MATHEMATICS (Revised) ©KTBS B¶Îmm Mm¡Wr 4 re be …ktbs.kar.nic.in/New/website textbooks/class4/4th-marathi-maths-1.pdfII III Young learners in their initial stages of learning

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MATHEMATICS

B¶Îmm Mm¡WrFourth Standard

‘amR>r ‘mÜ¶‘Marathi Medium

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Karnataka Text Book Society (R.)100 Feet Ring Road,

Banashankari 3rd Stage, Bengaluru - 85

(Revised)

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PREFACEThe Textbook Society, Karanataka has been engaged in producing

new textbooks according to the new syllabi prepared which in turn are designed based on NCF - 2005 since June 2010. Textbooks are prepared in 12 languages; seven of them serve as the media of instruction. From standard 1 to 4 there are the EVS, mathematics and from 5th to 10th there are three more core subjects namely mathematics, science and social science.

NCF - 2005 has a number of special features and they are:• Connecting knowledge to life activities• Learning to shift from rote methods• Enriching the curriculum beyond textbooks • Learning experiences for the construction of knowledge• Makingexaminationsflexibleandintegratingthemwith

classroom experiences

• Caring concerns within the democratic policy of the country• Make education relevant to the present and future needs• Softening the subject boundaries-integrated knowledge and

the joy of learning

• The child is the constructor of knowledge

The new books are produced based on three fundamental approaches namely Constructive Approach, Spiral Approach and Integrated Approach.

The learner is encouraged to think, engage in activities, to master skills and competencies. The materials presented in these books are integrated with values. The new books are not examination oriented in their nature. On the other hand they help the learner in the all round development of his/her personality, thus helping him/her become a healthy member of a healthy society and a productive citizen of this great country, India.

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Young learners in their initial stages of learning i.e., between the ages of 5 and 10, acquire most of the concepts which they need in consolidating learning in later stages. If this learning is properly planned andwellexecutedintheclassroom,childrenmayfindlearningeasyand enjoyable.

Based on these principles, in the early stages from class 1 to 5, the following subject areas have been introduced- Mother tongue, state language, English as a practice language, mathematics and environmental studies. Environmental studies include science and social science related to their daily life experiences, information about their environment, society, country, their duties and rights. These topics are presented through interesting situations and activities. Opportunities have been provided for self learning and creativity. At this stage importance is given to children sitting in pairs and groups and to exchange their experiences. The efforts have been made to make illustrations colourful, attractive and meaningful. Teachers are expected to make use of these and help children learn meaningfully and with pleasure. The textbooks aim at making learning interesting, enjoyable and satisfying.

The Textbook Society expresses grateful thanks to the chairpersons, writers, scrutinisers, artists, staff of DIETs and CTEs and the members of the Editorial Board and printers in helping the Text Book Society in producing these textbooks.

Prof. G.S. MudambadithayaCoordinator

Curriculum Revision and Textbook Preparation,

Karnataka Textbook Society (R),Bengaluru, Karnataka

NagendrakumarManaging Director

Karnataka Textbook Society (R),Bengaluru, Karnataka

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About the book.....

As Per 2005 National curriculum frame work children are expected to gain knowledge on their own by their day to day experience. The 2nd standard textbook has been designed on the basis of National curriculum frame work. the committee has tried to help teachers, students and par-ents by providing the favour able learning environments to take them to achieve the goal in a meaningful, joyful and day to experienced situation.

The main features of this textbook is to provide the students graded learning activities. to facilitate the students to draw the inference by understanding

the truth of concepts and to generalise the concepts on their own. to provide enough opportunities to the students to understand the

new concepts and to express the same on their own. to help the students to apply their mathematical knowledge in their

day to day affairs and in different circumstances. Each unit of this text book starts with teaching concrete examples,

activities and group activities. Teachers may use the same activities or the parallel activities designed by them.

‘Mathematical words’ or generalisation are used only after the child gets the experience of Mathematical operations by day to day experience. In other words from known to unknown.

Three new chapters are introduced in this textbook. ‘Mental Mathematics’ to give importance to mental arithmetic and

to achieve quick and correct calculation. ‘Pattern’ this unit provides an opportunity for the students to correlate the different patterns they observe around them in their day to day affairs and to appreciate the esthetic beauty of mathematics. ‘Data handling’ this chapter help the students to develop the skill to collect information, to arrange them in an order and tabulate them.

We welcome all positive suggestions from teachers, parents, students and general public to improve the standard of this text book.

Icongratulatetheguidingofficersofthedepartmentandmembersofall the teachers involving in the team of Mathematics framing textbook.

Sri D.R. Krishnaprasad Chair Person Textbook committee

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Text Book CommitteeChair Person :

Sri D.R. KrishnaprasadNo. 230, "Ganita Bharathi", 12th B Cross, 1st A main, West of cord road, II stage, Mahalakshmi puram Bengaluru -560076,

Members :Sri S. Gavisiddappa No. 263/17 A, 2nd cross, Basaveshwar nagar, Bellary -573103,Sri Vasudeva K.J Technical Assistant, DSERT, Hoskere halli Bengaluru.

Sri P.N Balakrishna Rao Assistant Mastar, Govt High school, Nambi Halli, Srinivaspur taluk, Kolar Dist.

Sri Ramachandra G Assistant Mastar, Govt High school, Kalkere Bengaluru South - 4.

Smt Asha Nayak Assistant Teacher,Sri V.S.S. 3rd Block, 3rd stage, Basaveshwaranagarr Bengaluru-560079

Sri Prakash Koti Drawing Teacher, Govt High school, Sakkare golla Halli, Dodda ballapur Taluk Bengaluru Rural DistScrutinizer : Sri. T.K Raghavendra, BEO Srinivaspur, Kolar DistrictEditorial Committee :

Sri Dr Ravindra Former NCERT Director, Arehalli BSK, 3rd stage, Bengaluru - 61.Sri Dr Upadya B.S Lecturer and Head of Department Maths, RIE, Mysuru.Sri Dr Prasad S.V Lecturer, RIE Mysore.

Sri Dr Sharad SureAssistant Proffessor Aziam Premji university Bengaluru -10 PES School of Engineering campus Konappa Agra Hara

Translation Committee :

Smt. Asha B. Nesarkar H.M. Mahila Vidyalay, H.S. Belagavi.

Sri. Vishwanath N. Patil A.M. Mahila Vidyalay, H.S. Belagavi.

Chief Co-ordinator:

Prof. G.S. Mudambadithaya, Co-ordinator, Curriculum Revision and Textbook Preparation, Karnataka Textbook Society, Bengaluru.GuidanceSri Nagendra Kumar, Managing Director, Karnataka Textbook Society, Bangaluru.Smt Nagamani, Deputy Director, Karnataka Textbook Society, Bengaluru.Programme Coordinators :Smt Vijaya Kulkarni Assistant Director, Karanataka Text Book Society.Smt Prema B. R. Technical Assistant ,Karanataka Text Book Society.

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About the Review of Textbooks

Honourable Chief Minister Sri Siddaramaiah who is also the Finance Minister of Karnataka, in his response to the public opinion about the New Textbooks from standard one to ten, announced, in his 2014-15 budget speech of constituting an expert-committee, to look into the matter. He also spoke of the basic expectations there in, which the Textbook experts should follow: “ The Textbooks should aim at inculcating social equality, moral values, development of personality, scientific temper, critical acumen, secularismand the sense of national commitment”, he said.

Later, for the production of the Textbooks from class one to tenth, the Department of Education constituted twenty seven committees and passed an order on 24-11-2014. The committees so constituted were subject and class-wise and were in accordance with the standards prescribed. Teachers who are experts in matters of subjects and syllabi were in the committees.

There were already many complaints, and analyses about the Textbooks. So, a freehand was given in the order dated 24-11-2014 to the responsible committees to examine and review text and even to prepare new text and review if necessary. Afterwards, a new order was passed on 19-9-2015 which also give freedom even to re-write the Textbooks if necessary. In the same order, it was said that the completely reviewed Textbooks could be put to force from 2017-18 instead of 2016-17.

Many self inspired individuals and institutions, listing out the wrong information and mistakes there in the text, had send them to the Education Minister and to the ‘ Textbook Society’. They were rectified. Before rectification

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we had exchanged ideas by arranging debates. Discussions had taken place with Primary and Secondary Education ‘ Teacher Associations’. Questionnaires were administered among teachers to pool up opinions. Separate meeting were held with teachers, subject inspectors and DIET Principals. Analytical opinions had been collected. To the subject experts of science, social science, mathematics and languages, textbooks were sent in advance and later meeting were held for discussions. Women associations and science related organistation were also invited for discussions. Thus, on the basis of all inputs received from various sources, the textbooks have been reviewed where ever necessary.

Another very important thing has to be shared here. We constituted three expert committees. They were constituted to make suggestions after making a critical study of the text of science, mathematics and social science subjects of central schools (N.C.E.R.T), along with state textbooks. Thus, the state text books have been enriched basing on the critical analysis and suggestions made by the experts. The state textbooks have been guarded not to go lower in standards than the textbooks of central school. Besides, these textbooks have been examined along side with the textbooks of Andhra, Kerala, Tamil Nadu and Maharashtra states.

Anotherclarificationhastobegivenhere.Whateverwehave done in the committees is only review, it is not the total preparation of the textbooks. Therefore, the structure of already prepared textbooks have in no way been affected or distorted. They have only been reviewed in the background of gender equality, regional representation, national integrity, equality and social harmony. While doing so, the curriculum frames of both central and state have not been transgressed. Besides, the aspirations of the constitution are incorporated carefully. Further, the reviews of the committees were once

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given to higher expert committees for examination and their opinions have been effected into the textbooks.

Finally, we express our grateful thanks to those who strived in all those 27 committees with complete dedication and also to those who served in higher committees. At the same time, wethankallthesupervisingofficersofthe‘TextbookSociety’who sincerely worked hard in forming the committees and managed to see the task reach it’s logical completion. We thank all the members of the staff who co-operated in this venture. Our thanks are also due to the subject experts and to the associations who gave valuable suggestions.

H.N. Gopalakrishna

Mangaging Director Karnataka Textbook Society

Bengaluru.

Prof. Baraguru Ramachandrappa

Chairman-in-Chief Textbook Review Committee

Bengaluru.

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Text Books Revision Committee

Chairman-in-chief.Prof. Barguru Ramchandrappa, State Revision Committee, Karnataka

textbooks Society®, Bengaluru. Revision Committee

ChairpersonDr. Narasimhamurthy S.K. Professor and Chairman, Department

of Mathematics , Kuvempu University, Shankaraghatta-577 451. Shivamogga

MembersDr. B . Chaluvaraju, Professor, Department of Mathematics,

Bengaluru University, Bengaluru.Sri. B. K. Vishwanatha Rao, Rtd., Principal, No.94, ''Prashanthi'', 30th

Cross, BSK 2nd Stage, Bengaluru.Sri Narasimha murthy G. N., ‘Beladingalu’ No.23/1,5th cross, Hosalli,

Bengaluru.Sri Shankarmurthy M.V. Rtd Headmaster, Sarvodaya High-school,

BengaluruSri H.N.Subbarao, Headmaster, Sadvidya Highschool,

N.S.Road, Mysuru.Smt S.S. Thara, Headmistress, Govt. High School,

Mavattur, K.R. Nagar taluk, Mysuru Dist,Smt Sushma NagarajRao, High School Teacher, Govt. Higher Primary

School, RamnagarSri Shrinath Shastri, Kannada Ganak Parishat, Chamrajpete,

Bengaluru.High Power CommitteeDr.Kashinath Biradar, Plot No.7, Gangasiri, Jayanagar,

Kalburgi - 585 105.Smt. L. Padmavathi, Vice-principal, Empress Girls

High-school, Tumkur.Sri T Gangadharaiah, Associate Professor, Department of

Mathematics, Govt. women’s college, Kolar TranslatorsSri. V.N. Patil, A.M. Mahila Vidyalaya, H.S.Belgavi.Sri. R.G. Kulkarni, Rtd. Teacher, Khanapur, Belgavi.Chief Advisors Sri H.N. Gopalakrishna, Managing Director, Karnataka Textbooks

Society®, Banashankari 3rd stage, Bengaluru-85.

Smt N.R. Shylaja Kumari Deputy Director, (Incharge), Karnataka Textbooks Society®, Banashankari 3rd stage, Bengaluru-85.

Programme co-ordinator:Smt. Vijaya Kulkarni,

Asst.Director, Karnataka Textbooks Society®, Banashankari 3rd stage, Bengaluru-85.

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1) _______________

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¶oWo joÌ’$i ho H$moUË¶mhr EH$H$m {edm¶ XmI{dbo Amho. Va joÌ’$imMo EH$H$H$moUVo? {dMma H$am.

Vwåhmbm ‘m{hV AmhoM AmH$mamMo joÌ’$i {‘i{dÊ¶mgmR>r bm§~r d é§XrMmJwUmH$ma Ho$bm OmVmo.

darb AmH¥$VrV 1ë¶m AmH$¥VrMr bm§~r {H$Vr?åhUOoM AB Mr bm§~r {H$Vr Amho?3 g§o.‘r.BC Mr é§Xr {H$Vr Amho?3 g§o.‘r.¶m XmoZ ~mOy§Mr ‘mno dmnê$Z 1 ë¶m AmH$mamMo joÌ’$i H$mT>y.XmoZ ~mOy§À¶m bm§~rMm JwUmH$ma H$am.1ë¶m AmH¥$VrMo joÌ’$i = 3 g§o.‘r. x 3 g§o.‘r. = 9 g§o.‘r2.ho joÌ’$imMo EH$H$ Amho, Ooìhm ‘moO‘mn g§o.‘r.‘Ü¶o AgVo.

{ZarjU H$am : Ooìhm XmoZ ‘moO‘mno g§o.‘r. ‘Ü¶o ê$nm§VarV H$am¶Mr AgVrbVa go§. ‘r.Mm JwUmH$ma H$am. JwUmH$mamMo EH$H$ g§o.‘r2. (Mm¡ag go§Q>r‘rQ>a AgodmMVmV.)

{ZarjU H$am : Imbr {Xboë¶m CXmhaUm§Mo {ZarjU H$am.H$mnS> 4 Mm¡ag ‘rQ>a, ImobrMo joÌ’$i 15 Mm¡ag ‘rQ>a, ‘moR>çm VbmdmMo joÌ’$i1Mm¡ag {H$bmo‘rQ>a, àmUr g§J«hmb¶mMo joÌ’$i 2 Mm¡ag {H$bmo‘rQ>a, B. dmnaboë¶mdoJdoJiçm EH$H$m§Mo {ZarjU H$am.

Oa ‘moO‘mn ‘rQ>a ‘Ü¶o Agob Va joÌ’$imMo EH$H$ Mm¡ag ‘rQ>a AgVo.

Oa ‘moO‘mn {H$bmo‘rQ>a ‘Ü¶o Agbo Va joÌ’$imMo EH$H$ Mm¡ag {H$bmo‘rQ>a AgVo.

gm‘mÝ¶nUo joÌ’$i ho Mm¡ag EH$H$ ‘Ü¶o gm§JVmV.

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Z‘yZm CXmhaU

J«m’$ nonada EH$m Mm¡agmMo joÌ’$i 1 Mm¡ag g|Q>r‘rQ>a Amho. {Xboë¶m AmH$mamMo

joÌ’$i AmoiIm

AmH$mam‘Ü`o Agboë¶m Mm¡agmMr g§»¶m ‘moOm. ¶oWo EHy$U 7 Mm¡ag AmhoV.

{Xboë¶m AmH$mamMo joÌ’$i =7 Mm¡ag g|.‘r.

ñdmÜ¶m¶ 1.3

I. J«m’$ nonada EH$m Mm¡agmMo joÌ’$i 1Mm¡. go|.‘r. Amho. Va J«m’$‘Ü¶o {Xboë¶m

AmH$mam§Mo joÌ’$i H$mT>m. 1

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2

3

4

5

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H$¥Vr :

1) Imbrb {Xboë¶m AmH$mam§Mo {ZarjU H$am.

darb AmH$ma Jm«’$ nonada H$mT>yZ ¶m§Mo joÌ’$i H$mT>Ê¶mMm à¶ËZ H$am.joÌ’$i

g‘OmdyZ KoÊ¶mgmR>r {ejH$m§~amo~a MMm© H$am.

1) J«m’$ nonada doJdJoio XmoZ AmH$ma H$mT>m.Á¶mMr EH$m AmH$mamMr n[a{‘Vr 20

g|.‘r. Am{U Xþgè¶m AmH$mamMr n[a{‘Vr 16 g|.‘r. Amho. Va XmoÝhr AmH$mamMo

joÌ’$i emoYm.

XmoÝhr AmH$mamÀ¶m n[a{‘VrMr Am{U joÌ’$imMr VwbZm H$am. ¶mdéZ Vwåhr H$m¶

{ZarjU H$obm? V‘wMo AZw^d H$m¶? Vw‘À¶m {ejH$m§~amo~a MMm© H$am.

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àH$aU -2 g§»¶m

¶m àH$aUmÀ¶m AÜ¶ZmZ§Va Vwåhr :

• H«$‘mZo 9999 n¶©VÀ¶m g§»¶m dmMy d {bhÿ eH$mb .

• ñWmZ ‘yë¶ V³Ë¶mV Mma A§H$s g§»¶m {bhmb.

• Mma A§H$s g§»¶o‘Yrb ‘mJrb, nwT>rb d ‘Yrb g§»¶m {bhÿ eH$mb.

• Mma A§H$s g§»¶m gm‘mÝ¶ Z‘yZm d {dñVm[aV Z‘yÝ¶mV {bhmb.

• Mma A§H$s g§»¶m§Mr ñWmZ ‘yë¶ qH$‘V d Xe©Zr {H$§‘V AmoiIy eH$mb.

• Mma A§H$s g§»¶m§Mm ‘moR>m d bhmZ Z‘wZm AmoiIy eH$mb.

• {Xboë¶m Mma A§H$s g§»¶m MT>Ë¶m d CVaË¶m H«$‘mV ‘m§Sy eH$mb.

• {Xboë¶m A§H$mnmgyZ ‘moR>r d bhmZ Mma A§H$s g§»¶m ~Zdy eH$mb.

Mma A§H$s g§»¶mlrdmUr Amnë¶m AmB©~amo~a KaJyVr dñVy àXe©Z d {dH«$s H|$Ðmbm Jobr hmoVr.

{Vbm AmdS>boë¶m dñVy§Mr {MÌ d Ë¶mMr qH$‘V Imbr XmI{dbr Amho. Vwåhr Ë¶m§Mo {Z[ajU H$am.>

15

Vwåhr ‘mJrb B¶ÎmoV VrZ A§H$s g§»¶m {b{hUo, dmMUo d {dñVma H$aUo {eH$bm

AmhmV. AmVm Vwåhr Mma A§H$r g§»¶m {eH$Ê¶mMm à¶ËZ H$aUma AmhmV.

VrZ A§H$s bhmZ g§»¶m H$moUVr ? (100)

VrZ A§H$s ‘moR>r g§»¶m H$moUVr ? (999) ?

Imbrb ñWmZ‘wë¶ V³Ë¶mV A§H$ {b{hbo AmhoV Ë¶m§Mo {Z[ajU H$am.

ghñÌ eVH$ XeH$ gwQ>o100×10 10×10 1×10 1

1 0 0 0

eVH$ ñWmZmÀ¶m S>mì¶m ~mOybm EH$ ñWmZ dmT>{dbo Va Vo ñWmZ eVH$ ñWmZmÀ¶m

Xhm nQ> AgVo. `mbm ghó ñWmZ åhUVmV.

dmMÊ`mMr nÜXV nhm : EH hOma

1,000hr Mma A§H$s

bhmZ g§»¶m Amho.

1000 Z§VaÀ¶m g§»¶m {b{hÊ¶mMr nÜXV:

1000 Z§VaM[ nwT>rb g§»¶m H$moUVr? (1000+1=1,001),

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¶mM à‘mUo, 1000 Z§Va ¶oUmè¶m g§»¶m§Mm Vº$m V¶ma H$ê$ d dmMy (1001+1=1,002),

‘mJrb V³Ë¶mMo {ZarjU H$ê$Z Imbrb V³Vm nyU© H$am.1001 1002 1003 1004 1005 1006 1007 1008 1009 1010

1011 1012 1013 1014 1015 1016 1017 1018 1019 1020

1021 1022 1023 1024 1025 1026 1027 1028 1029 1030

1031 1032 1033 1034 1035 1036 1037 1038 1039 1040

1041 1042 1043 1044 1045 1046 1047 1048 1049 1050

1051 1052 1053 1054 1055 1056 1057 1058 1059 1060

1061 1062 1063 1064 1065 1066 1067 1068 1069 1070

1071 1072 1073 1074 1075 1076 1077 1078 1079 1080

1081 1082 1083 1084 1085 1086 1087 1088 1089 1090

1091 1092 1093 1094 1095 1096 1097 1098 1099 1100

1101 1102

1200

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3701 3702

3741 3750

3800

9901 9902 9903

9991 9992 9993 9994 9995 9996 9997 9998 9999

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Mma A§H$s g»§¶o‘Yrb H$mhr g§»¶m {ZdSy>Z da XmI{dë¶mà‘mUo V³Vm V¶maH$am. ñV§^m‘Yrb g§»¶m§Mo {ZarjU H$am d AmH$¥Vr~Y§ AmoùIm.

Mma A§H$s _moR>r g§»`m H$moUVr?

Amh!

ñWmZ‘yë¶ VŠË`mV _r Mma ñWmZmV _moR>m

A§H$ {b{hUma

g e X gw9 9 9 9

Mma A§H$s ‘moR>r g§»¶m 9999 Amho. (ZD$ hOma ZD$eo Zì¶mZD$)

bhmZ g§»¶m 1000 _moR>r g§»¶m 9999

Mma A§H$s g§»¶m

g§»¶m dmMÊ¶mÀ¶m nÕVrMo {Z[ajU H$am :-

CXmhaU : 4009 ‘Ü¶o XeH$ ñWmZ d eVH$ ñWmZ 0 Amho. ho Mma hOma ZD$ Ago dmMVmV Am{U {bhrVmV.

g e XÀÀ gw dmMÊ`mMr nÕV

2 3 5 6 XmoZ hOma VrZeo N>ßnZ

3 2 5 0 VrZ hOma XmoZeo nÌmg

1 9 8 6 EH$ hOma ZD$eo ehmE|er

8 9 2 5 AmR> hOma ZD$eo n§Mdrg

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`mM à_mUo Vwåhr à`ËZ H$am :

Imbrb g§»¶m Ajar {bhm :

1) 5,004→ ------------------------------------------

2) 7,305→ -----------------------------------------

3) 9,000→ -----------------------------------------

4) 5876→ -----------------------------------------

Imbrb g§»¶m A§H$mV {bhm :

1) ghm hOma Mmaeo EH$mhÎma ------------

2) VrZ hOma ZD$ ------------

3) ZD$ hOma AmR>eo Zì¶mÊUd ------------

4) XmoZ hOma Mmaeo drg ------------

Vwåhr à¶ËZ H$am;

1)Imbrb g§»¶m dmMm : -

3,705 4,600 3,576 1,005 5,009 9,827

2) 1801 Vo 1900 n¶ªVÀ¶m g§»¶mMm Vº$m V¶ma H$am.3) ñWmZ‘wë¶ V³Ë¶mà‘mUo {MÌmV g§»¶m AmhoV Ë¶m§Mo {ZarjU H$am.

10 101

1 1 1 11

1001000g e X gw1 4 2 6

1000 100 10 10 10 10 1 1g e X gw

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‘mJrb, nwT>rb d ‘Yrb g§»¶m {b{hUo :

1) 3876 Mr nwT>rb g§»¶m H$moUVr?

3877 hmo¶ H$s Zmhr? Vwåhr H$go AmoiImb?

(nwT>rb g§»¶m {‘i{dÊ¶mgmR>r {Xboë¶m g§»¶oV EH$ {‘idm)

Ë¶mM à‘mUo 5938 Mr nwT>rb g§»¶m Amho 5939.

7999

8407

9000

2) 5863 Mr ‘mJrb g§»¶m H$moUVr ? 5862 Amho H$s Zmhr ? Våwhr H$go AmoiImb?

5863 Mr ‘mJrb g§»¶m Amho (5863-1) = 5862

Ë¶mM à‘mUo

4567

7659

8000

3) 6896 Am{U 6898 ¶m§À¶m ‘Yrb g§»¶m H$moUVr?

d 6896 d 6898 ¶m§À¶m ‘Yrb g§»¶m Amho 6897

Imbrb ‘Yrb g§»¶oMo {ZarjU H$am. BVa XmoZ g§»¶m d ‘Ybr g§»¶m ¶m§Mm

g§~§Y AmoiIm. 3695, 3696, 3697

8406, 8407, 8408

9000, 9001, 9002

8999, 9000, 9001

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ho Vwåhr H$am1) 3976 Mr nwT>rb g§»¶m ___________.2) 2900 Mr ‘mJrb g§»¶m __________.3) 3998 Am{U 4000 ¶mVrb ‘Yrb g§»¶m __________.4) 8477 hr 8476 Mr nwT>rb g§»¶m Amho. H$moUVr g§»¶m __________Zo ‘moR>r Amho.

ñdmÜ¶m¶ 2.1

I. Imbrb g§»¶m dmMm. Z§Va eãXm_Ü`o {bhm. 1) 697 2) 809 3) 1,576 4) 5298

5) 7005 6) 9899 7) 7203 8) 8004

II. Imbrb g§»¶m g§»¶m-‘yë¶ V³¶mV {bhm.

CXmhaU : 3594 g e X gw3 5 9 4

1) 307g e X gw

5) 8888 g e X gw

2) 611g e X gw

6) 9400 g e X gw

3) 5926 g e X gw

7) 9991g e X gw

4) 6000g e X gw

8) 7343g e X gw

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III. Imbrb g§»¶m eãXm‘Ü¶o {bhm :

CXmhaU : 2490 = XmoZ hOma Mmaeo ZìdX

1) 3524 = ____________________________________

2) 4967 = ____________________________________

3) 8740 = ____________________________________

4) 8001 = ____________________________________

IV. {MÌm‘Ü¶o XmI{dbobr g§»¶m ñWmZ-‘yë¶ V³Ë¶mV {bhÿZ dmMm:

CXmhaU :

10 10 10 1010011

1 1 1 11 1

1000

g e X gw3 5 4 8

10 1010011

1 1 111000

g e X gw

1111

1111 1

10 10 101001000

g e X gw

1000111

11 11 1

10 10100

g e X gw

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V. Imbrb g§»¶mMr nwT>rb g§»¶m {bhm.

1) 6820, ____________ 5) 4200, ____________

2) 3948, ____________ 6) 3999, ____________

3) 5201, ____________ 7) 2829, ____________

4) 7605, ____________ 8) 3007, ____________

VI. Imbrb g»§¶mMr ‘mJrb g§»¶m {bhm.

1) ____________, 3926 5) ____________, 4900

2) ____________, 5439 6) ____________, 5000

3) ____________, 6400 7) ____________, 3827

4) ____________, 3570 8) ____________, 4999

VII. Imbrb g§»¶mVrb ‘Yrb g§»¶m {bhm.

1) 2769, ____________, 2771

2) 5490, ____________, 5492

3) 3999, ____________, 4001

4) 5888, ____________, 5890

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g§»¶m§Mo {dñVmarV ñdê$nñWmZ ‘wë¶mZwgma VrZ A§H$s g§»¶mMo {dñVmarV ñdê$n AmnU ¶mnydu {eH$bmo

AmhmoV. hr H¥$Vr AmVm H$am.

H$¥Vr : H$mJX qH$dm H$mS>©~moS>© dmnê$Z g§»¶mH$mS>© V¶ma H$am. ’$i¶mda {b{hboë¶m

g§»¶oZwgma Vr ‘m§S>m.

1000 100 10 1

CXmhaU 1: 2496 hr g§»¶m ñWmZ ‘wë¶ A§H$mZwgma g§»¶mH$mS>© dmnê$Z ‘m§S>m.

2496 = 1000 + 100+

10 10+

1 1 11 1 1

g§»¶m dmnê$Z AmnU {dñVmarV ñdê$n ‘m§Sy : = 2 × 1000 + 4 × 100 + 9 × 10 + 6 × 1

∴ 2496 = 2000 + 400 + 90 + 6

CXmhaU 2 : 3214hr g§»¶m ñWmZ‘wë¶ A§H$mZwgma g§»¶mH$mS>© dmnê$Z ‘m§S>m.

3214 = 1000 + 100+

10+

1 11 1

g§»`m dmnê$Z AmnU {dñVmarV ñdén _m§Sy> = 3 × 1000 + 2 × 100 + 1 × 10 + 4 × 1

∴ 3214 = 3000 + 200 + 10 + 4

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Vwåhr H$am :

Vwåhr V¶ma Ho$boë¶m g§»¶mH$mS>© dê$Z Imbr {Xboë¶m g§»¶mMo {dñVmarV ê$n {bhm a) 5423 b) 3805

g»§¶mH$mS>© da {Xboë¶m A§H$mdê$Z g§»¶m V¶ma H$am.

CXmhaU 1. = 1000 + 100 + 10 1 1 1 = 2 × 1000 + 4 × 100 + 6 × 10 + 3 × 1

= 2000 + 400 + 60 + 3 h gm¡ X B2 4 6 3

= 2463

CXmhaU 2. =1000

+100

+10

= 4 × 1000 + 1 × 100 + 3 × 10 + 0 × 1

= 4000 + 100 + 30 + 0 h gm¡ X B4 1 3 0

= 4130

ñdmÜ¶m¶2.2

I. Imbrb g§»¶m {dñVmarV ñdê$nmV {bhm.

1) 6487 = ___________________________________________________

2) 2069 = ___________________________________________________

3) 5004 =___________________________________________________

4) 9678 = ___________________________________________________

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II. Imbrb g§»¶m gm‘mÝ¶ ñdê$nmV {bhm.

CXmhaU

3 × 1000 + 4 × 100 + 8 × 10 + 2 × 1 =g e X gw3 4 8 2

= 3482

1) 1 × 1000 + 3 × 100 + 6 × 10 + 5 × 1 = = ________

2) 4 × 1000 + 0 × 100 + 7 × 10 + 9 ×1 = = ________

3) 8 × 1000 + 1 × 100 + 5 × 10 + 5 × 1 = = ________

4) 6 × 100 + 3 × 10 + 2 × 1 = = ________

Imbrb g§»¶m gm‘mÝ¶ ñdê$nmV {bhm.

CXmhaU 1 : 8 × 1000 + 6 × 100 + 0 × 10 + 9 × 1 g e X gw8 6 0 9

= 8000 + 600 + 0 + 9

= 8609

CXmhaU 2 : 9 × 1000 + 4 × 100 + 0 × 10 +1 × 5 g e X gw9 4 0 5

= 9000 + 400 + 5 = 9405

Vwåhr H$am :Imbrb {dñVmarV ñdê$nmMo gm‘mÝ¶ ñdê$n {bhm. a) 5 × 1000 + 3 × 100 + 9 × 10 + 2 × 1 b) 8 × 1000 + 2 × 10 + 3 × 1

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ñWmZ‘yë¶ qH$‘V- Xe©Zr qH$‘Vg§»¶m§Mr ñWmZ‘yë¶ qH$‘V Våwhmbm AJmoXaM ‘mhrV Amho. Ë¶m g»§¶m H$em

dmMVmV d {b{hVmV ho gwÕm Vwåhmbm ‘mhrV Amho.

¶m CXmhaUm§Mo {ZarjU H$am.

4173

4237

4314

3125

3 ¶m A§H$mMr ñWmZ‘yë¶ qH$‘V AmoiIm.

ñWmZ ‘wë¶mZwgma 3 Mr qH$‘V H$er ~XbVo?

na§Vw, Oa Vwåhr 3 KoVbm Va ¶mMr qH$‘V ~XbVo?

Zmhr, hmo¶ {H$ Zmhr?

¶mMà‘mUo A§H$ qH$‘V ~Xby eH$V Zmhr. ¶m qH$‘Vrbm H$m¶ åhUVmV?

¶m qH$‘Vrbm Xe©Zr qH$‘V åhUVmV.

àË¶oH$ A§H$mMr ñdV…Mr Xe©Zr qH$‘V AgyZ Ë¶mÀ¶m H«$‘mZwgma Ë¶mMr ñWmZ‘wë¶

qH$‘V doJdoJir AgVo.

CXmhaU 1 : 34 78

‘mPr Xe©Zr{H$‘V Amho 3

‘mPr ñWmZ‘yë¶ {H§$‘VAmho.3×100 =300

5 847

‘mPr Xe©Z©r$ {H$‘V

Amho 5

‘mPr ñWmZ ‘yë¶ {H§$‘VAmho 5×1000 = 5000

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2367

‘mPr Xe©Zr$

{H$§‘V Amho 2

‘mPr ñWmZ‘yë¶ {H$§‘VAmh 2 × 1 = 2

CXmhaU 2 : 8 Mr Xe©Zr {H§$‘VAmho 8ñWmZ‘yë¶ {H$§‘V 8 × 100 = 800

ñWmZ‘yë¶ qH$‘V9 × 10 = 90

9 Mr Xe©Zr${H§$‘V Amho 9

3 8 9 5

CXmhaU 3 : 7 Mr Xe©Zr qH$‘VAmho 7ñWmZ‘yë¶ {H$§‘V

7 × 1000 = 7000

ñWmZ‘yë¶ {H$§‘V7 × 1 = 7

7 Mr Xe©Zr {H$§‘VAmho 7

7 3 2 7

darb CXmhaUmdê$Z ñWmZ‘yë¶ qH$‘V d Xe©Zr qH$‘V ¶m‘Yrb EH$ ’$aH$ gm§Jm.

ñWmZ‘wë¶ qH$‘V Am{U Xe©Zr qH$‘V ¶m‘Yrb ’$aH$ AmoiIÊ¶mÀ¶m nÕVr1) 2389 ‘Ü¶o 3 Mr ñWm{ZH$ qH$‘V d ñWmZ‘yë¶ qH$‘V ¶m‘Yrb ’$aH$ {H$VrAmho?

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2389 ‘Yrb 3 Mr ñWmZ‘yë¶ qH$‘V → 300

3 Mr Xe©Zr {H$§‘V → 3

\$aH$ → 297

2) 6547 ‘Ü¶o 6 Mr ñWmZ‘yë¶ {H$§‘V d Xe©Zr$ {H$§‘V ¶m‘Yrb ’$aH$ {H$Vr

Amho?

6547 ‘Yrb 6 Mr ñWmZ‘yë¶ qH$‘V → 6000

6 Mr ñWmZ‘yë¶ qH$‘V → 6

\$aH$ → 5994

3) 2998 ‘Ü¶o 9 Mr ñWmZ‘yë¶ {H§$‘V d Xe©Zr$ {H$§‘V ¶m‘Yrb ’$aH$ {H$Vr

Amho?

9 ho eVH$ñWmZr AgyZ ñWmZ‘yë¶ {H§$‘V → 900

9 ho XeH$ñWmZr AgyZ ñWmZ‘yë¶ {H§$‘V → 90

\$aH$ → 810

H$¥Vr : Imbr {Xboë¶m àË¶oH$ A§H$mMr Xe©Zr qH$‘V d ñWmZ ‘yë¶ qH$‘V ¶m§À¶mOmoS>¶m OwidyZ Imbr {Xë¶mà‘mUo aofoZo XmIdm.

g§»¶m Xe©Zr qH$‘V ñWmZ‘yë¶ {H$_V

1) 385 6 4 200

2) 23 67 3 4000

3) 4 673 2 30

4) 6907 9 900

5) 96 78 6 6

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ñdmÜ¶m¶ 2.3

I. ¶mo½¶ CÎmamZo Imbrb [aH$må¶m OmJm ^am.1)

69749 Mr Xe©Zr qH$‘V............................ Amho.¶mMr ñWmZ‘yë¶ {H§$‘V

Amho.......................


Amho.......................

2)


Amho.......................


Amho.......................

II. Imbr {Xboë¶m àË¶oH$ àíZmbm Mma n¶m©¶ {Xbobo AgyZ Ë¶mn¡H$s ¶mo½¶ CÎma{ZdS>m d {bhm.

1)4267 ‘Ü¶o 6 Mr ñWmZ‘ëy¶ {H§$‘V d Xe©Zr {H§$‘V ¶m‘Yrb ’$aH$______Amho

a) 0 b) 1 c) 9 d) 542) 3498 ‘Ü¶o 4 Mr ñWmZ‘yë¶ {H$§‘V d Xe©Zr {H$§‘V ¶m‘Yrb ’$aH$

________Amho a) 496 b) 409 c) 396 d) 903) 5435 ‘Ü¶o 5 Mr ñWmZ ‘yë¶ {H$§‘V________Amho a) 999 b) 4005 c) 4995 d) 5005

4) 1694 ‘Yrb ¶m A§H$mMr ñWmZ‘yë¶ {H$§‘V d Xe©Zr {H$§‘V g‘mZ Amhoo________

a) 0 b) 1 c) 4 d) 6

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g‘mZ A§Va Agboë¶m g§»¶m (Skip Numbers)

Imbrb CXmhaUmMo {ZarjU H$am:-~oSw>H$, ggm, h[aU Am{U {MÎmm ho Ë¶m§À¶m§ qH$_VrZwgma CS>r ‘maVmV. hr Ë¶m§Mr

CS>r g§»¶maofoda XmIdbr Amho. {ZarjU H$am

1) ~oSw>H$ àË`oH$ CS>r_Ü`o {H$Vr nwT>o OmVmo?

1)

990 995 1000 1005 1010 ?

~oS>H$mÀ¶m àË¶oH$ CS>r‘Ü¶o {H$Vr ’$aH$ Amho?= ------

¶oWo {H$Vr g§»¶m ~oS>H$m§À¶m CS>rZ§Va ~oarO Ho$ë¶m AmhoV?

995 - 990 = 5, 1000 - 995 = 5

∴ Ë¶mZo àË¶oH$ nm¶arbm 5 g§»¶m CS>r ‘mabr Amho. eodQ>r H$moUË¶m g§»¶obm

~oSy>H$ nmohMbm?

1010 + 5 = 1015

1250 1300 1350

_maboë m̀ CS>r_Yrb A§Va H$go H$mT>VmV? gí m̀À m̀ àË̀ oH$ CS>rVrb A§Va = --------

eodXn ª̀V nmohMVmZm gí`mZo H$moUH$moUË`m g§»`mZm ñne© Ho$bm Amho Vo Aoi>Im= ---------

‘maboë¶m CS>r‘Yrb A§Va Vwåhr H$go emoYyZ H$mT>mb?

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darb CXmhaUmdê$Z haU d {MÎmm `m§Z§r ~oS>H$mnojm {H$Vr OmñV A§Va H$mnbo Amho emoYyZ H$mT>m.3)

2100 2300 2500 2700 2900 ?àË¶oH$ doir haUmZo {H$Vr CS>r ‘mabr? (-----------)eodQ>r Vo H$moUË¶m g§»¶obm nmohMbo? (-----------)

4)

3025 4025 5025 6025 ? ?

àË¶oH$ doi {MË¶mZo {H$Vr CS>r ‘mabr? (-----------)

4 Ï¶m d 5 ì¶m CS>rbm {MÎmm H$moUË¶m g§»¶obm nmohMbm Vo AmoiIm.

CXmhaU 2 : Imbrb H«$‘m‘Ü¶o nwT>rb g§»¶m {bhm.1) 1572, 1574, 1576, ______, ______, ______

XmoZ g§»¶m‘Yrb ’$aH$ (1574 - 1572 = 2)

åhUyZ, H«$‘ {b{hVmZm àË¶oH $ doir 2 {‘idV Om.∴ 1572, 1574, 1576, 1578, 1580, 1582

2) 3480, 3500, 3520, ______, ______, ______

XmoZ g§»¶m‘Yrb ’$aH$ (3500 - 3480 = 20)

åhUyZ, H«$‘ {b{hVmZm àË¶oH $ doir 20 {‘idV Om.∴ 3480, 3500, 3520, 3540, 3560, 3580

3) 6205, 6505, 6805, 7105 ______, ______

XmoZ g§»¶m‘Yrb ’$aH$ (6505 - 6205) = 300∴ 6205, 6505, 6805, 7105, 7405, 7705

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Vwåhr ho H$am

1) Imbrb H«$‘ nyU© H$am.

a) 5240, 5250, 5260, ________, ________, ________,

b) 8425, 8450, 8475, ________, ________, ________,

c) 5049, 6049, 7049, ________, ________, ________,

ñdmÜ¶m¶2.4

I. Imbrb g§»¶maofodarb nwT>rb g§»¶m nyU© H$am.1)

2100 2125 2150

2)

3250 3350 3450

3)

7501 8001 8501

4)

2040 3040 4040

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II. Imbrb H«$‘mVrb nwT>rb g§»¶m {bhm.

1) 2326, 2330, 2334, ________, ________, ________

2) 1540, 1550, 1560, ________, ________, ________

3) 1850, 1900, 1950, ________, ________, ________

4) 3650, 3950, ________, 4550, ________, ________

5) 4107, ________, 6107, ________, 8107, ________

‘moRr g§»¶m d bhmZ g§»¶m AmoiIUo

Mma ^mOr {dH«o$Ë¶mZr J§wV{dbobr a¸$‘ Imbr {Xbr Amho. {MÌmM§o {ZarjU H$am.

arPdmZ

35

darb àíZm§Mr CÎmao {‘i{dÊ¶mgmR>r darb g§»¶m§Mr VwbZm H$am¶bm nm{hOo. VrZA§H$s g§»¶m§Mr VwbZm Vwåhr {eH$bm AmhmV. AmR>dm Am{U g§»¶oVrb ‘moR>o ñWmZ‘wë¶ VgoM ‘moR>r d bhmZ A§H$ AmoiIm.5,256 ; 4,900 ; 6,370 ; 3,480 ¶m Mma A§H$s g§»¶m AmhoV. ghó ñWmZmVrbA§H$ 5, 4, 6, Am{U 3 ho AgyZ ‘moR>m A§H$ 6' d bhmZ A§H$ 3 Amho.¶m g§»¶mVrb ‘moR>r g§»¶m Amho: 6,370 Am{U bhmZ g§»¶m Amho: 3480 ∴ Ë¶mVrb OmñV a¸$‘ Jw§V{dbr Amho Vmo Amho S>opìhS> (r IoimS>yZr EHy$U H$mT>boë¶m YmdmImbrb à‘mUo AmhoV. Ë¶m‘Yrb H$moUË¶m IoimSy>Zo OmñV Ymdm H$mT>ë¶m AmhoV?Va H$moUË¶m IoimSy>Zo H$‘r Ymdm H$mT>ë¶m AmhoV?

AemoH$ 1,856

\¡$æ`O 1,875

Omogo’$ 1,830

A{_V1,890

AaqdX 1,821

1856 , 1875 , 1830 , 1890 , 1821 ¶m {Xboë¶m g§»¶m AgyZ gd© g§»¶m

Mma A§H$r g§»¶m AmhoV.

àË¶oH$ ñWmZ‘yë¶ A§H$mMo {ZarjU H$am.

ghó ñWmZmV d eVH$ ñWmZmV A§H $ g‘mZ AmhoV . åhUyZ VwbZm H$aÊ¶mgmR>r

XeH$ ñWmZmVrb A§H$mMr VwbZm H$ê$. XeH$ ñWmZmVrb A§H$ 5, 7, 3, 9 Am{U

2 AmhoV.

∴ ¶m‘Yrb 9 hm ‘moR>m d 2 hm bhmZ A§H$ Amho.

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∴ ‘moR>r g§»¶m 1890 Amho.

bhmZ g§»¶m 1821 Amho.

Á¶m IoimSy>Zo OmñV Ymdm H$mT>ë¶m Vmo åhUOo Am{‘V (1890)

Á¶m IoimSy>Z H$‘r Ymdm H$mT>ë¶m Vmo åhUOo AaqdX (1821)

CXmhaU 3: Imbrb g§»¶m H$mS>© ‘Yrb ‘moR>¶m d bhmZ g§»¶oMo H$mS>© AmoiIm.

8692 8940 8629 8490 8094

ghó ñWmZmVrb A§H$ g‘mZ AmhoV. eVH$ ñWmZmVrb A§H$mMr Vwb§Zm H$ê$¶mH$m AmVm? eVH$ ñWmZmVrb A§H$ 6,9,4 Am{U 0 AmhoV. ¶mVrb ‘moR>m A§H$ 9åhUyZ ‘moR>r g§»¶m 8940. eVH$ ñWmZmVrb bhmZ A§H $ 0 Amho åhUyZ bhmZg§»¶m 8094 Amho.

ho Vwåhr H$am:

A) ‘moR¶m g§»¶obm Jmob H$am.

1) 3247, 3280, 3228, 2267 2) 5694, 5384, 5820, 5973

B) bhmZ g§»¶obm Jmob H$am.

1) 8826, 8823, 8821, 8829, 2) 5747, 4768, 6000, 3899

MT>Vm H«$‘ - CVaVm H«$‘

‘mJrb B¶ÎmoV Vwåhr VrZ A§H$s g§»¶m MT>Ë¶m d CVaË¶m H$«‘mV H$em {b{hVmV Vo {eH$bm AmhmV. Vo AmR>dyZ Imbrb g§»¶m MT>Ë¶m H$«‘mV {bhm.

CXmhaU : 679, 368, 796, 697

MT>Vm H«$‘ : 368, 679, 697, 796

darb nÕV dmnê$Z Mma A§H$s g§»¶m MT>Ë¶m d CVaË¶m H«$‘mV H$em {bhrVmV?

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CXmhaU : 5839, 5093, 5872, 5829

---------------, ---------------, ---------------, ---------------,

¶m g§»¶m MT>Ë¶m H«$‘mV {b{hÊ¶mgmR>r H$moUVr nÕV dmnabr? AmoiIm Am{U

{bhm.

------------------------------------------------,

------------------------------------------------,

------------------------------------------------

CXmhaU : 2167, 1679, 3847, 500

---------------, ---------------, ---------------, ---------------,

H$moUVr nÕV Vwåhr dmnabr?

------------------------------------------------,

------------------------------------------------,

{ZarjU :g§»¶m MT>Ë¶m H«$‘mV {bhrVmZm -

· àW‘ ghó ñWmZmMo {ZarjU H$am. · Z§Va eVH$ ñWmZmMo {ZarjU H$am.

· XeH$ ñWmZmMo {ZarjU H$am.

· gwQ>o ñWmZmMo {ZarjU H$am.

gd© ñWmZmMo {ZarjU Ho$ë¶mZ§Va A§H$ bhmZmnmgyZ ‘moR>çm A§H$mn¶ªV H«$‘mZo

{bhm

{dMma H$am : Oa gwédmVrbm eyÝ¶ {bhrbo Va Vr Mma A§H$r g§»¶m ~ZVo H$m?

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MT>Vm H«$‘:- (bhmZ g§» ò nmgyZ _moR>`m g§» ò n ©̀V)CXmhaU 1 :

Imbrb dOZm§Mo {ZarjU H$am. Ë¶m§Zm MT>Ë¶m H«$‘mV ‘m§S>m.

1000 J«°m‘ 5000 J«°m‘

2000 J«°m‘ 500 J«°m‘

MT>Ë¶m H«$‘mV {b{hÊ¶mgmR>r H$moUVr g§»¶m àW‘ ¿¶mdr?

bhmZ g§»¶mMm, àW‘ {bhmdr.

¶m‘Yrb bhmZ dOZ H$moUVo? (500 J«°‘)

amhrboë¶m dOZm‘Yrb, H$moUVo bhmZ dOZ Amho? (1000 J«°‘)

AmVm amhrbobr XmoZ dOZo 5000 Am{U 2000. Ë¶m XmoZ dOZm‘Yrb bhmZ

dOZ H$moUVo? (2000)

åhUZy H$moUVo dOZ eodQ>r Cabo Amho? (5000)

bhmZ dOZmnmgyZ gwédmV H$éZ eodQ>À¶m dOZm‘Yrb gd© dOZo H«$‘mZo {bhm.

hm MT>Vm H«$‘ Amho.

500 J«°m‘ 1000 J«°m‘ 2000 J«°m‘

5000 J«°m‘

∴ MT>Vm H«$‘ = 500, 1000, 2000, 5000

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CXmhaU 2: Imbrb g§»¶m-H$mS>© MT>Ë¶m H«$‘mV ‘m§Sm

3920 2890 5436 3860

bhmZ g§»¶m AmoiIyZ Vr {bhm (2890)

amhrboë¶m g§»¶o‘Yrb àË¶oH $doir bhmZ g§»¶m AmoiIyZ Ë¶m H«$‘mZo {bhm.

∴ MT>Vm H«$‘ : 2890, 3860, 3920, 5436

bjmV R>odm: Ooìhm AmnU MT>Ë¶m H«$‘mV g§»¶m {bhVmo, Voìhm n{hbr g§»¶m bhmZd eodQ²>Mr g§»¶m ‘moRr AgVo.

MT>Vm H«$‘ : (_moR>`m g§»`m nmgyZ bhmZ g§»`o n`©V) Imbr {Xboë¶m àË¶oH $ ^m§S>¶m‘Yrb XþYmMo ‘moO‘mn nhm. Ë¶m g§»¶m CVaË¶m

H«$‘mV {bhm.

4850 {‘br. 3500 {‘br 6250 {‘br 5450 {‘br

• CVaVm H«$‘ {b{hVmZm àW‘ H$moUVr g§»¶m {bhmdr ? ( ‘moR>r g§»¶m)

• H$moUVr ‘moR>r g§»¶m Amho? (6250)

• am{hboë¶m g§»¶m‘Yrb H$moUVr g§»¶m ‘moR>r Amho? (5450)

• AmVm 4850 d 3500 am{hë¶m. Ë¶m XmoZ ‘Yrb ‘moR>r g§»¶m H$moUVr?

(4850)

• H$moUVr g»§¶m amhrbr? (3500)

‘moR>¶m g§»¶onmgyZ gwédmV H$ê$Z eodQ>r amhrboë¶m g§»¶on¶ªV H«$‘mZo g§»¶m {bhUo.

{ZarjU H$am 6250, 5450, 4850, 3500

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hm CVaVm H«$‘ Amho.

6250 {‘br. 5450 {‘br. 4850 {‘br. 3500 {‘br.∴ CVaVm H«$‘---------------, ---------------, ---------------, ---------------,

CXmhaU 2: Imbrb g§»¶m-H$mS>© CVaË¶m H«$‘mV ‘m§S>m

5420 5840 4696 4890

• ‘moR>r g§»¶m AmoiIm (5840)

• am{hboë¶m g§»¶o‘Yrb àË¶oH$ doir ‘moR>r g§»¶m AmoiIyZ Ë¶m H«$‘mZo {bhm.

∴ CVaË¶m H«$‘mVrb g§»¶m = 5840, 5420, 4890, 4696

bjmV R>odm:: Ooìhm AmnU CVaË¶m H«$‘mV g§»¶m {b{hVmo Voìhm n{hbr g§»¶m ‘moR>r d eodQ>Mr g§»¶m bhmZ AgVo.

Vwåhr H$ê$Z nmhm:

A. Imbrb g§»¶m

MT>Ë¶m H«$‘mV {bhm.5026 2650 6520 5640

B. Imbrb g§»¶m

CVaË¶m H«$‘mV {bhm

3856 3656 3695 3965

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ñdmÜ¶m¶ 2.5

I. bhmZ g§»¶obm dV©wi (Jmob) d ‘moR>¶m g§»¶ogmR>r "' {MÝh {bhm.CXmhaU : 3675, 3765, 3265 , 34751) 8820, 3790, 6530, 2905

2) 9297, 8470, 9680, 5875

3) 5600, 6500, 6005, 5006

4) 9270, 9267, 9207, 9217

II. Imbrb g§»¶m MT>Ë¶m H«$‘mV {bhm.1) 679, 368, 796, 697

MT>Vm H«$‘ : ________________________________________2) 5839, 5093, 5872, 5829

MT>Vm H«$‘ : ________________________________________3) 2167, 1679, 3847, 5000

MT>Vm H«$‘ : ________________________________________4) 6493, 6394, 4693, 3625

MT>Vm H«$‘ : ________________________________________III. Imbrb g§»¶m CVaË¶m H«$‘mV {bhm.

1) 2765, 3847, 1629, 4867

CVaVm H«$‘: ________________________________________2) 3926, 3967, 3908, 3937

CVaVm H«$‘: ________________________________________3) 4798, 4792, 4087, 4800

CVaVm H«$‘ : ________________________________________4) 8620, 8629, 8630, 8624

CVaVm H«$‘ : ________________________________________

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{Xboë¶m A§H$mnmgyZ Mma A§H$s g§»¶m V¶ma H$aUo : {Xboë¶m A§H$mnmgyZ VrZ A§H$s g§»¶m H$er V¶ma H$aVmV ho AmnU AJmoXaM

{eH$bmo AmhmoV. AmVm AmnU Mma A§H$r g§»¶m H$em V¶ma hmoVmV Vo nmhÿ.

dJm©Vrb Q>o~bda VrZ A§H $ H$mS>© AmhoV . Vr A§H $ H$mS>© dmnê$Z {dÚmWu doJdJoù¶m g§»¶m V¶ma H$aVrb . ( A§H$ H$mS>© dmnê$Z Imbrb g§»¶m V¶ma H$aVrb)

A§H$ H$mS>© V¶ma Ho$boë¶m g§»¶m

5 3 7 →5 3 7 , 3 7 5 , 7 5 3 ,

3 5 7 , 7 3 5 , 5 7 3 ,

darb g§»¶oVrb H$moUVr gdm©V ‘moR>r g§»¶m V¶ma Ho$br? 753 ( gmVeo Í¶oßnZ)753 g§»¶o‘Yrb àË¶oH$ A§H$mMo {ZarjU H$am A§H$ 7,5 Am{U 3 ho H$moUË¶m

H«$‘mV AmhoV? (CVaË¶m H«$‘mV)

{ZarjU :- {Xboë¶m A§H$mnmgyZ ‘moR>r g§»¶m V¶ma H$am¶Mr Agob Va {Xbobo A§H$CVaË¶m H«$‘mV ‘m§S>m.

darb g»§¶m‘Yrb H$moUVr g§»¶m bhmZ Amho? (357)357 ‘Yrb àË¶oH$ A§H$mMo {ZarjU H$am.A§H$ 3,5 A{U 7 ho H$moUË¶m H«$‘mV AmhoV? (MT>Ë¶m H«$‘mV)

J{UV

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{ZarjU : {Xboë¶m A§H$mnmgyZ bhmZ g§»¶m V¶ma H$am¶Mr Agob Va {Xboboo A§H$ MT>Ë¶m H«$‘mV ‘m§S>m.

H$¥Vr1:

dJm©Vrb Q>o~bda EH$m ~m°³g ‘Ü¶o Imbrb A§H $H$mS>© R>odbr AmhoV.

8 0 3 7 6 9 5 1 4 2

H$moUVrhr Mma A§H$H$mS>© CMbyZ Q>o~bda R>odm. g‘Om Vwåhr

hr A§H$ H$mS>© CMbbr. 3 6 4 8

>darb A§H$ H$mS>© dmnê$Z Mma A§H$s ‘moR>r g§»¶m {bhm.

A§H$ CVaË¶m H«$‘mV ‘m§Sm.

A§H$mMm CVaVm H«$‘ 8 6 4 3

g§»¶m {‘imbr 8, 6, 4, 3 (AmR> hOma ghmeo )

∴ Mma A§H$s ‘moR>r g§»¶m 8,643 Amho.naV§y , bhmZ Mma A§H$s g§»¶m H$moUVr Amho? Vr 3,6,4 Am{U 8 ¶m A§H$mnmgyZ

{‘iVoA§H$ MT>Ë¶m H«$‘mV ‘m§S>m

MT>Ë¶m H«$‘mV A§H$ AmhoV 3 4 6 8

g§»¶m {‘imbr 3,468 (VrZ hOma Mmaeo AS>>wgï>)

∴ {‘imbobr Mma A§H$s bhmZ g§»¶m Amho = 3,468

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H$¥Vr 2: ‘§ÝWmZo ~m°³g ‘Yrb Mma A§H$-H$mS>© ~mhoa H$mT>br Vr AH§ $ H$mS© 7 , 5, 0 d 8 AmhoV .darb Mma A§H$ H$mS>© dmnê$Z H$moUVr Mma A§H$s ‘moR>r g§»¶m

V¶ma hmoVo?

‘moR>r g§»¶m {‘i{dÊ¶mgmR>r [VZo Vo A§H$ CVaË¶m H«$‘mV ‘m§S>bo.

CVaVm H«$‘ 8 7 5 0

g§»¶m V¶ma hmoVo 8750 (AmR> hOma gmVeo nÞmg).

∴ ‘moRr g§»¶m Amho 8,750

7 , 5 , 0 , 8 ho A§H$ dmnê$Z H$moUVr bhmZ g§»¶m V¶ma hmoVo?

‘§ÝWm Ë¶m§Zm MT>Ë¶m H«$‘mV ‘m§S>ob.CVaVm H«$‘ : 0, 5, 7, 8{VZo g§»¶m V¶ma Ho$br 0,578

0578 VrZ A§H$s g§»`m0578 ñWmZ ~Xbm 5078 (nmM hOma AÇ`m>Îma)

{VZo Vr dmMbr 0,578 (nm§Meo AÇ>¶mÎma) VrZ A§H$s g§»¶m0578 ñWmZ ~Xbm5078 (nmM§ hOma AÇ>¶mÎma), 0578 ‘Ü¶o ghó ñWmZ Zmhr.åhUyZ hr VrZ A§H$s g§»¶m ~Zbr.

{dMma H$ê$Z {VZo {ejH$m§H$S>o nmhrbo.{ejH$m§Zr {VMr e§H$m Imbrbà‘mUo Xwa Ho$br. Oa g§»¶oV 0 (eyÝ¶) ‘moR>¶m ñWmZ-‘yë¶mbm ¶oV Agob Va eyÝ¶ (0) Ë¶mg§»¶oV YaV ZmhrV.

(0578 = nm§Meo AÇ>¶mÎma)

0578 hr VrZ A§H$s g§»¶m Amho.Aem àg§Jr eyÝ¶mMo ñWmZ ‘yë¶ ‘moR>çm ñWmZ ‘yë¶mnmgyZ ~mOyÀ¶m

ñWmZ‘yë¶m~amo~a ~Xbbo. 0,5,7 Am{U 8 ¶m A§H$m nmgyZ 5078 hr Mma A§H$sg§»¶m ~ZVo (nm§M hOma AÇ>¶mÎma) ∴ 5078 hr Mma A§H$s bhmZ g§»¶m Amho. Vr 0,5,7 Am{U 8 ¶m A§H$mnmgyZ V¶maHo$br.

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bjmV R>odm: {Xboë¶m A§H$m‘Ü¶o Ooìhm eyÝ¶ A§H$ {Xbobm Agob Va bhmZ g§»¶m V¶ma

H$aVmZm Imbrb {Z¶‘ dmnam eyÝ¶ Yê$Z Vo A§H$ MT>Ë¶m H«$‘mV ‘m§Sm.eÝy¶ ñWmZ d nwT>rb ñWmZ ¶m§Mr AXbm ~Xb H$ê$Z amhrbobo A§H$ VgoM {bhm.

H$¥Vr 3 :

6, 2, 0 Am{U 5 ho A§H$ dmnê$Z H$moUVr bhmZ g§»¶m V¶ma hmoV?

{Xbobo A§H$ MT>Ë¶m H«$‘mV ‘m§S>m.

ewÝ¶ ñWmZ d Ë¶mnwT>rb ñWmZ ¶m§Mr

AXbm~Xb H$ê$Z amhrbobo A§H$

VgoM {bhm.

MT>Vm H«$‘ = 0, 2, 5, 6

= 2, 0, 5, 6

bhmZ g§»¶m = 2,056

{dMma H$am : darb CXmhaUmV 0256 hr bhmZ g§»¶m Zmhr H$m?

Vwåhr ho H$am.

1) , , ,6 9 7 1 ho {Xbobo gd© AH§ $ dmnê$Z

V¶ma H$aVm ¶oUmar ‘moR>r g§»¶m __________Amho. V¶ma H$aVm ¶oUmar bhmZ g§»¶m __________Amho.

2) , , ,4 0 3 7 ho {Xbobo gd© A§H$ dmnê$Z

V¶ma H$aVm ¶oUmar ‘moR>r g§»¶m __________Amho. V¶ma H$aVm ¶oUmar bhmZ g§»¶m__________Amho.

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ñdmÜ¶m¶ 2.6

I. Imbr [aH$må¶m OmJm ^am.1) , , ,4 6 8 5 ho AH§ $ dmnê$Z V¶ma hmoUmar ‘moR>r g§»¶m ________Amho2) 3,046 hr __________ A§H$s g§»¶oMo CXmhaU Amho.3) 0,734 hr __________ A§H$s g»§¶m Amho4) , , ,3 1 0 9 ho A§H$ dmnê$Z V¶ma hmoUmar bhmZ Mma A§H$s g§»¶m

__________AmhoII. gm§{JVë¶mà‘mUo {bhm.

1) 5, 8, 7, 2 ho A§H$ dmnê$Z Mma A§H$s -

gdm©V ‘moR>r g§»¶m V¶ma H$ê$ eH$Vmo Vr __________gdm©V bhmZ g§»¶m V¶ma H$ê$ eH$Vmo Vr __________2) 2, 8, 9, 0 ho A§H$ dmnê$Z Mma A§H$s -

gdm©V ‘moR>r g§»¶m V¶ma H$ê$ eH$Vmo Vr __________gdm©V bhmZ g§»¶m V¶ma H$ê$ eH$Vmo Vr __________3) 3, 5, 2, 9 ho A§H$ dmnê$Z Mma A§H$s -

gdm©V ‘moR>r g§»¶m V¶ma H$ê$ eH$Vmo Vr __________gdm©V bhmZ g§»¶m V¶ma H$ê$ eH$Vmo Vr __________

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47

àH$aU-3 ~oarO

¶m àH$aUmÀ¶m AÜ¶¶ZmZ§Va Vwåhr :

l Mma A§H$s g§»¶mMo JQ> Z H$aVm ~oarO H$amb.

l hmVMm KoD$Z Mma A§H$s g§»¶m§Mr ~oarO H$amb.

l Ë¶m§À¶m ñWmZ ‘yë¶ V³Ë¶mZwgma g§»¶m {bhÿZ X¡Z§{XZ$ OrdZmVrb CXmhaUo

gmoS>dy eH$mb.

l ~oaOooÀ¶m nÕVr g‘OmdyZ KoD$Z bJoM ~þÜXrMmVw¶m©Zo ~oarO H$amb.

VrZ A§H$s g§»¶m§Mr ~oarO Vwåhr ¶mnyduM {eH$bm AmhmV ¶m§Mo {ZarjU H$am-

CXmhaU : XþH$mZmV doJdoJù¶m dñVy Ë¶m§À¶m qH$‘Vrgh CnbãY AmhoV. {ZarjUH$ê$Z Imbr {Xboë¶m àíZm§Mo CÎma Úm.

`1349`324

`2454

`3298`3847

`2420

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48

Am) ¶m XþH$mZmV

• H°$ë³¶wboQ>aMr qH$‘V {H$Vr Amho? _____________

• {‘³ga>Mr qH$‘V {H$Vr Amho? _____________

• ao{S>AmoMr {H$‘§V {H$Vr Amho?_____________

• ‘mo~mB©bMr {H$§‘V {H$Vr Amho? _____________

Imbrb CXmhaUm§Mo {ZarjU H$am: XþH$mZm‘YyZ EH$m eoVH$è¶mZo Imbrb dñVy IaoXr Ho$ë¶m. Ë¶m§Mr EHy$U qH$‘V

{H$Vr?

`2454

`324

ñWmZ ‘yë¶mZwgma ¶m dñVy§À¶m {H§$‘VrMr ~oarO H$ê$.

darb qH$‘Vr {MÌH¥$Vr {MÝhmZwgma XmI{dë¶m AgyZ Ë¶m§Mr ~oarO H$am.

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49

= 1000 =100 =10 = 1

Vnerb JQ>

ghñÌ eVH$ XeH$ gwQ>o

1) ‘mo~mB©bMr qH$‘V aMrqH$‘V o ñWmZmVrb A§H$mMr àW‘

~oarO H$am.

Z§Va, AZwH«$‘o XeH$, eVH$,

Am{U ghó ñWmZm§M§r ~oarO H$am.

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50

2) EH$m J¥{hUrZo Imbrb dñVy XwH$mZmVyZ IaoXr Ho$ë¶m EH$yU Ë¶m dñV§yMr qH$‘V {H$Vr hmoVo ?

o

1) Q>onaoH°$mS>©²aMr[H$§‘V r KS>çmiMr qH$‘V onaoH°$mS>©²aMr [H$§‘V <2) ‘ZJQ>r KS>çmi Mr qH$‘V <

2 4 2 0

1 3 4 9

EHy$U < 3 7 6 9

EHy$U qH$‘V = < 3769 én¶o VrZ hOma gm§Veo EH$moUgÎma.

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51

Vwåhr ho H$am::1) dñVy§À¶m qH$‘Vr ñWmZ ‘yë¶ V³Ë¶mV {bhÿZ Ë¶m§Mr EHy$U~oarO H$am.

52

hmVMm KoD$Z ~oarO :CXmhaU 1: EH$m {J-hmB©H$mZo Imbrb dñVy IaoXr Ho$ë¶m Ë¶m dñVy§Mr EHy$U qH$‘V

{H$Vr Amho?

53

nmàr 1 gwQ>o ñWmZmV A§H$ 7 d 4 Mr ~oarO Ho$br Va

Amåhm§bm 11 {‘iVmV. ¶mV 1 XeH$ d 1 gwQ>o AmhVo.1 A§H$ gwQ>o ñWmZmV {bhm. XeH$ ñWmZmV 1 XeH$JQ>mV {bhm.

g e X gw

5 2 4 72 4 5 4

1

nmàr 2

AmVm1,4 d 5 XeH$ ñWmZr AmhoV . Ë¶m§Mr ~oarO Ho$ë¶mg 10 XeH$ {‘iVmV. 10 XeH$ ho 1 eVH$ d 0 XeH$ AmhoV. 0 ho XeH$ ñWmZmbm Am{U hmVMm eVH$ ñWmZmbm ¿¶m.

g e X gw

5 2 4 72 4 5 4

0

1

nmàr 3 eVH$ ñWmZr 1 eVH$, 8 eVH$ d 4 eVH$ ¶m§Mr

~oarO 13 eVH$ {‘iVo. 13 eVH$ ho 1 ghó d 3 eVH$ AmhoV. 3 ho eVH$ ñWmZmbm Am{U hmVMm ghó ñWmZmbm ¿¶m.

g e XÀ gw

5 2 4 72 4 5 4

7

0

1

nmàr 4 AmVm AmnU ghó ñWmZmVrb A§H$m§Mr ~oarO H$ê$.

¶oWo 1 ghó,3 ghó d 2 ghó, ¶m§Mr ~oarO ¶oVo 6 ghó. 6 ho ghó ñWmZr {bhm.åhUyZ {JèhmB©H$mZo IaoXr Ho$boë¶m dñVy§Mr EH$yU {H§$‘V Amho

54

CXmhaU 2: XþH$mZmVyZ {’$bmo{‘ZmZo Imbrb dñVy IaoXr Ho$ë¶m. Ë¶m§Mr EHy$U qH$‘V H$mT>m

©yaMr qH$‘V{‘³gaMr qH$‘V

g e X gw

3 2 9 8

3 8 4 7

7 1 4 5

EHy$U qH$‘V = hOma EH$eo n§MoMmirg) ¶oWo gwQ>oñWmZmnmgyZ g§»¶§mMr ~oarO Ho$br AgVm, Ë¶m§À¶m ¶mo½¶ ñWmZmV hmVMm COì¶m~mOybm {‘i{dbm OmVmo. {ZarjU H$am.

CXmhaU 3:

3895, 2436, 159 ¶§mMr ~oarO {H$Vr ¶oVo?g§»¶m àW‘ ñWmZ ‘wë¶mZwgma {bhm. Z§Va ‘mJrb CXmhaUmZwgma ~oarO H$am.

g e X gw

3 8 9 5

2 4 3 6

1 5 9

6 4 9 0

nwT>rb ñWmZmbm hmVMm Z KoVm, hmVMm ‘ZmV R>oD$Z AmnU ~oamoO H$ê$ eH$Vmo. 3,895

2 436 + 159 6,490

EHy$U qH$‘V = < 6,490

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ho Vwåhr H$am:1) 4675 + 3452

g e X gw

4 6 7 5

+ 3 4 5 2

2) 5368 + 2097

g e X gw

5 3 6 8

+ 2 0 9 7

3) 359 + 4276+ 2573

+

g e X gw

3 5 94 2 7 62 5 7 3

4) 3948 + 206 + 92

+

g e X gw

3 9 4 82 0 6

9 2

Vm|S>r CXmhaUo:

Am‘À¶m X¡Z§{XZ OrdZmV AZoH$ àg§Jr AZoH$ CXmhaUo AmnU ‘ZmV gmoS>{dVmo.

CXmhaU : ¶m à‘mUo XmoZ àg§J AmR>dyZ Vo {bhm

1) –––––––––––––––––––––––––––––––––––––––––––––––––

2) –––––––––––––––––––––––––––––––––––––––––––––––––

‘ZmZo CXmhaUo gmoS{dVmZm Amåhr doJdoJù¶m nÕVr dmnaVmo

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56

Imbrb CXmhaUm§Mo {ZarjU H$am.

1) 328 Am{U 241 `§mMr ~oarO {H$Vr òVo?

328 + 241 = ?= 328 + (200 + 40 + 1) 328 +200= 528

528 + 40 = 568 568 + 1 = 569 ∴ 328 +241= 569

nÕV-1{Xboë`m EH$m g§»òMm {dñVma H$am Am{U H«$_mZo ~oarO H$am

{Xboë`m EH$m g§»òMm {dñVma H$am Am{U gwQ>o ñWmZmZwgma H«$_mZo

~oarO H$am

nÕV-2

328 + 241 = ?

= 328 + (200 + 40 + 1)

328 329 369 569

+1 +40+200

∴ 328 + 241 = 569

2) 5347 Am{U 2635 `§mMr ~oarO {H$Vr òVo?

nÕV-1 5,347 + 2,635 = ?

= 5347 + (2000+600+30+5)

5347 + 2000 = 7347

7347 + 600 = 7947

7947 + 30 = 7977

7977 + 5 = 7982

~oarO = 7982

nÕV-1 5347 + 2635 = ?

= 5347 + (2000+600+30+5)

~oarO = 7982

5347

+5 +30 +600 +2000

5352 79825382 5982

ho Vwåhr H$am : XmoZ {Xboë¶m g§»¶o‘Yrb EH$m g§»¶oMm {dñVma H$ê$Z {VMr n{hë¶m

g§»¶o~amo~a ~oarO H$am.

1) 643 + 250 2) 6145 + 2236

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57

H$¥Vr : ~oaOoMm IoiImbrb V³Ë¶mVrb g§»¶m nhm. Cä¶m ñV§̂ mV qH$dm AmS>ì¶m n§º$sV Agboë¶m

XmoZ g§»¶mda EH$-EH$ qMMmoH$m Ro>dm (Xwgar EImXr dñVy). Ë¶m g§»`§mMr ~oarOH$am nU ~oarO 5000 nojm OmñV Agmdr.

3820 2200 1750 6300 3000 4137

4150 376 4920 2157 3156 1698

1598 2900 4213 1828 2986 3800

2520 4840 238 5786 2184 5790

1546 3275 3426 3248 2900 1000

6376 2821 1680 4495 1000 9000

Oa ~oarO 5000 nogm OmñV Ambr Va àË`oH$ ~amo~a J{UVmbm 5 JwUOa 100 JwU {‘i{dbog Va Vy {OH$erb. 150 JUw {‘iderb Va Vy M°pån¶Z

hmoerb. à¶ËZ H$am.

CXmhaU 2 {’$bmo{‘Zm ¶m nÕVrZo J{UV gmoS>{dVo.

1.+

382022006020

2.

+

4213 2384451

3.

+

298638006786

4.

+

154663767922

{’$bmo{‘Zmbm 15 JwU {‘imbo H$m? {dMma H$am.

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58

H¥$Vr1 _mH$S>mMr MoßQ>m¶oWo EH$ ’$im Amho. Ë¶mda A§H$H$mS>©Mm Cn¶moJ H$ê$Z ~oaOoMr CXmhaUo

gmoS>{dbr AmhoV . àË¶oH$ CXmhaUmMr EHy$U ~oarO Ho$bobr AgyZ Vr gwÕm {b{hbrAmho.

OdiM Agboë¶m PmS>mdarb ‘mH$S>mZo H$mhr A§H$ H$mS>© KoD$Z Jobr AmhoV .

‘mH$S>mZo KoD$Z Jobobr A§H$H$mS>© emoYm d Mm¡H$moZmV {bhm.

5 2 4 63 4 2 8 6 7

3 5 2 92 3 4 5 7 0

2 5 4 35 3 8 4 7 7

4 2 6 7 8 0 59 2 3

3 4 54 97 8 4

6 9 02 6 4

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59

ñdmÜ¶m¶ 3.1

I. Imbrb g§»¶m {MÌH¥$Vr {MÝhmZwgma AgyZ Ë¶m§Mr ~oarO ñWmZ ‘yë¶ V³Ë¶mVXmIdm.1) ghó eVH$ XeH$ gwQ>o

1000100

100

100

100

100

10 10 10 1111

1000 1000

1000100 100

10 1010 10 10

1 1

g eo X gw

2) ghó eVH$ XeH$ gwQ>o1000

1000

10001000

1000 100100100

10 10

1000

1000

1000 10010 10

10

g eo X gw

II. ñWmZ‘wë¶mZwgma Imbrb g§»¶m {bhÿZ Ë¶m§Mr ~oarO H$am.1) 6371 + 421

g go X gw

2) 6039 + 2920

g eo X gw

3) 3487 + 5203

g eo X gw

4) 4675 + 2397

g eo X gw

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60

III. ~oarO H$am: a. 1) 6 4 3 2

+ 3 2 6 4

2) 5 4 9 0 + 3 5 0 7

3) 6 7 5 4 + 2 1 3 5

4) 5 2 1 3 + 3 6 7 3

b. 1) 3 4 6 8 + 4 1 2 7

2) 5 8 9 4 + 3 2 6 3

3) 4 3 7 2+ 3 0 0 9

4) 5 0 9 7 + 3 8 6 5

c. 1) 2 4 9 3 3 7 1 + 4 4

2) 5 2 0 + 5 3 7 4

3) 8 2 6 7 3 2 9 + 1 4 9

4) 5 5 9 6 2 2 6 7 + 1 4 1 3

IV. OmXÿB© Mm¡agmMr eº$s -

OmXÿB© Mm¡agmZo g§»`m§Mr ~oarO ñV§̂ mZwgma, n§º$sZwgma d H$monè`mnmgyZ H$monè`mn ª̀V H$am. àË òH$ doir ~oaOoMr VwbZm H$am. Vw_Mo {ZarjU Vw_À`m {_ÌmZm d {ejH$m§Zm XmIdm.

H¥$Vr : Imbrb Mm¡agm_Yrb {ZarjU H$am.

2 7 69 5 14 3 8

àË¶oH$ n§³Vr d ñV§^mVrb A§H$m§Mr ~oarO H$am. VgoM {VaH$g gwÜXm ~oarO H$am.Vwåhr H$m¶ {ZarjU Ho$bmV?

gdmª‘Ü¶o A§H$m§Mr ~oarO g‘mZ ¶oVo Ago AmT>iVo. darb Mm¡agmMo {ZarjU H$éZ Ë¶mMà‘mUo 12 Zo gwédmV H$éZ Xwgam Mm¡ag aMm. (Vw‘À¶m {ejH$/[‘Ìm~amo~a MMm© H$am.)

1726 1558 2398

2566 1894 1222

1390 2230 2062

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61

IV Imbrb CXhamUo gmoS>dm-

1) EH$m YmÝ¶H$moR>mamV 2360 {Šd§Q>b Ádmar d 3427 {Šd§Q>b ‘H$m Amho. Va YmÝ¶H$moR>mamV EHy$U {H$Vr YmÝ¶ gmR>{dbo Amho?

2) n§Mm¶VrÀ¶m EH$m ^mJm‘Ü¶o 4275 nwéf, 4312 {ó¶m Am{U 1380 ‘wbo

AmhoV. Va Ë¶m ^mJm‘Ü¶o EHy$U bmoH$g§»¶m {H$Vr Amho?

3) EH$m gH©$g H§$nZrbm {XdgmÀ¶m n{hë¶m emobm < 6375 Am{U Xþgè¶m emobm < 2895 {‘imbo. Va Ë¶m {Xder EHy$U {H$Vr én¶o H§$nZrbm {‘imbo?

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62

àH$aU -4 dOm~mH$s

¶m àH$aUmÀ¶m AÜ¶¶ZmZV§a Vwåhr ho {eH$mb :

• hmVMm Z KoVm 4 A§H$s g§»`m§Mr dOm~mH$s H$amb.

• hmVMm KoD$Z 4 A§H$s g§»¶m§Mr dOm~mH$s H$amb.

• X¡Z§{XZ OrdZmVrb g‘ñ¶m gmoSdmb.

• dOm~mH$sÀ¶m nÕVr g‘OmdyZ KoD$Z ‘ZmZo d ËdarV dOm~mH$s H$amb.

VrZ A§H$s g§»¶m§Mr hmVMm KoD$Z d hmVMm Z KoVm dOm~mH$s Vwåhr ¶mAJmoXaM{eH$bm AmhmV. 4 A§H$s g§»¶m§Mr dOm~mH$s H$aÊ¶mÀ¶m nÕVr g‘OmdyZ KoÊ¶mgmR>rImbrb CXmhaUmMo {ZarjU H$am.

CXmhaU 1:

aoeZ XþH$mZ

OyZ ‘{hÝ¶mgmR>r aoeZ XþH$mZmbm 5890 {H$.J«±‘ Vm§Xÿi nwa{dbm Jobm. Ë¶m‘{hÝ¶mV 4650 {H$.J«±‘ Vm§Xþi {dH$bm Jobm. Va ‘{hÝ¶mÀ¶m eodQ>r {H$Vr Vm§Xÿi{e„H$ amhrbm?

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63

nÕV : nwa{dboë¶m EHy$U Vm§Xim‘YyZ {dH$bobm Vm§Xÿi dOm~mH$s H$am.

Vnerb g e X gw

nwa{dbobm EHy$U Vm§Xÿi 5 8 9 0 {H$.J«°‘ ì¶dH$ë¶

{dH$bobm EHy$U Vm§Xÿi 4 6 5 0 {H$.J«°‘ ì`dH$bH$

{e„H$ Vm§Xÿi 1 2 4 0 {H$.J«°‘ (~mH$s)\$aH$

∴ {e„H$ amhrbobm EHy$U Vm§Xÿi = 1,240 {H$.J«°‘

CXmhaU 2: OwZ ‘{hÝ¶mgmR>r 3268 {H$.J«°‘ Ádmar nwa{dbr hmoVr. Ë¶mVrb 125 {H$.J«°‘ Ádmar

‘{hÝ¶mÀ¶m eodQ>r {e„H$ amhrbr. Va Ë¶m ‘{hÝ¶mV EHy$U {H$Vr Ádmar {dH$br Jobr?

Vnerb g e X gw

nwa{dbobm Ádmar 3 2 6 8 {H$.J«°‘ ì¶dH$ë¶

{e„H$ amhrbobr Ádmar 0 1 2 5 {H$.J«°‘ ì`dH$bH$

{dH$bobr EHy$U Ádmar 3 1 4 3 {H$.J«°‘ (~mH$s)\$aH$

Imbrb CXmhaUm§Mo {ZarjU H$am :

1) 5647 ‘YyZ 3143 dOm H$am¶oWo 5647 hr ì¶dH$ë¶ Amho Am{U 3143 hr ì¶H$bH$ Amho. ì¶dH$ë¶VyZ

ì¶dH$bH$ dOm H$am.

5 6 4 7 ì¶dH$ë¶− 3 1 4 3 ì`dH$bH$

(~mH$s)\$aH$

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64

2) 9684 _YyZ 3041 dOm H$am

¶oWo H$moUVr g§»¶m ì¶dH$ë¶? (9684)

H$moUVr g§»¶m ì¶dH$bH$ Amho? (3041)

9684 _YyZ 3041 dOm H$am

9 6 8 4 ì¶dH$ë¶− 3 0 4 1 {ì`dH$bH$

(~mH$s)\$aH$

ho Vwåhr H$am :

1) 5876 _YyZ 3755 dOm H$am 2) 3800 _YyZ 6827 dOm H$am

hmVMm KoD$Z dOm~mH$s

CXmhaU 1: EH$m ñd¶§godr g§ñWoMo ~MV ImVo EH$m ghH$mar

~±Ho$V CKS>bo hmoVo.‘XV åhUyZ gaH$maZo Ë¶m§À¶m ~°H$ImË¶m§bm < 8950 O‘m H$obo g§ñWoZo {ebmB© ‘erZ IaoXr H$aÊ¶mgmR>r Ë¶m ImË¶mVrb bo.Va Ë¶m§À¶m ImË¶mV {H$Vr a³H$‘ {eëëH$ amhrbr?

O_m Ho$bobr aH$H$_ = bobr aH$H$_ =

65

¶m CXmhaUmMo CÎma nm¶è¶m nm¶è¶mZr nhm.

nmàr : 1ì¶dH$ë¶ ‘Ü¶o 0 gwQ>o ñWmZmV AmhoV . 0 ‘YyZ 7 dOm

H$aUo e³¶ Zmhr. åhUyZ XeH$ ñWmZm‘YyZ 1 XeH$ hm-VMm KoD$Z gwQ>o ñWmZmV {‘idm. AnZmbm 10 + 0 =10{‘iVmV. 10 ‘YyZ 7 dOm Ho$ë¶mg 3 {‘iVmV. AmVmì¶dH$ë¶ ‘Ü¶o XeH$ñWmZmV 4 {‘iVmV.

g e X gw 8 9 5 0− 5 3 9 7 3

4 10

nmàr : 2AmVm ì¶dH$ë¶ ‘Ü¶o XeH$ ñWmZmV 4 ‘YyZ 9

dOm~mH$s H$aUo e³¶ Zmhr.åhUyZ , eVH$ ñWmZm‘YyZ 1eVH$ hmVMm KoD$Z Vmo XeH$ ñWmZmV {‘idm. AmnUmbm10 + 4 = 14 XeH$ ñWmZmV {‘iVmV. 14 ‘YyZ 9 dOmHo$ë¶mg AmnUmbm 5 {‘iVmV. AmVm eVH$ ñWmZmV 8{‘iVmV.

8 9 5 0− 5 3 9 7 5 3

414

8 10

g e X gw

nmàr : 3ì¶dH$ë¶ ‘Ü¶o eVH$ ñWmZmV 8 ‘YyZ 3 dOm Ho$ë¶mg

AmnUmg 5 eVH$ [‘iVmV.

8 9 5 0− 5 3 9 7 5 5 3

414

8 10

g e X gw

nmàr : 4ì¶dH$ë¶ ‘Ü¶o ghó ñWmZmV 8 ‘YZy 5 dOm Ho$ë¶mg

AmnUmg 3 ghó {‘iVmV.

∴ ImË¶mda {e„H$ amhrbobr a¸$‘ Amho dy eH$Vmo? Imbrb CXmhaUmMo {ZarjU H$am.

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8 9 5 0 - 5 3 9 7

1000 1000

1000 1000

1000

1000

1000

1000

10 10 10 1010 10

10 10 10 10

100100100

100100100

100100 100

1010

10

10

10

11

11

11

11

11

\$aH$ : 3 5 5 3 3 5 5 3

ImË¶mda {e„H$ Agbobr a¸$‘ Amho < 3,553

CXmhaU 2:

IoimMo gm{hË¶ IaoXr H$aÊ¶mgmR>remiobm >q‘Q>Z, Wm«o~m°b, {H«$Ho$Q> goQ> B. ‘¡XmZrIoimgmR>r rKoVbr. Va ~m¡{ÕH$ IoimÀ¶m gm{hË¶mgmR>r{H$Vr {H$§‘VrMo gmhrË¶ IaoXr Ho$bo?

Vnerb g e X gw8 17 4 10

‘§Oay Pmbobr a¸$‘ = < 9 7 5 0

‘¡XmZr Ioi gm{hË¶mMr IaoXr {H$§‘V = < 5 9 1 8

~m¡{ÕH$ Iio gmhrË¶ IaoXr qH$‘V = < 3 8 3 2

~m¡{ÕH$ Ioi gm{hË¶ IaoXrgmR>r {eëbH$ a¸$‘ = < 3,832

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67

Imbrb CXmhaUm§Mo {ZarjU H$am :1) 5074 ‘YyZ 3267 dOm H$am¶oWo 5074 ì¶dH$ë¶ Amho Am{U 3267 ì¶dH$bH$ Amho.

g e X gw4 10 6 14

5 0 7 4 5 0 7 4 ì¶H$ë¶− 3 2 6 7 − 3 2 6 7 ì`dH$bH$

1 8 0 7 1 8 0 7 (~mH$s)\$aH$

2) 6300 _YyZ 3928 dOm H$am

WoWo 6300 ì¶dH$ë` Amho 3928 ì¶dH$ë` Amho

g e X gw

5 2 10 10

6 3 0 0 6 3 0 0 ì¶H$ë¶− 3 9 2 8 − 3 9 2 8 ì`dH$bH$

2 3 7 2 2 3 7 2 (~mH$s)\$aH$

912

ho Våhr H$am :1) 9372 ‘YyZ 8045 dOm H$am. 2) 8402 ‘YyZ 7835 dOm H$am.

Vm|S>r/ ~m¡{ÕH$ CXmhaUo Ooìhm g§»¶mMr dOm~mH$s H$aVmo Voìhm ‘ZmV dOm~mH$s H$aÊ¶mMr nÕV ¶oVo. àË¶oH$mMrdOm~mH$s H$aÊ¶mMr nÕV doJdoJir Agy eH$Vo. ¶m CXmhaUm§Mo {ZarjU H$am.

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CXmhaU 1: 673 ‘YyZ 241 dOm H$am. nÕV1

ì¶dH$bH$Mm {dñVma H$am Am{U H«$‘mZo dOm~mH$s H$am.

673 - 241 = ?

673 - (200 + 40 + 1)

673 - 200 = 473

473 - 40 = 433

433 - 1 = 432∴ 673 - 241 = 432

nÕV 2ì¶H$bH$Mm {dñVma H$am Am{U H«$‘mZog§»¶maofoda dOm~mH$s H$am.

673 - 241 = ?

673 - (200 + 40 + 1)

-200

432 632 672

-40-1

673∴ 673 - 241 = 432

CXmhaU 2: 900 ‘YyZ576 dOm H$am.nÕV 1

900 - 576 = ? = 900 - (500 + 70 + 6) 900 - 500 = 400 400 - 70 = 330 330 - 6 = 324

∴ 900 - 576 = 324

nÕV 2 900 - 576 = ?

= 900 - (500 + 70 + 6)

-500

324 824 894

-70-6

900

∴ 900 - 576 = 324

CXmhaU 3: 9000 ‘YyZ 5348 dOm H$am. {dYmZ 1

9000 - 5348 = ?= 9000 - (5000 + 300 + 40 + 8) 9000 - 5000 = 4000 4000 - 300 = 3700 3700 - 40 = 3660 3660 - 8 = 3652∴ 9000 - 5348 = 3652

{dYmZ 2

9000 - 5348 = ?

= 9000 - (5000 + 300 + 40 + 8)

-5000

36528652

89528992

9000-300-40

-8

∴ 9000 - 5348 = 3652

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ho Våwhr H$am: ì¶dH$bH$ Mm {dñVma H$ê$Z dOm~mH$s {‘idm. ¶mMà‘mUo àíZV¶ma H$am d ‘ZmV gmoS>{dÊ¶mMr nÕV V¶ma H$ê$Z à¶ËZ H$am.

1) 328 - 125 2) 693 - 258 3) 3690 - 1264 4) 8000 - 3578

ñdmÜ¶m¶4.1 I. Imbrb CXmhaUo gmoS>dm.

3 8 6 52 4 3 0−

1) 8 3 6 95 0 4 3−

2) 9 5 7 62 3 4 5−

3) 5 6 5 03 9 7 0−

4)

II.

5 3 7 2 3 8 5 9−

1) 6 9 0 73 2 4 5−

2) 8 7 0 03 2 9 7−

3) 9 0 0 05 3 8 2−

4)

8 0 3 0 3 8 6 7−

5) 6 0 0 42 3 4 5−

6) 3 9 2 82 5 9 3−

7) 8 0 0 43 1 0 8−

8)

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III. Imbrb CXmhaUo gmoS>dm.1) EH$m eoVH$è¶mZo 3290 {H$.J«‘ Ádmar {nH${dbr. Ë¶mVrb KamVrbCn¶moJmgmR>r 1376 {H$.J«‘ Ádmar R>odbr. amhrbobr Ádmar Ë¶mZo {dH$br.

Va EHy$U {H$Vr Ádmar Ë¶mZo {dH$br?

eoVH$è¶mZo {nH${dbobr EH$yU Ádmar = {H$.J«‘

KamVrb Cn¶moJmgmR>r R>odbobr EHy$U Ádmar = {H$.J«‘

amhrbobr Ádmar = {H$.J«‘

2) H$m‘Jma EH$m ‘{hÝ¶mbm Z emioÀ¶m e¡j{UH$ H$m¶m©gmR>r r IM© H$ê$Z r EH$yU {H$Vr én¶o IM© Ho$bo?

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4) nmÊ¶mMr Q>mH$s ^aÊ¶mgmR>r 8000 {bQ>a nmUr bmJVo Ë¶m Q>mH$sV 6398

{bQ>a nmUr Amho. Q>mH$s ^aÊ¶mgmR>r AOyZ {H$Vr {bQ>a nmUr bmJob?

ho g‘OmdyZ ¿¶m:

dOm~mH$s ‘Ü¶o VmimH$obm OmVmo

1) 2836 _YyZ 1329 dOm H$am2 16 Vmim :ì¶dH$bH$ +’$aH = ì¶dH$ë¶

2 8 3 6

1 3 2 9+ 1 5 0 7

2 8 3 6 ì¶dH$ë¶ 1 3 2 9 ì¶dH$bH$1 5 0 7 ’$aH$(~mH$s)

2) 8000 ‘| go 2593 KQ>mBE 7 9 9 10 Vmim :ì¶dH$bH$ +’$aH = ì¶dH$ë¶

8 0 0 0

2 5 9 3+ 5 4 0 7

8 0 0 0 ì¶dH$ë¶2 5 9 3 ì¶dH$bH$5 4 0 7 ’$aH$(~mH$s)

Vwåhr H$aV Agboë¶m àË¶oH$ CXmhaUmMm Vmim H$am.

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àH$aU -5 JwUmH$ma

¶m àH$maÀ¶m AÜ¶¶ZmZ§Va Vwåhr :

l JwUmH$ma hm nwZamdVuV ~oarO Amho ho g‘OmdyZ ¿¶mb.

l JwUmH$mam‘Ü¶o Agbobr AZoH$ nXo g‘OmdyZ ¿¶mb.

l JwUmH$ma‘Yrb ‘yi {H«$¶m AmoiImb

l g§»¶obm 1 A§H$mZo d 2 A§H$mZr JwUmb.( hmVMm KoD$Z/hmVMm Z KoVm Á¶m§Mm JwUmH$ma 9999 nojm OmñV Zmhr).

l X¡Z§[XZ OrdZm‘Ü¶o Ambobr JwUmH$mamMr CXmhaUo g‘OmdyZ ¿¶mb

l JwUmH$mamMr A§XmOo {H$§‘V H$mT>mb.

Vwåhr ¶m AJmoXa ‘mJrb dJm©V, EH$ A§H$s g§»¶m§Mm JwUmH$ma {eH$bm AmhmV.

CXmhaU : 1) 6 × 8 = 48 2) 12 × 6 = 72

darb CXmhaUmV {Xbobm JwÊ¶, JwUH$ d JwUmH$ma AmoiIm.

CXmhaU JwÊ¶ JwUH$ JwUmH$ma

1

2

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JwUmH$ma hm nwZamdVuV ~oarO Amho

H$¥Vr 3: amo{hVH$S>o 5 nopÝgb ~m°³g AmhoV. àË¶oH$ ~m°³g ‘Ü¶o 6 nopÝgb AmhoV.Va amo{hVH$S>o EHy$U {H$Vr nopÝgb AmhoV?

AmH$¥VrMo {ZarjU H$am.

AmH$¥Vr‘Yrb nopÝgb R>odÊ¶mÀ¶m ~m³°gMo {ZarjU H$am. àË¶oH$ ~m°³g‘YrbnopÝgbr ‘moOm.

6 + 6 + 6 + 6 + 6 = 30‘mJrb B¶ËVo ‘Ü¶o {eH$bobr ~oaOoMr nÕV AmR>dm. nm§M d¡im g§»¶m§Mr ~oarO

Z H$aVm AmnU "X' {MÝh dmnê$Z g§{já ñdê$nmV {bhÿ .

6 × 5 = 30

åhUyZ JwUmH$ma hm g‘mZ g§»¶oMr nwZamdVuV ~oarO Amho.

hmVMm Z KoVm JwUmH$maCXmhaU : EH$m ~m°³g‘Ü¶o 8 ImoS>a~a AmhoV . Aem 4 ~m°³g‘Ü¶o {H$Vr ImoS>a~aAgVrb?

EHy$U ~m°³g = 4

àË¶Ho $ ~m°³g‘Yrb ImoS>a~a = 8

∴ EHy$U ImoS>a~a = 8 + 8 + 8 + 8 = 32

¶oWo 8 Mr 4 doim nwZamd¥Vu Pmbr Amho.

∴ 8 × 4 = 32

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8 × 4 = 32

JwÊ¶ JwUH$ JwUmH$ma

bjmV R>odm:

l JwUmH$ma hm nwZamdVuV ~oaOoMr {H«$¶m Amho.

l Á¶m g§»¶obm AmnU JwUUma AmhmoV {Vbm "JwÊ¶' åhUVmV.

l Á¶m g§»¶oZo AmnU JwUUma AmhmoV {Vbm "JwUH$' åhUVmV.

l XmoZ g§»¶oMm JwUmH$ma H$ê$Z {‘iUmè¶m CÎmambm "JwUmH$ma' åhUVmV.

JwUmH$mamMo JwUY‘©

I . 1 Zo JwUyZ hmoUmao JwUmH$mamMo JwUY‘©- CXmhaU 1:

l¶oWo {H$Vr âbm°da nm°Q> AmhoV?

VrZ

làË¶oH$ âbm°da- nm°Q> ‘Ü¶o {H$Vr amonQ>r AmhoV?

EH$

l{VÝhr âbm°da-nm°Q> ‘Ü¶o {H$Vr amonQ>r AmhoV?

3 × 1 = 3

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CXmhaU 2 :

5 × 1 = 5

l darb AmH¥$VrV {H$Vr Am¶V AmhoV? nm§M l àË¶oH$ Am¶VmV {H$Vr q~Xÿ AmhoV? EH$ l gd© Am¶Vm‘Ü¶o EHy$U {H$Vr q~Xÿ AmhoV? 5 × 1 = 5

Oa Amåhr darb CXmhaUmMo {ZarjU Ho$bo Va

"EImXr g§»¶m Am{U 1 ¶m§Mm JwUmH$ma Zoh‘r Vr g§»¶m§M AgVo.

à¶ËZ H$am :1) 10×1 =............................. 2) 1×55 =.............................

3) 100×1=............................. 4) 8×1 =.............................

II. eyÝ¶À`m JwUmH$mamMm JwUY‘©-

{Xboë¶m CXmhaUmMo {ZarjU H$am:7 × 0 = 0

15 × 0 = 0

darb CXmhaUm§Mm JwUmH$ma {H$Vr? {ZarjU H$am.

darb CXmhaUmV, JwUmH$ma ewÝ¶ Amho. darb CXmhaUmdê$Z Amåhr Ago AZw‘mZH$mTy> eH$Vmo {H$,

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Ooìhm EImÚm g§»¶obm eyÝ¶ Zo JwUbo Va JwUmH$ma Zoh‘r eyÝ¶ AgVmo. .

JwUmH$mamÀ¶m H«$‘mMo VËd

AmH¥$Vr‘Ü¶o XmoZ doJdoJù¶m àH$mamZr Mm§XÊ¶m§Mr aMZm Imbr XmI{dbr Amho.

Cä¶m ñV§^mV aMZm AmS>ì¶m n§ŠVrV aMZm

AmH$¥Vr (a) ‘Ü¶o XmI{dboë¶m Mm§XÊ¶mÀ¶maMZoMo {ZarjU H$ê$Z Imbrb àíZm§MrCÎmao ¿¶m.

¶oWo {H$Vr ñV§^ AmhoV?

àË¶oH$ ñV§^mV {H$Vr Mm§XÊ¶m AmhoV?

gd© ñV§^mV {‘iyZ EHy$U {H$Vr Mm§XÊ¶m

AmhoV? 5 × 3 = 15

AmH$¥Vr (b) XmI{dboë¶m Mm§XÊ¶mÀ¶maMZoMo {ZarjU H$ê$Z Imbrb àíZm§MrCÎmao ¿¶m.

¶oWo {H$Vr n§º$s AmhoV?

àË¶oH$ n§º$sV {H$Vr Mm§XÊ¶m AmhoV?

gd© n§º$sV {‘iyZ EHy$U {H$Vr Mm§XÊ¶m

AmhoV? 3 × 5 = 15

darb H¥$VrVyZ AmnU H$moUVo {ZarjU Ho$bo?

5 × 3 = 3 × 5 = 15

XmoÝhr aMZo‘Ü¶o JwUmH$ma hm g‘mZ Amho. Ë¶mM à‘mUo,

5 × 7 = 7 × 5 = 35

20 × 8 = 8 × 20 = 160

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Oa Amåhr JwÊ¶ d JwUH$ ¶m§Mm H«$‘ ~Xbbm Va XmoZ g§»¶m§Mm JwUmH$ma ~XbVZmhr. ¶mbmM JwUmH$mamÀ¶m H«$‘mMo VËd åhUVmV.

ñdmÜ¶m¶ 5.1

I. ¶mo½¶ CÎmamZo [aH$må¶m OmJm ^am.

1) 9 + 9 + 9 = 9 × =

2) 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = × 8 =

3) 5 + 5 + 5 + 5 = × =

4) 6 + 6 + 6 + 6 + 6 = × =

II. àË¶oH$ gQ>mMr nwZamdVr©V ~oarO Am{U JwUmH$ma {bhm.

CXmhaU :

3 + 3 = 6

2 × 3 = 6

1) ___________________

___________________

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2)

___________________

___________________

3)___________________

___________________

III. JwUmH$mamMo JwUY‘© dmnê$Z Imbrb [aH$må¶m OmJm nyU© H$am.

1) 75 × _____ = 75

2) 93 × 0 = _____

3) 37 × 42 = 42 × _____

4) 1 × 555 = _____

5) 15 × _____ = 20 × 15

6) 7623 × _____= 0

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JwUmH$mamMm Vº$m (0 Vo 10)

× 0 1 2 3 4 5 6 7 8 9 10

0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9 10

2 0 2 4 6 8 10 12 14 16 18 20

3 0 3 6 9 12 15 18 21 24 27 30

4 0 4 8 12 16 20 24 28 32 36 40

5 0 5 10 15 20 25 30 35 40 45 50

6 0 6 12 18 24 30 36 42 48 54 60

7 0 7 14 21 28 35 42 49 56 63 70

8 0 8 16 24 32 40 48 56 64 72 80

9 0 9 18 27 36 45 54 63 72 81 90

10 0 10 20 30 40 50 60 70 80 90 100

darb V³Ë¶mMo {ZarjU H$am.JwUmH$mamÀ¶m darb Q>o~bdê$Z JwUmH$mamMo doJdoJio JwUY‘© Vw‘À¶m {ejH$m§À¶m

‘XVrZo AmoiIm.

10, 100 Am{U 1000 Zo JwUmH$ma

EH$m g§»¶obm XmoZ A§H$s g§»¶oZo H$go JwUVmV ho Vwåhr ¶mAJmoXa {eH$bm AmhmV-

AmnU EH$m g§»¶obm 10, 100 Am{U 1000 Zo H$go JwUVmV Vo {eHy$¶m -

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Imbrb JwUmH$mamMo {ZarjU H$am-

CXmhaU 1: 1) 9 × 10 = 9 × 1 XeH$ = 9 XeH$ = 90

2) 12 × 10 = 12 × 1 XeH$ = 12 XeH$ = 120

Vw‘Mo {ZarjU H$m¶ Amho?

Ooìhm EH$m g§»¶obm 10 Zo JwUVmo, Voìhm Ë¶m§Mm JwUmH$ma JwÊ¶À¶m COì¶m ~mOybm

eyÝ¶ XoD$Z {‘imboë¶m g§»¶oB©VH$m AgVmo.

CXmhaU 2: 1) 9 × 100 = 9 × 1 eVH$ = 9 eVH$ = 900

2) 12 × 100 = 12 × 1 eVH$ = 12 eVH$ = 1200

darb CXmhaUmMo Vw‘Mo {ZarjU H$m¶ Amho ?Ooìhm EH$m g§»¶obm 100 Zo JwUVmo, Voìhm Ë¶m§Mm JwUmH$ma hm JwÊ¶À¶m COì¶m

~mOybm XmoZ eyÝ¶ XoD$Z {‘imboë¶m g§»¶oB©VH$m AgVmo.

CXmhaU 3: 1) 9 × 1000 = 9 × 1 hOma = 9 hOma = 9000

Ooìhm EH$m g§»¶obm 1000 Zo JwUVmo, Voìhm Ë¶m§Mm JwUmH$ma hm JwÊ¶À¶m COì¶m

~mOybm VrZ eyÝ¶ XoD$Z {‘imboë¶m g§»¶oBVH$m AgVmo.

darb gd© CXmhaUmdê$Z Amåhr Ago g‘Oy eH$Vmo H$s, EImÚm g§»¶obm eodQ>r 0

A§H$ Agboë¶m g§»¶oZo JwUbo AgVm JwÊ¶ Am{U eyÝ¶ Agboë¶m JwUH$mMm JwUmH$ma

H$ê$Z eodQ>r JwUH$À¶m EH$yU eodQ>r Agbobo eyÝ¶ (0) {bhmdoV.

CXmhaU 4: 1) 8 × 10 = 80 2) 3 × 200 = 600

3) 2 × 4000 = 8000 4) 40 × 10 = 400

5) 60 × 30 = 1800

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ñdmÜ¶m¶ 5.2

I. ¶mo½¶ CÎmamZo {aH$må¶m OmJm ^am.

1) 3 × 100 = ________ 5) 24 × 200 = ________

2) 9 × 50 = ________ 6) 2 × 3000 = ________

3) 9 × 500 = ________ 7) ________ × 70 = 350.

4) 7 × 400 = ________ 8) 20 × 60 = ________

EH$ A§H$s Am{U XmoZ A§H$s g§»¶|Mm JwUmH$ma

H$¥Vr : 15 ‘wbm§Zm ~mobdyZ Ë¶m§Zm EH$m am§JVo C^o H$am. Ë¶m§Zm N>Ìr Mo {MÌ Agbobo d IaoXr qH$‘V © Úm. Z§Va Vo H$mS>© ‘wbmZm hmVmV Yam¶bm gm§Jm. EH$m ‘wbmbm ~mobmdyZ Ë¶mbm Imbrb àíZ {dMmam d CÎmao {‘idm.

{ejH$ : {H$Vr ‘wbo am§JoV C^r AmhoV?

‘wbJm : 15 ‘wbo{ejH$ : EH$m N>>ÌrMr IaoXr qH$‘V {H$Vr Amho?

‘wbJm : < 160{ejH$ : {H$Vr ‘wbm§Zr IaoXr {H§$‘V © hmVmV Yabr AmhoV? ‘wbJm : 15 ‘wbm§Zr [ejH$ : 160 hr g§»¶m {H$Vr doim Ambr Amho? ‘wbJm : 15 doim. AmVm Amåhmbm 15 N>Í¶m§Mr EHy$U qH$‘V H$mT>m¶bm nm{hOo. ho H$go H$mT>mb?

ho H$mT>Ê¶mgmR>r 160 d 15 Mm JwUmH$ma Ho$bm nmhrOo.åhUyZ 160×15

80016002400

160 bm 5 Zo JwUyZ`160 bm 10 Zo JwUyZ

åhUyZ, 15 N>Í¶m§Mr IaoXr qH$‘V =< 2400

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CXmhaU 1:EH$ Q´>H$‘Ü¶o H$m§ÚmMr 142 nmoVr AmhoV. Va 12 Q´>H$‘Ü¶o {H$Vr H$m§ÚmMr nmoVr

AgVrb?

H$mÚ§mMr EHy$U nmoVr = 142 × 12JwUmH$mamÀ¶m nÕVrZwgma 12 hm JwUH$ Amho. ¶m‘Ü¶o 1 XeH$ d 2 gwQ>o AmhoV.

àW‘ JwÊ¶ 142 bm 2 gwQ>o Zo JwUmdo Z§Va 1 XeH$ Zo JwUmdo.

nmàr 1 : 142 bm 2 gwQ>o Zo JwUm 284142 2#x

nmàr 2 : 142 bm 1XeH$ Zo JwUm

nmàr 3 : Ooìhm AmnU XmoÝhr JwUmH$mamMr ~oarO H$ê$

∴ EHy$U H$mÚm§Mr nmoVr 1704

CXmhaU 2 :

EH$m n°Ho$Q>‘Ü¶o 12 noÝg AmhoV. XþH$mZmV Aer 100 n°Ho$Q> AmhoV.Va EHy$U

{H$Vr noÝg XþH$mZmV AmhoV?

EH$m n°Ho$Q>‘Yrb noÝg = 24

XþH$mZmV Agbobr n°Ho$Q>g² = 100

∴ EHy$U XþH$mZmV Agbobr noÝg = 2400

1420142 10#x

284

17041420

142 2#x

240024 100#x

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MATHEMATICS (Revised) ©KTBS B¶Îmm Mm¡Wr 4 re be …ktbs.kar.nic.in/New/website textbooks/class4/4th-marathi-maths-1.pdfII III Young learners in their initial stages of learning