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§1.1. amocanebi naturaluri ricxvis Caweraze Tvlis Sedegad miRebul ricxvebs naturaluri ricxvebi ewodeba. naturaluri ricxvebia 1, 2, 3, 4, . . . . ricxvebis Casawerad specialur simboloebs, cifrebs viy-enebT. yvelaze gavrcelebulia aTobiTi poziciuri sistema, romelSic gamoiyeneba aTi cifri: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. am sistemaSi Cawerili ricxvi - 5327 oTxniSna ricxvia (mis Cana- werSi oTxi cifria gamoyenebuli), romelic 5 aTaseulis, 3 aseulis, 2 aTeulis da 7 erTeulis jamis mokle Canawers war-

moadgens. Tu am ricxvs Tanrigobrivi Sesakrebebis jamis saxiT CavwerT, miviRebT:5327=5·1000+3·100+2·10+7·1=5x103+3x102+2x101+7

amocana 1. CavweroT umciresi aTniSna naturaluri ricxvi, romelSic yvela cif-ri iqneba gamoyenebuli.amoxsna: radgan sul aTi cifri gvaqvs, aTniSna ricxvis Casawerad TiToeuli cifris mxolod erTxel gamoyeneba SegviZlia. umciresi ricxvis misaRebad maRal Tan-rigebSi SesaZlo umciresi cifrebi unda CavweroT. amasTan, Canaweris 0-iT dawyeba ar SeiZleba, amitom pirveli cifri iqneba 1, momdevno 0, Semdeg 2 da a.S. sabolood miviRebT Canawers 1023456789. pasuxi: saZiebeli ricxvia 1 023 456 789. amocana 2. davadginoT luwi samniSna ricxvebis raodenoba.amoxsna:pirvel rigSi davadginoT samniSna ricxvebis raodenoba. udidesi samniSna ricvia 999, e.i. 1-dan 999-is CaTvliT iqneba 999 ricxvi. magram maTgan pirveli 99 ricxvi araa sam-niSna. amitom samniSna ricxvebis raodenoba 999-99 sxvaobis tolia. am 900 ricxvidan nax-evari luwi ricxvia, naxevari ki kenti. e.i. luwi samniSna ricxvebis raodenobaa 450. pasuxi: luwi samniSna ricxvebis raodenobaa 450.amocana 3. ramdenia iseTi orniSna naturaluri ricxvi, romlis CanawerSi mxolod luwi cifrebia gamoyenebuli? amoxsna: amocana amovxsnaT ori gziT:I gza. zrdis mixedviT CavweroT luwi cifrebiT Sedgenili orniSna ricxvebi da da-viTvaloT:

20, 22, 24, 26, 28,40, 42, 44, 46, 48,60, 62, 64, 66, 68,80, 82, 84, 86, 88.

sul gamovida 20 ricxvi.II gza. sul gvaqvs 5 luwi cifri: 0, 2, 4, 6, 8. aqedan aTeulebis cifrad gamodgeba oTxi cifri 2, 4, 6, 8. TiToeul maTgans erTeulebad SegviZlia mivuweroT xuTi cifridan erT-erTi. magaliTad, Tu aTeu lebis TanrigSi 2-s davwerT, maSin saZiebeli saxis ricxvebi iqneba: 20, 22, 24, 26, 28, xolo, Tu 6-s davwerT, maSin saZiebeli saxis ricx-vebi iqneba: 60, 62, 64, 66, 68.

Tavi I. gayofadoba

mizani: viswavloT amo-canebis amoxsna aTobiTi pozi-ciuri sistemis gamoyenebiT

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ase, rom sul miviRebT 4 5× raodenobis ricxvs.

pasuxi: luwi cifrebiT sul 20 orniSna ricxvi iwereba.

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1. rogor ricxvs ewodeba naturaluri ricxvi? 2. ramdeni cifri gamoiyeneba aTobiT poziciur sistemaSi ricxvebis Casawerad? 3. ramdenniSna ricxvia 1 023 456 789? rogor ikiTxeba es ricxvi? 4. ra raodenobis luwi samniSna ricxvi arsebobs? kenti samniSna? 5. ramdeni orniSna ricxvis Caweraa SesaZlebeli luwi cifrebiT? 6. amocana 3-is amoxsnis romeli gza ufro moxerxebulia? ratom?

savarjiSoebi waikiTxe ricxvebi: a) 123 456 b) 90 090 090 g) 101 102 103 104. Cawere Tanrigobrivi Sesakrebebis jamis saxiT ricxvebi: a)13 592 b) 3 507 890 g) 100 100 100

Cawere SesaZlo umciresi samniSna ricxvi cifrebiT 0, 3, 4. Cawere SesaZlo udidesi oTxniSna ricxvi cifrebiT: 5, 7, 9, 0.

gamoiyene cifrebi 0, 2, 5, 7 TiTojer da Cawere SesaZlo udidesi luwi oTxniSna ricxvi. Cawere udidesi aTniSna naturaluri ricxvi, romelSic yvela cifri TiTojer iqneba gamoyenebuli.

ras udris umciresi eqvsniSna da udidesi samniSna naturaluri ricxvebis sxvaoba?

ras udris udidesi oTxniSna da umciresi samniSna naturaluri ricxvebis namravli? nikam ricxvSi 2597 cifri 5 Secvala 8-iT. ramdeniT meti ricxvi miiRo nikam Secvlis Sedegad?

Tedom ricxvSi 3481 cifrebi 4 da 1 gadaanacvla. gaizarda Tu Semcirda Tavda- pirveli ricxvi? ramdeniT?

Team samniSna ricxvs marcxnidan miuwera cifri 7. Tavdapirvelze ramdeniT meti ricxvi miiRo Team?

laSam oTxniSna ricxvs marcxnidan miuwera cifri 5. Tavdapirvelze ramdeniT meti ricxvi miiRo laSam?

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upasuxe kiTxvebs:

daadgine, ramdeni orniSna naturaluri ricxvi arsebobs da maT Soris ramdenia luwi da ramdeni kenti.

ramdenia iseTi orniSna ricxvi, romlis CanawerSi mxolod kenti cifrebia gamoyenebuli?

ras udris udidesi da umciresi samniSna ricxvebis namravli?

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lukam xuTive kenti cifris, xolo maTem xuTive luwi cifris gamoyenebiT Sesa- Zlo udidesi xuTniSna ricxvebi Caweres. lukas Cawerili ricxvia meti, Tu maTes Cawerili ricxvi? ramdeniTaa meti?

ramdenia iseTi samniSna ricxvi, romlis CanawerSi mxolod kenti cifrebia gam-oyenebuli?

ramdenia iseTi samniSna ricxvi, romlis CanawerSi mxolod gansxvavebuli ken-ti cifrebia gamoyenebuli?

salomem 48567-2573 sxvaobis gamoTvlisas maklebSi 5-s da 3-s adgilebi Seucva-la. am cvlilebis Sedegad gaizarda Tu Semcirda sxvaoba da ramdeniT?

naturaluri ricxvis Canawers marjvnidan miuweres cifri 7. miRebuli ricxvi 9-iT metia Tavdapirvel ricxvze. ipove Tavdapirveli ricxvi.

Cawere yvela orniSna ricxvi, romlis cifrTa namravli 24-is tolia.

gamoTvale gamosaxulebis mniSvneloba:

a) 1432 : 24 + 32575 : 25 b) 233 :184 - 10240 : 128 g) 16500 : (1100 : 11 - 5:17) d) (3357 : 36 - 317 : 18) : 11 : 99

Cawere wiladis saxiT: naxevari, meoTxedi, ori mesamedi, TerTmeti meSvidedi.

vaSli daWrilia 4 tol naWrad. vaSlis ra nawilia 1 naWeri? ori naWeri? sami naWeri?

TaTiam torti 8 tol naWrad daWra da maTgan sam-sami naWeri beqas da Tinikos gaunawila. tortis ra nawili darCa TaTias?

1. romeli ori ricxvis namravlia erT maTganze 10 - jer, meoreze ki 100_jer meti? 2. romeli ori ricxvis jamia erT maTganze 7-iT, meoreze ki 17-iT meti?3. ra cifriT dabolovdeba yvela erTniSna naturaluri ricxvis namravlis Canaweri?

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aba, gamoicani!

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§1.2. martivi da Sedgenili ricxvebi

mizani:amovxsnaT amo-canebi natura-luri ricxvis gamyofebsa da jeradebze.

amocana 1. ramdennairad SeiZleba 14 kurdRlis galiebSi Tanabrad ganawileba?amoxsna: 14 kurdRlis galiebSi Tanabrad ganawileba sxvadasx-vanairad SeiZleba. SesaZlebeli variantebis raodenoba im ricxvebis raodenobis tolia, romelzec 14 unaSTod iyofa. ricxvi 14 unaSTod iyofa Semdeg ricxvebze: 1, 2, 7, da 14. maSasa-dame, 14 kurdRlis galiebSi Tanabrad ganawileba oTxnairadaa SesaZlebeli:

I.erT galiaSi movaTavsoT yvela kurdReli;II.kurdRlebi 2 galiaSi movaTavsoT, TiToSi 7 kurdReli;III.kurdRlebi 7 galiaSi movaTavsoT, TiToSi 2 kurdReli;IV.kurdRlebi 14 galiaSi movaTavsoT, TiToSi TiTo kurdReli1, 2, 7 da 14 warmoadgenen 14-is gamyofebs. maSasadame, 14-s oTxi gamyofi aqvs. vTqvaT mocemulia ori naturaluri ricxvi M m da M nN. Tu M M m unaSTod iyofa M n N-ze, maSin N M n-s M M m-is gamyofi, xolo M M m-s N M n-is jeradi ewodeba.magaliTad, 7 gamyofia 14-is, xolo 14 jeradi 7-is. yovel naturalur ricxvs uamra-vi jeradi aqvs. magaliTad, 7-is jeradebia TviTon 7, 14, 21, 28 da a.S. ganxilul amocanaSi 14-is nacvlad 13 kurdReli rom yofiliyo gasanawilebeli, galiebSi maTi Tanabrad ganawileba mxolod ornairad iqneboda SesaZlebeli. ker-Zod, an cametives erT galiaSi, an TiTo kurdRels TiTo galiaSi movaTavsebdiT. am SemTxvevaSi galiebSi kurdRlebis Tanabari ganawilebis mxolod ori SesaZle-bloba imitomaa, rom 13-s mxolod ori gamyofi gaaCnia, 1 da 13. naturalur ricxvs, romelsac mxolod ori gamyofi aqvs, martivi ricxvi ewodeba. magaliTad, 13 martivi ricxvia. umciresi martivi ricxvia 2. martivi ricxvebia 2, 3, 5, 7, 11, 13, 17, 19, 23 da a. S. orze meti gamyofis mqone naturalur ricxvs Sedgenili ricxvi ewodeba.Sedgenili ricxvebia: 4, 6, 8, 9, 10, 12, 14, 15 da a. S.

1 araa marti-vi, radgan mas mxolod erTi gamyofi aqvs

magaliTi 1. martivia, Tu Sedgenili ricxvi 12075? amocana: gavixsenoT, rom 5-ze daboloebuli ricxvi unaSTod iyofa 5-ze. amitom 12075-s sul mcire, sami gamyofi mainc aqvs 1, 5 da 12075. pasuxi: 12075 Sedgenili ricxvia. magaliTi 2. ramdeni gamyofi aqvs: a) 9-s? b) 23-s? g) 30-s?

amoxsna: a) 9-is gamyofebia: 1, 3 da 9. e.i. 9-s sami gamyofi aqvs. b) 23-is gamyofebia: 1 da 23. e.i. 23-s ori gamyofi aqvs. g) 30-is gamyofebia: 1, 2, 3, 5, 6, 10, 15, 30. e.i. 30-s rva gamyofi aqvs. magaliTi 3. ramdeni martivi gamyofi aqvs 18-s?amoxsna: 18-is gamyofebia: 1, 2, 3, 6, 9, 18. maTgan martivi ricxvebia 2 da 3.pasuxi:. 18-s ori martivi gamyofi aqvs.

1. ras ewodeba ricxvis gamyofi? jeradi? 2. ra ricxvi iqneba mocemuli ricxvis udidesi gamyofi? umciresi gamyofi? 3. rogor ricxvebs hqvia martivi? Sedgenili? 4. arsebobs Tu ara luwi martivi ricxvi? kerZod romeli? 5. SeiZleba Tu ara iTqvas, rom yvela kenti ricxvi martivia? 6. ramdeni gamyofi aqvs 1-s? 7. ramdeni gamyofi aqvs martivi ricxvis kvadrats?

upasuxe kiTxvebs

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dawere a) 12-is b) 20-is g) 19-is d) 63-is yvela gamyofi. ramdeni gamyofi aqvs 4-s? 36-s? 23-s? 46-s?

daasaxele 45-is udidesi gamyofi.

ramdennairad SeiZleba 16 wignis Taroebze Tanabrad ganawileba?

ramden bavSvs SeiZleba Tanabrad gavunawiloT 25 vaSli ise, rom vaSlebi ar gavWraT?

savarjiSoebi

CamoTvale orniSna ricxvebi, romelic jeradia a) 10-is b) 15-is g) 17-is d) 33-is.

orniSna ricxvebidan ramdeni ricxvia a) 5-is b) 7-is g) 13-is jeradi?

Semdegi gamonaTqvamebidan romelia WeSmariti:

a) 27 gamyofia 9-is; g) 51 jeradia 17-is;b) 6-s aqvs ori gamyofi; d) 10 jeradia 100-is.

martivia Tu Sedgenili ricxvi 1? 2? 6?13? 27?

Semdegi ricxvebidan amowere martivi ricxvebi:1, 11, 21, 31, 41, 51, 61, 71, 81, 91.

Semdegi ricxvebidan amowere Sedgenili ricxvebi:3, 13, 23, 33, 43, 53, 63, 73, 83, 93.

ra ricxvia 17-is jeradi martivi ricxvi?

martivia Tu Sedgenili a) 135? b) 102576? g) 98530?

ramdeni martivi gamyofi aqvs a) 7-s? b) 25-s? 12-s? 70-s?

Cawere 0-iT daboloebuli 3-is jeradi orniSna ricxvebi.

Cawere 19-is jeradi luwi orniSna ricvebi.

daasaxele ricxvi, romelsac mxolod sami gamyofi gaaCnia.

daasaxele 5-is jeradi a) martivi ricxvi; b) umciresi Sedgenili ricxvi; g)udidesi samniSna ricxvi; d) umciresi SvidniSna ricxvi.

daasaxele ricxvi, romlis ori momdevno ricxvi martivia. ramdeni aseTi ricx vis dasaxelebaa SesaZlebeli?

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konkretul magaliTebze Seamowme Semdegi gamonaTqvamebis marTebuloba:a) Tu Sesakrebebi erTi da imave naturaluri ricxvis jeradia, maSin jamic am ricxvis jeradi iqneba.b) Tu ori Sesakrebidan erT-erTi raime naturaluri ricxvis jeradia, xolo meore ara, maSin jami ar iqneba am ricxvis jeradi.g) Tu erT-erTi Tanamamravli raime naturaluri ricxvis jera-dia, maSin namravlic am ricxvis jeradi iqneba.

Semdegi gamonaTqvamebidan romelia WeSmariti: a) yoveli martivi ricxvi kentia; b) yoveli kenti ricxvi martivia; g) yoveli naturaluri ricvi an martivia an Sedgenili; d) 2-ze meti yoveli luwi ricxvi Sedgenilia.

daasaxele ori martivi ricxvi, romelTa sxvaoba a) 1-is tolia; b) 2- is tolia; g) 4-is tolia.

Seamowme WeSmaritia Tu ara Semdegi gamonaTqvami: Tu samniSna ricxvs misi Canaweris cifrTa jams gamovaklebT, miviRebT 9-is jerad ricxvs.

ekam xuTive kenti cifris, xolo anam xuTive luwi cifris gamoyenebiT SesaZlo umciresi xuTniSna ricxvebi Caweres. ekas Cawerili ricxvia meti, Tu makas Caweri- li ricxvi? ramdeniTaa meti?

ramdenia iseTi samniSna ricxvi, romlis CanawerSi mxolod gansxvavebuli luwi cifrebia gamoyenebuli?

gamosaxe wiladiT figuris gaferadebuli nawili:

moifiqre wiladi, Aromlis a) mricxveli 3-iT metia mniSvnelze;b) mniSvneli 4-jer metia mricxvelze?

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mocemul orive naxatze saswori gawonasworebulia.naxatis mixedviT Seadare: a) kubis masa cilindris masas; b) cilindris masa birTvis masas; g) kubis masa cilindris masas;

gaiTvaliswine Sen mier Catarebuli gamoTvlebis Sedegebi da imis mixedviT gansazRvre, rogor gavawonasworoT saswori qvemoT mocemul TiToeul Sem- TxvevaSi.

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?1.3 gayofadobis niSnebi gayofadobis niSnebi gvexmareba gayofis moqmedebis Ses-rulebis gareSe davadginoT, iyofa Tu ara esa Tu is natu-raluri ricxvi mocemul naturalur ricxvze una-STod. rogorc mexuTe klasidan iciT imis dasadgenad, iyofa Tu ara unaSTod ricxvi 2-ze, 5-ze da 10-ze, sakmarisia vicodeT am ricxvis Canaweris bolo cifri. kerZod:2-ze iyofa is da mxolod is ricxvebi, romelTa Canaweris bolo cifri luwia.5 –ze iyofa is da mxolod is ricxvebi, romelTa Canaweris bolo cifria 0 an 5. 10 –ze iyofa is da mxolod is ricxvebi, romelTa Canaweris bolo cifria 0.

magaliTad, ricxvebidan 2570, 35007 pirveli iyofa 2-zec, 5-zec da 10-zec, radgan misi Canaweri akamayofilebs gayofadobis zemoTmocemul samive pirobas, xolo meore ar iyofa arc 2-ze, arc 5-ze da arc 10-ze, radgan misi Canaweris bolo cifri arc luwia, arc 0 da arc 5. sakmarisia Tu ara bolo cifris codna imis dasadgenad, iyofa Tu ara mocemuli ricxvi 9-ze. am kiTxvaze pasuxi uaryofiTia. magaliTad ric-xvebs 18-s da 28-s erTi da igive bolo cifri aqvT, magram 18 iyofa 9-ze, 28 ki ara. 9-ze gayofadobis niSnis dasadgenad ganvixiloT magaliTi: magaliTi 1. gavarkvioT iyofa Tu ara 9-ze ricxvi a) 756; b) 321. a) warmovadginoT 756 ori Sesakrebis jamad: 756=7:100+5:10+6=(7:99+7)+(5:9+5)+6=(7:99+5:9)+(7+5+6) miRebuli jamis pirveli Sesakrebi 9-is jeradi ricxvia. 9-is jeradia meore Se- sakrebic, radgan 7+5+6 = 18. amitom maTi jamic iqneba 9-is jeradi, anu 756 iyofa 9-ze. b) Tu 321-s warmovadgenT jamis saxiT miviRebT:

321=3:100+2:10+1=(3:99+3)+(2:9+2)+6=(3:99+2:9)+(3+2+1) am SemTxvevaSic, miRebuli jamis pirveli Sesakrebi 9-is jeradia, xolo meore Sesakrebi 3+2+1=6 - ara. amitom maTi jami ar gaiyofa 9-ze. ganxilul orive magaliTSi mocemuli ricxvebi davSaleT ori Sesakrebis jamad, romelTagan pirveli Sesakrebi iyofoda 9-ze, xolo meore Sesakrebi am ricxvebis cifrTa jams warmoadgenda. amitom, am ricxvebis 9-ze gayofadoba mxolod maT cif-rTa jamze aRmoCnda damokidebuli. sazogadod, nebismieri naturaluri ricxvi SegviZlia 9-is jeradi ricxvisa da am ricxvis cifrTa jamis saxiT warmovadginoT. magaliTad, oTxniSna naturaluri ricxvi, romlis aTaseulebis cifria a, aseulebis cifri b, aTeulebis cifri b da erTeulebis cifri d, Semdegi saxiT warmodgeba:

1000a +100b +10c +d =(999a + 99b + 9c)+(a +b +c+c )aqedan vaskvniT: 9-ze iyofa is da mxolod is naturaluri ricxvebi, romelTa Canaweris cifrTa jami iyofa 9-ze. imis gamo, rom zemoaRniSn ul warmodgenaSi 9-is jeradi Sesakrebi 3-is jeradi-caa, ricxvis 3-ze gayofadobac am ricxvis cifrTa jamze iqneba damokidebuli. 3-ze iyofa is da mxolod is naturaluri ricxvebi, romelTa Canaweris cifrTa jami iyofa 3-ze.

mizani1. viswavloT 3-ze da 9-ze gayofado-bis niSnebi;2. gamovi yenoT gayofadobis niSnebi wiladis Sesakvecad.

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magaliTi 2. davadginoT Semdegi ricxvebidan romlebia 3-is jeradi: 3512, 8.109+10, 18.107+4, 9.13+12amoxsna: 35012-is cifrTa jamia 3+5+0+1+2=11. 11 araa 3-is jeradi, amitom 35012 araa 3-is jeradi. 8:109+10 = 8 000 000 010. am ricxvis cifrTa jami 9-is tolia, amitom es ricxvi samis jeradia. 18.107+4 jamis pirveli Sesakrebi 18:107 3-is jeradia, radgan 18 jeradia 3-is, meore Sesakrebi 4 ki araa 3-is jeradi. amitom jami araa 3-is jeradi. 9.13+12 jamis TiToeuli Sesakrebi 3-is jeradia, amitom jamic 3-is jeradi iqneba. pasuxi: 8:109+10 da 9:13+12 3-is jeradi ricxvebia, xolo 35012 da 18:107+4 araa 3-jeradi. gayofadobis niSnebi SegviZlia gamoviyenoT wiladebis Sesakvecad. amisaTvis gavixsenoT wiladis ZiriTadi Tviseba: wiladis mricxvelisa da mniSvnelis nulis aratol ricxvze gamravleba-gayofiT wiladis mniSvneloba ar icvleba.magaliTi 3. SevkvecoT wiladi: a) b)

a) wiladis mricxveli da mniSvneli bolovdeba 5-iT, amitom orive maTgani unaSTod iyofa 5-ze.

b) -is rigorc mricxvelis, ise mniSvnelis cifrTa jami 3-is jeradia. amitom orive maTgani unaSTod iyofa 3-ze.

6555 ; 834

51 .

6555

83451

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65:555:5 =

1311 ;

83451 =

834:351:3 =

27817

1. rogor Seamowmeb mocemuli naturaluri ricxvi iyofa Tu ara 2-ze? 5-ze? 10-ze?2. sakmarisia Tu ara Canaweris bolo cifris codna imis dasadgenad, iyofa Tu ara mocemuli ricxvi 9-ze? 3-ze?3. rogor Seamowmeb mocemuli naturaluri ricxvi iyofa Tu ara 9-ze? 4. arsebobs Tu ara 9-is jeradi ricxvi, romlis Canaweris cifrTa jami ar iyofa 9-ze?5. rogor Seamowmeb mocemuli naturaluri ricxvi iyofa Tu ara 3-ze? 6. arsebobs Tu ara 3-is jeradi ricxvi, romlis Canaweris cifrTa jami ar iyofa 3-ze?7. gaiyofa Tu ara 9-ze jami, Tu a) yvela Sesakrebi iyofa 9-ze? b) ori Sesakrebidan erTi iyofa 9-ze, meore ki ara?8. SeiZleba Tu ara jami iyofodes 3-ze da arcerTi Sesakrebi ar iyofodes 3-ze?9. wiladis ra Tvisebas viyenebT Sekvecis dros?

upasuxe kiTxvebs

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savarjiSoebi Semdegi ricxvebidan amowere 5-is jeradi ricxvebi:

23354, 30795, 17001, 16940.

Semdegi ricxvebidan amowere 5-is jeradi luwi ricxvebi:73158, 3195, 230010, 2949, 13570.

ricxvebidan: 302, 45890, 1030, 5005, 5559, 557, 5023, 950 ramdeni ricxvia 5-is jeradi?

SeiZleba Tu ara 75 kanfeti Tanabrad gaunawiloT 5 bavSvs? 10 bavSvs?

mxolod luwi cifrebis gamoyenebiT dawere 5-is jeradi ricxvi.

daTvale 5-is jeradi orniSna ricxvebis raodenoba.

Semdegi ricxvebidan amowere 9-is jeradi ricxvebi:23354, 30795, 17001, 16940.

ricxvebidan: 3024, 236, 102, 1729, 9021, 9531, 19395 ramdenia 9-is jeradi? Semdegi ricxvebidan amowere 9-is jeradi kenti ricxvebi:

252, 3195, 530010, 2949, 330093.

Semdegi ricxvebidan amowere 3-is jeradi ricxvebi:111, 350, 10796, 1701, 16942.

mamam n TeTri sam Svils Tanabrad gaunawila. Semdegi tolobebidan romelia SesaZlebeli: a) n = 35 b) n = 75 g) n = 130.

SeiZleba Tu ara, rom klasSi iyos 28 moswavle, Tu moswavleTa mesamedi gogonaa?

gaarkvie Semdegi gamonaTqvamebidan romelia mcdari:

a)5-is jeradi yvela luwi ricxvi 10-is jeradia;b)3-is jeradi yvela luwi ricxvi 6-is jeradia;g) 3-isa da 9-is jeradi yvela ricxvi 27-is jeradia; d) 3-isa da 5-is jeradi yvela ricxvi 15-is jeradia.

Semdegi ricxvebidan amowere 6-is jeradi ricxvebi:114, 231, 796, 1062, 10042.

ricxvebidan: 3020, 1235, 1025, 5490, 2580, 9574, 23346 ramdenia 15-is jeradi? fifqis nacvlad ra cifrebis CasmiT miiReba 9-is jeradi ricxvi? a) 513*; b) 34*3; g) 1*370.

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