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rcAs ldentifyyour strongest skills, track year on year performance See clearlywhere you need to improve lreasure your true capabilities on a global scale In 2017the most comprehensive, annual, g oba benchnrarkol loa -i.gpo€rosc ^ngsbkFillalsLth^a.6tFudnd1erpdnas.lu.Accseas.ss.in<<Moa(thellmeatics, higher-order thlnk Science, Eng ish [C 2 12Jand 0 igilal Tech n ologles, [C 3-10]. Find out more at www.macmillaneducation.inlicas E\\+ uNswclobrl ff .rac.r' ar educdt on CAS isa product of IINSW Globa. a wholy owned ente.priseot UNSWAusralialThelJnversilyof NewSourhWalesl t'sdismbuted excrusiveiy n lnd a byMacmilan Education.

llq Vpq\"g.g*g _^ I.IERARY SPECNEIICOPY DA Dr Revothy Poromesworon Vice Principal, PS. Senior Secondary School Mylapore, Chennai yttvt.,tftft Lt eArAer, fIir ut.rfe A7V macmillan education

m MACMILLAN @ Macnillan Publishe^ India Prtuate Ltd, 2013, 2017 All rights resered under lhe copyright act. No parl of this lublication may be ftproduced, transffib€d, transmitted, stored in a retrieval syst€m or trdslaled hto aDy luglage or compuier lmglage, in dy fom or by any neans, electonic, rnechanical, magnetic, oplical, chernical, manual, photocopy or otheNise wi&out the prior pemission of th€ copridt oMq. Any p€rson who does any urauthorised act in relation to this publication nlay be liabl€ to crimiel pros@tion dd civil claims for dmases. Xpr6s edition 2014 Reptuted 20H €Aticel 201 5 Fhncd, 201 6 Revisedeai'td,20I7', Repnhtid 2017 (reice) MACMILLA}I PUBLISI{ERS II\\IDIA PR]VATE LIMITf, D Delhi Bengalm Ctemri Kolftata Munbai Almedabad Bliopal chmdisuh coimbatore Cun ck Guwahan Hyderabad Jaipur Lucknow Madurai Nagpu PatrE Pue ThiruvddrhaprraD \\4sakhapalDD ISBN: 9?8-9352-52164-7 Published by Macmillan Publishers India Private Ltd, - 21, Patullos Road, Chelmi 600002, Idia Pri.ted at KJiti, New Delhi 110 020 \"Ihis took is oeaDt for enucatioDl ud leming purposes. The autho(s) ofthe book has/have laken all rqsonable cde to ensE that the contents oflhe book do nol violale atry copyright or other inlcll€ctual property righrs ofary pqson in my mamer what- soever. In the event the authods) has/have te€n umble lo track any source and if any copyridt has beo inadveftenny inainsed, please nolify the publisher in *riting for any corrective action.\"

Pref ace Maths Xpress for Classes 1 to 8 has been developed by practising teachers and maths experts. Based on the latest pedagogical approaches toteaching 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. Special Features a Let's Recall recapitulates previous knowledge of concepts a Maths Around Us helps students apply mathematical concepts in real-life situations a HOTS/Target Olympiad empowers students to think out-of-the-box a Speed Maths/Mental Maths prepares students to carry out quick calculations a Take Care helps students avoid common errors a Maths Lab Activity and Project connect maths with reallife situations a Fun With Maths and Maths Game reinforce the concepts taught in a fun way a Enri€h Yourself provides deeper insight into the concept under study a Revision Station helps students in assessing their understanding ofthe concepts learnt a Worksheet helps in reinforcing the concepts learnt a Glossary serves as a ready reference a Practice Sheets aid in comprehensive evaluation a Maths Engine includes tasks that foster creative thinking and problem-solving skills amonq students

[.EEom Strueture 7 Recapitulates previous knowledge of concepts. Helps students apply mathematical concepts in real-life situations. It-' ,il^n5lj ''A .. sPEEo {l Prepares Students to carry our quick calculations. Connect maths with real-life situations.

Reinforce the concepts taught in i a fun way. ^ l Helps students in assessing their understanding of the concepts learnt. Helps in reinforcing the concepts learnt. al Wdksheet /' Serves as a ready reference. I. Aid in comprehensive evaluation. l

Dlgltul nssounoss s 0 $opdrol 4. Multipli.ation . JnrPes Symmetry 10. Time 'llIl* 12- Dlta Handling

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Comre'n!ts 1\" 1. Large Nu mbers 18 z. Addition 36 5. Su btraction 4. M ultiplication qt 5. Division 6. Fractions 67 7. Shapes 83 d. Patte rns and Symmetry 95 v. Metric Measures ro7 10. Time 1.1.6 LL. Money 12. Data Handling t-50 Pra ctice S heets _t_.+o Glossary IOJ Answers to Selected Questions 173 175 177 *

t !l'l.:t ';L L ' rqdr/// il HotT- oPunv gPun8ffi acevatuecards- :f:fli':;\"1m\":::;tiil1;,;:;;#iil,ijl:ii,l,:J-Jijl;\"l^#jl;?ill;:,*\" irii ,t, ii q. E ,..tIi -.- ii * ;':r\" E..--, ii E] f r\"r r qi one 11onu p\"rron is the calter. The caller turns over i G q qi l*nl:r:n*ru:t***u*:,:;: Lq 6lil :ii::lx;:*;JJril;i,f;:#,:t;:n:\",\"\", i 33 @ qi Olace, that is, 99. The caller con ;-' i i fr. fti Eiiri: :-l:h.\"e0c,ag:ll.e,,r.w*lr.lll.n,h.adveotnouke,pepr\"o.n\"ureu-s'tLacll:(:n\"g.''tihTeic:TaJr:d:'s ! ii cardrto generate different numbers for players to fill in their bingo ii il ii ii The first player to put a circle around all the 24 numbers shouts'Bingo' and is the winner. ii ,tii- --------'--------------------------------.tl -- - - - - - - - - - - - - - - - - - 4-d i git N u m be rs at:ter,'{r-'IuFr ; : The greatest 3-digit number is 999. When 1 is added to it, we get 1000. lt is read as one thousand. lt is the smallest 4-digit number. lt is equal to ten hundreds. So, 10 hundreds = l thousand When 1is added to 1000, we get 1001. lt is read as one thousand one. The greatest 4-digit number is 9999.

Number Names Let us see the number names of some of the numbers. 2487: Two thousand four hundred eighty-seven 5480: Five thousand four hundred eighty 6039: six thousand thirtv-nine 7458: Seven thdusand four hundred fifty-eight = 1000 = 2000 = s000 It is read as one thousand It is read as two thousand It is read as five thousand Place Value and Face Value Place va lue of a digit in a number is determined by the position of that digit in the number. We have four places in a 4-digit number, namely, ones (O), tens (T), hundreds (H) and thousands (Th). Examoles: The olace value of 5 in 1345 is 5. The olace value of 4 in t248 is 40. The olace value of 7 in 3726 is 7OO. The olace value of 2 in 2351 is 2000.

Let us illustrate a 4-digit number on the place value chart. 4 7 t947 46 9 2469 3 7 8 0 3780 Face value of a digit is the digit itself. Examples: The face value of 2 in L752 is 2. The face value of 9 in 1394 is 9. The face value of f. in 4164 is 1. The face value of 3 in 3284 is 3. The face value of a digit always remains the same, irrespective of its position in a number. Expanded Form Expanded form of a number is a way to wrlte the number as the sum of the place values of its digits in order. India got its independence in the year 1947. 1947 is a 4-digit number. 1947 has L thousand, g hundreds,4 tens and 7 ones. We read 1947 as one thousand nine hundred forty-seven. The expanded form of 1947 is 1000 + 900 + 40 + 7. Examples:The expanded form of 1326 is 1000 + 300 + 20 + 6. The expanded form of 2314 is 2000 + 300 + 10 + 4. The expanded form of 5232 is 5000 + 200 + 30 + 2. \"s1. Write the number name. a. 2385: b. 3869:

5027: d. 8852: 9753: 2. Write the expanded form. 2554 c. 3690 4146 f. 5567 a. 1964 h. 7072 i. 8181 d. 3900 g. 6899 c. 4131. f. 3000 3. Write in numerals. c. 5870 a. One thousand two hundred thirty-six f. 9845 b. Two thousand nine hundred ninety-nine c. Three thousand six hundred 4LO2 d. Five thousand five hundred fifty-five 1085 e. Eight thousand nine hundred seventy 4. Find the place value of A. 3in the following numbers. 1,463 b. 3787 e. 9839 o. 93t2 B. 8 in the following numbers. a. 1.810 b. 3L98 d. 7L81, e. 8000 5. Circle the number in which a. the place value of 2 is 2OO. 264L 1280 L620 2753 b. the place value of5 is 50. 2531 490s 6. Write down the face value and place value of 6 In a. 6400 b. 2640 tr-..\".

Fill in the grid with the corresponding numerals. Across j. a, Seven thousand five hundred i- th irty-five Down e. Four thousand nine hundred b. Three thousand four hundred eighty-nine sixty-four c. Five thousand nine hundred ninety d. Two thousand four hundred eighty-seven f, Five thousand seven hundred g. Eight thousand eight hundred thirty-two eighty-nine Nine thousand seven Three thousand twenty-four Two thousand three hundred eighty-eight k. Three thousand eight hundred thirty-eight Numbers on Abacus -fi.li;Represent 1467 on abacus. Place 7 beads in the ones column, 6 beads in the tens column, 4 beads in the hundreds column and 1 bead in the thousands cotumn, Th HT O 1 46 7 1. Write the number represented on each abacus. Then answer the questions that follow. Th Th HTO

a. Write the new number if 2 beads are removed from the ones column in A. b. Write the new number if 5 beads are added to the hundreds column in B. c. lWrite the new number if bead is removed from the thousands column and 1 bead is added to the ones column in C. Successor and Predecessor '-rys, '. The number that comes just after a given number Toke core! We con puf is called the successor of that number. o moximum of 9 beods Examples:The successor of 1 is 2. in one column on the The successor of 12 is 13. The successor of 99 is 100. The successor of 1245 is 1246. The number that comes just before a given number is called the predecessor of that number. Examples:The predecessor of 2 is L. The predecessor of 15 is 14. The predecessor of L28 is 127. The predecessor of 4589 is 4588. 1. Write the successor. b. 4897 c. 6838 8432 a. 3843 f. 5ro2 d. 7942 c. 23t4 2. Write the predecessor. b. 8474 f. 7400 4308 a. 3498 d. 1078 3. Write the successor and predecessor of 1,999. u-t s- _..

Kiran starts reading an animals' encyclopaedia from page 999 onwards. She finds the next 7 pages very interesting. Write down the next 7 page numbers. b. John paints every alternate page in his art and craft book starting from page 4L6. Write the page numbers if he paints 10 pages. Comparison of Numbers >iEWWt To compare any two numbers, count the number of digits in both the numbers. The number having more digits is greater. Example 1: Compare 867 and 1867. 1867 > 867 [1867 has 4 digits, and 867 has 3 digits] tf the numbers have the same number of digits, then compare the digits at the highest place. lf these two digits are the same, then compare the digits in the next highest place ano so on. Example 2: Compare the height of two trees. Which one is taller? 1Tree Tree 2 460 cm 450 cm Both 460 and 450 are 3-digit numbers. Compare the digits starting from the digit with the highest place value. We see that the digits at the hundreds place are same. So, compare the digits at the tens place. 6>5 Hence,460 > 450 Tree 1 Tree 2 Thus, Tree 1 is taller than Tree 2. Example 3: Compare 3263 and327t. Both 3263 and 3271have the same number of digits. Both numbers have 3 in their thousands place and 2 in their hundreds place. In tens place, 7 > 6. Hence,327t is greater than 3253.

Example 4: Compare 4268 and 4786. Exa mple 5: compare 7981 and 7934. 4268 4 786 798L 7934 Same Same Same Different Different Herc, Z <7 Here, 8 > 3 Thus,4268 < 4786 Thus, 798L > 7934 Torget OlymPiod lf A stands for 4, B stands for 2, C stands for 3 and D stands for which of the following is an incorrect statement? Put a cross (r) in the box front of the incorrect statement. n numbers hove a. ABCD is greater than DCAB. tl dilferent number of b. ABC is the successor of ABD. di-qiltess,stehrennuummbbeer rowf ith c. BCD + DDB is equalto CAC. n d. AB - BD is equal to BD. diqits is smoller E 1. Circle the smallest number in each row. a. 1286 4862 3368 2394 5252 5802 b. s963 s693 5469 7940 797L c. 79lo 79ot 7923 8324 3496 3093 8436 2. Circle the largest number in each row. 3002 a. 7286 2862 1368 8012 b. 8L02 8201 3086 c. 3014 3023

LS lf the number of students' bicycles parked in the campus of a school is 5 less than the smallest 4-digit number, how many students of the school use bicycles to commute? Write two benefits of riding bicycle over other modes of transport. Ascending and Descending Order Ascending order means arranging the given numbers in the order of the smallest to the largest. lt is also called increasing order. Descending order means arranging the given numbers in the order of the largest to the smallest. lt is also called decreasing order. Consider the numbers 2981, 1846, 9863 and 5143. 9863 ,\"D 1 Arrange in ascending order. b. 3864, r9a9,2L20, 6002 a. 4986, 3842, 2184,s026 2. Arrange in descending order. a. 9189, 9872, 9218, 9128 b. 8468,3794,3878,7398 3. In a factory warehouse, there are 3480 tables, 3860 chairs and 3940 benches. Arrange these items according to descending order of their numbers. iffCl on Independence Day, the students of class 3 of a school distributed 1320 l5l balloons, 1230 flags and 1310 sweets to the people in their neighbourhood. Arrange the above numbers in ascending order. Choose the most appropriate value associated with the above action. a. Regularity b. Patriotism c. Honesty

Aioths Around Us Kiran went to Ooty on a vacation with her parents. They travelled from Mettupalaiam to Ooty by train. While travelling, she asked her father about the height of the ooty hilltop. Her father told her that the height of the Ooty hilltop is 2240 metres. Her father also made her aware that the height of a hilltop is also known as altitude. He told her about the altitude of some hill stations. Mount Abu-1220 m Darjeeling-2050 m Kodaikanal-2133 m Shimla-2205 m The altitude of manv hill stations are in thousands of metres. Kiran could connect the altitude of hill stations with large numbers she has learnt in the class. Forming Largest and Smallest Numbers To form the largest 4-digit number, arrange the given digits in descending order. Example 1: The largest 4-digit number that -i can be formed using the digits t,2,3 and 4is 432L. To form the smallest 4-digit numbet arrange the given digits in ascending order. 'Example 2: The smallest 4-digit number that can be formed using the digits 1, 2, 3 and 4 is L234. Vishal's car number is the largest number formed using 4, 5, 1 and 6 Let us find the number. The number after arranging 4, 5, 1 and 6 in descending order is 654-. Surbhi's car, on the other hand, has the smallest number formed using 4, 5, 1 and 6. Let us find the number. Surbhi's car number after arranging 4, 5, 1 and 6 in ascending order is 1456.

1. Form the largest and the smallesl number using the given digits. Digits Largest number Smallest number a. 4, 6, O,3 b. 5,8,7,t oq12 d. 6,2, O, 4 e. 8,t,3,9 2. a. Kiran's lucky number is the smallest number that can be formed using 4, 3, 7 and 9. Her lucky number is b. Johnt lucky number is the largest number that can be formed using 4 3, 7 and 9. His lucky number is Even and Odd Numbers ,, -,.1-. Form two groups of children, one group with 6 children and the other with 5 children. Group them into pairs and observe. You will see that all the children are paired in the group of 6 children. On the other hand, in the group of 5 children, one child is left without a pair. Even numbers Odd numbers Numbers that can be divided into exact groups of twos are called even numbers. An even number ends with 0, 2,4,6 or 8. Numbers that cannot be divided into exact groups oftwos are called odd numbers. An odd number ends with 1,3, 5, 7 or 9.

Sheeba has a pack of 9 cards numbered from 1- to 9. She makes three unequal piles. What all combinations ofthree unequal piles can she make? Objective: To identify odd and even numbers' Materials required: A I'O x 10 grid and colour pencils What to do: Write the missing numbers. Colour even numbers blue and odd numbers red. L 2 3 4 5 6 7 8 9 10 11 L2 99 100 Number of odd numbers: Number of even numbers:

L. Circle the even numbers in each row. a. 2015 3218 ro2l 2084 1028 b. 62L9 1100 1099 7076 2. Circle the odd numbers in each row. a. 7226 9879 OzJ.I a4u 9723 b. t243 3468 4347 8696 7640 3. Fitl in the bianks. a. The largest 4-digit odd number is b. The smallest 4-digit even number ts Rounding Off Numbers ln real life, we round off numbers to make calculations easier and faster. When you go to any party, you might guess the number of people present there. . When you travel, you might guess the time taken to reach the destination. The rounded off value of a number is the approximate value and not the actual value. To the Nearest Ten -qqFlvr:For rounding off a number to the nearest ten, check the digit at the ones place. . lf the digit at the ones place is 0,1,2,3 or 4, change the ones digit to 0, keeping the ^fhar.lioii< <.ha . lf the digit at the ones place is 5, 6, 7, 8 or 9, add 1 to the tens digit and change the ones digit to 0. 38 is rounded off to 40, while 32 is rounded off to 30. But 35 is rounded off to 40 bv convention. 3+0lr31 32 33 34 35 36 37 38 39 4I0 rounded off to rounded off to To the Nearest Hundred For rounding off a number to the nearest hundred, check the digit at the tens place. . lf the tens digit is 0, 1, 2, 3 or 4, change both the tens and the ones digits to 0, keeping the other digits same.

. lf the tens digit is 5, 6, 7, 8 or 9, add 1to the hundreds digit and change both the tens and the ones digits to 0. 124 is rounded off to 100, while 182 is rounded off to 200. 1. Round off to the nearest ten. a. L3 b. 24 c. 27 d. 35 e. 68 f. I29 g. 409 h. 318 t. 792L j. 2707 2. Round offto the nearest hundreq. a. 156 b. 178 c. 412 o. 5db e. 907 f. Lr28 h. 2803 j. 7690 C. 1280 i. 4990 3. There are 1468 toy cars in a factory Round it offto the nearest LOO. 4. There are 1252 ice cream cones in a shop. Round it offto the nearest 10. 5. List all the numbers which when rounded off to the nearest ten become 240. 6. Write down the smallest and the greatest number which when rounded off to the nearest hundred becomes 500. Drive up a mountain Draw a mountain on a chart paper. WriIe O, 7,2,3 and 4 going up the left side of the rmruouu|n|rtda|in|r. WvvrrirtLee J5 daLt tLhnee tLooplJ t(ssliBghnUtlyy rtoawarqd5s frilgghntl), 1 and 6, 7, 8, 9 and L0 going down the right side of the I mountain. Also, draw a car going up the mountain. lf the number ends in 1 through 4, then the car rolls back towards 0 on the left side. lf the number ends in any digit greater than 5, the car will roll down the hill to 10. lf the number ends in 5, explain to the students that the car will roll down to 10.

--- =-_J Summer Time! The animals in the picture have number tags on tnem. The table given below the tree has numbers. Round off 2- and 3-digit numbers on the table to the nearest ten and 4-digit numbers to the nearest hundred. Use the siven colour code corresponding to the rounded off value to colour the animals. .. ', I /,, a{ rt: colour 29 106 Blue 1046 1998 Gr€y 921 Brown 42 134 Black 813 45 __.e-\\eiFi ------o-re-

^r# \"*b#Ir#1. Pair the objects and write odd (O) or even (E). t_---*l D. t----l 2. Write a number which has 4 thousands, 6 hundreds and 8 ones. 5. Write the place value of 6 in L645. A Write the greatest 4-digit number. 5. The Dredecessor of 1672 is and its successor is 6. The smallest 4-digit number that can be formed using 0, 1., 2 and 3 is 7. Write the number name and the exoanded form of 4598. 8. lf 499 is rounded off to the nearest hundred, it becomes 9. Write the smallest 3-disit odd number. 10. lf a number ends with 0,2, 4, 6 ot 8, it is called an number. L1,. Form the largest 4-digit number for each floweq using the digits only once. s sNow arrange these numbers in ascending and descending order. 12. Write allthe even numbers between 11.86 and 1220 (include both these numbers). s s L3. Write allthe odd numbers between 1011 and 1039 (include both these numbers). o o oo

{ WonrsHeer A Football Match A total of 2495 people went to watch a football match. out of 2495 people, 500 were women and 675 were children. Use the above information to fill in the blanks. a. The expanded form of 2495 is b. The place value of4 in 2495 is c. lf the number of people who watched the football match is rounded off to the nearest ten, it becomes The number of men who watched the football match is Which is greater-2000+400+90+ 5 or 2000 +900+40+ 5? What is the sum of the place values of 2 and 9 in 2495? g. Write the face values of all the digits in 2495. Scrambled Numbers Pick any three numbers from the clrcle to make three different 3-digit numbers and write them on the left side of the circle. On the right side of the circle, starting from the top, arrange the 3-digit numbers from the smallest to the greatest.

Adl Itlon ,t' ii ii i, il 1. onMake pairs of the penguins on both the sides so that the sum of the numbers ij ne risht. =---ls there a penguin which has no pair? (yes/No) i .; ii form?How many pairs of penguins did you li ,--i-l,:'e---..\\.!-'''.- ii ii obioined on oddition (*::'l:lT',ll*::gl\"\\zg*qt=+t*a-l2. Fill in the boxes. iii' u. .t res-ult ii ,o*o=o*fo is cqlled the sum. The numbers thqt ore odded iili a \"'T!1i\"\"'ffi't2r#zD-=--(c. ii fi|d. \\ ore coalled addcaiennddss. so+61+ze=61+[l+so -'\\=}-J, so+10+2s=10+f_l+so ti ii

Addition 3-digit Numbers Without Regrouping For adding 3-digit numbers, we start by adding the ones, then add the tens followed by the addition of hundreds. 3-digit number with a 1-digit number 3-digit number with a 2-digit number EEf sreo 1: ,\"oo rne ones. fEf steoi.: Addtheones. 5 5+3=8ones 28 8+1=9ones + Step 2: Add the tens. 5I Step 2: Add the tens. 3 8 2+0=2tens 9 2+3=5tens step 3: Add the hundreds. Step 3: Add the hundreds. 3+0=3hundreds 4+0=4hundreds Thus,325+3=328 Thus, 428 + 31 = 459 3-digit number with a 3-digit number trElil stepl: Addtheones. 4+5=9ones sPEcllllEll coPY Step 2: Add the tens. 2+4=6tens 324 Step 3: Add the hundreds. 3+1=4hundreds DATE.. l hl l +145 4 o 9 Thus, 324 + L45 = 469 With Regrouping Regrouping ones lf the sum of the digits in the ones column is more than 9, regroup 10 ones as 1 ten. Examole: Add 117 and 15. qrpn 1. A.l.l fha ^nac trEtr 7+5=12ones r@r 7 = l ten and 2 ones Carry over l ten to the tens column. I5 Write 2 in the ones column.

trEtr Step 2: Add the tens. r vI 7 L + L + L (carry over) = 3 tens L5 Step 3: Add the hundreds. 1 ten = 10 ones 1+0=lhundred 5 hundred = 10 tens EEE 1 thousond = 10 hundreds r@r 7 I5 L3 Thus, 117 + 15 = 132 Regrouping tens lf the sum of the digits in the tens column is more than 9, regroup 10 tens as t hundred. Example: Add 235 and L84. I|TTtr Step 1: Add the ones.5 +4 = 9 ones t^ 35 2 Step 2: Add the tens. 3 + 8 = 11tens = I hundred and l ten 84 Carry over t hundred to the hundreds column. 4 t9 Step 3: Add the hundreds. 2+L+L(carryover) = 4 hundreds Thus, 235 + 184 = 419 Regrouping hundreds lf the sum of the digits in the hundreds column is more than 9, regroup L0 hundreds as 1 thousand. Example: Add 792 and 4O3. tor7rs2|Etr Step 1: Add the ones.2 + 3 = 5 ones Step 2: Add the tens.9 +O = 9 tens +403 IIStep 3: Add the hundreds. 7 + 4 = hundreds = L thousand and t hundred 11 95 Carry over 1 thousand to the thousands corumn.

Step 4: Add the thousands. O + O + 1(carry over) = L thousand Thus, 792 + 403 = u95 Regrouping ones, tens and hundreds )ome mes ones, tens and hundreds columns are regrouped at the same time. Example: Add 876 and 257. Step 1: Add the ones.6 + 7 = 13 ones = L ten tortoraEoi tr and 3 ones 6 Carry over L ten to the tens cotumn. + z5 7 Step 2; Add the tens. 7 + 5 + 1 (carry over) L1 5 = 13 tens = L hundred and 3 tens Carry over t hundred to the hundreds column. Step 3: Add the hundreds. 8 + 2 + 1 (carry over) = 11 hundreds = l thousand and t hundred Carry over L thousand to the thousands column. Step 4: Add the thousands. O + O + L (carry over) = j. thousand Thus,876+257=1133 ' EEI!!1. Add the following: ,TEE . IIEE L28 347 +3L 34 +42 ' llEll c 'EEE 104 634 +651 \" EEE +3 5 3 525 +440

- EET ^ IIEE trEr 721 748 +120 +131 220 +5 6 8 j rEr \" rllE 86 589 trEr 4 +78 759 at5 m. \" EEE \" ITEE 587 L77 lJz +2 8 6 +343 rzov - EI|ET ' ErEr .ErEr 429 679 778 938 829 543 Word Problem Example: There are 328 red-coloured cars and j.39 blue-coloured cars parked in a parking area. How many cars are there altogether in the parking area? TIEtr (r^ Red-coloured cars 38 tBlue-coloured cars + 9 Total number of cars 4 67 There are 467 cars parked in the parking area.

1. In a primary school, there are 243 boys and 315 girls. Find the total number of students stidying in the school. 2. Vinay went to a beach and collected 165 seashells, while his ry* GI friends collected 435 seashells. How many seashells did Vinay and his friends collect in all? 3. In a grocery shop, there are 538 bags of rice and 376 bags @@ of wheat. Find the total number of bags in the shop. 4. 525 men and 579 women visited a fair. Find the total number of people who visited the fair. lry--grl On Ctritaren's Day, each boy and girl of Classes 3 and 4 were asked to bring an old storybook to donate it to children in nearby NGOs. lf there are 102 boys and 98 girls in Class 3 and 115 boys and 120 girls in Class 4, how many books were collected in all? Suggest some other ways to help people in need. Expanded Form Follow the steps and add. L(Dg4+@2s = iZOO +iOOl + [90 + 20] +[4+31 =600+ r1O+7 =717 2. 236 + L12 - I-T-J T [-+-] +[_+ l= 3. 318 + 430 [-+-] r'It_'_t- r l- 4. 465 + 524 - t_-_l r [-+-] + [_+_] = 5. 685 + 312 - t_,_t ? [-+-] + [_+_] =

Express the given numbers as a sum of an odd number and an even number' One has been done for You. Addition Using a Map \":'*t-\"z:+z'+''\"t' Use the information given in the map and answer the following questions. The distance between 1. Agra and Jaipur via Delhi is kilometres f---lm * tIf__-lt'\" = 2. Jaipur and Shimla via Delhi is kilometres l-lt' * l---lr,' E= 3. Agra and Shimla via Delhi is kilometres l_lm * Ef---]r.'\" = More on Addition of 3-digit Numbers Example: Add 243, 128 and 308. IlEtr step 1: Addtheones'3+8+8= leones= ltenand Z @q 3 Carry over I' ten to the tens column' | 2 8 Step2: Add the tens. 4 + 2 + 0 + 1 (carry over) =7tens + 3 O I Step3: Addthe hundreds' 2+1+3=6hundreds 6 79 Thus, 243 + 128 + 308 = 679

. EEE1. Add the following: , ETET . EEE t26 2L2 234 265 442 435 +127 346 +123 ,TEE 247 \" llElil 'rEr 285 253 254 +7 3 8 128 s39 +3 8 5 +129 g. h. t. ETET 278 334 329 313 L63 +148 498 DE,4 199 Pattern in Maths Fill in the blank boxes. One has been done for you. B.E.E=@ so,@*@*@=fr*l E.E.@=O so,D*C*D=E Word Problem Example: In an orchard, there are 186 apple trees, Apple trees o\"I @80 274 mango trees and 134 coconut trees. Find the total number of trees in the Mango trees 74 orcha rd. 34 Coconut trees +1 Thus, there are 594 trees in the orchard. Total number of trees ) 94

1- 243 men,178 women and 358 children visited a zoo on Sunday. Find the total number of visitoB to the zoo on Sunday. 2. Remya counted 157 men, L40 women and 70 children in the Christmas fair organised by her school. How many people did she count in all? 3. In a cricket match, Sunil scored 135 runs, Amit scored L48 runs and Aliscored 125 runs. How many runs did they score in all for the team? A A cold storage has 349 cartons of apples, 239 cartons of pears and 421 cartons of oranges. Find the total number of canons. \\ Write the numbers verticallv and add. a. 545 + 111+ 266 b. 133 + 284 + 499 c. 109 + 518 + 99 f. 276 + 589 + 100 d. 88 + 136 + 333 e. 1L4+44!+L49 ttAoths Around Us On the event of World Environment Day, a school planned to plant at least 1000 flowering plants. Students were told to participate in this event. In the event, Class 3 planted 270 plants, Class 4 planted 355 plants and Class 5 planted 385 plants. Did all the three classes together meet the school's planning of planting ].OOO plants? lf yes, how many more plants were planted than the minimum requirement of LOOO plants? Express the given numbers as the sum of two even numbers.

q#o@@ The Bakery Shop Look at the picture given below ind answer the questions that follow. 1. Vinay orders a birthday cake and a pizza. How much money trEtl will he have to pay? 2. Arthur buys a cup of ice cream and a glass of orange juice. How much will these things cost him? 3. lfJaya orders a birthday cake, a pizza and a cup of ice cream, how much money will she have to pay?

1. The sum ofthe smallest 3-digit number and 99 is 2. The sum ofthe largest 2-digit number and the largest 3-digit number is 3. The sum of 999 and L ii 4. When we add the smallest 3-digit number to O, the sum is 5. 999+99+9= Estimating the Sum In daily life, estimation is used for intelligent guesses about possible amounts. you might see a jar of marbles and estimate that there are about 25OO marbles in the jar. lf the actual number is 2479, it is a close estimate. while estimating the sum, we first round off the given numbers to the nearest tens or ones as asked and then we add the numbers. Example 1: Estimate the sum of 274 and 3I2 fir;ifllll ru ]fSumEstimated Actual Sum by rounding off the numbers to the nearest ten. 270274 We round ofI274 to the nearest ten to get 270 and +310+31,2 round off 312 to the nearest ten to get 310. Then we add the rounded-off numbers. 580 586 We observe here that the estimated sum is lesser than the actual sum. Example 2: Estimate the sum of274and3!2 Estimated Sum Actual Sum 600 by rounding off the numbers to the M rEl nearest hu ndred. 24 We round off 274 to the nearest hundred to get 300 and round off 312 to the nearest hundred to 31 2 300. Then we add the rounded-off numbers. 586 We observe here that the estimated sum is greater than the actual sum. 'fixrilfEstimate the sum by rounding off the numbers to the nearest ten. Also, find the actual sum. b c. 506 6L3 4 2 492 +2O4 +1 9

. EINET 323 ' EEII 789 +418 -1 59 304 +zt3 h. 972 845 867 288 161 325 2. Estimate the sum by rounding off the numbers to the nearest hundred. Also, find the actuat sum. a. D. c. 525 455 1nE +179 +5Lt +2 6 8 o. e, 655 +120 709 598 +108 +299 3. Anuj obtained 389 marks in the quarterly examination and 423 marks in the half-yearly examination. Estimate his total marks by rounding off the marks obtained to the nearest hundred. 4. Vicky bought a T-shirt for { 378 and a pair of sunglasses for { 322. Estimate his total expenditure by rounding off the costs to the nearest ten. Addition of 4-digit Numbers Without Regrouping While adding two or more 4-digit numbers, arrange the digits of the given numbers in the correct columns and then add. For adding 4-digit numbers, we start by adding the ones, then add the tens, then the hundreds. followed bv the addition of thousands. Ft -##.

I Ste p L: Addtheones.4+3=7ones Examole: Add 2634 and 1253. Step 2: Addthetens.3+5=8tens E!|ET 2634 Step 3: Add the hundreds. 6 + 2 = 8 hundreds +1253 Step 4: Add the thousands. 2 + 1= 3 thousands 3887 Hence. 2634 + 1253 = 3887 1. Add the following: b. E trc. 5 043 \" EEEIil 240 03 3 b25 3152 +4 3 1 0 +51 'ETET 8642 ro. E +10 5 5 iIUI 2 7 064 With Regrouping If the sum of the digits in any column is more than 9, regroup as given below ten10 ones = L 10 tens = t hundred 10 hundreds = l thousand Example: Add 4348 and 2479. Step 1: Add the ones.8 + 9 = L7 ones E = L ten and 7 ones o, 4 Carry over l ten to the tens column. 6827 Step 2: Add the tens.4 + 7 + L (carry over) = 12 tens = t hundred and 2 tens Carry over L hundred to the hundreds column.

Step 3: Add the hundreds. 3 + 4 + 1 (carry over) = 8 hundreds Step 4: Add the thousands.4 + 2 = 6 thousands Hence, 4348 + 2479 -- 6827 1883 6767 .ETET +2 3 4 8 +2 4 7 8 525:t , EEET \" ETET 4986 7973 +4 8 7 4 +3245 +1457 'EEET ' ErElil 'Etr|ET 2665 L655 3547 +2 6 8 9 +4 9 8 3 +2 4 9 6 , ETET -EEET r 7824 435 7 +1999 5358 +19 8 8 +344 5 EEET 4613 +2 3 4 9 More on Addition EIIEtr @, @, Example: Add: 4238 + 425 + L238 8 425 Arrange the numbers in the correct columns and add. 238 Step 1: Addtheones. 8+ 5+8= 21ones 59 07 = 2 tens and 1 one Carry over 2 tens to the tens column.

Step 2: Add the tens. 3 + 2 + 3 + 2 (carry over) = 10 tens L0 tens = L hundred + 0 tens (only L digit can come in a column) Carrv over L hundred to the hundreds column. step 33: Addthehundreds. 2+4+2+ L(carryover)=thundreds Step 44: Add the thousands.4 + 1= 5 thousands Hence, 4238 + 425 + 1238 = 5901 1. Add the following: 'ETET .E|trET 65L7 \"ETEE 1836 54 638 +291 87 4944 45 +235 2. Arrange the following in the correct columns and find the sum b. 35 + 6241+ 2304 c. 4539+24+1299 trEET trtrEr trtrEra. 2653 + 3M +2359 3.5957,!242and23gstticolourballoonswerereleasedduringlndependenceDay celebrations in three consecutive years. How many balloons were released in the three years altogether? lyEil n milt van supplied 4528 bottles of milk to a milk booth and 4265 bottles to l5l 3n616g1 slilk booth. Find the total number of milk bottles supplied by the van' lf these two booths receive their milk supply always on time, what value is portrayed by the milk suPPlier?

Properties of Addition .'4l7wr,;:,., . When zero is added to a number, the sum is the number itseli Examples: 42+0=42; 63+0=63; 84+0=84 . When one is added to a number, the sum is the successor of the given number, Examples: 36+L=37; 59+1=50; 95+L=96 1. Fitl in the boxes. u. zr+r=f_-] c. sa+f_l=g+ 14+o=f_-] e. zo + l---l = zo r aq+o=T_l d. s++l-l=ss D[srH{s, A-UTU!7 Obiective: To understand the formation of 4-digit numbers. Materials required: Ten number cards each for 1000, 100, 10 and 1 Method: Teacher writes three 4-digit numbers on the board (for example: 2253,3347 and 4334). Each student forms the 4-digit numbers with the help of the number cards. Students place the number cards combination and verifv with the teacner. @ffiffi@@trtrtrtrtrIlI @ffi@@@@@EEtrEI @ ffiffiMffi@@@ElE4Elrrr The activity can be extended for explaining addition of 4-digit numbers. mmwE@2253 + 334'r.= sss4 = @trtrL00 100 100 100 trtrtrtrtrtrtr1trt

Choose the correct answer from the given options. 1. 240 + 790 is the same as a. 630 + 300 b. 850 + 280 c. 400 + 630 \" EEE o rEr2. Which of the following gives the correct sum? c. 5 52 55 4 o8 9 +5 6 7 +1 5 795 79 7 793 3. A shopkeeper sells 139 cones of chocolate ice cream and 241 cones of strawberry ice cream. Altogether, he sells a.3T0conesoficecream b. 280 cones of ice cream c. 380 cones of ice cream 4. 360 people visited a science exhibition in the first week of May. The number of people increased by 100 in the second week. The total number of people who visited the exhibition in the first two weeks is a.820 b. 460 c. 560 5. 4166 men, 3980 women and 750 children live in a village. The total population of the village is b. 8896 c. 8869 a. 8900 6. In a train, there are 245 first-class seats and 662 second-class seats. The total number of seats rounded off to the nearest hundred is a. 890 b. 900 c. 800 7. 243 + 483 is equal to b. 443 + 384 c. 443 + 284 a. 483 + 243 Add the number at the top to each number and fill in the box. One has been done for you in each option. b. 146 c. 568 a. 36 t92 +87 a t, rczz + 77 7 1345 +15 +2 +9 + o +9 L

1. There lived many different wild animals in a forest as given below. Animal I Number crid You kn6,r, 1530 Elephant The Royal Bengal Ltons L15 Tigers 434 Tiger is the national animal of lndia. Rhinoceroses 2260 NoW answer the following questions. a. How manv eleohants and rhinoceroses were there in the forest? b. What is the total number of animals in the forest? How many animals other than elephants lived in the forest? d. How many lions and tigers were there in the forest? 2. Add the numDers in columns and rows and then fill in the empty boxes. a. b. 760 980 256 680 238 342 277 c. 9IL 122 1s0 506 328 t43 883 555 100 747 385 460 t,|t.H tttttHttrtttr: I. t-.4,,t-.-.n_-I._-_I-_-.-H-.

stl)Olllt Subtraction means taking away one n um ber from another number. Subtraction is the reverse process of additlon. The number from which another number is subtracted is called the m in uend. The number which is subtracted from the minuend is called rthe subtrahend. The result is called the difference. 7 .- M in uend - 3 i- Subtrahend ,-f+-l Difference 1. In a basketball match between Team A and Team B, Team A scored 38 points and Team B scored 54 points. How many more points did Team B score than Team A? -Team Bscored Tea mAsco red [] 2. In the match between Team B and Team C, Team B scored 44 points while Team C scored 52 points. How many more points did Team C score than Team B? Team C scored - Team Bscored

Subtraction .:,*, Subtracting 2-digit Number from a 3-digit Number Without Regrouping We start by subtracting the ones, then we subtract the tens followed by the subtraction of hundreds. Example: Subtract 28 from 359. Stepl: Subtract the ones. Step2; Subtract the tens. Step3: Subtract the hundreds. 9-8=1one rEr5-2=3tens rEE3-0=3 hundreds 59 J9 88 1, 5I 55r Thus, 359 - 28 = 331 . EEIT1. Subtract the following: ' rElil . EEE 28 348 87 I5 -38 ,TEE trEr 546 \" ENE 648 559 -47 - EEE -45 778 EET -24 ^ trIEE 99 893 73 -62

2. Arrange the fotlowing in the correct columns and subtract' qzt-fi=f-l =f-lb. zqz -zz c. 6ss-+2=[----_l oog - az =[---_l ez+-oo=[----_l f. gs+-zr=[---_-l With Regrouping Examole: Subtract 39 from 228. EEtr Step l-: Subtract the ones. %@t@t Since 8 is smaller than 9, borrow L ten from the tens column and regroup the ones column as 8 ones + 10 ones = l'8 ones. Hence, 18-9=9ones t 89 step 2: Subtract the tens. since l ten was borrowed by the ones column' l ten is left' Since 1 is smaller than 3, borrow t hundred from the hundreds column and regroup the tens column as l ten + 10 tens = Ll\" tens' Hence, 11-3=8tens Step 3: Subtractthe hundreds. L-O = t hundred Thus, 228 - 39 = 189 1. Subtract the following: , IIEE . IIEE 5+ 476 a. -t6 _JJ 323 \" EEE ' EEIil 510 05z -IO -38 -49 ,TEE 432 -2J

* EEE h. 645 45 3 75 -38 5 9 2. Fill in the boxes with the appropriate sign (., , ot =1. ).^+^z-o-^v(-Lt-J-^lou-rf\",- f. eeo - s7 a-l s72 - 88 a. -tz^/ -- 5-\"+rl--)-t2-L\"!\"- \"L-z D. 252- 2r l__) 3ZO- +! .l 5O4 - 50 LJ rr) - r5 e. s74-29[ 1880-89 Subtracting 3-digit Number from a 3-digit Number Without Regrouping Examole: Subtract 123 from 346. StepL: Subtract the ones. 6 - 3 = 3 ones Step 2: Subtract the tens. 4- 2 = 2 tens Step 3: Subtract the hundreds. 3 - 1= 2 hundreds 23 Thus,346 - L23 -- 223 With Regrouping Example 1: subtract 1.45 from 382. Step Subtract the ones. 237 Since 2 is smaller than 5, borrow 1 ten from the tens column and regroup the ones column as L0 ones + 2 ones = L2 ones. Hence, 12-5=7ones Step 2: Subtract the tens. 7 -4 = 3 tens step3: subtractthe hundreds. 3-1=2 hundreds rhus, 382 - 745 = 237

Example 2: Subtract 145 from 327. Subtractthe ones. 7 - 5 = 2 ones 1 87 Subtract the tens. Since 2 is smaller than 4, borrow fhus,327 - I45 = I82 t hundred from the hundreds column and regroup the tens column as L0 tens + 2 tens = 12 tens' Hence, 12-4=8tens subtract the hundreds. 2-1=lhundred 1.. Subtract the following: Ob. -325 L02 -- tI^ 21a - 111 = tlt 689-100= Oa. 236- lZO = tIe.48a-277= Dd.486-486= tlh. 873 - 642 = Oi. 9M- I23 = De. 789 - 556 = Ol. 42L-236= OK. 555 - rO4 = Do. 716 - 442 = Ol, 242- r5O = On. 643 - 468 = Or. 922 - 644 = Om. 532- 327 = Dq. 854 - 235 = DP. 820 - 31s = Subtracting 4-digit Number from a 4-digit Number The subtraction of 4-digit numbers is the same as that of 3-digit numbers. Regroup if in any column, the digit of the subtrahend is greater than the digit of the minuend' Without RegrouPing Subtract the ones. 8 -4 = 4 ones Subtractthe tens. 3 - L = 2 tens Example; Subtract 32L4 from 6438. Subtract the hundreds. 4 - 2 = 2 hundreds Subtract the thousands. 6 - 3 = 3 thousands EtrET eA2q -5ZL 3224 rhus, 6438 - 32!4 = 3224