trlr Objective: To understand the concept of addition and subtraction of 5- and 6-digit numbers Materials required: Strips of paper with 5- or 6-digit numbers written on them Method: The teacher makes groups with two students in each group. she then shuffles the strips of paper and keeps them one on top of the other. One student from each group picks up two paper strips and arranges them to make a question. The teacher instructs whether to add or subtract. The students solve the sums in their notebooks. The teacher can also ask them to estimate the sum or difference. MY Proiect 8(' I l .da*---Conduct an election in Your class I'or selecting the monitor of the as shown' Find the actual and estimated class. Make a table of votes lo Write three factors that influenced ,ui of uot\", to tt'e nearest your choice for the monitor of the class' Number of Votes Rounded off to the nearest 10 Candidate L Candidate 2 candidate 3 Sum of votes .-t #8.

Add the following: b. 56353 + o. 823782 + 625623 a. 34266 + L3242 c. 763767 + 724572 Subtract the following: D. 46575 - 24367 o. 923825 - 693832 a. 24364- t5623 c. 723762-536378 Estimate the answer of the following by rounding off the numbers to the nearest 1000. a. 25623 + L3425 J5+5) - 2555b c. 632623 - 343626 d. 823723 - 812723 So lve. b. 43324-24354+2435 a. L3245+34353-13254 d. 8237 623 - 25267 I + 524236 c. 762354 + 153533 - 343536 e. 58456 + 78352 - 70040 f. 90000-85500+111020 Solve and check the subtraction using addition. EEITETO EETTETa. 45730 s3200 -13982 -42771\" ' EEErEr, EE[ErEr 774210 904327 -327942 -42L765 A company manufactured 35,623 motorcycles in 2014 and 3g,653 motorcvctes in 20L5. In 2016, it manufactured 2O,OOO more motorcycles than the combined oo oonumber in 201,4 and 2015. How many motorcycles were manufactured in 2016?

The number of tourists who visited shimla, Darjeeling and Kullu-Manali in the months of May, lune and July is recorded. Find the missing data and answer the questions below Place May June July Total Shimla 28,755 35,L22 -j1s0,5,6r8si _;o,aio our.leeiing , r;,bo r 61,250 Kullu-Manali 20,735 23,760 a. How many people visited Shimla, Darjeeling and Kullu-Manali in the month of Mav? b. How many total people visited Darjeeling in the months of May and June? c. How many more people visited Darjeeling than Kullu-Manali in all the three months? d. Which month had the highest number of tourists altogether? Multiple Choice Questions 1. 10000 people attended a musical concert. 2755 people reached in white cars, and 1500 people came in black cars. The number of people who came neither in white nor in black cars is a. 4652 b. 5645 c. 3650 d. 2373 2. The difference between the largest 6-digit number and the smallest 6-digit number is b. L0000 c. 899999 d. L2000 a. 99999 3. A public library has 12,465 books. An NGO donates 4120 books to the library. The total number of books in the library is a. 16,585 b. 16,680 c. 18,505 d. 16,013 4. The sum of the smallest 6-digit odd number and the largest s-digit even number ts a. 19,999 b. 8,99,999 c. 1,99,999 d. I,27,300

The number that is to be multiplied by another .- Multiplicand Multiplier numbernumber is called the multiplicand. The x -a-l+<- e.odr.t by which we multiply is called the multiplier. fr The answer is known as the product. 1. Fill in the boxes. One has been done for you. a. f+-lxso= so+so+so+50 b. 34+34+34+34+3a=f-_lx3+ f_.lxc. 52 + 52 + 52 + 52 + 52 + 52 + 52 + 52 +52 = 52 e. | jxzs:253 + 253 + 253 + 253 + 2s3 + 253 = ffi 2. 3. H: ffi:::JTil :J::HH: :l\":ffi [:::::ffT\"' wd24 benches? in trFfil:\"J;li:y.o4. appres. How manv apples will be there .@ the5. A goods train can carry 25 containers in one trip. Calculate number of containers the train can carrv in a. 7 trips b. 12 trips c. 21 trips d. j.9 trips

\\ 6. Find the product. 243 x 1.00 = a. 153xL0= 562 x 100 = 735 x L000 = 423 x 1000 = 635x10= Moths Around Us A group of children, along with their parents, were managing an event to celebrate Earth Day on 22nd April in a city council. There were l-1 districts in the city and each district was asked to plant at least 1000 saplings in their area. The children wanted to find out the minimum number of saplings needed for the event. The children wanted to find out the answer without using pen and paper. Seeing this, Mr Sharma taught them that the result of 11 x 1000 can be easily found by putting 3 zeros after 11, i.e. 11000 saplings. Similarly, if any number is multiplied by 10, 100 or 1000, then we have to put subsequent number of zeros after that number. Properties of Multiplication . Order property of multiplication: Even if the order of multiplicand and multiplier is changed, the product remains the same. Examples:32x43=43x32; l24x$)=$2v124' 245x52=52x245 . Property of one: Any number multiplied by 1 gives the number itself as the product. Examples: 4].3xL=4t3; 735xL=735) 23Ox1,=23O . Property of zero: Any number multiplied by 0 gives 0 as the product Exa mples: 23'J,x O = O; 745xO=O) 837x0=0 . The product of a number (either odd or even) with an even number is always an even n um ber. Exa mples: 325 x2 = 650) 562x4=2248; 2252x8=78076 . The product of two odd numbers is always an odd number. Examples: 323 x3=969; 56Lx7 = 3927; 727x9=6543

1. Find the product using the properties of multiplication. a. L2Lx82= x I21\" b. 53x751 =75Lx c. 164 x t= e. 735x0= d. 823 x = 823 f. 600x0-- 8. 534x2= n. bZJ xtr= i. 651 x3= j. 323 x9 = 2. Match the following: a. 534x2 is an odd number 0 b.457xL is an even number 457 c. 237 x0 d. product of 522 and 4 2x534 e. product of311 and 9 Multiplication of a Number by 100, 1000 and 1O,OO0 o While multiplying a number by 100, insert two zeros to the right of the number. Examples: 52 x 100 = 5200. 280x100=28,000; 1456x1O0=1,45,600 . While multiplying a number by 1OOO, insert three zeros to the right of the number. Examples: 34 x 1000 = 34,000. 153 x 1000 = 1,53,000; 630 x 1000 = 6.30.000 r While multiplying a number by 1O,OOO, insert four zeros to the right of the number. Examples: 55 x 10,000 = 6,50,000. 34 x 1o,ooo = 3,4O,OOO. 87 x 1O,OOO = 8,7O,OOO Smart Multiplication To multiply a number by 99, multiply that number by j.OO and then subtract the number from the product. Exampie 1: 37 x0S = 37 y 1199- 11 Example 2: 70 x 99 = 70 x (l.OO - 1) -= 37 x 'J.OO 37 =7Oxl0O-70 = 37OO - 37 -= TOOO 70 = 3663 = 6930 Fr Let us extend this learning to other numbers also. l38lf -b,lt

Example 3: 83 x 29 = 83 x (30 - 1) Example 4: 72x49= 72x(50-1, =83x30_83 =72x5O_72 = 249O - 83 = 36O0 _ 72 = 3528 = 2407 . 1. Find the product. a. 11 x 100 b. 18 x 1OOO c. 130 x 1000 o. 403 x 100 e. 2634 x 100 g. 4 x 10,000 i. 426 x IOO f. 110 x 1.00 h. 73 x lggg j. 723 x LOOl k. 24 x 1000 918 x 1000 2. Find the product using smart multiplication. d. 79x99 a. 11x 99 b. 28x99 c. 65x99 h. 94x9 e. 36x99 l. 68x59 i. 15x49 I 52x99 8. 47x99 p. 72 >< 89 j. 2g'ag k. 34x39 m. 67 x79 n. 53x29 o. 86x49 Wro@EEID Flnd me! When you multiply me by 15, you get a number that is 50 more than 4oo. Who am t? Mu|tiplication Ta b|es ).:r::yiiii|7,:trj; - . You already know the multiplication tables up to 10. Let us learn the multiplication tables from 11 to 20. Multiplication Table of 11 We know, L1 = 10 + 1 so' the murtiprication tabre of 11 wit be the sum of the murtiprication tabres of 10 and 1. 1x 11 = 1x 10+1x 1= 10+ L= 11 Slmilarly, 2 x 7L = 2 x lO + 2 x I = 20 + 2 = 22 5 x 11=5 x 10+5x1=50+5=55 10x 11 = 10x 10+ 10 x 1 = 1OO+ L0 = 110

So, the table of 11. is E f;)@ t1u @ @ (;) @TLJ;-Jt \\G:: ;'lJ t!9 J E @ L::J @@@ @@ t(;l;f)J E@ @ @ @ \\G:!:a;I) L\\rl;:!;:_-J)t @@ GN In any multiplication table, say in the table of 11, the multiplier would be the first term and multiplicand would be the second term. For example, 2x t), ,,h 44 Multiplier Multiplicand Product We can find tables of other numbers in the same way. Multiplication Tables from 12 to 15 Table of 12 Table of 13 Table of 14 Table of 15 !1_',_:\" 1x13=13 '),xL4=t4 lil= 2xL3--26 2xL4=28 2_x12=24 2x15=30 3x15=45 3x72=36 3x13=39 3xL4=42 4x15=60 5x15=75 4x12=48 4x73=52 4x14=55 6x15=90 7x15=105 5x12=60 5x13=65 5x14=7Q 8x15=120 9xL5=135 6xt2=72 6xL3=78 6x14=84 10x15=150 7xt2=84 7xt3=97 7x74=98 8x12=96 8x1.3=104 8x!4=LI2 9x12=108 9xL3=7I7 9xL4=126 70x12=I2O 10x13=130 tOxt4=74O Create multiplication tables of 16, 17, 18, L9 and 20 in the same wa\\,.