ii

H$Zm©Q>H$ gaH$ma

J{UV{hÝXr ‘mܶ‘

MATHEMATICSHindi Medium

H$jm - Mm¡Wr^mJ - 1

Fourth StandardPart - 1

KARNATAKA TEXT BOOK SOCIETY (R).,

100 Feet Ring Road, Banashankari 3rd Stage,Bengaluru - 560 085

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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),Bangalore, Karnataka

Nagendra KumarManaging Director

Karnataka Textbook Society (R),Bangalore, 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 Bangalore -560076,

Members :Sri S. Gavisiddappa No. 263/17 A, 2nd cross, Basaveshwar nagar, Bellary -573103,

Sri Vasudeva K.J Technical Assistant, DSERT, Hoskere halli Bangalore.

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 Bangalore South - 4.

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

Sri Prakash Koti Drawing Teacher, Govt High school, Sakkare golla Halli, Dodda ballapur Taluk Bangalore Rural Dist

Scrutinizer :

Sri. T.K Raghavendra, BEO Srinivaspur, Kolar District

Editorial Committee :

Sri Dr Ravindra Former NCERT Director, Arehalli BSK, 3rd stage, Bangalore - 61.

Sri Dr Upadya B.S Lecturer and Head of Department Maths, RIE, Mysore.Sri Dr Prasad S.V Lecturer, RIE Mysore.

Sri Dr Sharad Sure Assistant Proffessor Aziam Premji university Bangalore -10 PES School of Engineering campus Konappa Agra Hara

Translation Committee :

Sri. Vilas G. Pudale Head Master, Shri Shantinath Hindi High School, Hubli

Smt. Shanavaz Begum Asst. Teacher, Dhanaraj Phoolchand Hindi Medium High School, Bengalore

Chief Co-ordinator:

Prof. G.S. Mudambadithaya, Co-ordinator, Curriculum Revision and Textbook Preparation, Karnataka Textbook Society, Bangalore.

GuidanceSri Nagendra Kumar, Managing Director, Karnataka Textbook Society, Bangalore.Smt Nagmani C, Deputy Director, Karnataka Textbook Society, Bangalore.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 Revision 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 sent them to the Education Minister and to the ‘Textbook Society’. Theywere 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 Revision Committee

Bengaluru.

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Text Books Revision CommitteeChairman-in-chief.Prof. Barguru Ramchandrappa, State Revision Committee, Karnataka

textbooks Society®, Bengaluru. Review Committee

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

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

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

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

Cross, BSK 2nd Stage, Bengaluru.Sri Narasimha murty 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. Tara, 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,

Kalaburgi - 585 105.Smt. L. Padmavati, Vice-principal, Empress Girls

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

Mathematics, Govt. women’s college, Kolar Translators Smt Shanwaz Begum, A.M. Sri VSK H.S. Srinivasnagar, Bengaluru.Chief Advisors Sri H.N. Gopalakrishna Managing Director, Karnataka Textbooks

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

Sri S.G. Nagesh Deputy Director, Karnataka Textbooks Society®, Banashankari 3rd stage, Bengaluru-85.

Programme co-ordinator: Asst.Director, Karnataka TextbooksSmt. Vijaya Kulkarni, Society®, Banashankari 3rd Stage,

Bengaluru-85.

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AZwH«$‘{UH$m

H«$‘ g§»¶m KQ>H$ n¥ð> g§»¶m

1 n[a‘mn Am¡a gab AmH$ma Ho$ joÌ ’$b 1 - 12

2 g§»¶mE± 13 - 46

3 ¶moJ’$b 47 - 61

4 KQ>mZm 62 - 71

5 JwUZ’$b 72 - 91

6 {d^mOH$ 92 - 109

7 d¥Îm 110 - 117

8 ‘mZ{gH$ A§H$J{UV 118 - 138

9 {^Þ Am¡a Xe‘bd$ 139 -158

^mJ - 1

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KQ>H$-1 gab AmH¥${V`m| Ho$ n[a_mn

Bg KQ>H$ H$mo Aܶ¶Z H$aZo Ho$ ~mX Amn :

AmH¥${V`m| Ho$ n[a‘mn kmV H$a|Jo &

n[a‘mn H$s n[aH$ënZm H$m {dñVma H$aHo$ J{UV hb H$a|Jo&

AmH¥${V`m| Ho$ joÌ’$b H$mo g‘P|Jo &

AmH$ma Ho$ joÌ’$b kmV H$a|Jo &

amOy Ho$ {nVm Zo EH$ O‘rZ IarXr h¡& BgHo$ Mmam| Amoa Vma S>mbZm& {H$VZr bå~r Vma H$s Amdí¶H$Vm h¡? H¡$go kmV H$a gH$Vo h¡?

arVm Q>¡~b na ~m°S>©a bJmZm MmhVr h¡& {H$VZo ‘rQ>a Vma H$s Amdí¶H$Vm h¡&?H¡$go kmV H$a gH$Vo h¢ ?

Xmo ì¶{º$¶mo§ H$s g‘ñ¶m H¡$go hb H$a gH$Vo h¡? gmo{ME& XmoZmo g§X^© ‘| b§~mB© ³¶m h¢? gmo{ME&

gab AmH¥${V`m| H$m n[a‘mn

nyd© H$s H$jm ‘| gab AmH¥${V H$m Aܶ¶Z {H$¶m h¡& Hw$N> aoImH¥${V`m| {MÌ Ûmam {XImB©E & EH$ H$m CXmhaU {X`m h¡&

1) 2)

............................................

3) .

............................................

4)

............................................

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Bg {MÌ H$m {ZarjU H$s{OE&

‘B’ go ‘A’ H$s Xÿar Š`m h¡ ?

‘C’ go ‘B’ H$s Xÿar Š`m h¡ ?

‘D’ go ‘C’ H$s Xÿar Š`m h¡ ?

‘A’ go ‘D’ H$s Xÿar Š`m h¡ ?

4 go§.

‘r.

8 go§.‘r.

6 go§.‘r.

7 go§.‘

r.A B

CD

ABCD gab aoImJ{UVr¶ AmH¥${V & AmH¥${V ‘| ‘mnm| H$m {ZarjU H$s{OE&

{ZarjU A go B H$s Xyar H$mo AB {Z{X©ï> H$aVo h¡&

AB = ........ go§.‘r.

BC = ........ go§.‘r.

CD = ........ go§.‘r.

DA = ........ go§.‘r.

A go B, B go C, C go D Am¡a D go A , H$s Hw$b Xÿar ³¶m h¡?

AB + BC + CD + DA = 8 + 7 + 6 + 4

= 25 go§.‘r.

A go ewé H$aHo$ {’$a A nhþMZo Ho$ {bE Hw$b Xÿar 25 g|.‘r Hw$b Xÿar H$mo ³¶m H$hVo h¡? gmo{ME

aoImJ{UVr¶ AmH¥${V Ho$ g^r ^wOm Ho$ ¶moJ H$mo n[a_mn H$hVo h¡&

H$m`©H$bmn : nmR>ç nwñVH$ H$m n[a‘mn kmV H$s{OE& H$jm H$s {IS>H$s, Q>o~b Ho$ D$nar gVh Ho$ n[a‘mn _| {H$gH$m A{YH$ h¡?

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Z‘yZm àíZ

1) 6 go§.‘r

7 go§.‘r

4 go§.‘r

A

B C

Bg AmH$ma H$m n[a‘mn kmV H$s{OE&

XÎm AB = 4 go§.‘r BC = 7 go§.‘r CA = 6 go§.‘r

n[a‘mn = AB + BC + CA

= 4 + 7 + 6 = 4 go§.‘r + 7 go§.‘r + 6 go§.‘r

= 17 go§.‘r

Aä¶mg 1.1

I. XÎm AmH$ma H$m n[a‘mn kmV H$s{OE :

1)E

I

HG

F 3 go§.‘r

4 go§.‘r

5 go§.‘

r

7 go§.‘r

4 go§.‘

r

2)

N

J K

L

M5 go§.‘r

6 go§.‘r

6 go§.‘

r

5 go§.‘r

4 go§.‘

r

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3)

T S

RU

P Q

4 go§.‘r

4 go§.‘r

3 go§.‘r

4 go§.

‘r 2 go§.‘r2 go§.‘r

4)

4 go§.‘r

8 go§.‘

r

7 go§.‘r

3 go§.‘r

2 go§.‘

rW X

CN

MR

II. A g_Vb AmH¥${V h¡ Am¡a gyMr B CZHo$ n[a‘mn h¡& XmoZmo gyMr H$mo Omo{S>E :

A B CÎma

1)

6 go§.‘r

4 go§.‘r

3 go§.‘r

5 go§.

‘r

A

B

CD

a) 20 go§.‘r ___________

2)

K

LM 6 go§.‘r

7 go§.‘r

5 go§.‘

r

2 go§.‘r

b) 15 go§.‘r. ___________

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3) 5 go§.

‘r

5 go§.‘r

5 go§.‘r

P

QR

c) 24 go§.‘r ___________

4)

6 go§.‘r

6 go§.‘r

6 go§.‘

r

6 go§.‘

r

W X

YZ

d) 22 go§.‘r ___________

e) 18 go§.‘r

g_Vb AmH¥${V H$s ^wOm H$s b§~mB© XoZo go n[a‘mn kmV H$a gH$Vo h¡& EH$ ^wOm

H$s b§~mB© N>moS>Zo go n[a‘mn AmH$ma H$mo {X¶m h¡ Vmo eof ^wOm H$mo H¡$go kmV H$a gH$Vo

eof ^wOm H$s b§~mB© kmV H$aZo Ho$ {bE n[a‘mn ‘| go KQ>mBE&

eof ^wOm H$s b§~mB© kmV H$aZo Ho$ {bE n[a‘mn ‘o go KQ>mBE & Z‘yZm àíZ

1)

5 go§.

‘r

?

6 go§.‘r

P

QR

XÎm AmH$ma Ho$ Xmo ^wOmAm| H$s b§~mB© 5 go§.‘r Am¡a 6 go§.‘r& CgH$m n[a‘mn 15 go§.‘r hmo Vmo Vrgar ^yOm H$s b§~mB© kmV H$s{OE&

XÎm Xm o ^wOmAm| H$m ¶m oJ = 5 go §.‘r + 6 go §.‘r = 11 go§.‘r

Vrgar ^wOm H$s b§~mB© =n[a‘mn-Xmo ^wOmAm| H$m ¶moJ

Vrgar ^wOm H$s b§~mB© = 15 go§.‘r- 11 go§.‘r = 4 go§.‘r

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Aä¶mg 1.2

1)

10 go§.‘r

10 go§.‘r

2 go§.‘

r

?

P Q

SR

XÎm AmH$ma H$m {ZarjU H$s{OE & BgH$m n[a‘mn 24 go§.‘r& Mm¡Wr ^wOm H$s b§~mB© ³¶m h¡?

2)

8 go§.‘r

4 go§.‘r3 go§.‘r

?

4 go§.‘

rA B

D

E

C

{MÌ ‘| Mma ^wOm H$s ‘mn {X¶o h¡& BgH$m n[a‘mn 24 go§.‘r h¡ Vmo eof ^wOm H$s b§~mB© Š`m h¡&

3)

8 go§.‘r

K M

NL

{MÌ ‘| EH$ ^wOm H$s b§~mB© 7 go§.‘r& ¶{X g^r ^wOm g‘mZ hmo Vmo n[a‘mn ³¶m h¡?

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H$m¶©H$bmn: AmH$ma H$m n[a‘mn {Og‘o§ gr{‘V ̂ wOm hmo Vmo kmV H$a gH$Vo h¡& AJbo

{MÌ H$m {ZarjU H$s{OE&

BZ AmH$ma H$m n[a‘mn H¡$go kmV H$a gH$Vo h¡& AmnHo$ {ejH$ go MMm© H$s{OE

Am¡a Om{ZE&

gab AmH$a H$m joÌ’$b

Q>o~b(1)

ãb°H$ ~moS>© (2)

nwñVH$ (3)

Cnamoº$ {MÌ ‘| {ZarjU H$s{OE {H$ Q>o~b H$s gVh, ãb°H$ ~moS>©, nwñVH$ H$r

gVh& Bg‘| {H$gH$m AmH$ma ~S>m Am¡a N>moQ>m h¡ ? {H$gHo$ AmYma na {ZíM¶ {b¶m

OmVm h¡& gmo{ME&

ãbmH$ ~moS>© H$m Xÿgam {MÌ ~S>m h¡ Am¡a Vrgam g~go N>moQ>m h¡&

Xÿgam {MÌ Á¶mXm ñWmZ boVm h¡ Am¡a Vrgao ‘| H$‘ ñWmZ bJVr h¡&

AmH$ma Ho$ {g{‘V ñWmZ ¶m joÌ H$mo ³¶m H$hVo h¡, Bgo AmH$ma H$m joÌ’$b H$hVo

h¡, XÎm AmH$ma H$m joÌ’$b H$hVo h¡&

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XÎm AmH¥${V Ho$ ñWmZ ¶m joÌ H$mo joÌ’$b H$hVo h¡&

AmH¥${V H$m joÌ’$b H¡$go kmV H$a gH$Vo? gmo{ME :

1) {H$gHo$ AmYma na H$man|Q>a joÌ’$b kmV H$aVo h¡? H$man|Q>a H$s XÿH$mZ H$mo OmH$a ‘mby‘ H$s{OE&

2) XOu H$s XH$mZ H$mo OmH$a ‘mby‘ H$s{OE {H$ eQ>© {gbmZo Ho$ {bE {H$VZo ‘rQ>a H$nS>o H$s Amdí¶H$Vm h¡?

H$m¶© H$bmn : H$m¡Zgo AmYma na joÌ’$b kmV {H$¶m OmVm h¡? Mma CXmhaU H$s{OE&

CXmhaU : H$‘ao H$m joÌ’$b 1) _______________ 2) _______________

3) _______________

Cnamoº$ CXmhaU ‘| joÌ’$b H¡$go kmV H$aVo h¡? gmo{ME& H$mo{ee H$s{OE&

AmH¥${V H$m joÌ’$b àmßV H$aZo Ho$ {bE b§~mB© Am¡a Mm¡S>mB© H$m JwUZ’$b h¡&

joÌ’$b H$s BH$mB©

D

A(1)

C

B

N

(2)K

M

L

Xmo {MÌm| H$mo {ZarjU H$s{OE Omo J«m’$ erQ> na ~Zo h¡& H$m¡Zgm ~S>m h¡? H¡$go

kmV H$a gH$Vo h¡ & nhbm {MÌ {H$VZo dJ© go gr{‘V h¡?

Zm¡ dJ© go {g{‘V h¡& BgH$m AW© àW‘ {MÌ H$m joÌ’$b 9 h¡ Am¡a Xÿgao {MÌ

H$m joÌ’$b 8 h¡&

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¶hm± na joÌ’$b ‘o§ H$moB© BH$mB© Zht h¡&

joÌ’$b H$s BH$mB© ³¶m h¡? gmo{ME&

Amn nhbo go Aܶ¶Z {H$¶o h¡ {H$ AmH$ma H$m joÌ’$b b§~mB© Am¡a Mm¡S>mB© H$m

JwUZ’$b h¡&

Cnamo³V {MÌm| ‘| à¶ËZ AmH¥${V H$s b§~mB© ³¶m h¡ AWm©V A B H$m ‘mn ³¶m h¡?

3 go§.‘r Mm¡S>mB© BC H$m ‘mn ³¶m h¡?

Xmo ̂ wOmAmo§ Ho$ ‘mn Ho$ Cn¶moJ go àW‘ {MÌ H$m joÌ’$b kmV H$s{OE àW‘

{MÌ H$m joÌ’$b = 3 go§.‘r X 3 go§.‘r = 9 dJ© go§.‘r

dJ© go§.‘r joÌ’$b H$s B©H$mB© h¡ O~ ‘mn go§.‘r ‘| h¡&

{ZarjU H$s{OE : Xmo ‘mnm| H$mo g|.‘r ‘| 춺$ H$aZo Ho$ {bE JwUZ’$b H$s BH$mB©

àmáH$aZo Ho$ {bE dJ© goÝQ>r‘rQ>a ‘| 춊V {H$¶m OmVm h¡& go‘r2 (dJ© go‘r)

{ZarjU XÎm H$WZmo§ H$m {ZarjU H$s{OE&

4 dJ© ‘rQ>a H$nS>m, Xrdma H$m joÌ’$b 15 dJ© ‘rQ>a, EH$ ~S>m Vmbm~ H$m

joÌ’$b 1 dJ© {H$bmo ‘rQ>a, àmUr g§J«hmb¶ H$m joÌ’$b 2 dJ© {H$bmo‘rQ>a h¡&

¶{X ‘mn ‘rQ>a ‘| hmo Vmo joÌ’$b H$s B©H$mB© dJ© ‘rQ>a& ¶{X ‘mn {H$bmo ‘rQ>a hmo

Vmo joÌ’$b H$s BH$mB© dJ© {H$bmo ‘rQ>a h¡&

gm‘mݶV… joÌ’$b H$s BH$mB© dJ© BH$mB© ‘o§ 춳V H$aVo h¡&

joÌ’$b H$s b§~mB© = dJ© g|_r, dJ© _r, dJ© {H$bmo {_Q>a `{X

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Z‘yZo Ho$ àíZ

J«m’$ erQ> na à˶oH$ dJ© H$m joÌ’$b 1 dJ© go‘r& XÎm AmH$ma H$m joÌ’$b kmV

H$s{OE&

{MÌ ‘| dJm] H$s kmV H$s{OE& H$w$b 7 dJ© h¡& {MÌ H$m joÌ’$b = 7 dJ© go§.‘r

Aä¶mg 1.3

I. J«m’$ erQ> na à˶oH$ dJ© H$m joÌ’$b 1 dJ© go‘r XÎm AmH$ma H$m joÌ’$b kmV H$s{OE& 1

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2

3

4

5

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12

H$m¶© H$bmn :

1) XÎm AmH$ma H$mo {ZarjU H$s{OE&

BZ AmH$ma H$mo J«m’$ erQ> na ~ZmH$a joÌ’$b kmV H$aZo H$s H$mo{ee H$s{OE&

{ejH$ go MMm© H$aHo$ Om{ZE& 2) J«m’$ erQ> na Xmo AmH$ma ~ZmB©E EH$ H$m n[a‘mn

20 go‘r Am¡a Xÿgam 16 go‘r h¡& XmoZmo§ AmH$ma H$m joÌ’$b kmV H$s{OE&

n[a‘amn H$s VwbZm H$s{OE Am¡a AmH$ma H$m joÌ’$b ̂ r VwbZm H$s{OE& AmnH$m

{ZíM¶ ³¶m h¡? AmnHo$ {ejH$ go MMm© H$s{OE&

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KQ>H$-2 g§»¶mE±

Bg KQ>H$ Ho$ Aܶ¶Z H$aZo Ho$ ~mX :

9999 g§»¶m H$mo {bIZo Am¡a nT>Zo H$m H«$‘ grI|Jo &

Mma A§H$m| ‘| ñWmZ ‘yë¶ {bI|Jo &

Mma A§H$m| Ho$ nhbo, ~mX Ho$ _Ü` H$s g§»`m {bI|Jo &

Mma A§H$m| H$s g§»¶m H$m {dñVma ê$n, gm‘mݶ ê$n {dñVma g§Ho$V ‘| {bI|Jo&

g§»¶m Ho$ ñWmZ ‘yë¶ Am¡a A§{H$V ‘yë¶ nhMmZ|Jo &

Mma A§H$mo H$s g§»¶m ‘| go ~S>r Am¡a N>moQ>r g§»¶m nhMmZ|Jo &

Mma A§H$m| H$s g§»¶m H$mo AamohU Am¡a AdamohU H«$‘ ‘| Omo‹S>|Jo &

Mma A§H$mo H$s g§»¶m

lrdmZr AnZr ‘m± Ho$ gmW àXe©Zr H|$ÝÐ H$mo OmVr h¡& dñVwE± Omo ngÝX AmVr h¡ dh {MÌ ‘| Xm‘ Ho$ gmW h¡& {ZarjU H$s{OE& >>>

<796<2356

<687

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<425 <3250

<990

<1986<8925

lrdmUr Zo dñVwAm| Ho$ Xm‘ H$mo nT>Zm ewé {H$¶m h¡&

<796 = gmV gm¡ N>r¶mZã~o én¶o<687 = N>… gm¡ gV«mgr én¶o <425 = Mma gm¡ nƒrg én¶o <990 = Zm¡ gm¡ Zã~o én¶o

<2356

<3250

<1986

<8995

BZH$mo H¡$go nT>Vo h¡&

VrZ A§H$m| H$s g§»¶m H$mo OëXr nT>Zo hmoVm h¡& CgZo AnZo {ejH$ go Mma A§H$modmbr g§»¶m H$mo nT>Zo ewé {H$¶m h¡& ³¶m Amn Mma A§H$modmbr g§»¶m H$mo nT>

gH$Vo h¡?

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VrZ A§H$modmbr g§»¶mH$mo nT>Zo {bIZm Am¡a {dñVma H$aZo nhbr H$jm ‘| grIo

h¡& A~ nwZ… Mma A§H$m|dmbr go H$mo{ee H$a|Jo&

g~go N>moQ>r VrZ A§H$dmbr g§»¶m H$m¡Z gr ?(100)

?

g~go ~S>r VrZ A§H$dmbr g§»¶m H$m¡Z gr ? (999)

ñWmZ ‘yë¶ MmQ>© ‘| g§»¶m {bIZo H$mo {ZarjU H$s{OE&

hOma gm¡ Xgdm± BH$mB©100×10 10×10 1×10 1

1 0 0 0

gm¡ d| ñWmZ Ho$ ~m¶o Va’$ EH$ ñWmZ ~T>mZo h¡& dh ñWmZ gm¡ d| ñWmZ H$m Xg

JwZm h¡& nT>Zo H$s nÕ{V : EH$ hOma

1,000 Mma A§H$m|dmbr

g~go N>moQ>r g§»¶m h¡&

g§»¶m 1000 H$mo {bIZm H$m {dYmZ

1000 Ho$ ~mX H$m¡Zgr g§»¶m h¡? (1000+1=1,001),

1001 Ho$ ~mX H$m¡Zgr g§»¶m (1001+1=1,002),

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Bgr àH$ma g§»¶mAm| H$m MmQ>© ~ZmBE 1000 Ho$ ~mX AmVo h¡ Am¡a n{T>E&

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$mo§ H$s g§»¶m ‘| H$B© g§»¶m H$mo Mw{ZE Am¡a MmQ>© H$mo V¡¶ma H$s{OE& nÕ{V H$mo nhMm{ZE&

g~go ~S>r Mma A§H$mo ‘| g§»¶m H$m¡Z gr h¡?

hm± !

ñWmZ ‘yë¶ MmQ>© ‘| Mma A§H$mo§ ‘| ~S>r g§»¶m {b{IE&

h gm¡ X À B9 9 9 9

Mma A§H$modmbr g~go ~S>r g§»¶m 9999 (Zm¡ hOma Zmo gm¡ {ZݶmZdo)

N>moQ>r g§»¶m 1000 9999 ~S>r g§»¶m

Mma A§H$modmbr g§»¶m

g§»¶m H$mo nT>Zo H$m {dYmZ H$m {ZarjU H$s{OE 4009 H$mo H¡$go nT>m OmVm h¡?

h gm¡ XÀÀ B nT>Zo H$m {dYmZ

2 3 5 6 Xmo hOma VrZ gm¡ N>ßnZ &

3 2 5 0 VrZ hOma Xmo gm¡ nMmg&

1 9 8 6 EH$ hOma {N>¶mgr&

8 9 2 5 AmR> hOma Zm¡ gm¡ nƒrg&

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Bgr Vah H$mo{ee H$s{OE&

{ZåZm{b{IV g§»¶mAmo§ H$mo eãXm| ‘| {b{IE:- {ZarjU H$s{OE :

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

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

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

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

{ZåZ{b{IV eãXm| H$mo g§»¶m ‘o§ {b{IE:- {ZarjU H$s{OE :

1) N>… hOma Mma gm¡ BH$Îma → ------------

2) VrZ hOma Zm¡ gm¡ → ------------

3) Zm¡ hOma AmR> gm¡ {ZÞ¶mZdo → ------------

4) Xmo hOma Mma gm¡ ~rg → ------------

H$mo{ee H$s{OE

1) {ZåZ{b{IV g§»¶mAmo§ H$mo n{T>E&3,705 4,600 3,576 1,005 5,009 9,827

2) 1801 go 1900 H$m MmQ>© ~ZmB©E& 3) g§»¶m H$mo {MÌ ‘| Xem©BE J¶m h¡& ñWmZ ‘yë¶ MmQ>© ~ZmBE&

10 101

1 1 1 11

1001000h gm¡ X B1 4 2 6

1000 100 10 10 10 10 1 1 h gm¡ X B

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nyd©nX, AZwdVu Am¡a ‘ܶ Ho$ g§»¶m H$mo {bIZm&

1) 3876 H$m AZwdVu g§»¶m H$m¡Z gr h¡?

XÎm g§»¶m H$m AZwdVu g§»¶m 1 OmoS>Zo go àmßV hmoVr h¡& 1 Omo{S>E&

3876 H$m AZwdVu g§»¶m → 3876 + 1 = 3877 Bgr àH$ma

7999

8407

9000

2) 5863 H$m nyd©nX H$m¡Z gm h¡?

nyd©nX kmV H$aZo Ho$ {bE 1 KQ>Zm h¡&

5863 H$m nyd©nX 5863-1 = 5862

Bgr àH$ma

4567

7659

8000

3) 6896 Am¡a 6898 H$s ~rM H$s g§»¶m H$m¡Z gr h¡, 6896 Am¡a 6898 H$s ~rM

H$s g§»¶m 6897 {ZåZ{b{IV g§»¶m H$s ~rM H$s g§»¶m H$s {ZarjU H$s{OE& ‘ܶ

H$s g§»¶m Am¡a Xÿgao Xmo g§»¶m H$m gå~ÝY nhMm{ZE& 3695, 3696, 3697

8406, 8407, 8408

9000, 9001, 9002

8999, 9000, 9001

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ñd¶§ H$s{OE

1) 3976 H$s AZwdVu g§»¶m __________.

2) 2900 H$s nyd©nX g§»¶m__________.

3) 3998 Am¡a 4000 H$s ‘mܶ g§»¶m__________.

4) 8476 H$s AZwdVu g§»¶m 8477 h¡& ¶h g§»¶m __________go A{YH$ h¡&

Aä¶mg 2.1

I. {ZåZ{b{IV g§»¶mAm| H$mo n{T>E : 1) 697 2) 809 3) 1,576 4) 5298

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

II. {ZåZ{b{IV g§»¶m ñWmZ ‘yë¶ MmQ>© ‘| {b{IE&

CXmhaU : 3594 h gm¡ X B3 5 9 4

1) 307h gm¡ X B

5) 8888 h gm¡ X B

2) 611h gm¡ X B

6) 9400 h gm¡ X B

3) 5926 h gm¡ X B

7) 9991h gm¡ X B

4) 6000h gm¡ X B

8) 7343h gm¡ X B

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III. {ZåZ{b{IV g§»¶mAm| H$mo eãXm| ‘| {b{IE :

CXmhaU : 2490 = Xmo hOma Mma gm¡ Zã~o&

1) 3524 = ____________________________________

2) 4967 = ____________________________________

3) 8740 = ____________________________________

4) 8001 = ____________________________________

IV. {MÌ ‘| {XIm¶o J¶o g§»¶m ñWmZ ‘yë¶ MmQ>© ‘o {b{IE Am¡a n{T>E&

CXmhaU :

10 10 10 1010011

1 1 1 11 1

1000h gm¡ X B3 5 4 8

10 1010011

1 1 111000

h gm¡ X B

1111

1111 1

10 10 101001000 h gm¡ X B

1000111

11 11 1

10 10100

h gm¡ X B

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V. {ZåZ{b{IV g§»¶mAmo§ H$s AZwdVu g§»¶m {b{IE:

1) 6820, ____________ 5) 4200, ____________

2) 3948, ____________ 6) 3999, ____________

3) 5201, ____________ 7) 2829, ____________

4) 7605, ____________ 8) 3007, ____________

VI. {ZåZ{b{IV g§»¶mAm| Ho$ nyd©nX {b{IE:

1) ____________, 3926 5) ____________, 4900

2) ____________, 5439 6) ____________, 5000

3) ____________, 6400 7) ____________, 3827

4) ____________, 3570 8) ____________, 4999

VII. {ZåZ{b{IV g§»¶mAmo§ H$s ‘ܶ H$s g§»¶m {b{IE:

1) 2769, ____________, 2771

2) 5490, ____________, 5492

3) 3999, ____________, 4001

4) 5888, ____________, 5890

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g§»¶mAmo§ H$m {dñVma ê$n

VrZ A§H$m|dmbr g§»¶mAm| H$m {dñVma H$aZm grIo h¡& A~ H$m¶© H$bmn H$a|Jo&

H$m¶© H$bmn : nona Ho$ Cn¶moJ go g§»¶m H$mS>© V¡¶ma H$s{OE& ¶m H$mS>© ~moS>© V¡¶ma

H$aHo$ Omo{S>E& ~moS>© H«$‘ Ho$ AZwgma Omo{S>E&

1000 100 10 1

CXmhaU 1: 2496 g§»¶m H$mS>© H$mo ñWmZ ‘yë¶ Ho$ AZwgma Omo{S>E&

2496 = 1000 +100

+10 10

+1 1 11 1 1

{dñVma én ‘| g§»¶m H$mo Bg àH$ma {bIVo h¡& = 2 × 1000 + 4 × 100 + 9 × 10 + 6 × 1

2496 = 2000 + 400 + 90 + 6

CXmhaU 2 : 3214 à˶oH$ A§H$ H$mo ñWmZ Ho$ AZwgma H$mS>© Omo{S>E&

3214 = 1000 +100

+10

+1 11 1

g§»¶mAm| H$mo {ZåZ én go {bIm OmVm h¡& = 3 × 1000 + 2 × 100 + 1 × 10 + 4 × 1

3214 = 3000 + 200 + 10 + 4

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ñd¶§ H$s{OE

{ZåZ{b{IV g§»¶mAm| g§»¶m H$mS>© Ho$ Cn¶moJ go {dñVma én {b{IE :- a) 5423 b) 3805

{dñVma g§»¶m H$mo gm‘mݶ én ‘| {bIZm Am¡a g§»¶m H$mS>© H$s g§»¶m {bIZm&

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

Aä¶mg 2.2

I. {ZåZ{b{IV g§»¶m H$mo {dñVma én ‘| {b{IE :

1) 6487 = ___________________________________________________

2) 2069 = ___________________________________________________

3) 5004 =___________________________________________________

4) 9678 = ___________________________________________________

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II. gm‘mݶ én ‘| g§»¶mAm| H$mo {b{IE:

CXmhaU

3 × 1000 + 4 × 100 + 8 × 10 + 2 × 1 =h gm¡ X B3 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 = = ________

BZ g§»¶mAmo° H$mo gm‘mݶ ê$n ‘| {b{IE

CXmhaU 1 : 8 × 1000 + 6 × 100 + 0 × 10 + 9 × 1 h gm¡ X B8 6 0 9

= 8000 + 600 + 0 + 9

= 8609

CXmhaU 2 : 9 × 1000 + 4 × 100 + 0 × 10 +1 × 5 h gm¡ X B9 4 0 5

= 9000 + 400 + 5

= 9405

ñd¶§ H$s{OE {dñVma ê$n H$s g§»¶mAm| H$mo gm‘mݶ ê$n ‘| {b{IE& a) 5 × 1000 + 3 × 100 + 9 × 10 + 2 × 1 b) 8 × 1000 + 2 × 10 + 3 × 1

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ñWmZ ‘yë¶- A§{H$V ‘yë¶

AmnZo A§H$ Ho$ ñWmZ _yë` Ho$ ~mao _| n‹T>m h¡& Amn CZHo$ ñWmZ _yë` Ho$ AZwgma n‹T>Zm Am¡a {bIZm OmZVo h¢ &

{ZåZ{b{IV CXmhaU H$mo {ZarjU H$s{OE :

4173

4237

4314

3125

à˶oH$ CXmhaU ‘o§ 3 Ho$ ñWmZ _yë` na Ü`mZ Xr{OE & ñWmZ _yë` Ho$ AZwgma 3

H$m _yë` H¡$go ~XbVm OmVm h¡? naÝVw `{X Amn 3 na {dMma H$ao, Š`m BgH$m _yë`

~XbVm h¡ ? Zht& Bg Vah EH$ A§H$ AnZm _yë` Zht ~XbVm & Bgo Š`m H$hVo h¢?

Bgo A§{H$V _yë` H$hVo h¢ & àË`oH$ A§H$ H$m ñd`§ H$m _yë` hmoVm h¡ {Ogo A§{H$V _yë`

H$hVo h¢& naÝVw ñWmZ _yë` CgHo$ ñWmZ Ho$ AZwgma ~XbVm ahVm h¡& {ZåZ CXmhaU

na Ü`mZ Xr{OE &

CXmhaU 1 : 34 78

A§{H$V ‘yë¶ 3 h¡ ñWmZ ‘yë¶ 3 × 100 = 300

5 847

A§{H$V ‘yë¶ 5 ñWmZ ‘yë¶ 5 × 1000 = 5000

2367

A§{H$V ‘yë¶ 2 h¡ ñWmZ ‘yë¶ 2 × 1 = 2

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CXmhaU 2 : 8 H$m A§{H$V ‘yë¶ 8

ñWmZ ‘yë¶ 8 × 100 = 800

ñWmZ ‘yë¶ 9 × 10 = 90

9 H$m A§{H$V ‘yë¶ 9 h¡&

3 8 9 5

CXmhaU 3 :

7 H$m A§{H$V ‘yë¶ 7 h¡

ñWmZ ‘yë¶ 7 × 1000 = 7000

ñWmZ ‘yë¶7 × 1 = 7

7 H$m A§{H$V ‘yë¶ 7 h¡

7 3 2 7

ñWmZ ‘yë¶ Am¡a A§{H$V ‘yë¶ Ho$ ~rM A§VaJ©V H$aZo H$m {dYmZ

ñWmZ ‘yë¶ Am¡a A§pŠV ‘yë¶ Ho$ ~rM H$mo A§Va kmV H$s{OE &

1) 2389 ‘| ñWmZ ‘yë¶ 3 Am¡a A§{H$V ‘yë¶ _| A§Va ³¶m h¡&

2389 go 3 H$m ñWmZ ‘yë¶ 300

3 H$m A§{H$V ‘yë¶ 3

A§Va 297

2) 6547 ‘| ñWmZ ‘yë¶ Am¡a A§{H$V ‘yë¶ 6 H$m A§Va ³¶m h¡?

6547 ‘| 6 H$m ñWmZ ‘yë¶ 6000

6 H$m A§{H$V ‘yë¶ 6

A§Va 5994

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3) 2998 ‘| A§Va kmV H$s{OE O~ ñWmZ ‘yë¶ A§{H$V _yë` XmoZm| 9 h¡

2998 ‘| 9 g¡H$S>o ñWmZ ‘| h¡ 900

ñWmZ ‘yë¶ 9 H$m XhmB© ñWmZ 90

A§Va 810

H$m¶© H$bmn : à˶oH$ g§»¶m H$mo XÎm ZrMo {X¶o J¶o h¡? ñWmZ ‘yë¶ Am¡a A§{H$V ‘yë¶ H$mo Omo{S>E aoIm H$mo ItMH$a A§{H$V H$s{OE&

g§»¶m A§{H$V ‘yë¶ ñWmZ ‘yë¶

1) 385 6 4 200

2) 23 67 3 4000

3) 4 673 2 30

4) 6907 9 900

5) 96 78 6 6

Aä¶mg 2.3

I. C{MV CÎma go [aŠV ñWmZ ^[aE: 1)

69749 H$m ñWmZ ‘yë¶ ............................

BgH$m A§{H$V ‘yë¶ .......................

7 H$m ñWmZ ‘yë¶ ............................

BgH$m A§{H$V ‘yë¶ .......................

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2)

30933 H$m ñWmZ ‘yë¶ ............................

BgH$m A§{H$V ‘yë¶ ..........................

3 H$m ñWmZ ‘yë¶ ............................

BgH$m A§{H$V ‘yë¶ ..........................

II. à˶oH$ àíZ ‘| Mma {dH$ën {X¶o J¶o h¡& ghr CÎma H$mo MwZH$a {b{IE:- 1) 4267 ‘| ñWmZ ‘yë¶ Am¡a A§{H$V ‘yë¶ 6 h¡ A§Va _______h¡ a) 0 b) 1 c) 9 d) 54

2) 3498 ‘| ñWmZ ‘yë¶ Am¡a A§{H$V ‘yë¶ 4 Ho$ ~rM H$m A§Va ________h¡ a) 496 b) 409 c) 396 d) 90

3) 5435 ‘| ñWmZ ‘yë¶ 5 Ho$ ~rM H$m A§Va ________h¡ a) 999 b) 4005 c) 4995 d) 5005

4) 1694 ‘| ñWmZ ‘yë¶ Am¡a A§{H$V ‘yë¶ A§{H$V ‘yë¶ g‘mZ hmo Vmo A§H$________h¡

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

gm_mÝ` A§Va g§»`mE±

{ZåZ{b{IV CXmhaUm| H$mo {ZarjU H$s{OE

AnZr eº$s Ho$ AZwgma ‘|T>H$, IaJmoe, {haU Am¡a {MVm Hy$XVo h¡& à˶oH$ ~ma do

g‘mZ Xÿar na Hy$XVo h¡& CZH$m Hy$XZm g§»¶m aoIm na {XIm¶m J¶m h¡& {ZarjU H$s{OE&

1)

990 995 1000 1005 1010 ?

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‘|T>H$ à˶oH$ Hy$X _| {H$VZo g§»¶m Hy$XVm h¡?

‘¢T>H$ Ho$ à˶oH$ Hy$X ‘| A§Va ³¶m h¡?

995 - 990 = 5, 1000 - 995 = 5

à˶oH$ ñVa ‘| 5 g§»¶mAm| H$mo Hy$Xm h¡&

A§V ‘| ‘|T>H$ {H$VZo g§»¶m Hy$Xm h¡&

1010 + 5 = 1015

2) BZHo$ Xmo H«$_mJV Hy$XZo H$s ~rM H$s Xÿar Š`m h¡?

1250 1300 1350

IaJmoe Ho$ à˶oH$ Hy$X> Ho$ ~rM H$m A§Va = (------------)

IaJmoe O~ A§{V‘ {~ÝXþ nhþ±MVo H$m¡Z gr g§»`m H$mo ñne© H$aVm h¡&

Cnamoº$ CXmhaU ‘| MrVm Am¡a {haZ H$s Hy$X kmV H$s{OE&

3)

2100 2300 2500 2700 2900 ?

{haZ à˶oH$ ~ma {H$VZr g§»`m Hy$XVm h¡& (-----------)

A§V ‘| H$m¡Zgr g§»¶m nhþ§MVm h¡? (-----------)

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4)

3025 4025 5025 6025 ? ?

MrVm à˶oH$ ~ma {H$VZm bå~m Hy$XVm h¡? (-----------)

Mm¡Wo Am¡a nm±Mdr Hy$X _| MrVm go Hy$XZodmbr g§»¶m nhMm{ZE &

CXmhaU 2 : {ZåZ{b{IV AZwH«$‘ ‘| AkmV g§»¶m {b{IE&

1) 1572, 1574, 1576, ______, ______, ______

Xmo H«$_mJV g§»¶mAm| H$m A§Va (1574 - 1572 = 2)

Bg{bE à˶oH$ ~ma OmoS>Zo Ho$ g‘¶ 2 OmoS>Zm&

1572, 1574, 1576, 1578, 1580, 1582

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

Xmo H«$‘JV g§»¶mAm| H$m A§Va (3500 - 3480 = 20)

Bg{bE AZwH«$‘ à˶oH$ ~ma 20 OmoS>Zm h¡&

3480, 3500, 3520, 3540, 3560, 3580

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

Xmo H«$‘JV g§»¶mAm| H$m A§Va (6505 - 6205) = 300

6205, 6505, 6805, 7105, 7405, 7705 Bg{bE AZwH«$‘ ‘| Eogo {bIm OmVm h¡&

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ñd¶§ H$s{OE

1) {ZåZ{b{IV AZwH«$‘ H$mo nyU© H$s{OE :

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

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

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

Aä¶mg 2.4

I. {ZåZ{b{IV g§»¶maoIm na AkmV g§»¶mAm| H$mo kmV H$s{OE: 1)

2100 2125 2150

2)

3250 3350 3450

3)

7501 8001 8501

4)

2040 3040 4040

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II. {ZåZ{b{IV AZwH«$‘ ‘| AkmV g§»¶mAm| H$mo kmV H$s{OE:

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

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

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

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

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

~S>r Am¡a N>moQ>r g§»¶mAm| H$s nhMmZ

{MÌ H$m {ZarjU H$s{OE& Mma g~Ordmbo Ho$ {Zdoe {X¶o J¶o h¡& {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE Am¡a {ZarjU H$s{OE&

arÁdmZ <5,256

Jm¡aå‘m <4,960

S>o{dS> <6,370’$mVr‘m <3,480

Mmam| ‘| H$m¡Z A{YH$ YZam{e H$m {Zdoe {H$¶m h¡? Mmam| ‘| H$m¡Z g~go H$‘ YZam{e H$m {Zdoe {H$`m h¡?

BZ àíZm| Ho$ CÎma OmZZo Ho$ {bE g§»¶mAm| H$s VwbZm H$s{OE& nhbr MaU ‘|

VrZ A§H$m| H$s g§»¶m H$s VwbZm H$s{OE& nwZ… g§»¶m H$s VwbZm H$s{OE A{YH$ V‘

ñWmZ ‘yë¶ Am¡a ~S>r Am¡a N>moQ>r g§»¶m H$mo nhMm{ZE&

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5,256 ; 4,900 ; 6,370 ; 3,480 Mma A§H$dmbr g§»¶m h¡& 5,4,6 Am¡a 3 H$m H«$‘

hOma d| ñWmZ ‘| h¡& Bg‘| 6 ~S>m Am¡a 3 N>moQ>m&

BZ g§»¶m ‘|, ~S>r g§»¶m 6370 Am¡a N>moQ>r g§»¶m 3480 h¡&

Bg‘|, S>¡{dS> g~go A{YH$ {Zdoe H$aVm h¡& (<6,370)

’$m{V‘m g~go H$‘ {Zdoe H$aVr h¡ & (<3,480)

CXmhaU 2 : EH$ {H«$Ho$Q> ‘¡M loUr, {Ibm{S>¶m| H$s Hw$b aZ {ZåZ h¡& Bg‘o§ A{YH$

aZ {H$gHo$ h¡? ݶyZVZ aZ {H$gHo$ h¡?

AemoH$ 1,856

’$m¶O 1,875

Omogo’$ 1,830

A‘rV1,890

AaqdX 1,821

¶hm± g§»¶mE°§ 1856, 1875, 1830, 1890, 1821 dh Mma A§H$dmbr g§»¶m& à˶oH$ ñWmZ ‘| A§H$ H$m {ZarjU H$s{OE&

hOma Ho$ ñWmZ Am¡a gm¡ d| ñWmZ ‘| A§H$ g‘mZ h¡& VwbZm H$aZo Ho$ Xgdm± ñWmZ br{OE&

XhmB© Ho$ ñWmZ ‘| A§H$ 5,7,3,9 Am¡a 2 Bg‘| 9 ~S>r g§»¶m Am¡a 2 N>moQ>r h¡&

~S>r g§»¶m1890 h¡&

N>moQ>r g§»¶m 1921 h¡&

{IbmS>r Omo A{YH$V‘ aZ {b¶m h¡ dh A{‘V (1890) h¡&

{IbmS>r Omo ݶyZV‘ aZ {b¶m h¡ dh AaqdX ( 1821) h¡&

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CXmhaU 3: {ZåZ{b{IV g§»¶m H$mS>© ‘| nhMm{ZE H$m¡Zgm A{YH$V‘ Am¡a ݶyZV‘

‘yë¶ H$mS>© h¡&

8692 8940 8629 8490 8094

hOma d| ñWmZ ‘| A§H$ g‘mZ h¡& gm¡ dm ñWmZ ‘o§ VwbZm H$s{OE& gm¡do ñWmZ ‘o§

6,9,4 Am¡a 0 Bg‘| A{YH$V‘ 9 h¡ Bg{bE ~S>r g§»¶m 8940, gm¡ d| ñWmZ ‘| 0

N>moQ>r g§»¶m h¡& N>moQ>r g§»¶m 8094 h¡&

ñd¶§ H$s{OE

A) ~S>r g§»¶m H$mo A§{H$V H$s{OE&

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

B) N>moQ>r g§»¶m H$mo A§{H$V H$s{OE&

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

AamohU - AdamohU H«$‘

nhbo Ho$ H$jm ‘o§ Amn VrZ A§H$dmbr g§»¶m nT>o h¡& AamohU Am¡a AdamohaU

H«$‘ & nwZ… ¶mX H$aHo$ AamohU H«$‘ {bIZm &

CXmhaU : 679, 368, 796, 697

AamohU H«$‘ : 368, 679, 697, 796

Bgr àH$ma Mma A§H$dmbr g§»¶m {bIVo h¡&

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CXmhaU : 5839, 5093, 5872, 5829

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

H$m¡Zgo {dYmZ go AamohU H«$‘ {bIm OmVm h¡& nhMmZ H$a {b{IE

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

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

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

CXmhaU : 2167, 1679, 3847, 500

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

H$m¡Zgm {dYmZ Cn¶moJ H$aVo h¡&

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

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

AamohU H«$‘ {bIZo ‘|

àW‘ hOma Ho$ ñWmZ H$mo {ZarjU H$s{OE&

{’$a g¡H$‹S>o H$m ñWmZ &

g§»¶m XhmB© ñWmZ ‘| &

{’$a BH$mB© ñWmZ &

‘Z ‘| {dMma aIHo$ N>moQ>r Am¡a ~S>r g§»¶m {b{IE gmo{ME 4 A§H$dmbr g§»¶m O~ eyݶ àW‘ ñWmZ ‘| {bIm OmVm h¡&

gmo{ME: O~ ewédmV ‘| ewݶ {bIm V~ 4 A§H$dmbr g§»¶m ~ZVr h¡ ³¶m?

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AamohU H«$‘ (N>moQ>o go ~S>m)CXmhaU 1 :

ZrMo {X¶o dOZm| H$m {ZarjU H$s{OE& CZH$mo AmamohU H«$‘ ‘| {bImo&

1000 J«°m‘ 5000 J«°m‘

2000 J«°m‘ 500 J«°m‘

AamohU H«$‘ _| H$m¡Zgr g§»¶m àW‘ {bIZm h¡?

àW‘ N>moQ>r g§»¶m {bIr OmVr h¡&

Bg‘| H$m¡Zgr g§»¶m N>moQ>r h¡? (500)

g§»`mAm| ‘| H$m¡Zgr N>moQ>r h¡? (1000)

5000 Am¡a 2000 ‘| H$m¡Zgr N>moQ>r h¡& N>moQ>r 2000 h¡,

A§V ‘o§ H$m¡Z gr g§»¶m eof h¡&

N>moQ>r g§»¶m ewê$ H$aHo$ ~m¶| Va’$ go Xÿgar g§»¶m {bIr OmVr h¡&

AamohU H«$‘

500 J«°m‘ 1000 J«°m‘ 2000 J«°m‘

5000 J«°m‘

AamohU H«$‘ = 500, 1000, 2000, 5000

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CXmhaU 2: {ZåZ g§»¶m H$mS>© H$mo AamohU H«$‘ ‘| {b{IE&

3920 2890 5436 3860

N>moQ>r g§»¶m H$mo nhMm{ZE & (2890)

eof g§»¶mAm| _| N>moQ>r g§»¶m H$mo H«$‘ ‘| {b{IE&

AamohU H«$‘ : 2890, 3860, 3920, 5436

¶mX a{IE: O~ AamohU H«$‘ ‘| {bIVo h¡ Vmo N>moQ>r g§»¶m nhbo ~mX ~S>r g§»¶m {bIVo h¢&

AdamohU H«$‘ (~S>o go N>moQ>m)

{ZåZ nmÌm| _|XÿY H$s ‘mÌm {ZarjU H$s{OE& AdamohU H«$‘ ‘o§ {b{IE&

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

AdamohU H«$‘ ‘| H$m¡Zgr g§»¶m àW‘ {bIr OmVr h¡? (~S>r g§»¶m)

~S>r g§»¶m H$m¡Zgr h¡? (6250)

eof g§»¶mAm| ‘| H$m¡Zgr ~S>r g§»¶m h¡? (5450)

A~ 4850 Am¡a 3500 h¡& Bg‘| H$m¡Z gr ~S>r g§»¶m h¡? (4850)

eof g§»¶m H$m¡Z gmo h¡? (3500)

~S>r g§»¶m ewê$ H$aHo$ eof g§»¶m VH$ {bIm OmVm h¡&

{ZarjU H$s{OE 6250, 5450, 4850, 3500

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hm CVaVm H«$‘ Amho.

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

∴ CVaVm H«$‘ ---------------, ---------------, ---------------, ---------------,

CXmhaU 2: {ZåZ g§»¶m H$mS>© H$mo AdamohU H«$‘ ‘| Omo{S>E&

5420 5840 4696 4890

• ~S>r g§»¶m H$mo nhMm{ZE& (5840)

• eof g§»¶mAm| ‘| à˶oH$ ~ma ~S>r g§»¶m H$mo nhMm{ZE

∴ AdamohU H«$‘ = 5840, 5420, 4890, 4696

¶mX a{IE: AdamohU H«$‘ ‘| àW‘ ~S>r g§»¶m Am¡a A§V ‘| N>moQ>r g§»¶m {bIr OmVr h¡&

ñd¶§ H$s{OE

A. {ZåZ g§»¶m H$mo AamohU H«$‘ ‘| à˶oH$ ñVa ‘| {b{IE:

5026 2650 6520 5640

B. {ZåZ g§»¶m H$mo AdamohU H«$‘ à˶oH$ ñVa ‘| Omo{S>E

3856 3656 3695 3965

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Aä¶mg 2.5

I. N>moQ>r g§»¶m H$mo A§{H$V H$s{OE Am¡a ~S>r g§»¶m H$mo {Q>H$ `' bJmB¶o&

CXmhaU : 3675, 3765, 3265 , 3475

1) 8820, 3790, 6530, 2905

2) 9297, 8470, 9680, 5875

3) 5600, 6500, 6005, 5006

4) 9270, 9267, 9207, 9217

II. {ZåZ g§»¶mAm| H$mo AamohU H«$‘ ‘| {b{IE& 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«$‘ : ________________________________________III. {ZåZ g§»¶mAm| H$mo AdamohU H«$‘ ‘| {b{IE&

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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XÎm g§»¶m ‘| go Mma A§H$modmbr g§»¶m ~ZmZm& : nyd© H$s H$jm ‘| VrZ A§H$dmbr g§»¶m ~ZmZm {gIm h¡& nwZ… ¶mX H$aHo$ Mma

A§H$dmbr g§»¶m ~Zm`|Jo &

Bg‘| H$m¡Z gr ~S>r g§»¶m h¡(gmV gm¡ {VanZ) 753 & g§»¶m 753 ‘| à˶oH$ A§H$ H$mo {ZarjU H$s{OE& A§H$ 7 ,5 Am¡a 3 H$m¡Z go H«$‘ ‘| h¡&

A§H$ H$mS>© ~Zo g§»¶m

5 3 7 →5 3 7 , 3 7 5 , 7 5 3 ,

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

Bg‘| H$m¡Z gr ~S>r g§»¶m h¡ ( gmV gm¡ {VanZ ) 753 g§»¶m 753 ‘| à˶oH$ A§H$ H$mo {ZarjU H$s{OE& A§H$ 7,5 Am¡a 3 H$m¡Z go H«$‘ ‘| h¡ (AdamohU H«$‘)

{ZarjU :- XÎm A§H$ ‘| ~S>r g§»¶m Am¡a A§H$ H$mo AdamohU H«$‘ ‘| Omo{S>E&.

BZ g~ go N>moQ>r g§»¶m H$m¡Z gr h¡= 357 (VrZ gm¡ gÎmmdZ h¡&)357 H$mo à˶oH$ A§H$ H$m {ZarjU H$s{OE

A§H$ 3,5 Am¡a 7 H$m¡Z go H«$‘ ‘| h¡? AamohU H«$‘

J{UV

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{ZarjU :

N>moQ>r g§»¶m XÎm ‘| go Omo{S>E& AamohU H«$‘ ‘| Omo{S>E&.

H$m¶©H$bmn 1:

H$jm Ho$ Q>o~b na {S>ã~m {Og‘| g§»¶m H$mS>© h¡& {S>ã~m ‘| {ZåZ{b{IV H$mS>© h¡&

8 0 3 7 6 9 5 1 4 2

Mma g§»¶m H$mS>© H$mo Mw{ZE Q>o~b na a{IE&

3 6 4 8 ‘m{ZE ¶h Mma H$mS>© h¡

Bg g§»¶m H$mS>© A{YH$V‘ Mma A§H$dmbr g§»¶m {b{IE AdamohU H«$‘ ‘| Omo{S>E& AdamohU H«$‘ ‘| Omo{S>E&

AdamohU H«$‘ ‘| 8 6 4 3

àmá 8, 6, 4, 3 (AmR> hOma N> gm¡ {M¶m{bg)

∴ ~S>r g§»¶m 8,643

3, 6, 4 Am¡a 8 go N>moQ>r g§»¶m H$m¡Z gr h¡? {b{IE ?

A§H$ H$mo AamohU H«$‘ ‘o§ {b{IE AamohU H«$‘ ‘o‘ A§H$ H$mo Omo{S>E&

g§»¶m AamohU H«$‘ ‘o§ h¡ 3 4 6 8

àmá g§»¶m 3,468 (VrZ hOma Mma gm¡ AS>gR> h¡)

∴ N>moQ>r g§»¶m = 3,468

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H$m¶© H$bmn 2: {S>ã~m ‘| go ‘Z¶m Mma H$mS>© {ZH$mbVr h¡& g§»¶m H$mS>© 7 , 5, 0 Am¡a 8 & Mma A§H$m|dmbr ~S>r g§»¶m BZ H$mS>© H$mo Cn¶moJ H$aVo hþE ~ZmB©E&

do AdamohU H«$‘ ‘| OmoS>H$a ~S>r g§»¶m àmá H$aVr h¡&

AdamohU H«$‘ ‘o§ 8 7 5 0

~S>r g§»¶m 8750 (AmR> hOma gmV gm¡ nƒmg)

∴ ~S>r g§»¶m 8,750

7 , 5 , 0 , 8 H$mo Cn¶moJ H$aHo$ N>moQ>r g§»¶m {b{IE& ‘Z¶m AamohU H«$‘ ‘| OmoS>Vr h¡&

AamohU H«$‘ : 0, 5, 7, 8do g§§»¶m 0,578 ~ZmVr h¡&

0578 VrZ A§H$r g§»`m0578 ñWmZ ~Xbm 5078 (nm±M hOma AmÇ>`mÎma)

nT>Zo Ho${bE 0,578 (nm±M gm¡ AmR>Îma )h¡& 0,578 ‘| hOma Zht h¡& Bg{bE ¶h VrZ A§H$dmbr g§»¶m h¡&

gmoMH$a dh {ejH$ H$mo XoIr, {ejH$ e§H$m H$mo Xÿa H$aVr h¡& ¶{X eyݶ A{YH$ V‘ ñWmZ ‘| hmo Vmo dh Zht ‘mZm OmVm h¡&

(0578 = nm±M gm¡ AR>Îma)

H$B© g§X^© ‘| eyݶ H$m ñWmZ n[adV©Z

H$aZo go 0578 H$mo 5078 {b{IE& A~ nm±M hOma AR>Îma h¡& ¶h Mma A§H$dmbr

g§»¶m h¡&

5078 Mma A§H$dmbr g§»¶m 0, 5, 7, Am¡a 8 H$mo Cn¶moJ go ~Zr h¡&

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¶mX a{IE

N>moQ>r g§»¶m ~ZmZo Ho${bE {ZåZ H$mo ¶mX a{IE& {X¶o hþAm A§H$m| ‘| eyݶ hmo Vmo

eyݶ H$mo ‘mZH$a A§H$ H$mo AamohU H«$‘ ‘| Omo{S>E&

eyݶ H$m ñWmZ H$m n[adV©Z H$s{OE AJbm A§H$ go Am¡a eof A§H$ {b{IE&

H$m¶© H$bmn 3 :

6,2,0 Am¡a 5 ‘| N>moQ>r Mma A§H$dmbr g§»¶m H$m¡Z gr h¡&

AamohU H«$‘ ‘| A§H$ H$mo Omo{S>E&

eyݶ H$mo AJbm A§H$ go n[adV©Z H$s{OE Am¡a eof g§»¶m {b{IE&

g§»¶m H$mo {b{IE& .

AamohU H«$‘ = 0, 2, 5, 6

= 2, 0, 5, 6

N>moQ>r g§»¶m = 2,056

gmo{ME : CXmhaU ‘| g~go N>moQ>r Mma A§H$dmbr g§»¶m 0256 h¡&

ñd¶§ H$s{OE

1) XÎm A§H$ , , ,6 9 7 1 Cn¶moJ H$aHo$

~S>r g§»¶m ~ZVr h¡ __________

N>moQ>r g§»¶m ~ZVr h¡ __________

2) , , ,4 0 3 7 XÎm Cn¶moJ H$aHo$

~S>r g§»¶m ~ZVr h¡ __________

N>moQ>r g§»¶m ~ZVr h¡ __________

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Aä¶mg 2.6

I. N>moQ>r g§»¶m H$mo A§{H$V H$s{OE Am¡a ~S>r g§»¶m H$mo {Q>H$ bJmBE&1) , , ,4 6 8 5 A§H$ go ~S>r g§»¶m ~ZVr __________ h¡&

2) 3,046 H$m CXmhaU __________ A§H$ g§»¶m h¡&

3) 0,734 H$m CXmhaU _________ A§H$ g§»¶m

4) , , ,3 1 0 9 N>moQ>r Mma A§H$ g§»¶m __________

II. {ZXoe AZwgma {b{IE &

1) 5, 8, 7, Am¡a 2 Mma A§H$mo H$s g§»¶m

Bg ‘| ~S>r g§»¶m __________

Bg ‘| N>moQ>r g§»¶m __________

2) 2, 8, 9, Am¡a 0 Ho$ Cn¶moJ Mma A§H$dmbr g§»¶m

Bg‘| ~S>r g§»¶m __________

Bg‘| N>moQ>r g§»¶m __________

3) 3, 5, 2, Am¡a 9 Ho$ Cn¶moJ go Mma A§H$dmbr g§»¶m

Bg‘| ~S>r g§»¶m __________

Bg‘| N>moQ>r g§»¶m __________

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KQ>H$ - 3 ¶moJ’$b

Bg KQ>H$ H$m Aܶ¶Z H$aZo Ho$ ~mX:

{~Zm g‘yh Ho$ Mma A§H$modmbr g§»¶m H$mo OmoS>Zm grI|Jo &

Mma A§H$dmbr g§»¶m H$mo eof go OmoS>|Jo &

X¡{ZH$ OrdZ ‘| àíZm| H$mo hb H$aZm Am¡a ñWmZ ‘yë¶ Ho$ AZwgma {bI|Jo &

‘mZ{gH$ OmoS>Zm Am¡a OmoS>Zo H$s ar{V OmZ|Jo &

VrZ A§H$modmbr g§»¶m H$mo OmoS>Zm grIm h¡& Bg CXmhaU H$m {ZarjU H$s{OE&

CXmhaU :

EH$ XþH$mZ ‘| {d{^Þ dñVw Xm‘ Ho$ gmW h¡& {ZarjU H$aHo$ àíZm| Ho$ CÎma {b{IE &

`1349``324`3

`2454

`3298`3847

`2420`

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Cg XwH$mZ ‘o§

● JUH$¶§Ì H$m Xm‘ ³¶m h¡? _____________

● {_Šgr H$m Xm‘ ³¶m h¡? _____________

● ao{S>¶mo H$m Xm‘ ³¶m h¡? _____________

● ‘mo~mBb H$m Xm‘ ³¶m h¡? _____________

{ZåZ{b{IV CXmhaUm| H$mo {ZarjU H$s{OE

EH$ ì¶{º$ Zo XþH$mZ go {d{^Þ dñVwE± IarXr h¡& CgH$m Hw$b Xm‘ ³¶m h¡?

`2454

`324

454

`3

OmoS>Zo Ho$ {bE ñWmZ ‘yë¶ go Omo{S>E&

BZHo$ Xm‘ g§Ho${VH$ {MÌm| ‘| {Z{X©ï> {H$¶m h¡ Omo{S>E& {ZarjU H$s{OE&

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49

= 1000 =100 =10 = 1

ã¶moamo g‘yh

hOma gm¡ Xgdm± BH$mB©

1) ‘mo~mBb H$m Xm‘ <2454

1000 1000100 100

10010010 10 10

10 10 11

11

2) JUH$¶§Ì H$m Xm‘ <324

100

100100

10 10 11

11

Hw$b Xm‘ <27781000 1000

100

100100

100

100 100

1001010

1010

1010

10

11

11

11

1 1

OmoS>Zo Ho$ {dYmZ H$mo {ZarjU H$s{OE Am¡a ñWmZ ‘yë¶ MmQ>© ‘| {b{IE&

h gm¡ X B1) ‘mo~mBb H$m Xm‘ <2) JUH$¶§Ì H$m Xm‘ <

2 4 5 43 2 4

2 7 7 8

Hw$b Xm‘ = ` 2778.

Ho$db Xmo hOma gmV gm¡ AR>Îma én¶o

ñVa 1

BH$mB© ñWmZ ‘| OmoS>m OmVm

~mX ‘| Xgdm±, gm¡, hOmadm°§ H«$‘e… OmoS>m OmVm h¡&

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50

2) EH$ J¥hrUrZo {ZåZ{b{IV dñVwAm| H$mo IarXm h¡& BgH$m Hw$b Xm‘ ³¶m h¡?

<1349

<2420

<

dñVw H$m Xm‘ gm§Ho$[VH$ {MÌ ‘| {Z{X©ï> {H$¶m h¡& Omo{S>E {ZarjU H$s{OE &

ã¶moam g‘yh hOma gm¡ Xgdm± BH$mB©

1) ¶§Ì H$m Xm‘ <2420

2) KS>r H$m Xm‘ <1349

1000 1000

100 100

100

10010 10

1000100 100 100 10 10 10 10

1 1 1 1 11111

Hw$b <37691000 1000

1000100

100 100 100

100 100 100

10 10 10 1010 10

1 1 1 1 11111

OmoS>Zo H$m {dYmZ H$mo {ZarjU H$s{OE Am¡a ñWmZ ‘yë¶ MmQ>© ‘| {b{IE&

ã¶m¡am h gm¡ X B OmoS>Zo H$m {dYmZO~ A§H$mo§ H$mo OmoS>m OmVm Am¡a H«$‘e… ñWmZ ‘| {bIm OmVm BH$mB© go ewé H$aVo h¡&

1) ¶§Ì H$m Xm‘ <2) KS>r H$m Xm‘ <

2 4 2 0

1 3 4 9

Hw$b < 3 7 6 9

Hw$b Xm‘ = < 3769

VrZ hOma gmV gm¡ CZgÎma

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51

ñd¶§ H$s{OE :1) ñWmZ ‘yë¶ MmQ>© ‘| dñVwE± H$m Xm‘ {bIH$a CZH$m Hw$b Xm‘ kmV H$s{OE :

<3847

<2420

a)

h gm¡ X B

<

<

Hw$b <

b) BgH$m ¶moJ’$b ³¶m h¡?

<3626 + <5243

h gm¡ X B

<

<

Hw$b < c) ¶moJ’$b kmV H$s{OE&

1) 5476 + 213

2) 3048 + 2851

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52

hm{gb go OmoS>Zm:

CXmhaU 1: {ZåZ{b{IV dñVwE± H$mo EH$ J«mhH$ Zo IarXm h¡& BZ dñVwAm| H$m Hw$b Xm‘ ³¶m h¡?

<3847

<2454

<3847 + <2454 = ? gm§Ho${VH$ {MÌ ‘| dñVwE± Ho$ Xm‘ {Z{X©ï> {H$¶m h¡& Omo{S>E {ZarjU H$s{OE&

ã¶m¡am

g‘yh hOma gm¡ Xgdm± BH$mB©

1000 10

1) Q>r.dr. H$m Xm‘ <3847

1000 1000

1000 1000

1000100 100

10 10

10 10 1 1 1 1111

2) ‘mo~mBb H$m Xm‘ <2454

1000 1000

10 1010 10 10

1 1 1 1

Hw$b Xm‘ <6301

1000 1000

1000 1000

1000 1000100 100

1001

100

100 100

100 100

é 6301 Hw$b Xm‘ N>h hOma VrZ gm¡ EH$ h¡&

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53

ñVa 1 7 Am¡a 4 BH$mB© ñWmZ ‘| OmoS>Zo go 11 àmá hmoVm h¡& Bg 1 Xgdm± Am¡a 1 BH$mB© h¡& BH$mB© ñWmZ ‘| 1 {b{IE& Xgdm± ñWmZ ‘| 1 {b{IE&

h gm¡ X B

5 2 4 72 4 5 4

1

ñVa 2

Xgdm°§ ñWmZ 1,4 Am¡a 5 OmoS>Zo go 10 Xg h¡& 10 Xgdm± 1 gm¡ Am¡a 0 Xg h¡& Xgdm± ñWmZ ‘| 0 {b{IE Am¡a 1 gm¡ do ñWmZ hm{gb {b{OE&

h gm¡ X B

5 2 4 72 4 5 4

0

1

ñVa 3

gm¡ do ñWmZ ‘| 1 gm¡ 2 gm¡ Am¡a 4 gm¡ h¡& OmoS>Zo go 7 gm¡ àmá hmoVm h¡& Bg‘| Ho$db gm¡ h¡&

Bg{bE hOma ‘| hm{gb Zht h¡&

h gm¡ XÀ B

5 2 4 72 4 5 4

7

0

1

ñVa 4

hOma H$o ñWmZ ‘| 5 Am¡a 2 OmoS>Zo go CZH$m ¶moJ 7 hOma h¡& 1 hm{gb H$m OmoS>Zo go 6 àmá hmoVm h¡&

h gm¡ XÀ B

5 2 4 72 4 5 4

77

0

1

dñVwAm| H$m Hw$b Xm‘ <6301 h¢& gmV hOma gmV gm¡ EH$ h¡&

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54

CXmhaU 2: {ZåZ{b{IV dñVwAm| H$mo EH$ J«mhH$ Zo IarXm h¡& Hw$b Xm‘ kmV H$s{OE&

<3298 <3847

1.Q>on [aH$mS>©a H$m Xm‘ 2.Q>r.dr. H$m Xm‘ Hw$b Xm‘

h gm¡ X B

3 2 9 8

3 8 4 7

7 1 4 5

Hw$b Xm‘ = <7,145 (gmV> hOma EH$ gm¡ n¡Vmbrg )

BH$mB© ñWmZ g§»`m OmoS>H$a Xm`o OmoS>Zm h¡&

CXmhaU 3:

3895, 2436, Am¡a 159 H$m ¶moJ ³¶m h¡?

nyd© CXmhaU Ho$ O¡go g§»¶m H$mo ñWmZ ‘yë¶ go hm{gb AmJo Zht {bIVo hþE ‘Z ‘| aI gH$Vo h¡&

h gm¡ X B

2 4 3 6

1 5 9

6 4 9 0

hm{gb AmJo Zht {bIVo hþE ‘Z ‘| aI gH$Vo h¡& 3,895

2 436 + 159 6,490

Hw$b Xm‘ = < 6,490

©

KTBS

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55

ñd¶§ H$s{OE 1) 4675 + 3452

h gm¡ X B

4 6 7 5

+ 3 4 5 2

2) 5368 + 2097

h gm¡ X B

5 3 6 8

+ 2 0 9 7

3) 359 + 4276+ 2573

+

h gm¡ X B

3 5 94 2 7 62 5 7 3

4) 3948 + 206 + 92

+

h gm¡ X B

3 9 4 82 0 6

9 2

‘m¡{IH$ àíZ

O~ g§»¶mAm| H$mo OmoS>Vo h¡ Vmo OmoS>Zo H$m {dYmZ ‘Z ‘| H$aZm h¡& à˶oH$ ì¶mpŠV

OmoS>Zo H$m àH«$‘ AnZo {dYmZ go H$aVo h¡& AmnH$m {dYmZ AbJ hmoVm h¡&

CXmhaU : gyMZm Ho$ AZwgma XþH$mZ ‘| ~Xbr h¡&

Bgr Vah Xmo CXmhaU {b{IE&

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

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

O~ ‘m¡{IH$ J{UV H$aVo h¡ Vmo H$B© {dYmZ H$m Cn¶moJ H$aVo h¡&

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56

{ZåZ{b{IV CXmhaUmo§ H$mo {ZarjU H$s{OE&

1) 328 Am¡a 241 H$m ¶moJ ³¶m h¡?

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

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

{dYmZ-1EH$ g§»¶m H$mo {dñVma H$aHo$

EH$ H«$‘ ‘| Omo{S>E& EH$ H$mo {dñVma H$aHo$ BH$mB©

ñWmZ ‘| Omo{S>E&

{dYmZ-2

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

328 329 369 569

+1 +40 +200

328 + 241 = 569

2) 5347 Am¡a 2635 H$m ¶moJ ³¶m h¡?

{dYmZ-1 5,347 + 2,635 = ?

= 5347 + (2000+600+30+5) 5347 + 2000 = 7347

7347 + 600 = 7947

7947 + 30 = 7977

7977 + 5 = 7982

¶moJ = 7982

{dYmZ-1 5347 + 2635 = ?

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

¶moJ = 7982

5347

+5 +30 +600 +2000

5352 79825382 5982

ñd¶§ H$s{OE : XÎm g§»¶mAm| ‘|, EH$ g§»¶m H$mo {dñVma H$s{OE Am¡a àW‘ g§»¶m go Omo{S>E

1) 643 + 250 2) 6145 + 2236

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57

H$m¶© H$bmn : OmoS>Zo H$m Iob{ZåZ{b{IV g§»¶mAm| H$mo MmQ>© H$mo {ZarjU H$s{OE& B‘br Ho$ ~rO H$mo Xmo

g§»¶mAm| H$mo ñne© n{H$b ¶m ñVå^ H$ao, CZH$m ¶moJ kmV H$s{OE& CZH$m ¶moJ’$b 5000 go ~T>Zm Zhr h¡&

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

5000 go A{YH$ hmo Vmo 5 A§H$ &

100 A§H$ àmá hmoZo go {dOoVm h¡& 150 A§H$ àmá hmoZo go dra H$mo{ee H$s{OE&

CXmhaU 2 {’$bmo{‘Zm {ZåZ ¶moJ H$aVr h¡&

1.+

382022006020

2.+

4213 2384451

3.+

298638006786

4.+

154663767922

{’$bmo{‘Zm 15 A§H$ àmá H$aVr h¡& ³¶m|? gmo{ME&

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58

H$m¶© H$bmn 1 ~§Xa H$s eamaV

¶h ~moS>© h¡& g§»¶m H$mS>© na àíZ h¡& à˶oH$ àíZ H$m OmoS> kmV H$aZm h¡&

nS>mog go ~§Xa AmH$ma H$B© H$mS>© bo {b¶m h¡&

~§Xa go H$mS>© {b¶m J¶o g§»¶m kmV H$s{OE Am¡a CZH$m ñWmZ {b{IE&

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

Aä¶mg 3.1

I. {ZåZ{b{IV {MÌ go ñWmZ ‘yë¶ MmQ>© {b{IE Am¡a CZH$m ¶moJ kmV H$s{OE&

1) hOma gm¡ Xgdm§ BH$mB©

1000100

100

100

100

100

10 10 10 1111

1000 1000

1000100 100

10 1010 10 10

1 1

h gm¡ X B

2) hOma gm¡ Xgdm§ BH$mB©1000

1000

10001000

1000 100100100

10 10

1000

1000

1000 10010 10

10

h gm¡ X B

II. g§»¶mAm| H$mo ñWmZ ‘yë¶ go OmoS>H$a {b{IE:-1) 6371 + 421

h gm¡ X B

2) 6039 + 2920

h gm¡ X B

3) 3487 + 5203

h gm¡ X B

4) 4675 + 2397

h gm¡ X B

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60

III. ¶moJ kmV H$s{OE: 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. OmXþB© dJ© H$s e³Vr OmXþB© dJ© n§{º$, ñVå^ Am¡a H$moZo go Omo{S>E& à˶oH$

~ma ¶moJ H$s VwbZm H$s{OE AnH$m {ZarjU XmoñVmo Am¡a {ejH$ H$mo ~VmB©E ñd¶§ H$s{OE& OmXwB© dJ© ‘| g§»¶m H$mo {ZarjU H$s{OE& Cgr àH$ma OmXwB© dJ© ~ZmB©E& {ejH$ Ho$ Cn¶moJ go ~ZmB©E&

1726 1558 2398

2566 1894 1222

1390 2230 2062

ñd¶§ H$s{OE : OmXþB© dJ© ‘| g§»¶m H$mo {ZarjU H$s{OE& Cgr àH$ma OmXwB© dJ©

~ZmB©E& {ejH$ Ho$ Cn¶moJ go ~ZmB©E&

2 7 69 5 14 3 8

àË`oH$ ñVå^ Am¡a n§{º$ H$s g§»`m H$mo Omo{S>E& {dH$U© H$s g§»`m H$mo Omo{S>E&

AmnH$m {ZarjU H$s{OE Š`m h¡& `moJ g_mZ h¡& dJ© H$mo {ZarjU H$s{OE Xÿgao dJ© H$s aMZm H$s{OE 12 OmoS>Zo go {_Ì Am¡a {ejH$ go MMm© H$s{OE&

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61

IV {ZåZ{b{IV àíZm| H$mo hb H$s{OE:

1) EH$ JmoXm‘ ‘| 2360 q¹$Q>b amJr h¡ Am¡a 3427 q¹$Q>b ‘¸$mB© h¡& JmoXm‘ ‘| Hw$b AZmO {H$VZm h¡?

2) n§Mm¶V joÌ ‘| 4275 nwéf, 4312 ‘{hbm Am¡a 1380 ~ƒo 1 Cg joÌ H$s Hw$b OZ g§»¶m {H$VZr h¡ >>?

3) EH$ gaH$g H$ånZr àW‘ emo ‘| é>>6375 Am¡a é 2895 Xÿgao emo ‘| àmá hmoVm& Cg {XZ H$ånZr H$s H$‘mB© ³¶m h¡?

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KQ>H$-4 KQ>mZm

Bg KQ>H$ H$mo Aܶ¶Z H$aZo Ho$ ~mX :

{~Zm hm{gb {b¶o Mma A§H$modmbr g§»¶m H$mo KQ>mZm grI|Jo &

Mma A§H$modmbr g§»¶m hm{gb boH$a KQ>m`|Jo &

X¡{ZH$ OrdZ ‘| ‘m¡{IH$ àíZ hb H$a|Jo &

‘mZ{gH$ KQ>mZm go KQ>mZm H$m àH«$‘ OëXr go H$a|Jo &

VrZ A§H$m|dmbr g§»¶m H$mo KQ>mZm nhbo H$jm ‘| nT>o h¡& 4 A§H$mo H$mo KQ>mZo Ho$

{bE {ZåZ{b{IV àíZm| H$s {ZarjU H$s{OE&

CXmhaU 1:

AZmO H$s XþH$mZ

OyZ Ho$ ‘hrZo ‘| 5890 Ho$ Or Mmdb XþH$mZ H$mo {X¶m J¶m h¡& Bg‘| 4650 Ho$ Or Mmdb ~oMo J¶o h¡? Cg ‘hrZo ‘| Mmdb {H$VZm ~Mm h¡?

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63

{Z¶‘ : àmá Mmdb H$s ‘mÌm go ~oMo J¶o Mmdb H$mo KQ>mB©¶o&

h gm¡ X B

àmá Mmdb H$s‘mÌm 5 8 9 0 Ho$Or ì¶dH$ë¶

~oMo J¶o Mmdb H$s‘mÌm

4 6 5 0 Ho$Or {d¶moOH$

eof Mmdb 1 2 4 0 Ho$Or A§Va

eof Mmdb H$s ‘mÌm = 1,240 Ho$Or

CXmhaU 2:

EH$ XþH$mZ H$mo 3268 Ho$Or amJr àmá h¡& OyZ ‘hrZo Ho$ A§V ‘| 125 Ho$Or amJr ~MVr h¡& Cg ‘hrZo Ho$ A§V ‘| ~oMr J¶r amJr H$s ‘mÌm kmV H$s{OE&

h gm¡ X B

àmá amJr H$s ‘mÌm 3 2 6 8 Ho$Or ì¶dH$ë¶

‘mÌm ~oMr J¶r amJr H$s ‘mÌm 0 1 2 5 Ho$Or {d¶moOH$

eof amJr 3 1 4 3 Ho$Or A§Va

{ZåZ{b{IV àíZmo§ H$mo hb H$s{OE :

1) 5647 ‘| go 3143 KQ>mB©E &

5647 ì¶dH$ë¶ h¡ Am¡a 3143 {d¶moOH$ ì¶dH$ë¶ ‘o§ {d¶moOH$ KQ>mB©E&

5 6 4 7 ì¶dH$ë¶ 3 1 4 3 {d¶moOH$

A§Va

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64

2) 9684 ‘| go 3041 KQ>mB©E&

Bg‘o§ ì¶dH$ë¶ ³¶m h¡? (9684)

{d¶moOH$ ³¶m h¡? (3041)

9684 H$mo 3041 KQ>mB©E

9 6 8 4 ì¶dH$ë¶ 3 0 4 1 {d¶moOH$

A§Va

ñd¶§ H$s{OE:

1) 5876 ‘o§ go 3755 KQ>mB©E& 2) 3800 ‘| go 6827 {ZH$m{b¶o&

G$U boZo go KQ>mZm

CXmhaU 1: EH$ ~¢H$ ‘| <8950 O‘m hþAm h¡& Bggo <5397

H$m {gbmB© ¶§Ì IarXm h¡& ImVo ‘| {H$VZo n¡go ~Mo h¡&

ImVo ‘| O‘m H$s J¶r YZamer = <8950

{ZH$mbr hþB© YZamer = <5397

eof YZamer = < ?

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65

EH$ àíZ H$m hb H$m {ZarjU H$s{OE&

ñVa : 1

ì¶mH$ë¶ ‘o§ 0 BH$mB© ñWmZ ‘| h¡& 0 _| go 7 KQ>m Zht gH$Vo & Bg{bE EH$ Xg boH$a BH$mB© ñWmZ ‘| Omo{S>E& 10+ 0 =10 BH$mB© 10 ‘| 7 H$mo KQ>mZo go 3 àmá hmoVm h¡& ì¶H$ë¶ Xg Ho$ ñWmZ ‘| 4 hmoVm h¡&

h gm¡ X B 8 9 5 0− 5 3 9 7 3

4 10

ñVa : 2

4 ‘| go 9 H$mo KQ>mZm g§^d Zht h¡& Bg{bE gm¡d| ñWmZ ‘| 10 boH$a XhmB© ñWmZ Omo{S>E 10 + 4 = 14 Xg & 14 ‘| 9 H$mo KQ>mZm go 5 àmá hmoVm h¡& 8 ñWmZ ‘| Nw>Q>m h¡&

8 9 5 0− 5 3 9 7 5 3

414

8 10

h gm¡ X B

ñVa : 3

ì¶H$ë¶ 8 ‘| 3 KQ>mZm na 5 àmá hmoVm h¡&

8 9 5 0− 5 3 9 7 5 5 3

414

8 10

h gm¡ X B

ñVa : 4

hOma do ñWmZ ‘| ì¶dH$ë¶ ‘| 8 ‘| go 5 KQ>mZm h¡& eof 3 h¡&

ImVo ‘| eof é 3553 {MÌ Ho$ Ûmam ^r àíZ H$mo hb H$a gH$Vo h¡& {ZarjU H$s{OE&

8 9 5 0− 5 3 9 7 3, 5 5 3

414

8 10 h gm¡ X B

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66

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

A§Va : 3 5 5 3 3 5 5 3

ImVo ‘| ~MV < 3,553

CXmhaU 2:

EH$ ñHy$b ‘| < 9750 ñnmoQ>©g Ho$ dñVwE± IarXZo Ho$ {bE àmá hmoVo h¢& Bg‘| ~mhar ñnmoQ>©g gm_J«r na IM© <5918 dm°br~mb 1 ~mb, {H«$Ho$Q> goQ> IarXZo Ho$ {bE Cn¶moJ H$aVo h¡& eof ‘| go H¡$a‘, Mog, B. IarXVo h¡& A§V… Iob Ho${bE Xm‘ kmV H$s{OE&

h gm¡ X B8 17 4 10

àmá YZamer = < 9 7 5 0

~mhar ñnmoQ>©g H$m Xm‘ = < 5 9 1 8

A§V… ñnmoQ>©g dñVwE± H$m Xm‘ = < 3 8 3 2

A§V… ñnmoQ>©g dñVwE± H$m Xm‘ = < 3,832

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67

1) 5074 ‘| go 3267 KQ>mBE&

5074 ì¶H$ë¶ Am¡a 3267 {d¶moOH$ h¡&

h gm¡ X B4 10 6 14

5 0 7 4 5 0 7 4 ì¶H$ë¶ 3 2 6 7 3 2 6 7 {d¶moOH$

1 8 0 7 1 8 0 7 A§Va

2) 6300 ‘o§ go 3928 KQ>mB©E&

6300 ì¶H$ë¶ Am¡a 3928 {d¶moOH$

h gm¡ X B

5 2 10 10

6 3 0 0 6 3 0 0 ì¶H$ë¶ 3 9 2 8 3 9 2 8 {d¶moOH$

2 3 7 2 2 3 7 2 A§Va

912

ñd¶§ H$s{OE

1) 9372 ‘o§ go 8045 KQ>ZmE 2) 8402 ‘| go 7835 KQ>mBE

KQ>mZo H$m {dYmZ ‘Z go {H$¶m OmVm h¡& ¶h {dYmZ EH$ ì¶{º$ go Xÿgao ì¶{º$ go AbJ hmoVm h¡& {ZåZ CXmhaU H$m {ZarjU H$s{OE&

{ZåZ{b{IV àíZm| H$mo {ZarjU H$s{OE

_m¡{IH$ àíZ

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68

CXmhaU 1: 673 ‘| go 241 KQ>mBE {dYmZ 1

XÎm g§»¶m go {d¶moOH$ H$mo {dñVma H$s{OE Am¡a KQ>mBE&

673 - 241 = ? 673 - (200 + 40 + 1) 673 - 200 = 473

473 - 40 = 433

433 - 1 = 432 673 - 241 = 432

{dYmZ 2{d¶moOH$ H$mo {dñVma H$s{OE Am¡a g§»¶m aoIm ‘o§ go KQ>mBE

673 - 241 = ? 673 - (200 + 40 + 1)

-200

432 632 672

-40-1

673 673 - 241 = 432

CXmhaU 2: 900 ‘| go 576 KQ>mBE

{dYmZ 1 900 - 576 = ? = 900 - (500 + 70 + 6) 900 - 500 = 400 400 - 70 = 330

330 - 6 = 324

900 - 576 = 324

{dYmZ 2 900 - 576 = ? = 900 - (500 + 70 + 6)

-500

324 824 894

-70-6

900

900 - 576 = 324

CXmhaU 3: 9000 ‘| go 5348 KQ>mBE

{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

8952 8992 9000-300 -40 -8

9000 - 5348 = 3652

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ñd¶§ H$s{OE: {ZåZ àíZ ‘| ì¶H$ë¶ H$mo {dñVma H$aHo$ A§Va kmV H$s{OE Am¡a A§Va kmV H$r{OE

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

Aä¶mg 4.1{ZåZ àíZm| H$mo hb H$s{OE& I.

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. {ZåZ{b{IV àíZm| H$mo hb H$s{OE& 1) EH$ {H$gmZ 3290 Ho$ Or Ádma CJmVo h¡& 1376 Ho$ Or Ka Ho$ {bE aIVm h¡ Am¡a eof ~oMVo h¡& {H$VZo Ho$.Or Ádma ~oMVm h¡&

{H$gmZ go CJmZodmbr Ádma = Ho$.Or.

{H$gmZ go Ja ‘| aIdmbr Ádma = Ho$.Or.

eof Ádma = Ho$.Or.

eof Ádma

2) EH$ ‘hrZo ‘| ‘OXÿa < 9500 H$‘mVo h¡& do <3268 IMm© H$aVo h¡& {H$VZr

YZamer ~MVr h¡& ‘hrZo ‘| H$‘mZodmbr YZamer ~MVr h¡&

‘hrZo ‘| H$‘mZodmbr YZamer =

‘m{gH$ IMm© =

~MV =

3) ñHy$b H$m¶©H«$‘ Ho${bE XmZr go <8250 BH$Å>m {H$¶o h¡& H$m¶©H«$‘ Ho$ ~mX

<894 ~MVo h¡. H$m¶©H«$‘ Ho$ ~mX {H$VZr YZamer ~MVr h¡?

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4) nmZr Q>¢H$ ^aZo Ho$ 8000 brQ>a nmZr H$s Adí¶H$Vm ¶{X Cg‘| 6398 brQ>a

nmZr h¡& Q>¢H$ ^aZo Ho$ {bE {H$VZm nmZr Ada Mm{hE?

Om{ZE:

KQ>Zm na g˶mnZ

1) 2836 ‘| 1329 KQ>mBE2 16 g˶mnZ :{d¶moOH$ + A§Va=

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 {d¶moOH$1 5 0 7 A§Va

2) 8000 ‘| go 2593 KQ>mBE 7 9 9 10 g˶mnZ :{d¶moOH$+A§Va =ì¶dH$ë¶

8 0 0 0

2 5 9 3+ 5 4 0 7

8 0 0 0 ì¶dH$ë¶2 5 9 3 {d¶moOH$5 4 0 7 A§Va

KQ>mZm Ho$ à˶oH$ àíZ H$s{OE&

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KQ>H$ -5 JwUZ’$b

Bg KQ>H$ H$mo Aܶ¶Z H$aZo Ho$ ~mX :

JwUZ’$b XmoharV Omo‹S> h¡ `h OmZ|Jo &

JwUZ’$b ‘| {d{^Þ Cn`wŠV nX OmZ|Jo &

‘yb JwUZ’$b g§H$ënZm nhMmZ|Jo&

b°{Q>g$ {dYmZ go JwUm H$a|Jo &

1 A§H$ Am¡a 2 A§H$ g§»¶m H$mo JwUm H$aZm (hm{gb Ho$ gmW 1 hm{gb Ho$ {~Zm 1 JwU’$b 9999 go ~T>Zm) OmZ|Jo &

X¡{ZH$ OrdZ ‘| JwUZ’$b àíZ g‘P|Jo &

JwU’$bZ kmV H$a|Jo &

EH$ A§H$ H$m JwUZ’$bZ nhbr H$jmAm| ‘| nT>o h¡&

CXmhaU : 1) 6 × 8 = 48 2) 12 × 6 = 72

D$na Ho$ CXmhaU ‘| Jwʶ, JwUH$ Am¡a JwU’$b H$mo nhMmZm&

CXmhaU Jwʶ JwUH$ JwU’$b

1

2

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JwUZ’$b XmoharV OmoS> h¡

H$m¶© H$bmn 3: amo{hV Ho$ nmg nm±M nopÝgb H$n h¡ à˶oH$ H$n ‘| 6 nopÝgb h¡& amo{hV Ho$ nmg {H$VZo nopÝgb h¡?

{MÌ H$mo {ZarjU H$s{OE&

{MÌ ‘| nopÝgb H$n H$mo {ZarjU H$s{OE& à˶oH$ H$n ‘| nopÝgb H$s g§»¶m H$s {JZVr Ir{OE Hw$b {H$VZo nopÝgb h¡& H$mo{ee H$s{OE&

6 + 6 + 6 + 6 + 6 = 30

nwZ… OmoS>Zo Ho$ àH«$‘ H$mo ¶mX H$s{OE&

6 × 5 = 30

JwUZ’$b XmoharV OmoS>Zm h¡&

JwUZ’$b {~Zm hm{gb

CXmhaU : EH$ {S>ã~o ‘| 8 a~a h¡& 4 {S>ã~m| {H$VZo a~a ‘| hmoVo h¡&

{S>ã~o H$s g§»¶m = 4

à˶oH$ {S>ã~o ‘| a~a H$s = 8

a~a H$s Hw$b g§»¶m = 8 + 8 + 8 + 8 = 32

8 H$mo 4 ~ma XmoharV

8 × 4 = 32

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8 × 4 = 32

Jwʶ JwUH$ JwUZ’$b

¶mX a{IE :

JwUZ’$b H$m àH«$‘ XmoharV OmoS>Zm&

g§»¶m {Ogo JwUm H$aZm h¡ dh Jwʶ h¡&

g§»¶m {Oggo JwUm H$aVo h¡ dh JwUH$$ h¡&

Xmo g§»¶m H$mo JwUm H$aZo Ho$ & n[aUm‘ H$mo JwUZ’$b H$hVo h¡&

JwUZ’$b H$m JwUY‘©

I . JwUZ’$b Ho$ JwUY‘© 1 go JwUm H$aZo na

CXmhaU 1: AmH¥${V H$m {ZarjU H$s{OE&

D$na Ho$ {MÌ {H$VZo ’y$b XmZ h¡?

VrZ

à˶oH$ nm°Q> ‘| {H$VZo nm¡Yo h¡?

EH$

VrZ nm°Q> ‘| Hw$b nm¡Yo {H$VZo h¡?

3 × 1 = 3

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CXmhaU 2 :

5 × 1 = 5

D$na Ho$ {MÌ ‘| {H$VZo Am¶V h¢? nm±M à˶oH$ Am¶V ‘| {H$VZo S>mQ> h¡? EH$ Am¶V ‘| Hw$b {H$VZo S>mQ> h¡ ? 5 × 1 = 5

D$na Ho$ CXmhaU ‘|

O~ {H$gr g§»¶m H$mo 1 JwUm H$aVo h¡ dhr JwUZ’$b àmá hmoVm h¡&

H$mo{ee H$s{OE :1) 10×1 =............................. 2) 1×55 =.............................

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

II. JwUZ’$b H$m Xÿgam JwUY‘© O~ H$moB© eyݶ go JwU H$aVo h¡&

XÎm CXmhaU H$mo {ZarjU H$s{OE &

CXmhaU ‘| JwUZ’$b eyݶ h¡& 7 × 0 = 0

15 × 0 = 0

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O~ {H$gr g§»¶m H$mo eyݶ go JwUm H$aVo h¡ JwUZ’$b eyݶ h¡& .

JwUZ’$b H$m H«$‘ {d{Z_` JwU

{MÌm| ‘| ZjÌ H$mo Xmo {d{^Þ ar{V go {H$¶m OmVm h¡&

jo{VO ñVå^ ‘| OmoS>Zm D$Üdm©Ya n§{º$ ‘| OmoS>Zm

{MÌ (a) ‘| ZjÌ H$m OmoS>Zm h¡ Am¡a

{ZåZ{b{IV àíZm| H$mo CÎma {b{IE&

{H$VZo ñVå^ h¡?

à˶oH$ ñVå^ {H$VZo ZjÌ h¡? ñVå^ ‘|

ZjÌm| H$s g§»¶m 5 × 3 = 15

{MÌ (b) ZjÌm| H$s ì¶dñWm Xo{IE&

{ZåZ{b{IV àíZm| Ho$ CÎma {b{IE&

{H$VZr n§{º$ h¡?

à˶oH$ n§{º$ ‘o§ {H$VZo ZjÌ h¡?

ZjÌ H$s Hw$b g§»¶m 3 × 5 = 15

Bg H$m¶© H$bmn go ³¶m {ZarjU H$aVo h¡?

5 × 3 = 3 × 5 = 15

XmoZmo ì¶dñWm ‘| JwUZ’$b g‘mZ h¡&

5 × 7 = 7 × 5 = 35

20 × 8 = 8 × 20 = 160

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Jwʶ Am¡a JwUH$ H$mo n[adV©Z H$aZo go Xmo g§»¶mAm| H$m JwUZ’$b g‘mZ hmoVm

h¡& Bg H$mo JwU’$b H$m H«$‘ {d{Z_` JwU H$hVo h¡&

Aä¶mg 5.1

I. ghr CÎma go Imbr ñWmZ ^[a¶o:

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. à˶oH$ g‘wƒ¶ Ho$ {bE OmoS> H$m XmoharV ê$n {b{IE :

CXmhaU :

3 + 3 = 6

2 × 3 = 6

1) ___________________

___________________

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2)

___________________

___________________

3)___________________

___________________

III. JwU’$b Ho$ JwUY‘© go Imbr ñWmZ ^[aE:

1) 75 × _____ = 75

2) 93 × 0 = _____

3) 37 × 42 = 42 × _____

4) 1 × 555 = _____

5) 15 × _____ = 20 × 15

6) 7623 × _____= 0

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JwUZ’$b nhmS>o ( 0 go 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

JwUZ’$b Ho$ {d{^Þ JwUY‘© {ejH$ Ho$ gh¶moJ go ~ZmB©E&

nhbr H$jm ‘| 2 A§H$modmbr g§»¶m go EH$ A§H$dmbr g§»¶m H$mo JwUm H$aZo {gIo h¡&

A~ 10, 100 Am¡a 1000 H$mo JwUm H$a|Jo&

gmaUr H$mo {ZarjU H$s{OE

JwUZ\$b 10, 100 Am¡a 1000

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{ZåZ{b{IV JwUZ’$b H$mo {ZarjU H$s{OE&

CXmhaU 1: 1) 9 × 10 = 9 × 1 Xg = 9 Xg = 90

2) 12 × 10 = 12 × 1 Xg = 12 Xg = 120

AmnH$m ³¶m {ZarjU h¡?

O~ g§»¶m H$mo 10 go JwUm H$aVo h¡ Vmo JwUZ’$b ‘| 0 eyݶ H$s ñWmZ JwUZ’$b

Ho$ Xm¶o Va’$ ahVr h¡&

CXmhaU 2: 1) 9 × 100 = 9 × 1 gm¡ = 9 gm¡ = 900

2) 12 × 100 = 12 × 1 gm¡ = 12 gm¡ = 1200

Cnamoº$ CXmhaU ‘| ³¶m {ZarjU H$aVo h¡. O~ g§»¶m H$mo 100 go JwUm H$aVo

àmá JwUZ’$b Xmo eyݶ JwUZ’$b Xm¶o go Xmo eyݶ hmoVo h¡&

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

O~ g§»¶m H$mo 1000 go JwUm H$aVo h¡ Vmo JwUZ’$b ‘| VrZ eyݶ hmoVo h¡&

Cnamoº$ CXmhaU ‘| O~ EH$ g§»¶m H$mo JwUm H$aVo h¡& {Og‘| A§V ‘| eyݶ hmo&

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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Aä¶mg 5.2

I. C{MV CÎma go Imbr ñWmZ ^[a¶o:

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$ Am¡a Xmo A§H$ g§»¶m H$m JwUZ’$b

H$m¶© H$bmn: 15 ~ƒo H$mo ~wbmB¶o Am¡a n§{º$ IS>o hmoZo Ho$ {bE ~mo{bE& CZH$mo N>mVo H$m {MÌ Xr{OE Am¡a Xm‘ é 160.00 {b{IE& ~ƒo H$mo H$mS>© hmW ‘| nH$S>Zo {bE H${h¶o& EH$ ~ƒo H$mo ~wbmB©¶o Am¡a {ZåZ{b{IV àíZm| Ho$ CÎma ‘mby‘ H$s{OE&

{ejH$ : EH$ n§{º$ ‘| {H$VZo ~ƒo IS>o h¡ ?

~ƒo : 15 ~ƒo

{ejH$ : KVar H$m H«$¶ ‘yë¶ ³¶m h¡?

~ƒo : é 160

{ejH$ : {H$VZo ~ƒo Ho$ nmg H$mS>© 160.00 Ho$ h¡?

~ƒo : 15 ~ƒo

[ejH$ : 160 g§»¶m {H$VZo ~ma hmoVr h¡?

~ƒo : 15 ~ma JwUZ’$b H$aZo H$s H$mo{ee H$s{OE 160×15

80016002400

160 H$mo 5 go JwUm H$r{OE`160 H$mo 5 go JwUm H$r{OE

15 N>Var Ho$ Hw$b H«$¶ ‘yë¶ =é 2400

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CXmhaU 1:

EH$ bmar ‘o§ 142 ߶mO Ho$ ~moao h¡& ߶mO Ho$ Hw$b {H$VZo ~moao h¡& {Og‘| 12

bmar ‘| {H$VZr ߶mO hmoVr h¡&

߶mO H$s Hw$b g§»¶m = 142 × 12

JwUZ’$b Ho$ {Z¶‘ Ho$ AZwgma 12 JwZH$ h¡ {Og‘| 1 Xg Am¡a 2 EH$ h¡ àW‘

Jwʶ 142 H$mo 2 go JwZm H$s{OE 142 H$mo 2 EH$ Am¡a 142 H$mo 10.

ñVa 1 : 142 H$mo 2 go JwUm H$s{OE 284142 2#x

ñVa 2 : 142 H$mo 1 Xg

ñVa 3 : O~ JwUZ’$b H$mo OmoS>Vo h¡ Vmo ߶mO H$s Hw$b g§»¶m

1704 ߶mO H$s ~moar h¡&

CXmhaU 2 :

EH$ n¡H$Q> ‘| 24 noZ h¡& EH$ XþH$mZXma Ho$ nmg 100 n¡H$Q> h¡& XþH$mZ ‘| {H$VZo noZ hmoVo h¡?

EH$ n¡H$Q> ‘| noZ H$s g§»¶m = 24

XþH$mZ ‘| n¡H$Q>m| H$s g§»¶m = 100

noZm| H$s Hw$b g§»¶m = 2400

1420142 10#x

284

17041420

142 2#x

240024 100#x

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Aä¶mg 5.3

I. {ZåZm| H$mo JwUm H$s{OE :

1)31 × 4 2)

50 × 3 3)210 × 40

4)52 × 22

5)231 × 31

6)102 × 43

II. {ZåZ{b{IV àíZm| H$mo hb H$s{OE 1) 1 ‘rQ>a H$nS>m H$m Xm‘ é 32 h¡& 4 ‘rQ>a H$nS>m H$m Xm‘ ³¶m h¡?

2) ¶{X 1 {H$bmoJ«m‘ Mmdb H$m Xm‘ é 40 h¡& 5 {H$bmoJ«m‘ Mmdb H$m Xm‘ ³¶m h¡?

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3) EH$ {gZo‘mhm°b ‘| 32 n§{º$¶m± h¡ Am¡a à˶oH$ n§{º$ ‘| 42 grQ> h¡& {gZo‘m hmb ‘| grQ>mo§ H$s g§»¶m kmV H$s{OE?

4) gmo‘Þo 122 BªQ> à˶oH$ {XZ ‘| ~ZmZm h¡& 24 {XZ ‘| BªQ>mo§ H$s g§»¶m kmV H$s{OE?

JwUZ’$b hm{gb go

H$m¶© H$bmn :

am‘m EH$ XþH$mZ ‘| {nVm Ho$ gmW OmH$a 3

gm~wZ IarXVo h¡& à˶oH$ gm~wZ <18 H$m h¡&

XþH$mZXma H$mo {H$VZr YZamer XoZm h¡&

³¶m {nVm am‘m H$s ‘XX H$a|Jo? gmo{ME&

XþH$mZ

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am‘m {nVm H$mo {ddaU XoVm h¡& {nVm ‘‹¡Zo 3 gm~wZ {b¶m hÿ± & à˶oH$ gm~wZ H$m

Xm‘ <18& Bg{bE < 54 ^aZm h¡& ³¶m ¶h ghr h¡? {nVmOr Zo nyN>m ¶h H¡$go

kmV {H$¶m h¡&

ñVa 1: 8 H$mo 3

8 × 3 = 24

1 8 × 3 2

4

4 BH$mB© Am¡a 2 hm{gb (Xgdm§ ñWmZ) ñVa 2 : 1 H$mo 3 go JwUm H$s{OE 1 × 3 = 3 Xg 2 H$mo JwUZ’$b ‘| Omo{S>E 3 + 2 = 5

5 H$mo Xg Ho$ ñVå^ ‘| {b{IE

1 8 × 3 2

54 3 gm~wZ H$m Xm‘ <54

CXmhaU 1 : EH$ ~¡J ‘| 47 Z[a¶b h¡& 8 ~mJm| Ho$ Hw$b Zm[a¶b H$s g§»¶m ³¶m

h¡& Zm[a¶b H$s Hw$b g§»¶m ³¶m h¡&

Zm[a¶b H$s Hw$b g§»¶m 47 × 8

ñVa 1: 7 H$mo 8 go JwUm H$s{OE 4 7×8 6

5 7 × 8 = 56

6 BH$mB© Am¡a hm{gb 5 Xgdm§ ñWmZ ‘| h¡&

ñVa 2: 4 H$mo 8 go JwZm H$s{OE

32 + 5 = 37.

4 7×8376

5 5 JwUZ’$b H$mo Omo{S>E

7 BH$mB© ñWmZ ñWmZ Am¡a 3 gm¡ao ñWmZ ‘| h¡. Zm[a¶b H$s Hw$b

g§»¶m = 376

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CXmhaU 2:

¶{X EH$ n§Im H$m Xm‘ 655 hmo Vmo 15 n§Imo H$m Xm‘ ³¶m h¡?

1 n§Im H$m Xm‘ = <655

15 n§Imo H$m Xm‘ = <9825

Aä¶mg 5.4

I. {ZåZm| H$mo JwUm H$s{OE

1)75 × 8

2)627 × 7 3)

445 × 6

4)83 × 26

5)75 × 48

6)395 × 24

II. {ZåZm| H$mo hb H$s{OE

1) EH$ ñHy$b H$m bS>H$m ha ‘hrZo <25 ~MmVm h¡& 1 df© ‘| {H$VZo YZamer

~Mm`oJm ?

3275

9825655

655 15#x

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2) EH$ n¡H$Q> ‘| 75 Mm°H$boQ> hmoVo h¡& 7 n¡H$Q> ‘| {H$VZo Mm°H$boQ> hmoVo h¡?

3) EH$ W¡bo ‘| 25 Ho$.Or Mmdb h¡& 68 W¡bo ‘| Mmdb {H$VZo {H$bmo Ho$ hmoVo h¡?

4) EH$ nwñVH$ ‘| 96 nÞo h¡& 45 nwñVH$ ‘| {H$VZo nÞo hmoVo h¡?

5) ñHy$b H$m¶©H«$‘ H$m IMm© <900 & Eogo 11 H$m¶©H«$‘m| H$m Hw$b IMm© ³¶m h¡?

6) ZrVm EH$ ‘hrZo ‘| 200 {Ibm¡Zo ~ZmVr h¡& 3 df© ‘o§ dh {H$VZo {Ibm¡Zo

~ZmVr h¡?

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JwUZ’$b H$m Am¡a EH$ {dYmZ grI|Jo {OgH$m Am{dîH$ma OmZ Zo[n¶a (John Na-pier) {H$¶m h¡&

CXmhaU 1 : 43 × 6

1

84

4

2

3

6

2 5(4+1=5)

8

ñVa :

Xmo ~m°³g ~ZmB©E&

Jwʶ ~m°Šg Ho$ D$na n§pŠV ‘| {b{IE&

JwUH$ H$mo ~m`t Va’$ {b{IE&

XhmB© ñWmZ H$mo 6 go JwUm H$s{OE Am¡a

JwUZ’$b H$mo àW‘ ~m³g ‘o {b{IE&

4 × 6 = 24

BH$mB© H$mo JwUm H$s{OE Am¡a Xÿgao ~m³g

‘| {b{IE&

3 × 6 = 18

CXmhaU Ho$ O¡go Omo{S>E&

43 × 6 = 258. ~S>r g§»¶mAm| H$m JwUZ’$b kmV H$aZo Ho$ {bE Cn¶moJ H$aVo h¡&

CXmhaU 2 : 57 × 48

2

4

4

7(1+4+0+2=7)

3(0+5+8=13)

6

20

0

5

6

8

8

2

75

1 57 × 48 = 2736

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CXmhaU 3 :

273 H$mo 36 go JwUm H$s{OE

0

4

9

1

9(1+6+2=9)(1+2+4+1+0=8) (2+1+9=12)

28 8

06

0

2 2 6

1

18

2

72 3

3

1 273 × 36 = 9828

Aä¶mg 5.5

I. b°{Q>g JwUZ’$b Ho$ Cn¶moJ JwUZ’$b kmV H$s{OE&

1) 52× 95 2

9

52 × 9 =

2) 712 × 57 1 2

5

712 × 5 =

3) 75 × 36 7 5

3

6

75 × 36 =

4) 242 × 422 4 2

4

2

242 × 42 =

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JwUZ’$b H$m AZw‘mZ

{MÌ (1)

< 99

{MÌ (2)

<102

{MÌ H$mo {ZarjU H$s{OE

{MÌ 1 ‘| Q>r-eQ>© H$m Xm‘ ³¶m h¡? <99

{MÌ 2 ‘| Q>r-eQ>© H$m Xm‘ ³¶m h¡? < 102

gm‘mݶV… Q>r-eQ>© H$m Xm‘ <100 Ho$ nmg h¡& Bg g§H$ënZm H$mo AZw‘mZ H$hVo h¡&

¶h Cnm¶m¡{JH$ h¡ O~ ghr CÎma Zht ‘mby‘ hmoVm h¡& ghr JwUZ’$b go àmá

CÎma ^r Cn¶moJr h¡&

{Z¶‘ : ¶{X g§»¶m AmYr hmoVr h¡ Cgo A{YH$ 10,100,1000 ¶{X H$mo ~T>mBE&

¶{X AmYr go H$‘ hmo ݶyZV‘ 10,100,1000 ¶[X

CXmhaU 64 - Xg AZw‘{ZV 60 h¡&

68 - Xg AZw‘{ZV 70 h¡&

65- Xg AZw‘{ZV 70 h¡&

Bg{bE ≥ 5 AZw‘{ZV AJbo nyU© g§»¶m

< 5 AZw‘{ZV nyd© nyU© g§»¶m

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CXmhaU 1:

10 Ho$ ZOX{H$ Jwʶ Am¡a JwUH$ kmV H$s{OE&

10 H$mo A§{H$V H$s{OE

76 → 80

34 → 30

dmñV{dH$ JwUZ’$b go

CXmhaU 2 :

286 × 32 H$m AZw‘m{ZV JwUZ’$b àW‘ g§»¶m gm¡ Ho$ ZOXrH$ Xÿgar g§»¶m

Xg Ho$ ZOXrH$

10, 100 Ho$ ZOXrH$

286 → 300

32 → 30

dmñV{dH$ JwUZ’$b

30476 34

25842280

#x

240080 30#x

572286 32

91528580

#x

9000300 30#x

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Aä¶mg 5.6I. Jwʶ Am¡a JwUH$ H$m JwUH$’$b kmV H$s{OE

1) 44 × 39 2) 19 × 21 3) 23 × 28

4) 86 × 53 5) 77 × 62

II. Jwʶ gm¡ Ho$ ZOXrH$ Am¡a JwUH$ Xg ZOXrH$ JwUZ’$b kmV H$s{OE

1) 308 × 17 2) 240 × 42

3) 195 × 34 4) 335 × 23

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KQ>H$ -6 {d^mOZ

Bg KQ>H$ H$mo Aܶ¶Z H$aZo Ho$ ~mX :

g‘yh go {d^mOZ grImZm &

S>mQ²>g Ho$ Cn¶moJ {d^mOZ grImZm &

{d^mOZ XmoharV KQ>mZm h¡&

JwUZ’$bZ Am¡a {d^mOZ H$s VwbZm &

^mÁ¶ go {d^mOZ EH$ eof Ho$ gmW H$aZm &

X¡{ZH$ OrdZ ‘| Cn¶moJr àíZ H$mo {d^mOZ H$aZm &

g‘mZ g‘yh go {d^mOZ H$aZm

H$m¶© H$bmn : H$aZ Ho$ nmg 12 J|X h¡, do Mma XmoñV am‘, Jmonmb, AemoH$ Am¡a amOy H$mo g‘mZ ê$n ‘| XoZo MmhVo h¡&

J|Xm| H$mo {ZarjU H$s{OE Omo H$aZ Ho$ nmg h¡&

Mma XmoñVm| H$mo {dV[aV H$aZo Ho$ {bE Amn ‘XX H$a gH$Vo h¡?

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à˶oH$ XmoñV H$mo EH$ Jo§X XoVo? {dVaU Ho$ ~mX H$aZ nmg {H$VZo Jo§X h¡?

am‘ Jmonmb AemoH$ amOy H$aU Ho$ nmg eof J|X

Xÿgar ~ma à˶oH$ 2 J|X Xo gH$Vm h¡ ³¶m? H$aZ Ho$ nmg {H$VZo J|X

am‘ Jmonmb AemoH$ amOy H$aZ Ho$ nmg eof J|X

Am¡a EH$ J|X Xo gH$Vm h¡ ³¶m? A~,

H$aU Ho$ nmg eof Jo§X {H$VZo h¡ ?

am‘ Jmonmb AemoH$ amOy H$aZ Ho$ nmg eof J|X

Zhr§ h¡&

H$aZ Ho$ à˶oH$ XmoñV Ho$ nmg VrZ J|X

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Bg{bE 12 J|Xm| 4 g‘yh ‘| à˶oH$ H$mo 3 J|X àmá hmoVm h¡&

`' {MÝh H$m Cn¶moJ H$aHo$ 124=3

g‘mZ {dVaU ¶m ^mJ H$aZo H$mo {d^mOZ H$hVo h¡&

CXmhaU 1: 4 XmoñV EH$ Am‘ Ho$ ~mJ H$mo OmH$a 32

Am‘ VmoS>Vo h¡& ¶h Am‘ g‘mZ ê$n go {dV[aV

H$aVo h¡ Vmo à˶oH$ H$mo {H$VZo Am‘ àmá hmoVo h¡&

XmoñVm| H$s g§»¶m = 4

{dV[aV H$aZo Ho$ Am‘ H$s g§»¶m = 32

à˶oH$ XmoñVmo§ H$mo àmá Am‘ H$s g§»¶m = 32÷ 4=8

S>mQ²>g go {d^mOZ

H$m¶© H$bmn 1: EH$ Q>moH$ar ‘| 16 ’y$b h¡& BZ ’y$bm| H$mo Xmo g‘mZ g‘yh ‘o§ {dVaU

H$s{OE&

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Bg CXmhaU à˶oH$ ’y$b H$mo S>mQ> ‘mZ H$a {b¶o h¡&

A~ {H$VZo S>mQ²> ‘| boZo h¡?

Xmo g‘yh BZH$mo OmoS> gH$Vo h¡? H$mo{ee H$s{OE&

à˶oH$ g‘yh ‘| AmR> S>mQ²> h¡&

BgH$mo {d^mOZ Ho$ ê$n ‘| H¡$go {bIVo h¡&

16 2 = 8

CXmhaU 1:

EH$ {S>ã~o ‘| 15 Mm°H$boQ> h¡& BgH$mo 3 g‘yh ‘| {dV[aV H$s{OE& à˶oH$ g‘yh

‘| {H$VZo Mm°H$boQ> hmoVo h¡?

• • • • • • • • • • • • • • •

VrZ g‘yh ‘| OmoS>Zo H$s H$mo{ee H$s{OE&

à˶oH$ g‘yh ‘| Mm°H$boQ> H$s g§»¶m=_________

BgH$mo {d^mOZ ê$n ‘| {b{IE

{d^mOZ XmoharV KQ>mZm h¡&

{d^mOZ g‘mZ g§»¶m H$m XmoharV KQ>mZm h¡&AWdm KQ>mZo H$m gm‘mݶ én {d^mOZ h¡&

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H$m¶© H$bmn : amYm Ho$ {nVmOr Zo 20 H$hmZr H$s nwñVH$ br h¡& ¶{X dh 5 nwñVH$ EH$ {XZ ‘| nT>Vr h¡& {H$VZo {XZm| ‘o§ dh nyao nwñVH$ nT>Vr h¡&

³¶m Amn amYm H$s ‘XX H$aZo Ho$ {bE V¡¶ma h¡ {H$ 20 nwñVH$ nT>o&

do nm±M nwñVH$ à[V{XZ nT>Vr h¡&

EH$ {XZ Ho$ ~mX nwñVH$m| H$r g§»¶m

20 - 5 = 15

Xÿgao {XZ Ho$ ~mX

15 - 5 = 10

Vrgao {XZ Ho$ ~mX

10 - 5 = 5

Mm¡Wo {XZ

5 - 5 = 0

Mm¡Wo {XZ Ho$ ~mX eof nwñVH$ h¡ ³¶m?

KQ>mZm Am¡a {d^mOZ ‘| gå~ÝY h¡&

{d^mOZ g‘mZ g§»¶m H$m XmoharV {X`o ga§d`m go KQ>mZm h¡&

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Aä¶mg 6.1

I. {ZåZm| H$m {d^mOZ XmoharV KQ>mZo go H$s{OE

CXmhaU 20 4 =

20 - 4 = 16

16 - 4 = 12

12 - 4 = 8

8 - 4 = 4

4 - 4 = 0

20 4 = 5

1)

18 3 =

18 - 3 =

- 3 =

- 3 =

- 3 =

- 3 =

- 3 =

18 3 =

2)

25 5 =

25 - 5 =

- 5 =

- 5 =

- 5 =

- 5 = 0

25 5 =

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3)

40 10 =

40 - 10 =

- 10 =

- 10 =

- 10 =

40 ÷10=

4)

35 7 =

35 - 7 =

- 7 =

- 7 =

- 7 =

- 7 =

35 ÷ 7=

{d^mOZ Am¡a JwUZ’$bZ Ho$ gå~ÝY H$m VwbZm H$s{OE

hm±! JwUZ’$bZ XmoharV OmoS>Zm g‘mZ g§»¶m H$m h¡& {d^mOZ KQ>mZo H$m XmoharV g‘mZ g§»¶m H$m h¡&

{d^mOZ Am¡a

JwUZ’$bZ Ho$

~rM gå~ÝY

OmZVo h¡?

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100

JwUZ’$bZ Am¡a {d^mOZ Ho$ ~rM gå~ÝY

CXmhaU 1: {MÌ H$mo {ZarjU H$s{OE

{MÌ : (a)

{MÌ (a) Vmam| H$s g§»¶m H$mo {JZVr H$s{OE&

n§{º$¶m| H$s g§»¶m Am¡a Vmam| H$s g§»¶m H$mo {ZarjU

H$s{OE& 20 Vmao 4 n§{º$¶m| ‘| {dV[aV hmoVo h¡& à˶oH$

n§{º$ ‘| 5 Vmao h¡& BgH$mo {d^mOZ Am¡a JwUZ’$b ‘|

{bIm OmVm h¡&

4×5=20 JwUZ’$b go

204=5 {d^mOZ go

{MÌ (b)

{MÌ (b)

20 Vmam| H$mo 5 n§{º$¶m| ‘| {d^mOZ {H$¶m h¡& à˶oH$

‘| 4 Vmao h¡& ³¶m Amn {d^mOZ Am¡a JwUZ’$b Ho$

ê$n go H$a gH$Vo h¡&

5 × 4 = 20 JwUZ’$bZ go

20 ÷ 5 = 4 {d^mOZ go

gyMZm : JwUZm’$bZ ‘| Xmo g§»¶mAm| H$m JwUZ’$bZ h¡& {d^mOZ ‘| AkmV kmV

H$aVo h¡ O~ Xÿgar g§»¶m Am¡a JwUZ’$b ‘mby‘ h¡&

CXmhaU 2: {d^mOZ kmV H$s{OE 6 × 8 = 48

{d^mOZ go 48 ÷ 6 = 8 48 ÷ 8 = 6

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CXmhaU ‘| {d^mOZ KQ>Zm {b{IE

CXmhaU : 8×5= 40 ÷ 8 = 5

40 ÷ 5 = 840

1) 7 × 3 =

2) 6 × 9 =

3) 5 × 4 =

4) 8 × 9 =

5) 3 × 6 =

EH$ A§H$dmbr g§»¶m H$m {d^mOZ {~Zm eof Ho$ Amn {d^mOZ nhbo nT>o h¡&

nwZ… ¶mX H$s{OE 284=7

~S>r g§»¶m H$mo Bgr àH$ma H$m {d^mOZ H$a gH$Vo h¡& {dÚmWu H$mo dJ© 4 AmB©gH«$s‘

H$s H$mS>r ~ZmZo Ho$ {bE H$hVo h¡& 148AmB©gH«$s‘ H$s H$mS>r go {H$VZo dJ© ~ZVo h¡?

^mÁ¶

eof

^mJ’$b ^mOH$ 4)148(3712

2828

0

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ñVa 1: 1 < 4 Bg{bE 2 A§H$ br{OE 14 Xg H$mo 14 go ^mJ H$s{OE 4×3=12

3 H$mo ^mJ’$b {b{IE Am¡a 14-12 KQ>mBE=2, 2 eof {b{IE

ñVa 2 : BH$mB© ‘| go 8 br{OE 2 Ho$ ~mOw 28 BH$mB© 4 go 4×7=28

7 H$mo ^mO’$b ‘o§ 3 Ho$ ~mOw ‘o‘ {b{IE 28-28=0 eof 0 {b{IE&

¶mX a{IE

g§»¶m {Oggo ^mJ H$aZm h¡ Cgo ^mÁ¶ H$hVo h¡&

^mÁ¶ go ^mJ hmoZodmbr g§»¶m H$mo ^mOH$ H$hVo h¡&

{d^mOZ H$m n[aUm‘ H$mo ^mJ’$b H$hVo h¡&

{d^mOZ Ho$ ~mX Omo ~MVm h¡ Cgo eof H$hVo h¡&

eof h‘oem ^mOH$ go N>moQ>m hmoVm h¡&

CXmhaU 1: 7434 6 ^mJ H$s{OE

) (6 7434 1239

146

2312

5418

054

CXmhaU 2: 8428 H$mo 7 go ^mJ H$s{OE

) (7 8 4 28 1204

147

00214

28

0028

0

ñVa 1: 8 hOma H$mo 7 go ^mJ H$s{OE 7×1=7, 1 H$mo ^mJ’$b

‘| {b{IE 8-7=1 KQ>mBE eof 1 {b{IE

ñVa 2 : 4 gm¡ H$mo ZrMo br{OE 14 gm¡ H$mo 7 ^mJ H$s{OE&

7×2=14, 2 H$mo Xÿgar A§H$ ‘| {b{IE 14-14=0

eof 0

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ñVa 3: 2 Ho$ ZrMo {b{IE 0 Ho$ ~mOy ‘| 7,2 go ~S>m h¡ 7×0=0, 0, 2 go N>moQ>m h¡,

0 H$mo Vrgao ñWmZ ‘| ^mJ’$b ‘| {b{IE, 2-0=2 KQ>mBE eof 2 h¡&

ñVa 4: ZrMo 8 br{OE 2 Ho$ ~mOy ‘| 28 H$mo 7 go ^mJ H$s{OE, 7×4=28

'4' H$mo ^mJ’$b ‘| {b{IE [28-28=0] KQ>mBE&

eof 0 {b{IE

CXmhaU 3: 5 ñHy$bm| ‘| 1735 nwñVHo$ {dVaU H$aVo h¡& à˶oH$ ñHy$b H$mo nwñVH$m|

H$s g§»¶m kmV H$s{OE&

) (5 17 35 347

2315

03520

0035

nwñVH$m| H$s g§»¶m = 1735

ñHy$bm| H$s g§»¶m = 5

nwñVH$m| H$s g§»¶m Omo à˶oH$ ñHy$b H$mo àmá hmoVr h¡ = 347 nwñVH$

Aä¶mg 6.2

I. Imbr ñWmZ ^[a¶o

1) 42 6 = ______________

2) 24 8 = 3 ‘| ^mÁ¶ ______________h§¡&

3) 45 9 = 5 ‘| '9' ______________ h¢&

4) 72 8, ‘| ___________ ^mJ’$b Am¡a ___________eof h¡&

II. ^mJ H$s{OE

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2) 88 (a) 7) 91 (b) 5) 850 (c)

6) 792 (d) 4)8464 (e) 9) 9567 (f)

III. hb H$s{OE

1) 4 {dÚmWu EH$ ~|M ‘| ~¡R> gH$Vo h¡& 64 ~ƒm| H$mo {H$VZo ~|Mm| H$s Amdí¶H$Vm

h¡?

2) 240 ‘mo‘~Îmr 8 {S>ã~m| ‘| OmoS>m OmVm h¡& à˶oH$ {S>ã~m| ‘| ‘mo‘~Îmr H$s

g§»¶m kmV H$s{OE&

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3) 255 ~ƒo ^«‘U Ho$ {b¶o {ZH$bVo h¡& 5 ~g go ¶mÌm H$aVo h¡& à˶oH$ ~g

‘| {H$VZo ~ƒo ~¡R>Vo h¡?

4) EH$ aob JmS>r 672 {H$‘r 6 K§Q>mo ‘| Xÿar V¶ H$aVo h¡& 1 K§Q>o ‘| aob JmS>r

{H$VZo {H$bmo ‘rQ>a MbVr h¡?

5) EH$ gámh ‘| ‘OXÿa <952 H$‘mVo h¢& X¡{ZH$ H$‘mB© ³¶m h¡?

6) ñdV§ÌVm {Xdg ‘| 3 Mm°H$boQ> à˶oH$ ~ƒo H$mo àmá hmoVr h¡& 246 Mm°H$boQ>

~m±Q>o J¶o h¡& à˶oH$ ~ƒo H$mo {H$VZo Mm°H$boQ> àmá hmoVo h¡?

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^mÁ¶ go A§H$dmbr g§»¶m H$m {d^mOZ H$aVo h¡ Vmo eof àmá hmoVm h¡&

EH$ g§»¶m H$m {d^mOZ nhbo nT>o h¡& 9 bmSy>Am| H$mo 4 {‘Ìm| ‘| ~mQ>Zo h¡&

4)9(2

18

eof

à˶oH$ {‘Ì H$mo {H$VZo bmSy> àmá hmoVm h¡?

{H$VZo bmSw> ~m§Q>o J¶o h¡?

g‘mZ ê$n go ~mQ>Zo Ho$ ~mX {H$VZo bmSw> ~M J¶o h¡& CgH$mo eof H$hVo h¡&

gyMZm : ^mOH$ go H$‘ eof hmoVm h¡& gyÌ go g˶mnZ H$s{OE&

(^mJ’$b × ^mOH$ ) + eof = ^mÁ¶ (2×4)+1=9

CXmhaU 1 : 86 H$mo 5 go ^mJ H$s{OE& ^mJ’$b Am¡a eof kmV H$s{OE& ) (5 86 17

365

0135

eof

ñVa 1: 8 Xg H$mo 5 H$mo ^mJ H$s{OE, 5×1=5, EH$ H$mo àW‘ A§H$ ‘| {b{IE

8-5=3 KQ>mBE& 3 eof h¡&

ñVa 2: 6 BH$mB© 3 Ho$ ~mOy ‘| {b{IE 36 H$mo 5 go ^mJ H$s{OE, 7 H$mo ^mJ’$b

Xÿgar A§H$ ‘| {b{IE& 36-35=1, 1 eof h¡&

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Aä¶mg 6.3

I. {ZåZ{b{IVmo à˶oH$ ‘| ^mJ’$b Am¡a eof kmV H$s{OE:

6) 76 (1)

^mJ’$b =

eof =

8) 93 (2)

^mJ’$b =

eof =

5) 345 (3)

^mJ’$b =

eof =

6) 911 (4)

^mJ’$b =

eof =

8) 9254 (5)

^mJ’$b =

eof =

5) 8374 (6)

^mJ’$b =

eof =

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5) 2437 (7)

^mJ’$b =

eof =

7) 6218 (8)

^mJ’$b =

eof =

6) 3452 (9)

^mJ’$b =

eof =

8) 5715 (10)

^mJ’$b =

eof =

4) 2375 (11)

^mJ’$b =

eof =

7) 4238 (12)

^mJ’$b =

eof =

àíZm| H$mo hb H$s{OE {Og‘| EH$ go A{YH$ à{H«$¶mMo&

¶mX ao{I¶o: - OmoS>Zm (+), KQ>Zm (_), JwU’$bZ () Am¡a {d^mOZ (hr J{UV Ho$ Mma à{H«$¶mE± h¡&

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Mma ‘yb^yV à{H«$¶m Ho$ AbJ AbJ hb H$aZm AmVm h¡& A~ h‘ EH$ gmW Xmo

¶m VrZ à{H«$¶m Cn¶moJ H$ao§Jo&

CXmhaU 1:

amKw ` 8000 ha ‘hrZm H$‘mVo h¡& do ` 2000 Ka H$mo {H$am¶m ` 3500 ImZo na

Am¡a ` 1000 H$nS>m| na IM© H$aVo h¡& eof YZamer ~MmVm h¡& do {H$VZr YZamer

~MmVm h¡&

amKw H$s H$‘mB© ha ‘hrZo = ` 8000

Hw$b IMm© = ` 6500

~MV KZamer ` 1500

IMm©

YZamer {H$am¶o na ` 2000

YZamer ImZo na ` 3500

YZamer H$nS>m| na ` 1000

Hw$b YZamer ` 6500

CXmhaU 2:

gdrVm 25 Ho$Or Am‘ ` 12 à{V Ho$Or ~oMo h¡& Bg YZamer ‘| 10 Ho$Or

Mmdb IarXr h¡& Mmdb H$m H«$¶ ‘yë¶ à{V Ho$Or kmV H$s{OE&

1 Ho$Or AmJ H$m Xm‘ ` 12

25 Ho$Or Am‘ H$m Xm‘ = 30025 12#

` 300 do Mmdb H$s ‘mÌm = 10 Ho$Or

) (10 300 30

000

0000

30

1 Ho$Or Mmdb H$m Xm‘ = ` 30

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Aä¶mg 6.4

1) nyOm EH$ {‘³ga ` 2300 H$mo IarXVr h¡ Am¡a Hw$H$a {OgH$m Xm‘ ` 1750 IarXVr h¡& ¶{X CgHo$ nmg ̀ 3500 h¡& Vmo Am¡a {H$VZo YZamer H$s Amdí¶H$Vm h¡?

2) Johþ Ho$ 9 W¡bm| H$m Xm‘ ` 4050 h¡& 21 Johþ Ho$ W¡bm| H$m Xm‘ kmV H$s{OE&

3) 4 eoë’$ ‘| 520 nwñVH$ OmoS>o J¶o h¡& 32 eoë’$ ‘| {H$VZo nwñVH$ O‘m gH$Vo h¡?

4) nwñVH$ H$m Xm‘ `15 Am¡a nopÝgb H$m Xm‘ `4 h¡, ‘mohZ 2 nwñVH$ Am¡a 3 nopÝgb IarXZm MmhVm h¡& CgH$m Xm‘ ³¶m h¡?

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KQ>H$ - 7 d¥Îm

Bg KQ>H$ H$m Aܶ¶Z H$aZo Ho$ ~mX :

{~Zm CnH$aU go d¥Îm H$s aMZm&

d¥Îm H$s aMZm naH$ma go H$a|Jo &

Ho$ÝÐ, {ÌÁ¶m Am¡a ì¶mg H$mo nhMmZo&

nhbo Ho$ H$jm ‘| Amn d¥Îm O¡go AmH$ma ‘| nT>o h¡& X¡{ZH$ OrdZ ‘| d¥Îmr¶ AmH$ma Ho$ dñVwE±

CXmhaU : 1) H$m±M H$s MyS>r

2) ........................................

3) ........................................

4) ........................................

H$m¶© H$bmn: Vmbm~ ‘| nËWa ’|${H$E& ~ZVo Va§Jm| H$mo {ZarjU H$s{OE& do H$m¡Z go AmH$ma ‘| hmoVo h¡?

AmnH$mo d¥Îm H$m AmH$ma ‘mby‘ h¡& d¥Îm H$s aMZm H¡$go H$aVo h¡? gmo{ME&

d¥Îmmo§ H$s aMZm

MwS>r br{OE& Bggo Jmobm ~Zm gH$Vo& H$mo{ee H$s{OE&

{MÌ - 1 {MÌ - 2

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EH$ erQ> nona na MyS>r aIr {MÌ Ho$ O¡go&

1) {MÌ Ho$ O¡go nopÝgb Ho$ Cn¶moJ MyS>r na bJmB¶o&

2) MyS>r {ZH$m{bE& àmá AmH$ma H$m¡Z gm h¡? ¶hm± d¥Îm h¡&

¶hm± d¥Îm h¡&

X¡{ZH$ OrdZ ‘| {d{^Þ dñVwE± ~VmBE {Oggo d¥Îm ~ZmVo h¡& gyMr ~ZmBE&

1) ....................................................................................................................

2) ....................................................................................................................

3) ....................................................................................................................

4) ....................................................................................................................

gy{MV dñVwE± dÎmm| H$s aMZm H$s{OE& .

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XÎm {~ÝXþAm| H$mo Omo{S>E& {H$gH$m AmH$ma àmá hmoVm h¡? {ZarjU H$s{OE&

aoImJ{UVr¶ {S>ã~m Imo{bE& H$m¡Zgo CnH$aU d¥Îm ~Zm gH$Vo h¡? gmo{ME&

d¥Îm H$s aMZm naH$ma Ho$ Cn¶moJ go

naH$ma ‘| no{Ýgb bJmB¶o& KmpËdH$ gyB© Am¡a nopÝgb H$s H$‘ Xÿar a{IE

KmpËdH$ gyB© nona na a{IE&

nopÝgb nona H$mo ñne© H$aZm h¡& àH$ma H$m YyU©Z H$r{OE&

A~ àmá AmH$ma H$m¡Z gm h¡?

YmpËdH$ gyB© àH$ma H$s aIZodmbr OJh H$mo ³¶m H$hVo h¡? .gmo{ME&

¶h d¥Îm H$m Ho$ÝÐ h¡& {MÌ ‘| 0 d¥Îm H$m Ho$ÝÐ h¡&

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gyMZm :

YmpËdH$ gwB© Ho$ A§V H$mo hmo{e¶mar go H$aZm h¡&

nopÝgb H$m ZmoH$ Am¡a àH$ma H$m A§V XmoZm| EH$ g‘mZ aoIm ‘| hmoZo Mm{hE&

YmpËdH$ gwB© Am¡a nopÝgb H$mo pñWa aIZm h¡& Am¡a nwñVH$ H$mo Kw‘mZm Zht&

Aä¶mg 7.1

I. d¥Îm H$m Ho$ÝÐ `A' ‘mZH$a d¥Îm H$s aMZm H$s{OE&

A

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II. C Am¡a D Ho$ÝÐ ‘mZH$a d¥Îm H$s aMZm H$s{OE& {Oggo do XmoZm| Amng ‘| nañna Zht {‘bVo h¡&

DC

III. XÎm ZrMo Ho$ ñWmZ g~go ~S>m d¥Îm H$s aMZm H$s{OE&

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H$m¶© H$bmn: EH$ {~ÝXþ go {H$VZo d¥Îm ~Zm gH$Vo h¡? gmo{ME H$mo{ee H$s{OE&

d¥Îm H$s {ÌÁ¶m

d¥Îm H$s aMZm H$s{OE

.

D

O

C

BA

d¥Îm na A, B, C, Am¡a D H$mo A§{H$V H$s{OE {MÌ Ho$ O¡go A, B, C, D "0' go Xÿar kmV H$s{OE&

OA = ........................................ g|‘r

OB = ........................................ g|‘r

OC = ........................................ g|‘r

OD = ........................................ g|‘r

d¥Îm na H$B© Am¡a {~ÝXþ ~ZmB©E Am¡a Xþar ‘{n¶o&

d¥Îm Ho$ g^r {~ÝXþ ‘| g‘mZ Xÿar na h¡&

OA, OB, OC, Am¡a OD H$mo ³¶m H$hVo h¡? BZ H$mo d¥Îm H$s {ÌÁ¶mE± H$hVo h¡&

H$m¶© H$bmn:

EH$ d¥Îm H$s aMZm H$s{OE& Bg d¥Îm go {H$VZo {ÌÁ¶m¶o§ ~Zm gH$Vo h¡? aMZm

H$s{OE& Bggo Amn ³¶m OmZVo h¡? AmnH$m {ZíM¶ ³¶m h¡?

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d¥Îm H$m ì¶mg

AJbr AmH¥${V H$m {ZarjU H$s{OE&

D

O

C B

A

A, B, C, Am¡a D {~ÝXþ H$hm± na h¡? do {~ÝXþE± d¥Îm na h¢&

A Am¡a B Omo{S>E& Cgr àH$ma C Am¡a D Omo{S>E&

AB Am¡a CD {H$gHo$ Ûmam OmVm h¡? [ZarjU H$s{OE&

do d¥Îm Ho$ Ho$ÝÐ Ho$ Ûmam OmVm h¡&

AB Am¡a CD H$mo ³¶m H$hVo h¡?

BZH$mo d¥Îm Ho$ ì¶mg H$hVo h¡&

AB Am¡a CD d¥Îm Ho$ ì¶mg h¡&

H$m¶© H$bmn :

EH$ d¥Îm H$s aMZm H$s{OE& Bggo {H$VZo ì¶mg ~Zm gH$Vo h¡& aMZm H$s{OE& g^r ì¶mgm| H$mo ‘m{n¶o& Bggo ³¶m OmZVo hmo? AmnH$m ³¶m {ZíM¶ h¡?

Om{ZE :

ì¶mg d¥Îm H$mo Xmo ^mJm| ‘| {d^m{OV H$aVo h¡&

Xmo ì¶mgm| H$m à{VÀN>oXZ H$mo d¥Îm H$m Ho$ÝÐ H$hVo h¡&

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H$m¶© H$bmn :

àH$ma Ho$ {~Zm d¥Îm H$s aMZm H$s{OE& Ho$ÝÐ, {ÌÁ¶m Am¡a ì¶mg H$mo nhMm{ZE&

Aä¶mg 7.2

1)

d¥Îm H$s {ÌÁ¶m ~ZmB©E&

2) A

d¥Îm H$m ì¶mg ~ZmB©E&

3)M

P

Q

R

{ZarjU H$aHo$ Imbr ñWmZ ^[aE&

a) d¥Îm H$m Ho$ÝÐ ..........................

b) {ÌÁ¶m ......................................

c) ì¶mg ....................................

d) d¥Îm go {ÌÁ¶mAm| H$s g§»¶m ............................

H$m¶© H$bmn :

Iob Ho$ ‘¡XmZ ‘| ~S>r d¥Îm ~ZmZm h¡& H$m¡Z go {dYmZ go ~ZmVo h¡? {ejH$ go MMm© H$s{OE&

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KQ>H$-8 ‘mZ{gH$ A§H$J{UV

Bg KQ>H$ H$mo Aܶ¶Z H$aZo Ho$ ~mX :

10 Am¡a 100 Ho$ JwUZIÊS> ‘mZ{gH$ ê$n go Omo‹S>|Jo &

10 Am¡a 100 Ho$ JwUZIÊS> ‘mZ{gH$ KQ>m`|Jo &

Xmo g§»¶mAm| H$m JwUZ’$b AnyU© JwUZ’$b Ho$ gmW&

X¡{ZH$ OrdZ ‘| ‘mZ{gH$ kmV H$aZm h¡&

{ZåZ{b{IV g§X^m] ‘| {ZarjU H$s{OE&

CXmhaU : XÿY IarXVo g‘¶ Xmo brQ>a XÿY H$m ‘yë¶, Bg g§X^© ‘o§ H¡$go kmV H$a

gH$Vo h¡& Eogo g§X^© ‘| ‘mZ[{gH$ ~w{Õ H$m Cn¶moJ H$aVo h¡&

3 Eogo g§X^m}§ H$mo gmo{ME:

1) ..........................................................................

..........................................................................

2) ..........................................................................

..........................................................................

Bgr Vah ‘Z go kmV H$aZodmbo H$B© {dYmZ h¡&

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CXmhaU 1: 60 H$mo 50 go Omo{S>E&

{dYmZ 1: 60 H$mo ~Xb H$a 50+10

50 H$mo Omo{S>E 50+10

50+50+10=110

{dYmZ 2: 60 H$mo ^mJ H$aHo$ 30+30 50+30+30

80+30=110

{dYmZ 3: BH$mB© ñWmZ ‘| g§»¶m H$mo Omo{S>E 5+6=11

BH$mB© ñWmZ ‘| 0 hmoZo go

50+60=110

Bg Vah gdmb H$aZm H$m Cn¶moJ h¡& AmnHo$ {ejH$ go MMm© H$aHo$ gyMr ~ZmB©E&

..............................................................................

..............................................................................

..............................................................................

..............................................................................

Bg go A{YH$ AmnH$mo ‘mZ{gH$ gdmb H$aZm hmo Vmo {ejH$ Am¡a XmoñVm| ‘| ~m{Q>E&

‘mZ{gH$ J{UV OmoS>Zm KQ>Zm Am¡a JwUZ’$b Ho$ g‘¶ Cn¶moJ H$aVo h¡& gmo{ME

Am¡a {b{IE&

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CXmhaU 2:

{ejH$ : gwaoe ¶h àíZ H$amo 40+20

{dÚm : ‘¢ H$aZm MmhVr hÿ±&

{ejH$ : XoI|Jo H$m¡Z H$aoJm àW‘

nhbm CÎma {dÚm Zo {X¶m h¡&

CÎma : 60

{ejH$ : AmnZo H¡$gm {H$¶m h¡?

{dÚm: ‘Z ‘| {H$¶m h¡&

gm¡ Xg B 4 02 06 0

~mX ‘o§ gwaoe Zo CÎma {X¶m {H$ 60

nwñVH$ ‘| àíZ {bIH$a ñWmZ ‘yë¶ go OmoS>m h¡&

àW‘ 20 H$mo 10+10 go ^mJ H$s{OE& ~mX ‘o‘ 40 H$mo 10 OmoS>Zm h¡& 50 àmá hmoVm h¡& 50 H$mo 10 OmoS>Zo go 60 àmá&

àíZ ‘Z ‘| H$aZo go ‘mZ{gH$ àíZ H$hVo h¡&

{ejH$ {dÚm go nyN>Vo h¡ {H$ dh H¡$gm {H$¶m h¡?

40 + 20

(4+2) (0+0)60

1) Xgdm± ñWmZ ‘| A±H$m| H$mo Omo{S>E( 4+2=6)

2) BH$mB© ñWmZ ‘| eyݶ {bIm h¡&

3) CÎma 60 àmá homoVm h¡&

‘mZ{gH$ OmoS>Zm:

10 H$mo 100 go OmoS>Zm&

CXmhaU 3 : a{d Ho$ nmg 40 Am‘ h¡ Am¡a amIr Ho$ nmg 30 Am‘& Hw$b {H$VZo Am‘ h¡?

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Z‘yZm 1:

1) 40 + 30 Omo{S>E

XÀ B4 03 07 0

1) 4 Xg Am¡a 3 Xg 7 Xg àmá hmoVm h¡&

2) {bIZo Ho$ {bE 70 h¡&

BH$mB© ñWmZ ‘| ewݶ hmo Vmo Xgdm± ñWmZ ‘o‘ OmoS>Zm Am¡a BH$mB© ñWmZ Hw$b Am‘ =70

Z‘yZm 2: a{d Ho$ nmg 40 Am‘ h¡& amIr Ho$ nmg 30 Am‘ BgH$mo 10+10+10 Ho$

O¡go {b{IE&

nhbo 40 H$mo 10 OmoS>Zo go 50 àmá hmoVm h¡&

60 H$mo 10 OmoS>Zo go 70 àmá hmoVm h¡&

CÎma 70 Am‘ h¡&

40 + 10 + 10 + 10 =70

H$aZo H$s H$mo{ee ‘Z go H$s{OE

1)

50 {‘br brQ>a 20 {‘br brQ>a

50 + 20,

________ {‘br brQ>a 2) a‘oe H$mo gmá{hH$ ~mOma go {ZåZ{b{IV g{ãO¶m± IarXZr h¡&

~oÊS>r

1 Ho$Or = <30

Q>‘oQ>mo

1 Ho$Or = <50

a‘oe Zo XþH$mZXma H$mo Hw$b {H$VZo n¡go {X¶m h¡? --------------

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3) arZm Xmo gm~wZ XþH$mZ go IarXo h¡&

<20àW‘ gm~wZ

+ <50Xÿgam gm~wZ

arZm XþH$mZ Xma ..................................Ho$ {X¶o h¡&

4) {ZåZ{b{IV àíZm| H$mo H$s{OE&

a)

b)

c)

d)

5) Cgr g§»¶m H$mo Cn¶moJ H$s{OE& jo{VO ¶m CÜdm©Yma OmoS>Zo go CÎma g‘mZ ahZo Mm{hE& BgràH$ma Imbr ñWmZ ^[aE&

10

20

30

.

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6) doZw a§Jmobr ‘| é.30 ‘| IarXVr h¡& ^mñH$a Xÿgar é.40 ‘| IarXVm h¡& Hw$b {H$VZo n¡go XoZo h¡?

7) erbm {Ibm¡Zm H$m IaJmoe <50 Am¡a {Ibm¡Zm H$m V~bm <30 ‘| IarXo h¡& Hw$b {Ibm¡Zm| na {H$VZm IM© {H$¶m?

CXmhaU 4: 1) 23+20 Omo{S>E

Z‘yZm 1 : 20 H$mo 10+10 {b{IE (Xmo Xg ~ZmB©E)

23+10 Omo{S>E& 23+10=33

{’$a 33 H$mo 10 Omo{S>E 33+10=43

Z‘yZm 2: 23 H$mo 20+3 Omo{S>E&

20 + 3 + 20

40 + 3 = 43

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2) 47+30 Omo{S>E&

Z‘yZm 1: 47 H$mo 40 + 7 {d^m{OV H$s{OE (4 Xg + 7 BH$mB©)

40 + 7 + 30

70 + 7 = 77

Z‘yZm 2:

30 H$mo 3 Xg ‘| {d^m{OV H$s{OE &

47+10+10+10 57+10+10 67+10 =77

{{

{

3) arQ>m Am¡a nrQ>a EH$ XþH$mZ go <75 H$m¶© H$bmn H$s nwñVH$ Am¡a <10 ‘o§

noZ IarXVo h¡& h¡& Hw$b {H$VZo n¡go IM© hmoVo h¡?

CXmhaU 5: 32 + 45 Omo{S>E

Z‘yZm 1:

{ {

(30 + 2) + (40 + 5)

30 +40 + 2 + 5

70 + 7 =77

gm¡ X B 3 24 5

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1) 32 H$mo (30+2) {d^m{OV H$s{OE &

2) 45 H$mo (40+5) {d^m{OV H$s{OE &

3) nhbo 3 Xg Am¡a 4 Xg H$mo Omo{S>E 7 Xg àmá hmoVm h¡& Bgr àH$ma 2 BH$mB© Am¡a 5 BH$mB© H$mo OmoS>H$a 7 BH$mB© àmá hmoVm h¡&

4) 7 Xg H$mo 7 BH$mB© Omo{S>E {Oggo 77 àmá hmoVm h¡&

Z‘wZm 2 : 32 + 45 (45 = 10+10+10+10+5)

32+10+10+10+10+5 42+10+10+10+5 52+10+10+5 62+10+5 72+5 77

{{

{{{

CXmhaU 6: 1) 53+37 Omo{S>E

Z‘yZm 1: 53 ‘| 5 Xg Am¡a 3 BH$mB©

37 ‘| 3 Xg 7 BH$mB©

8 Xg 10 BH$mB© = 9053+37 80+10

Z‘yZm 2:

5 3 + 3 7

(5+3) Xg + 8 Xg +

(3+7) BH$mB©10 BH$mB©

80+10=90

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2) 62+26 Omo{S>E

Z‘yZm 1:

62

60 + 2

26

20 + 6 nhbo Xg H$mo Omo{S>E 60+20=80

{’$a BH$mB© ñWmZ H$mo Omo{S>E 2+6=8

80 + 8 = 88

Z‘yZm 2: 26 +62 H$m OmoS>Zm

26 H$mo 10 + 10 + 6 H$mo Vmo{S>E Am¡a 62

62 + 10 + 10 + 6

72 + 10 + 6

82 + 6

88

{{ {

3) H$mdoarå‘m Ho$ nmg 40 ~H$ao, 20 Jm¶ Am¡a 10 gmS> h¡& CgHo$ nmg {H$VZo

new h¡?

Bg àH$ma Ho$ H$B© CXmhaU h¡&

CÎma ‘mby‘ H$aZo H$s H$mo{ee H$aHo$ kmV H$s{OE&

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CXmhaU : gmo‘dma H$mo ahr‘ Ho$ nmg 30 brQ>a XÿY h¡ Am¡a ‘§Jbdma 20 brQ>a

XÿY h¡& Xmo {XZ ‘| {H$VZo brQ>a XÿY h¡& Hw$b = 30 + 20 brQ>a?

I. {ZåZm| H$mo Omo{S>E Am¡a CÎma {b{IE&

1) 26 + 40 = ____________ 2) 20 + 33 = ____________

3) 53 + 30 = ____________ 4) 72 + 10 = ____________

II. {ZåZ{b{IV àíZm| H$mo ‘Z go Omo{S>E Am¡a CÎma H$mo ñWmZ ‘§o {b{IE:

1) 45 + 23 = ____________

2) 33 + 25 = ____________

3) 45 + 43 = ____________

4) 85 + 22 = ____________

5) 68 + 21 = ____________

6) 55 + 45 = ____________

7) 33 + 45 = ____________

8) 46 + 51= ____________

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III. ‘Z go H$s{OE:-

1) 10 + 20 + 30 = _______

2) 20 + 20 + 10 = ________

3) 50 + 30 + 10 = ________

4) 40 + 30 + 20 = ________

300 + 200 Omo{S>E

gm¡ XÀ B3 0 02 0 05 0 0

Z‘yZm 1: 3 gm¡ H$mo 2 gm¡ Omo{S>E 5 gm¡ àmá hmoVm h¡&

Z‘yZm 2: BH$mB© Am¡a gm¡ ñWmZ ‘| eyݶ h¡& gm¡ do ñWmZ ‘|

Omo{S>E Am¡a BH$mB© ñWmZ ‘| eyݶ Am¡a Xgdo ñWmZ ‘| eyݶ h¡&

Am±I H$mo Q>oñQ> H$aHo$ EoZH$ <500 ‘| IarXVo 1 arVm IarXVr

gy¶© EoZH$ <400 ‘| IarXVo h¡& Hw$b {H$VZm KZamer XoZo h¡&

` 500 ` 400 CÎma : __________

Zgram ~oJ‘ 2 ~mëQ>r IarXr h¡& EH$ ~mëQ>r ` 200 Am¡a Xÿgam H$m ` 300 h¡& Hw$b {H$VZm n¡go XoZo nS>Vm h¡&

` 200 ` 300

CÎma : __________

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1) gwZrb Ho$ XþH$mZ ‘| 500 dñVwE°§ Wr& XþH$mZ ~T>mZo na 200 dñVwE°§ AJa O‘m

gH$Vm h¡ Vmo Hw$b {H$VZo dñVwE± hþB©?

2) 200 {dÚmWu ñHy$b ^«‘Z OmZo Ho$ {bE V¡¶ma Wo& A§V ‘| 100 {dÚmWu Am¡a

AmH$a O‘Vo h¡& ^«‘Z Ho$ {bE {H$VZo {dÚmWu OmVo h¡ ?

3) àUmVr OZdar ‘| ` 200 O‘m H$aVr h¡ Am¡a nadar ‘| ` 700 O‘m H$aVr

h¡& Hw$b {H$VZm n¡gm O‘m hmoVm h¡?

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‘mZ{gH$ KQ>mZm

amZr AnZo OÝ‘ {XZ na 25 Mm°H$boQ> bmVr h¡ Am¡a AnZo gho{b¶m| ‘| 10 ~mm|Q>Vr h¡& eof {H$VZo Mm°H$boQ> hmoVm h¡?

Z‘yZm 1: 25 -10

20+5, 25 H$mo {d^m{OV H$s{OE & 20+5-10 (20-10=10)

10+5

= 15

amZr Ho$ nmg 15 Mm°H$boQ> hmoVo h¡&

Z‘yZm 2: 25 H$mo 20+5 {d^m{OV H$s{OE &

= 15 Mm°H$boQ> eof h¡&

2) KQ>mBE:

50− 30

=50-30

=40-10

=30-10

=20

30=10+10+10

3) 24 ‘| go 17 KQ>mBE:

24 - 17

24

20 4

17

10 7

20 + 4 - 10 - 7

20 - 10 - 7 + 4

10 - 7 + 4

3 + 4

= 7

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Z‘yZm 1 : 24 Am¡a 17 H$s ‘m§S>Ur Xg Am¡a BH$mB© ‘| H$amo& A~r KQ>mBE& KQ>mBE ‘| N>moQ>r g§»¶m ~S>r g§»¶m go KQ>mB© OmVr h¡&

4) 3517-

35 ‘| 3 Xg Am¡a 5 BH$mB© 17 ‘| 1 Xg Am¡a 7 BH$mB© 3 Xg ‘| go 1 Xg KQ>mBE& {Oggo 2 Xg àmá hmoVm h¡ (30-10=20) 20 ‘o go ‹7 KQ>mBE& 13 àmá hmoVo h¡& (20-7=13) 13 H$mo 5 Omo{S>E 18 àmá hmoVo h¡&

3530

517

10

7

20-7

30-10

13 5

18

5+

5+

+

4)

64 − 34 = ?

KQ>mZo H$s nÕV 64-34 64 ‘| 6 Xg Am¡a 4 BH$mB© = 60+4

34 ‘| 3 Xg Am¡a 4 BH$mB© = 30+4

64 ‘| go 34 KQ>mBE = 30+0

64 go 34 KQ>mZo go 30 {‘bVo h¡& >¶{X N>… Xg ‘| 3 Xg KQ>mZo go 30 àmá hmoVo h¡& --------4 BH$mB© ‘| go 4 BH$mB© KQ>mVo h¡ Vmo 0 àmá hmoVo h¡& -------- 30+0=30

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Z‘yZm 2 : 64 - 34

64 ‘| go 10 KQ>mBE

64 -10 = 54 ( nhbm Xg)

54 -10 = 44 (Xÿgam Xg)

44 -10 = 34(Vrgam Xg)

34 - 4 = 30

34 H$s ‘mZZr 10 + 10 + 10 + 4

eoIaßnm 600 nm¡Yo Zg©ar ‘| bJmVm h¡& ~mare Ho$ H$maU 300 nm¡Yo Iam~ hmo

OmVo h¡& eof {H$VZo nm¡Yo ~Mo h¡?

600 - 300 = ?

1) Xgdm ñWmZ ‘| eyݶ hmoZo go gm¡ do ñWmZ ‘| 6 - 3 = 3 eyݶ H$mo d¡go hr

aoIrE& CÎma 300 H$mo{ee H$s{OE&

2) X¡{ZH$ OrdZ ‘| H$moB© Xmo CXmhaU {b{IE&

‘Z go CXmhaU hb H$aZo Ho$ ’$m¶Xo H$m¡Z go h¡? gmo{ME&

1)

2)

3)

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134

H$mo{ee H$s{OE: - 1) aoIm Ho$ nmg <40 h¡& XþH$mZ H$mo OmH$a <25 H$s nwñVH$ IarXVr h¡& aoIm

Ho$ nmg {H$VZr YZamer h¡&

2) ‘oKm 400 Zm[a¶b ~mOma ‘| ~oMZo Ho$ {bE bmVr h¡& CgZo 100 Zm[a¶b ~oMo h¡& Vmo {H$VZo Zm[a¶b ~Mo h¡?

10 Ho$ JwUZIÊS> (‘mZ{gH$ àíZ) 1) ZmJdoZr XÿY H$s S>oAar H$mo à{V{XZ 10 brQ>a XÿY ~oMVr h¡& 20 {XZm| ‘| do {H$VZo

brQ>a XÿY ~oMVr h¡? ‘m± Zo ~ƒm| go Bg àíZ H$mo nyN>m& àW‘ ~mobZodmbm| H$mo nwañH$ma XoVr h¡& {à¶m Am¡a ahr‘ CÎma XoVo h¡&

{à¶m ahr‘

200

brQ>a XÿY

200

brQ>a XÿY

{à¶m OëXr CÎma XoVr h¡ Am¡a ahr‘ ~mX ‘|& ‘m± Zo ~wbmH$a nyN>Vr h¡ {H$ H$m¡Z àW‘ CÎma {X¶m h¡& {à¶m?

{à¶m Zo H$hm {H$ dh ‘Z go CÎma {X¶m h¡&

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{à¶m :- ‘m± ‘oZo JwUZ’$b ‘Z ‘| {H$¶m h¡&

‘m± :- H¡$go ?

{à¶m :- 10 brQ>a×20

{à¶m :- BH$mB© ñWmZ ‘| eyݶ ahZo go BH$mB©

ñWmZ ‘| eyݶ h¡& O~ 2 ×1 = 2

2 Ho$ ~mOw Xmo ewݶ bJmB©E& 200 brQ>a XþY

~oMo OmVm h¡ &

ahr‘:- JwUZ’$b {dYmZ ‘| {H$¶m

h¡& ahr‘ :- nwñVH$ ‘| {bIm h¡&

10×20

00

20020

10 20#

ahr‘ :- 200 brQ>a

Bg‘| H$B© àíZ hb H$a gH$Vo h¡:-

2) amOy ~hZ H$s emXr H$mo gmS>r IarXVo h¡& à˶oH$ gmS>r H$m Xm‘ <200 h¡& 30

gm{S>¶m| H$m Xm‘ ³¶m h¡?

{ejH$ : H$m¡Z àW‘ ~Vm¶oJm?

OmZ : ga, ‘¡ àW‘ ~VmD§$Jm&

{ejH$:- OmZ, CÎma H¡$go {‘bm?

EH$ gmS>r H$m Xm‘ 200

30 gmS>r H$m Xm‘? 2 0 0 × 3 0

6 0 0 0

ñVa 1: ‘Z ‘| 200×30 go JwUm {H$¶m h¡&

ñVa 2: Jwʶ H$mo JwUZ’$b H$s{OE 2 gm¡ do

ñWmZ Am¡a 3 Xg do ñWmZ H$s{OE&

CÎma 6 h¡ 200 × 30

Jwʶ JwUO

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ñVa 3: AmJo VrZ ewݶ {b{IE&

ñVa 4: 6000

{ejH$ : JwUZ’$b H$mo AnZo VarHo$ go {H$¶m h¡& nwñVH$ ‘| Eogo H$aZm h¡& 6000

200 30#

ñd¶§ H$s{OE :-

1) Hw$gr© H$m Xm‘ ` 600 g§Vmof Zo 3 Hw$gu IarXm h¡& CgH$m Xm‘ {H$VZm h¡?

?`600

2) IoV ‘| 6 n{º$¶m°§ h¡& ¶{X 100 ~rO EH$ n§{º$ ‘| ~mo gH$Vo h¡ Vmo Hw$b {H$VZo

~rO ~mo gH$Vo h¡?

3) à˶oH$ Jwbm~ H$m Xm‘ <7 h¡& 6 bS>{H$¶m± à˶oH$ Jwbm~ IarXVr h¡& Vmo Jwbm~ dmbm| H$mo {H$VZo n¡go XoVo h¡?

EH$ Jwbm~ H$m Xm‘<7

àíZm| H$mo ‘Z ‘| hb H$a|Jo

‘mZ{gH$ ê$n go àíZ H$mo H¡$go hb H$aVo h¡? CXmhaU :5

à˶oH$ Mm°H$boQ> ~ma H$m Xm‘ é25 h¡& Eogo 5 Mm°H$boQ ~ma H$m Xm‘ ³¶m hmoJm? >

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1) 25 × 5 (20 + 5) × 5 VmoS>H$a {b{IE&

2) 20 ×5 + 5×5 = 100 + 25

3) OmoS>H$a CÎma H$mo a{IE = 125

I. ‘Z go àíZ H$mo hb H$aHo$ Imbr ñWmZ ‘| ^[a¶o:

1) 6 × 5 = 2 × 5 + × 5

2) 5 × 9 = 5 × 3 + 5 ×

3) 35 × 6 = 30 × 6 + 5 × II. ‘Z go àíZ H$s{OE& {ZåZ ¶moJ H$m JwUZ’$b 2 g§»¶mAm| H$m JwUZ’$b h¡&

1) 3 × 6 + 3 × 2 = + =

2) 20 × 4 + 5 × 4 = + =

3) 400 × 2 + 4 × 2 = + =

III. {ZåZ{b{IV àíZm| Ho$ CÎma {b{IE Am¡a H$m JwUZ’$b ‘Z ‘| H$s{OE:-

1) EH$ ñHy$b ‘| ImZo Ho$ {bE 5 Ho$.Or. Mmdb H$s Amdí¶H$Vm h¡& EH$ ‘hrZo

‘| ñHy$b ‘| {H$VZo Mmdb H$s Amdí¶H$Vm hmoJr?

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138

2) EH$ H$jm ‘| Zm¡ ~o§M h¡& à˶oH$ ~|M H$mo 4 nm±d h¡& g^r ~|Mm| H$mo {H$VZo

nm±d hmoVo h¡?

3) aobdo ~moJr ‘| 8 n{h¶o hmoVo h¡& 6 aobdo ~moJr ‘| {H$VZo n{h¶o hmoVo h¡?

4) ew^m Ho$ nmg 16 JwbXñVo h¡& à˶oH$ JwbXñVo ‘| 9 ’y$b h¡, JwbXñVo ‘| Hw$b

{H$VZo ’w$b h¡?

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139

KQ>H$-9 {^Þ Am¡a Xe‘bd

Bg KQ>H$ Ho$ Aܶ¶Z Ho$ ~mX :

{^Þ H$m AW© OmZ|Jo &

{^Þ Ho$ ha Am¡a A§e H$mo nhMmZ|Jo &

{^Þ Ho$ g‘Vwë¶ {^Þ kmV H$a|Jo &

Xe‘bd 0.1, 0.2, 0.3 H$m AW© OmZ|Jo &

, ,21

41

43 H$m AW© nhbo H$s H$jm ‘| nT>o h¡& H$B© CXmhaUm| H$mo {ZarjU H$s{OE&

12

{MÌ ‘| {^Þ Ho$ N>m¶mH¥$V àXoe H$m ^mJ 12

h¡& BgH$mo EH$ ~Q>o 2 H$hVo h¡&

14

{MÌ ‘| {^Þ Ho$ N>m¶mH¥$V àXoe H$m ^mJ 14

h¡& nT>Zo Ho$ {bE EH$ ~Q>o Mma h¡&

34

{MÌ ‘| N>m¶mH¥$V ^mJ 34 h¡& nT>Zo Ho$ {bE 3 ~§Q>o Mma h¡&

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{^Þ H$mo nhMm{ZE Omo AmH¥${V Ho$ ~m¶o Va’$ Am¡a ñWmZ ‘| ^[a¶o.

a) (Z‘yZm)

1) CXmhaU 21 EH$ ~Q>o 2 h¡&

b) 2)

c)

3)

d)

4)

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141

1. {MÌm| H$mo nhMm{Z¶o Omo {^ÝZ Ho$ N>m¶mH¥$V àXoe h¡ Am¡a ~am~a H$mo "' bJmB¶o&

CXmhaU 2:

a) 21

A B C

b) 41

A B C

c) 43

A B C

d) 31

AA

BB

CC

e) 32

A

B

C

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142

Aä¶mg 9.1

I. {ZåZ{b{IV H$mo nyU© H$s{OE&

a) 14 H$mo a§J ^[aE b) 1

2 H$mo a§J ^[aE

c) 34

H$mo a§J ^[aE d) 23

H$mo a§J ^[aE

II. XÎm {MÌ ‘| H$m¡Z gm {^Þ {Z{X©ï> H$aZm d¥Îm{V¶ H$s{OE

a) 12

13

14

b) 12 1

3 14

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III. {ZåZ{b{IV {MÌm| H$mo N>m¶mH¥$V H$s{OE Omo {^Þ 31 H$mo {Z{X©ï> H$aVo h¡&

a) b)

{^Þ

nona H$mo Mma g‘mZ ^mJ ‘| ‘mo{S>E&

EH$ Mm¡Wo ^mJ H$mo N>m¶m H¥$V H$s{OE&

Cnamoº$ {MÌ H$mo {^Þ H$m {bIZo go

___________ nT>o OmVo h¡& __________

4 ³¶m gy{MV H$aVo h¡?

erQ> Ho$ 4 g‘mZ ^mJm| H$mo {Z{X©ï> H$aVm h¡ ³¶m?

1 ³¶m {Z{X©ï> H$aVm h¡?

Bgo aoIm§{H$V ^mJ H$hVo h¡&

AmnH$mo ‘mby‘ h¡ {^Þ 14 h¡ , nT>Zo Ho$ {bE 1 ~Q>o 4 H$hVo h¡&

4 ha h¡ Am¡a 1 A§e h¡&

14

A§e

ha

gmo{ME H$moB© ^r {^Þ ‘o A§e Am¡a ha H$mo ³¶mo {Z{X©ï>

H$aVm h¡?

14

MwZo hþE g‘mZ ^mJ H$mo {Z{X©ï> H$aVo h¡&

nyU© dñVw Omo g‘mZ ^mJm| ‘| {d^m{OV H$aVo h¡& =

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¶mX a{IE: {^Þ nyU© dñVw Ho$ g‘mZ ^mJ h¡& CXmhaU :

nyU© dñVw Xmo g‘mZ ^mJ g‘mZ ^mJ N>m¶mH¥$V EH$ ~Q>o Xmo&

(Fraction){^Þ Numerator

Denominator= =A§e

ha A§e : {^Þ Ho$ g‘mZ ^mJm| H$s g§»¶m Omo MwZo h¡

ha : g‘mZ ^mJm| H$mo g§»¶m {Og‘| nwU© dñVw {d^m{OV H$aVo h¡&

CXmhaU :

a) {MÌ H$m¡Z gm {^Þ N>m¶mH¥$V h¡?

¶h 23 h¡&

2 Am¡a 3 ³¶m {Z{X©ï> H$aVm h¡& 2 __________ h¡&3 __________ h¡&

b)

b) {^Þ H$m N>m¶mH¥$V àXoe {Z{X©ï> H$s{OE&

15 ‘| 1 Am¡a 5 ³¶m {Z{X©ï> H$aVo h¡? {b{IE&

_______________ _______________

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c)

c) {^Þ H$m N>m¶mH¥$V àXoe __________{Z{X©ï> H$aVm h¡&

A§e __________ ha __________

d) d) {^Þ H$m N>m¶mH¥$V àXoe __________H$mo {Z{X©ï> H$aVm h¡&

A§e __________ ha __________

e) e) {^Þ H$m nmZr ^am {Jbmg _______h¡&

{ZåZ{b{IV H$m¶©H$bmn H$mo D${MV CÎma go nyU© H$s{OE&

OÝ‘ {XZ na Om°Z Ho$ {nVm EH$ N>moQ>m Ho$H$ bm¶m h¡& 10 g‘mZ ^mJm| ‘| H$mQ>o J¶o h¡&

EH$ ^mJ Om°Z H$mo {X¶o J¶o h¡&

Xmo ^mJ aodVr H$mo {X¶o J¶o h¡&

ahr‘ H$mo 3 ^mJ {X¶o J¶o h¡&

nrQ>a H$mo 4 ^mJ {X¶o J¶o h¡&

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Om°Z Ho$ {nVm go Ho$H$ Ho$ g‘mZ ^mJ _________ h¡&

Om°Z go {b¶m J¶m Ho$H$ H$m ^mJ ___________ h¡&

aod[V go {b¶m J¶m Ho$H$ H$m ^mJ ___________h¡&

ahr‘ go {b¶m J¶m Ho$H$ H$m ^mJ ___________h¡&

nrQ>a go {b¶m J¶m Ho$H$ H$m ^mJ __________h¡&

1,2,3,4 __________ {Z{X©ï> H$aVm h¡&

à˶oH$ go {b¶m J¶m Ho$H$ H$m ^mJ ~VmBE& {MÌ go à˶oH$ Ho$H$ H$m ^mJ ____________{Z{X©ï> H$aVm h¡&

{MÌ‘¶ go Ho$H$ Ho$ {b¶o hþE ^mJ XoI|Jo&

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H$m¶© H$bmn :

{eënm, hþg¡Z Am¡a ZdrZ {XbngÝX ImZm MmhVo Wo& Bg{bE ~oH$ar H$mo OmVm h¡&

{eënm : h‘ {XbngÝX Im¶|Jo&

hþg¡Z : à˶oH$ EH$ Im¶|Jo&

ZdrZ : ‘wPo EH$ {XbngÝX

Im¶o J¶o {XbngÝX H$s ‘mÌm

Zm‘ nyam {Xb

ngÝX

^mJm| H$s

g§»¶m

Im¶o J¶o à˶oH$ ^mJ

{eënm do AmYm ImB© h¡& do Xmo

g‘mZ ^mJ ~ZmH$a do

Im¶o& {eënm 21 ^mJ

ImVr h¡&

hþg¡Z 4 ^mJm| ‘| go 2 ^mJ ImVo

h¡ 42

ZdrZ 8 g‘mZ ^mJm| ‘| do Mma

^mJ ImVo h¡ 84 = 2

1

Im¶o J¶o {XbngÝX H$s g§»¶m {^Þ ‘| {bI|Jo&

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{eënm 12 ^mJ ImB© h¡ &

hþg¡Z 24 ^mJ Im¶o h¡&

ZdrZ 48 ^mJ Im¶o h¡&

¶h ^mJ {MÌ {Z{X©ï> H$aVo h¡&

{eënm 12

hþg¡Z 42

ZdrZ 48

12 ,

24 , 4

8 ¶h ^mJ nyU© {Xbng§X {XImVo h¡ ³¶m? gmo{ME&

12 , 2

4 , 4

8 à˶oH$ ^mJ H$m ‘yë¶ 1

2 h¡ ³¶m? h¡ H$s Zht? Bgo g‘mZ {^Þ

H$hVo h¡&

Omo {^Þ g‘mZ à‘mU {XImVo h¡, Cgo g‘mZ {^Þ H$hVo h¡&

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CXmhaU :

1) VrZm| Ho$ g‘mZ ^mJ ~ZmB¶o& EH$ ^mJ H$mo bmb a§J H$s{OE&

¶h ^mJ ____________ gy{MV H$aVo h¡&

2) 6 ^mJm| go ~Zo ^mJ Xmo ^mJmo§ H$mo Ho$gar a§J ^[aE& ¶h {^Þ ____________h¡&

3) 9 ̂ mJ ~ZmB©E& VrZ ̂ mJm| ‘| nrbm a§J ̂ [aE& BZH$m {^Þ ________________ h¡&

VrZ CXmhaUm| H$mo {ZarjU H$s{OE& VrZ H$m ^mJ 13

h¡& BZH$m {^Þ ____________h¡&

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EH$ XÎm {^Þ go g‘mZ {^Þ ~Zm gH$Vo h¡&

Bg CXmhaU H$mo {ZarjU H$s{OE&

23 {^Þ go EH$ g§»¶m go JwUm H$aZm h¡&

32

3 22 2

64

##= = 2 go JwUm H$aZm h¡&

3 go JwUm H$aZo go

32

3 32 3

96

##= =

4 go JwUm H$aZo go 32

3 42 4

128

##= =

, ,64

96

128 H$mo 2

3 BgH$m g‘ {^Þ H$hVo h¡&

CXmhaU 2: 45 Ho$ VrZ g‘Vwë¶ {^Þ {b{IE& A§e Am¡a ha H$mo 2 go JwUm H$aZm h¡&

54

5 24 2

108

##= = 3 H$mo JwUm H$aHo$ ^mJ H$s{OE&

54

5 34 3

1512

##= = A§e Am¡a ha H$mo 4 go JwUm H$s{OE&

54

5 44 4

2016

##= = A§e Am¡a ha H$mo 4 go JwUm&

, ,54

108

1512

2016= g‘Vwë¶ {^Þ

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Aä¶mg 9.2

I. Imbr ñWmZ ^[a¶o : -

1) , , ____83

166

2) _______51

153

3) , ______32

64

4) ______ ,64

96

II. {ZåZ {b{IVmo {^Þm| Ho$ g‘Vwë¶ {^Þ ‘| {b{IE&

1) 41

2) 161

3) 31

4) 32

5) 52

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Xe‘bd

{ZåZ{b{IV CXmhaUm| H$mo {ZarjU H$s{OE&

ImZo nH$mZo Ho$ {bE BªYZ

(J¡g 14.6 kg h¡ )

14.6kg

eQ>© ~ZmZo Ho$ {bE H$nS>m H$s Amdí¶H$Vm 2.5 ‘rQ>a h¡& Cnamoº$ CXmhaU ‘| ‘mÌm

H$mo H¡$go 춺$ H$aVo h¡&

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

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

{ZåZ{b{IV CXmhaU go g§»¶mAm| H$mo {ZarjU H$s{OE& CXmhaU 1:

dJ©

dJ© H$mo Xg g‘mZ ^mJm| ‘| {d^m{OV H$s{OE Am¡a EH$ ^mJ

H$mo a§JrZ H$s{OE& BgH$mo {bIZo Ho$ {bE 101 ¶h Xg H$m

EH$ ^mJ h¡, Xe‘bd H$mo {bIZo Ho$ {bE 0.1 & Bg {dYmZ

H$mo Xe‘bd H$hVo h¡& nT>Zo Ho$ {bE eyݶ Xe‘bd 1 h¡&

Bgr àH$ma dJ© H$mo 100 ̂ mJm| ‘| {d^{OV H$aVo h¡& {bIZo Ho$

{bE 0.01 {bIVo h¡& nT>Zo Ho$ {bE eyݶ eV‘bd EH$ h¡&

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CXmhaU 2: Bg ‘| Xg g‘mZ Am¶V h¡& 1 ^mJ H$mo bmb a§J go ^[aE&

Xe‘mbd {bIZo Ho$ {bE N>m¶mH¥$V H$s{OE&

Xe‘mbd ‘| 101 H$mo Xÿgam ^mJ ‘mZm OmVm h¡& Xe‘bd ê$n ‘| {bIZo Ho$ {bE

0.1 ‘mZo OmVm h¡&

1) Xg g‘mZ ^mJm| H$mo Am¶V ‘| {bIm OmVm h¡& ham a§J go ^[a¶o&

2) ¶h 3 Am¶V h¡ Omo Zrbm a§J ^aVo h¡& Xe‘bd 0.3 h¡&

IV. {ZåZ{b{IV d¥Îm H$m {ZarjU H$s{OE&

1. {H$VZo ~mJm| N>m¶mH¥$V {H$¶m h¡?_________.

2 {^Þ ‘| {bIZo Ho$ {bE ___________. h¡&

{^Þ 101 H$mo {bIZo Ho$ {bE 0.1 h¡& ....................

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102 Xe‘bd g§»¶m 0.2 h¡& .................................. .

103 Xe‘bd g§»¶m 0.3 h¡& .................................. .

gmo{ME: 0.1, 0.2, 0.3 ³¶m Xem©Vo h¡?

D$na {X¶o CXmhaU H$m {ZarjU H$aZo Ho$ ~mX Xe‘bd H$m g§~§Y ahVm h¡&

gyMZm : Xe‘bd g§»¶m H$mo 춺$ H$aZo Ho$ {bE Xg ^mJ ahZm Mm{hE&

1 go 10 H$mo g§»¶m aoIm ‘o§ {Z{X©ï> H$a|Jo &

{ZåZ{b{IV g§X^© ‘o§ {ZarjU H$s{OE&

1 2 3 4 5 6 7 8 9 10

1 go 2 Ho$ ~rM 10 aoIm h¡& ñHo$b {ZarjU H$s{OE&

0 Am¡a 1 {MÌ Ûmam {Z{X©ï> H$aVo h¡&

0.1 0.30.2 0.50.4 0.6 0.90.8 1.00.7

VoOm

VoOm H$m¡Z go {~ÝXþ ‘o§ IS>m h¡? ~mobZo Ho$ 0.1 EH$ Xe‘bd ‘o‘ {bIZo Ho$ {bE

hgrZm H$m¡Z go {~ÝXþ na IS>r h¡? 0.3

‘§Oy H$m¡Z go {~ÝXþ na ISr h¡? 1.0

hgrZm ԤOy

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gyMZm : 0 Am¡a 1 Ho$ g§»¶m aoIm ‘| 10 g‘mZ ^mJ hmoVm h¡& 101 1 10

1# =

Om{ZE

^mJm| H$s g§»¶m 10 ‘| {b¶m

OmVm h¡&

EH$ ~Q>o Xgdmm± .10

1 0 1=

^mJm| H$s g§»¶m 100 ‘o‘ {b¶m OmVm

h¡&

EH$ ~Q>o gm¡dm 0.01100

1 =

Xe‘bd {^Þ H$mo ñWmZ ‘yë¶ ‘o H¡$go {bIZm h¡&

nwZ… ñWmZ ‘yë¶ MmQ>© ~ZmZo Ho$ ¶mX H$a|Jo &

hOma gm¡ do Xgdm± eyݶ 1000 100 10 1

10 Am¡a 100 H$mo ñWmZ ‘yë¶ MmQ>a ‘o‘ {bIZm {gIm h¡&

hOma gm¡ Xg eyݶ . EH$ ~Q>o Xg

dm± ^mJ

EH$ ~Q>o gm¡ do

^mJ 1000 100 10 1 .

101

1001

nyUmªH$ ^mJ Xe‘bd {MÝh({~ÝXþ)Xe‘bd ^mJ

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ñWmZ_yë` MmQ>© H$m {Z[ajU H$s{OE& Xe_bd q~Xÿ Ho$ ~m`r Va\$ A§H$ hmoVo

h¡ Am¡a Xm`r Va\$ ^r A§H$ hmoVo h¡& {ZarjU H$s{OE H$s Xe_bd H$s Xm`r Va\$

A§H$ H$m H«$_ ~T>Vm h¡ O~ Xm`r go ~m`r Va\$ MbVo h¡&

ñWmZ_yë` MmQ>© H$m {ZarjU H$s{OE& O~ Xe_bd q~Xÿ Ho$ XmE Va\$ MbVo

h¡, H«$_ ~T>Vm `m KQ>Vm h¡? kmV H$s{OE&

{ZåZ{b{IV MmQ>© H$m {ZarjU H$s{OE

{^Þ A§e ha Xe‘bd ê$n

1) 101

2) 102

3) 103

4) 1001

5) 1002

6) 1003

1

2

3

1

2

3

10

10

10

100

100

100

0.1

0.2

0.3

0.01

0.02

0.03

Xe‘bd Ho$ ê$n ‘| {bIZo Ho$ {bE ha H$s g§»¶m H$mo {ZarjU H$s{OE&

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gyMZm

¶{X Xe‘bd {~ÝXþ ‘| g§»¶m hmo Vmo Cgo Xe‘bd g§»¶m H$hVo h¡&

Xe‘bd H$m Xÿgam ê$n {^Þ H$mo 춺$ H$aZm h¡&

Xe‘bd H$m AW© {^Þ H$m ha 10, 100, 1000 .......... ¶{X

H$m¶© H$bmn: XÎm AmH¥$Vr H$m {ZarjU H$s{OE&

nrQ>a N>moQ>r nopÝgb H$s b§~mB© nT>Zo H$m à¶ËZ H$aVm h¡&

‘oar : nrQ>a nopÝgb H$s b§~mB© ³¶m h¡?

nrQ>a : nopÝgb H$s b§~mB© 3 go‘r go Á¶mXm Am¡a 4 g|.‘r. go H$‘ h¡&

‘oar : Omo g§»¶m nyU© Zht h¡ CZH$mo nT>Zo Ho$ {bE ~mobVr h¡&

{ZåZ{b{IVm| H$mo {ZarjU H$s{OE&

1 g|.‘r. H$mo 10 ^mJm| ‘| {d^{OV H$s{OE& ha EH$ ^mJ H$mo 0.1 H$hVo

h¡&

EH$ ~Q>o Xgdm± ^mJ H$mo 0.1 H$hVo h¡&

nT>Zo Ho$ {bE eyݶ Xe‘bd 1 H$hVo h¡&

nrQ>a A~ ghr b§~mB© ~mo{bE&

¶h 3 g|.‘r. Am¡a 8 Xe‘bd g|.‘r. h¡&

BgH$m AW© 3.8 g|.‘r. BgH$mo nT>Zo Ho$ {bE VrZ Xe‘bd 8 h¡&

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Aä¶mg 9.3

1) {ZåZ{b{IV Xe‘bd H$mo nT>H$a eãXm| ‘| {b{IE& 1) 0.2 2) 0.5 3) 0.7 4) 0.21 5) 0.02 6) 0.15

2) {ZåZ{b{IV eãXm| go Xe‘bd ‘| {b{IE&

1) eyݶ Xe‘bd VrZ

2) eyݶ Xe‘bd N>…

3) eyݶ Xe‘bd gmV

4) eyݶ Xe‘bd eyݶ Mma

5) eyݶ Xe‘bd eyݶ nm±M

3) {ZåZ{b{IV {^Þm| H$mo Xe‘bd ê$n ‘| {b{IE&

1) 101

2) 102

3) 103

4) 105

5) 1002

6) 1005

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