I Tavi

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I <strong>Tavi</strong> 32 jgufuri mecadineoba TamaSobs ori moTamaSe. viTamaSoT! I TamaSi. I moTamaSe asaxelebs ricxv 1-s an 2-s, meore moTamaSes SeuZlia dasaxelebul ricxvs daumatos 1 an 2 da asaxelebs miRebul jams. igebs is, vinc pirvelad daasaxelebs 51-s. ver mixvdiT? CaatareT erTmaneTSi es TamaSi ramdenjerme. romelma moTamaSem moigo? aRwereT, rogor unda iTamaSos moTamaSem (romelma?) sworad, rom moigos. II TamaSi. qvebis grovaSi 100 qvaa. moTamaSes erT svlaze SeuZlia aiRos 1 an 3 qva. igebs is moTamaSe, romelic bolo qvas aiRebs. romeli moTamaSe moigebs, Tu a) pirveli moTamaSe aiRebs 3 qvas; b) pirveli moTamaSe aiRebs 1 qvas. III TamaSi. qvis grovaSi 120 qvaa. moTamaSeebi, monacvleobiT, survilisamebr iReben a) 1, 2, 3 an 4, b) 1, 2, 3, 4 an 5 qvas. romeli moTamaSe moigebs da rogori wesiT unda iTamaSos man, rom moigos, Tu mogebulad iTvleba is moTamaSe, romelic aiRebs bolo qvas?
5 ricxvTa gayofadobis zogierTi Tviseba 1. saaxalwlo zeimze Tovlis babuam I a da I b klasis moswavleebs saCuqrad TiTo yuTi Sokoladis fila miutana. ganawile bis Semdeg aRmo Cnda, rom: a) I a klasis TiToeul moswavles Sexvda sam-sami fila, xolo I b klasis moswavleebs ki _ oTx-oTxi fila. SeeZlo Tu ara Tovlis babuas imave raodenobis Sokoladis fila (1 yuTi) 12 bavSvisTvis Tanabrad gaenawilebina? b) I a klasis TiToeul moswavles ergo eqvs-eqvsi fila, I b klasisas _ oTx-oTxi. SeeZlo Tu ara Tovlis babuas imdenive Sokoladis fila (1 yuTi) 24 bavSvisTvis Tanabrad gaena wilebina? Tqven ukve iciT zogierT ricxvze, magaliTad, 2-ze, 3-ze, 5-ze, 9-ze, 10-ze gayofadobis niSnebi. SeiZleba Tu ara davadginoT, kidev sxva ricxvebze, magaliTad 12-ze, 24-ze, 15-ze da a. S. gayofadobis niSnebi? amisTvis gavecnoT ricxvTa gayofadobis ramdenime Tvisebas. Tviseba 1. Tu a (bc), maSin a b da a c. marTlac, a (bc) niSnavs, rom ganayofSi miiReba mTeli ricxvi da sruldeba toloba: a=(bc)·n (1) Tu gamoviyenebT gamravlebis jufTebadobis Tvisebas, (1)-s SeiZleba aseTi saxe mivceT a=b(cn). radgan cn-ic mTeli ricxvia, es imas niSnavs, rom a b. analogiurad, a=c(bn), saidanac Cans, rom a c. marTlac, radgan 24 8, amitom 24 2 da 24 4 (2·4=8). 36 6, amitom 36 2 da 36 3 (2·3=6). sainteresoa, sruldeba Tu ara zemoT Camoyalibebuli winadadeba piriqiT? e.i. Tu a b da a c gaiyofa Tu ara a ricxvi maT namravlze, bc-ze? ganixileT ramdenime magaliTi. rogorc xedavT, Cvens mier Camoyalibebuli winadadeba zogjer sruldeba, zogjer ara. magaliTad, 12 iyofa 6-zec da 4-zec, magram 12 ar iyofa 6·4-ze. mocemul sqemaze kargad Cans rom 4·6=24 martiv mamravlebad daSlaSi u. s. g. (6;4)=2 orjer Sedis _ erTxel, rogorc 4-is, meored ki rogorc 6-is gamyofi. amitom cxadia, 12 aRar gaiyo maT namravlze. meores mxriv, 12 3 da 12 4. amasTan 12 12 (12=3·4) da u. s. g. (3;4)=1. yuradReba! C a n a w e r i a b ( a i y o f a b - z e ) a r aRniSnavs raime moqmedebas a da b ricxvebs Soris. igi aris winadadeba, romelic a-sa da b-s zogierTi mniSvne lobisTvis WeSmaritia, zogierTisTvis ki _ mcdari. 12 24 2 · 2 · 3 2 · 2 · 2 · 3 4 · 6 33
Page 3: nana jafariZe � maia wilosani �
Page 6 and 7: III Tavi . . . . . . . . . . . . .
Page 8 and 9: 6 rogor visargebloT wigniT wignze m
Page 10 and 11: I Tavi 8 1 VI klasSi Seswavlili mas
Page 12 and 13: I Tavi 10 savarjiSoebi: gamoiangari
Page 14 and 15: I Tavi msgavsi wevrebi rom Sevkribo
Page 16 and 17: I Tavi 14 Tvlis sistemebi Tema Tvli
Page 18 and 19: I Tavi 16 Tbilisi 180 km 2 gamosaxu
Page 20 and 21: I Tavi 18 SeavseT gamotovebuli adgi
Page 22 and 23: I Tavi (7,24,25) 20 (35,12,37) (5,
Page 24 and 25: I Tavi 22 imetyvele sworad! a 5 1.
Page 26 and 27: I Tavi 2,51 = = 5 1 2 + + 2 10 10 2
Page 28 and 29: I Tavi 26 Seamowme Seni codna: 1 mT
Page 30 and 31: I Tavi „ar iyofa“ aRiniSneba
Page 32 and 33: I Tavi 30 3 mwkrivSi dgas 137 jaris
Page 36 and 37: I Tavi naSTi yovelTvis nak lebia ga
Page 38 and 39: I Tavi 353 = 3·100 + 10·5 + 3 478
Page 40 and 41: I Tavi 38 22 ramdeni samniSna ricxv
Page 42 and 43: I Tavi 40 1 ∇ 2 3 ∇ 2 2 ∇ 1 s
Page 44 and 45: I Tavi 42 naxiri rema arve fara xal
Page 46 and 47: I Tavi 44 amoxsna: gamoviyenoT 3-ze
Page 48 and 49: I Tavi 46 7 simravleTa toloba . qve
Page 50 and 51: I Tavi 48 B A C 4. K qarTvel xelova
Page 52 and 53: I Tavi 50 8 simravleTa 1, 2, 3, 4,
Page 54 and 55: I Tavi 52 magaliTi 1. vTqvaT A={3;5
Page 56 and 57: I Tavi 54 I Tavis damatebiTi savarj
Page 58 and 59: I Tavi 56 26 udidesi orniSna ricxvi
Page 60 and 61: I Tavi 58 Seamowme Seni codna: 1. m
Page 62: 60 I TavSi Seswavlili masalis mokle

I Tavi

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