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Lesson 4 Math Class 5th.pdf
1.
v/;k; & 4
fgLls vkSj iwjs iz’u 1- gekjs >.Ms ds fdrus Hkkx esa dkSu dkSu ls jax gSa mRrj & gekjs >aMs dk Åijh fgLlk dslfj;k jax dk gS chp ds Hkkx dk lQsn jax ,oa e/; esa v’kksd pØ gS] rFkk Hkkx uhps okyk gjk jax dk gS iz’u 2- eatw ds ikl ,d pkWdysV Fkh mlus ,d pkSFkkbZ jkth dks] ,d frgkbZ lqxa/kk dks vkSj NBk Hkkx 'khyk dks fn;kA ckdh fgLlk mlus [kk fy;k gjsd dks pkWdysV ds fdrus fgLls feys ;gak fy[kksA mRrj & jkth us ,d pkSFkkbZ ¾ 12 x = 3 Hkkx lqxa/kk us ,d frgkbZ ¾ 12 x = 4 Hkkx 'khyk us NBk Hkkx ¾ 12 x = 2 Hkkx eatw us pkWdysV dk fgLlk [kk;k ¾ dqy Hkkx & fn;k Hkkx = 12 – 9 (3+4+2) = 3 Hkkx vr% eatw us pkWdysV dk ,d pkSFkkbZ Hkkx 3 Hkkx [kk;k iz’u 3- Vksfi;ksa dks jaxks mRrj & dqy Vksih 15 Vksfi;ksa dks yky jaxks vFkkZr 15 x Vksfi;ksa dks uhyk jaxks vFkkZr 15 x rqeus fdruh Vksfi;ksa esa yky jax Hkjk ¾ 5 rqeus fdruh Vksfi;ksa esa uhyk jax Hkjk ¾ 9 Vksfi;ksa ds dkSu ls Hkkx esa dksbZ jax ugha Hkjk x;k ¾ 1 iz’u 4- f=Hkqt ds cjkcj fgLls djks
2.
lQsn f=Hkqt dks
3 cjkcj fgLlksa esa ckaVk x;k gS gjsd frgkbZ Hkkx dks vyx vyx jax ls HkjksA D;k rqe fn[kk ldrs gks fd ;s Hkkx cjkcj gSa lkspks dSls vc bl f=Hkqt dks vyx rjhds ls rhu cjkcj fgLlksa esa ckaVus dh dksf’k’k djksA gjsd frgkbZ Hkkx esa vyx&vyx jax HkjksA iz'u 5- fuEu vk;r dks N% cjkcj Hkkxksa esa fdl rjg ckaVk tk ldrk gS iz’u 6- rqe ;g dSls irk djksxs fd vk;r dk gj Hkkx fgLlk gh gS mRrj & Ldsy dh lgk;rk ls ekidj iz’u 7- gjh vk;r uhyh vk;r ls cMh gS D;k ge dg ldrs gSa fd gjh vk;r dk Hkkx uhyh vk;r ds Hkkx ls cMk gS mRrj & ugha nksuksa vk;r ds Hkkx cjkcj gSaA iz’u 8- chjcy us buke ds :Ik esa 100 FkIiM gh D;ksa ekaxs mRrj & rkdh ykyph pkSdhnkj dks lcd fl[kk ldsA iz’u 9- blds ckn D;k gqvk gksxk dgkuh dks iwjk djks dfo dks buke dk fdruk fgLlk feyk mRrj & igys pkSdhnkj dks 100 dk fgLlk vFkkZr 10 FkIiM feys nwljs pkSdhnkj dks 100 dk fgLlk vFkkZr 40 FkIiM feys rhljs pkSdhnkj dks 100 dk vk/kk fgLlk vFkkZr 50 FkIiM feysA vkSj bl izdkj chjcy dks dksbZ FkIiM ugha feykA iz’u 10- fgLlksa esa iSVuZ ¼1½ B, C, D fxzM ds dqN [kkuksa dks jax dj vyx&vyx iSVuZ cukvksA rqeus fxzM dk fdruk fgLlk jaxk gS fxzM dk fdruk fgLlk lQsn jgk fy[kksA
3.
A B C
D uhyk lQsn uhyk lQsn uhyk lQsn uhyk lQsn ¼2½ fxzM dks fQj ls ns[kks D;k fxzM esa Hkjk gqvk jax & ¼d½ uhyk] lQsn ¼[k½ uhyk] lQsn ¼x½ uhyk] lQsn (x) ¼?k½ uhyk] lQsn xyr mRrj ij fu’kku ¼x½ yxkvksA ¼3½ 16 [kkuksa dh viuh fxzM cukvks vkSj ,sls isVuZ cukvks ftlesa ¼d½ yky] ihyk] gjk gks ¼[k½ yky] ihyk] gjk gks iz’u 11- jkew dk lfCt;ks dk [ksr ¼1½ [ksr ds lcls cMs fgLls esa og dkSu lh lCth mxk jgk gS fdruk fgLlk mRrj & VekVj ¼2½ fdrus fgLls esa og vkyw mxk jgk gS mRrj & ¼3½ fdruk fgLlk ikyx mxkus ds fy;s mi;ksx fd;k x;k mRrj & fdruk fgLlk cSaxu mxkus ds fy;s mi;ksx fd;k x;k mRrj & ¼4½ vc rqe bl fp= dks ns[kdj dqN iz’u fy[kks & v½ jkew vius [ksr esa dqy fdrus izdkj dh lCth mxk jgk gS mRrj & ikap
4.
c½ fdrus Hkkx
esa cSaxu o fdrus Hkkx esa VekVj mxk jgk gS mRrj & cSaxu mxkus & Hkkx rFkk VekVj mxkus ds fy;s Hkkx iz’u 12- jkew us dqN lfCt;ka vius nksLrksa dks nsus dh lksphA mlus vcwcdj dks fgLlk VekVj vkSj fgLlk vkyw fn, l`tk dks fgLlk VekVj vkSj fgLlk vkyw feysA uSUlh dks cph gqbZ lfCt;ka feyhaA vcwcdj ds fgLls ij uhys jax ls xksyk cukvksA l`tk dks feys Hkkx dks ihys xksys ls fn[kkvksA mRrj & dqy VekVj ¾ 20 rFkk dqy vkyw ¾ 18 vr% vcwodj dks ¾ 4 VekVj rFkk 6 vkyw VekVj dk fgLlk ¾ 20 x = 4 VekVj fn, vkyw dk fgLlk ¾ 18 x = 6 vkyw fn, vr% l`tk dks ¾ 8 VekVj rFkk 9 vkyw VekVj dk fgLlk ¾ 20 x = 8 VekVj fn, vkyw dk fgLlk ¾ 18 x = 9 vkyw fn, vr% cph gqbZ lfCt;ka uSUlh dks ¾ 8 VekVj rFkk 3 vkyw feys 20 – 12 (4 + 8) = 8 VekVj rFkk 18 – 15 (6 + 9) = 3 vkyw feysA iz’u 13- vanktk yxkvks vkSj tkapks & ¼d½ gjsd vkd`fr dk fdruk Hkkx jaxk gqvk gS igys vanktk yxkvks vkSj fQj mRrj dks tkapksA ¼1½ ¼2½ ¼3½ ¼2½
5.
¼[k½ D;k rqEgsa
;g fp= ;kn gS NksVs f=Hkqt dks ns[kks ;g oxZ dk dkSu lk fgLlk gS rqe ;g dSls irk yxkvksxs mRrj & cMs f=Hkqtksa vkSj nwljh vkd`fr;ksa dks NksVs&NksVs f=Hkqtksa esa ckaVks ¼yky f=Hkqt dh rjg½ dqy fdrus NksVs f=Hkqt cusaxs mRrj & 16 iz’u 15-jaxhu fgLls bUgsa iwjk djks & mRrj & bl o`Rr dkss nks cjkcj fgLlksa esa ckaVk x;k gSA 2 cjkcj fgLlksa esa ls ,d Hkkx esa uhyk jax fd;k x;k gSA bl o`Rr dkss 4 cjkcj fgLlksa esa ckaVk x;k gSA 4 cjkcj fgLlksa esa ls 2 Hkkx esa uhyk jax fd;k x;k gSA bl o`Rr dkss 6 cjkcj fgLlksa esa ckaVk x;k gSA 6 cjkcj fgLlksa esa ls 3 Hkkx esa uhyk jax fd;k x;k gSA bl o`Rr dkss 8 cjkcj fgLlksa esa ckaVk x;k gSA 8 cjkcj fgLlksa esa ls 4 Hkkx esa uhyk jax fd;k x;k gSA rks ge dg ldrs gSa fd iz’u 16- gYkos dks dkVuk ¼1½ mlus nksuksa ds fy, bldk nks cjkcj Hkkxksa esa ckaVkA gjsd dks gyos dk vk/kk fgLlk feysxkA
6.
¼2½ vc vEew
us fQj VqdMksa dks fQj ls vk/kk vk/kk ckaVkA ;g gyos dk fdruk fgLlk gS ¼3½ vc gjsd cPps dks fdrus VqdMs feysaxs & 4 ¼4½ gj VqdMk gyos dk fdruk fgLlk gS ¼5½ vxj jes’k us gyos dks 6 cjkcj fgLlksa esa dkVk gksrk rks gjsd dks fdrus VqdMs feys gksrs iz'u 17- igys % D;k ;g cjkcj gS vfeuh dgrh gS fd vk/ks dk vk/kk vkSj rhu pkSFkkbZ dk ,d frgkbZ cjkcj gSaA D;k rqe ;g ekurs gks rqe dSls fn[kkvksxs mRrj & vk/ks dk vk/kk rhu pkSFkkbZ dk ,d frgkbZ nksuksa cjkcj gSaA iz’u 18- fgLls ls iwjs dh vksj & ¼1½ ;gak ij ,d Qwy dh ifRr;ka fn[kkbZ xbZ gSa ckdh ifRr;ksa dk fp= cukdj Qwy dks iwjk djksA ¼2½ fp= esa ia[ks ds ,d frgkbZ CysM fn[kkbZ ns jgs gSa ckdh CysM cukdj fp= dks iwjk djksA ¼3½ ,d nwljs ia[ks ds vk/ks CysM ;gka fn[kk, x, gSa ckdh vk/kk fgLlk cukdj fp= dks iwjk djksA rqeus fdrus CysM cuk, gSa mRrj & geusa nks CysM cuk, gSaA
7.
izz’u 19- :Ik;s
vkSj iSls ¼1½ fdrus 50 iSls ,d :Ik;k cuk;saxs & nks 50 iSls feydj 1 :I;k cuk;saxhA ¼2½ D;k 50 iSls ,d :Ik;k dk vk/kk gS & gk¡ ¼3½ fdrus 25 iSls ,d :Ik;k cu,saxs & pkj 25 iSls feydj 1 :Ik;k cuk,asxhA ¼4½ 25 iSlk ,d :Ik;s dk fgLlk gSA ¼5½ 20 iSlk ,d :Ik;s dk fgLlk gSA ¼6½ fdrus 10 iSls feydj ,d :Ik;k cuk,sa & nl 10 iSls feydj 1 :Ik;k cuk,saxs ¼5½ nl iSls ,d :Ik;s dk fgLlk gSA iz'u 20- ,d cw<h vkSjr dh clh;r dk cVokjk dSls gqvk ppkZ djks mRrj & pkph us clh;r dk cVokjk fd;kA 19 Å¡ esa viuk ,d Å¡V feykdj 20 dj fn, fQj cVokjk bl izdkj gqvk & cMh csVh dks Å¡Vksa dk Hkkx ¾ Å¡V feys nwljh csVh dks Å¡Vksa dk Hkkx ¾ Å¡V feys rhljh csVh dks Å¡Vksa dk Hkkx ¾ Å¡V feys bl izdkj dqy 19 Å¡V caV x, ckdh cpk 1 Å¡V pkph us okfil ys fy;kA iz’u 21- v:.k fdrus ?k.Vs ysrk gS crkvks & [ksyuk & fnu dk vkBoka fgLlk] i<uk & fnu dk fgLlk mRrj & ,d fnu dk ,d frgkbZ fgLlk ¾ ?k.Vs] lksus ds fy;s ,d fnu dk vkBoka fgLlk ¾ ?k.Vs] [ksyus ds fy;s ,d fnu dk ,d pkSFkkbZ fgLlk ¾ ?k.Vs] i<+us ds fy;s iz’u 22- ,d fnu esa fdrus ?k.Vs gksrs gSa mRrj & 24 ?k.Vs iz’u 23-Ldwy if=dk dc fudyrh gS vkSj dkSu&dkSu ls eghus esa fudyrh gS
8.
mRrj & Ldwy
if=dk lky ds gj frekgh vFkkZr gj rhljs eghus esa fudyrh gS 1 2 3 4 5 6 7 8 9 10 11 12 3 & ekpZ ] 6 & twu ] 9 flrEcj ] 12 fnlEcj ekg esas fudysxhA iz’u 24- dqaHkdj.k dkSu Fkk og D;ksa izfl) Fkk mRrj & dqaHkdj.k jko.k dk HkkbZ FkkA og vk/ks lky vFkkZr 6 ekg lksus ds fy;s izfl) FkkA iz’u 25- dhfrZ dh [kjhnnkjh lwph & ¼1½ 2 fdyks VekVj fdrus ds gSa pawfd 1 fdyks 12 :Ik;s ds rks 2 fdyks VekVj 2x12 = 24 :Ik;s ¼2½ fdyks VekVj fdrus ds gksaxs pawfd 1 fdyks 12 :Ik;s ds rks vk/kk fdyks VekVj 12 x = 6 :Ik;s ¼3½ fdj.k dks 2 fdyks VekVj pkfg, mls os fdrus ds feysaxs pawfd 1 fdyks 12 :Ik;s ds rks 2 <kbZ fdyks VekVj ¾ 24 + 6 = 30 :Ik;s ¼4½ fdyks vkyw dh dher D;k gksxh pawfd 1 fdyks vkyw dh dher ¾ 10 :Ik;s gSA rks 3 lk<s rhu fdyks VekVj dh dher ¾ 30 + 5 = 30 :Ik;s ¼5½ fdyks xktj dh dher D;k gksxh pawfd 1 fdyks xktj dh dher ¾ 18 :Ik;s gSA rks 1 lok fdyks xktj dh dher ¾ 18 + 4.5 = 22 :Ik;s 50 iSls ¼6½ mlus fdyks ykSdh [kjhnk mldh dher D;k gS pawfd 1 fdyks ykSdh dh dher ¾ 8 :Ik;s gSA rks 4 fdyks ykSdh dh dher ¾ 8 x 4 = 32 :Ik;s gSA rks 4 ikSus ikap fdykss ykSdh dh dher ¾ 32 + 6 = 38 :Ik;s gksxhA Pkht dher :Ik;ksa esa ¼fdyks ds fy;s½ VekVj vkyw I;kt Xktj ykSdh 12 10 16 18 8
9.
¼7½ dhfrZ ds
gkFk esa [kjhnnkjh lwph dks ns[ksaA mls ;g lc [kjhnus ds fy;s fdrus :Ik;s nsus iMsaxs & pht dher :Ik;ksa esa ¼fdyks ds fy;s½ ek=k [kpZ VekVj 12 2 24.00 vkyw 10 3 30.00 xktj 18 1 22.50 ykSdh 8 38.00 dqy 114.50 ¼8½ rqe tks lfCt;ka [kjhnuk pkgrs gks mudk fcy [kqn cukvksA irk yxkvks fd rqEgsa fdrus iSls nsus iMsaxs pht dher :Ik;ksa esa ¼fdyks ds fy;s½ ek=k [kpZ VekVj 12 42.00 vkyw 10 15.00 xktj 18 40.50 ykSdh 8 14.00 dqy 111.50 iz’u 26- vH;kl dk le; & ¼1½ jghe dh ;k=k & jghe dks vius Ldwy igqpaus ds fy;s fdyksehVj lQj djuk iMrk gSA mls Ldwy tkus vkSj ogka ls ?kj vkus esa dqy fdruh nwjh r; djuh iMrh gS mRrj & ?kj ls Ldwy igqpaus ds fy;s r; dh xbZ nwjh ¾ fdyksehVj
10.
Ldwy ls ?kj
igqpaus ds fy;s r; dh xbZ nwjh ¾ fdyksehVj dqy r; dh xbZ nwjh ¾ $ ¾ fdyksehVj ¾ fdyksehVj ¼2½ dkSu ls flDds & yrk us 7-50 :Ik;s esa ,d isafly vkSj ,d dye [kjhnkA mlus dqy 10 :Ik;s fn,A nqdkunkj us mls vBUuh vkSj poUuh ds flDds okil fn, crkvks mls dkSu ls flDds feys mRrj & 10 :- & 7-50 :Ik;ss ¾ 2 :Ik;s 50 iSls vr% nqdkunkj 4 vBUuh ¾ 2 :Ik;s vkSj 2 poUuh ¾ 50 iSls ns nsxkA ¼3½ jsYos LVs’ku ij & cSaxykSj ls fr:vuUriqje tkus okyh xkMh eaxykSj ,Dlizsl vk/ks ?k.Vs ihNs py jgh gSA jsyxkMh dk lgh le; ikSus 7 cts dk gSA ¼d½ jsy ds vkus dk vuqekfur le; D;k gksxk & mRrj & lgh le; ikSu lkr vFkkZr & 6 ctdj 45 fefuV ysV vkus dk le; vk/kk ?k.Vk & 30 fefuV vuqekfur le; gksxk lok lkr & 7 ctdj 15 fefuV ¼[k½ ukft;k bl LVs’ku ls 2 ?kaVs ckn nwljs LVs’ku ij ?kaVs ckn nwljs LVs’ku ij mrjsxh og fdrus cts mrjsxh mRrj & bl LVs’ku ls jokuk gksxh Vsªsu & 7 ctdj 15 fefuV vr% nwljs LVs’ku 2 ?kaVs ckn ij igqapsxh Vsªsu & 9 ctdj 45 fefuV ¼x½ 'kkth dks bl jsy ls ,ukZdqye igqapus esa 5 ?kaVs yxsaxsA og fdrus cts ,ukZdqye igqapsxk mRrj & bl LVs’ku ls jokuk gksxh Vsªsu & 7 ctdj 15 fefuV vr% ,ukZdqye 5 ?kaVs ckn igqapsxh Vsªsu & 12 ctdj 15 fefuV ij
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