GM EMAT 6 ESP - 22 23 Fusionado
September 19, 2022 | Author: Anonymous | Category: N/A
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bks euhvks okths
Duïk nhb okhstrf 0.³ ]riokrik / ueinknhs ;-7-1 Duïk nh ouhstrk
okthoëtiaks aks gksknf HOK^ hs ue prfdrkok pkrk bk heshûkezk nh bks okthoëti he ohtfnfbfdïks ieefvknfrks quh phroithe ue kprhenizkch sidei`iaktivf. Drkaiks kb cuhdf, bk okeipubkaiñe y bks kativinknhs afethxtukbizknks, okthoëtiakss. tus kbuoefs nis`rutkrëe nh bks okthoëtiak
Knhoës, ohniketh bk shauheaikaiñe aïabiak nh bfs afetheinfs y bk nivhrsinkn nh hxphriheaiks nh kprhenizkch afeshduirës ue kprhenizkch prf`uenf y nurknhrf nhsnh hnknhs thoprkeks, rhsphtkenf tfnfs bfs ritofs nh kprhenizkch. K afetieukaiñe, heafetrkrës uek shbhaaiñe nh pëdieks nh bk Duïk nhb okhstrf, hb nfauohetf he hb quh sh nhskrrfbbke tfnks bks kativinknhs kb nhtkbbh y bfs ksphatfs phnkdñdiafs abkvhs pkrk prfdrkokr tu nïk k nïk. Y tfnf hb prfdrkok hstë nishûknf pkrk nkr rhspuhstk k bk euhvk bhy nh hnuakaiñe BFOBFH3
Nhskrrfbbf nh bks afophtheaiks hsphaï`iaks
Hvkbukaiñe afophtheaikb y afetieuk
Hstrkthdiks nh hnuakaiñe ieabusivk
^haefbfdïk kb shrviaif nhb kprhenizkch AighrHOK^ hs bk kpbiakaiñe pkrk bk prëatiak shokekb nh HOK^ nh okehrk kutñefok y phrsfekbizknk. AighrHOK^ AighrHOK^ phroith ue kprhenizkch knkptktivf, afe kativinknhs quh sh kcustke kb prfdrhsf nhb kbuoef.
Afe `hhngkaj ieohniktf pkrk `kaibitkr bk kutfefoïk.
¶Añof uskrbf6 He bk Duïk nhb okhstrf heafetrkrës nhtkbbknfs bfs afetheinfs quh sh trkgkcke he aknk shsiñe nh AighrHOK^.
^u dhstfr nh kubk, nïk k nïk He oyrffo, tu pbktk`frok nfaheth febieh, heafetrkrës tfnf bf quh ehahsitks pkrk iopbhohetkr hb prfdrkok he tu kubk. He oyrffo thenrës tfnk bk ie`frokaiñe frdkeizknk, afe tfnfs bfs rhaursfs ehahskrifs nhb nïk, pkrk rhkbizkr bks kativinknhs ¡he ue sfbf abia!
oyrffo.thjokehnuaktife.afo
;.³ ]riokrik
Nïk ; - X;
Afesubtk bfs okthrikbhs nh aknk shsiñe
^ u d h s t f r n h k u b k , n ï k k n ï k
Kaahnh k bks pbktk`froks niditkbhs
Nis`rutk nh vïnhfs sfgrh hb prfdrkok
¡Hb Bigrf nhb kbuoef tkogiée hs niditkb!
Hvkbók nh `frok afophtheaikb ]krk rhkbizkr uek hvkbukaiñe afetieuk y afophtheaikb th ieniakofs qué kativinknhs puhnhs rhkbizkr, auëenf y afe qué iestruohetfs auhetks.
Fgshrvkr hb nhshophûf
Whkbizkr ue nikdeñstiaf
Ksidekr ue eivhb
Xtibizk bfs ieniaknfrhs nh aknk shsiñe ksfaiknfs k aknk uek nh bks afophtheaiks, pkrk fgshrvkr hb prfdrhsf nh bfs kbuoefs.
He shsifehs hsphaïaks, utibizk ni`hrheths iestruohetfs pkrk rhkbizkr ue nikdeñstiaf nhb eivhb nh bfs kbuoefs.
Kb ekbizkr bk ueinkn f aursf, utibizk tfnk bk hvkbukaiñe rhkbizknk pkrk shûkbkr he qué eivhb nh bfdrf nh bk afophtheaik okthoëtiak sh heauhetrk aknk kbuoef.
• Whdistrf nh hvkbukaiñe.
7
b k i a e h t h p o f a k o r f ` h n k ó b k v H
• Hvkbukaiñe nh vhbfainkn nh aëbaubf ohetkb. • @ialk afof pruhgk. • ]feth k pruhgk. • ]ruhgk nh bk ueinkn.
• Wógriaks nh afophtheaik okthoëtiak pfr aiabf.
]krk uek hvkbukaiñe oës ëdib, pfehofs k tu nispfsiaiñe hb Whdistrf nh hvkbukaiñe y hb rhstf nh iestruohetfs he Knnitif `fr salffbs. ]fnrës hvkbukr nhsnh aukbquihr nispfsitivf afe ue sfbf abia y afopkrtir bfs rhsubtknfs he tihopf rhkb afe bks `koibiks. Kaahnh k trkvés nh oyrffo y nis`rutk nh tfnks sus vhetkcks. vhetkcks.
]krk rhkbizkr uek hvkbukaiñe afopkrtink afe tus kbuoefs, quh bhs phroitk tfokr afeaiheaik nh sus kprhenizkchs, k bf bkrdf nh bk ueinkn heafetrkrës3
Kativinknhs nh kutfhvkbukaiñe Kativinknhs quh phroithe kb kbuoef rhhxifekr sfgrh su kprhenizkch y kutfrrhdubkrsh. • • • • • •
Hsakbhrk nh ohtkafdeiaiñe Nikrif nh okthoëtiaks ]bketibbk nh rhsfbuaiñe nh prfgbhoks Wógriak nh rhsfbuaiñe nh prfgbhoks Kutfhvkbukaiñe ekb nh afetheinfs ]fr`fbif nh kprhenizkch
Kativinknhs nh hvkbukaiñe nhb kprhenizkch affphrktivf Kativinknhs quh phroithe kb kbuoef hvkbukr añof lk trkgkcknf he hquipf, añof trkgkcke sus afopkûhrfs y añof trkgkcke hbbfs. • • • •
Wógriak nh afhvkbukaiñe Drëak nh hvkbukaiñe nhb trkgkcf affphrktivf ^hbkrkûk nh hvkbukaiñe nhb trkgkcf affphrktivf Itiehrkrif nh hvkbukaiñe nhb trkgkcf affphrktivf
b k i a e h t h p o f a k o r f ` h n k ó b k v H
Whafefah bfs ofohetfs nh kprhenizkch Bks ueinknhs nh HOK^ hstëe iethrafehatknks hetrh sï, nh `frok quh bfs afetheinfs siduhe uek prfdrkokaiñe aïabiak y sh rhtfoke phriñniakoheth nhsnh uek drke nivhrsinkn nh hxphriheaiks nh kprhenizkch. Bk sisthoksideiaktivf y hb nhskrrfbbf nh bks tizkaiñe y shauheaikaiñe nh hstks kativinknhs lkahe pfsigbh hb kprhenizkch sideiaktivf lkgibinknhs okthoëtiaks nh `frok prf`uenk y nurknhrk, nhsnh ie`ketib lkstk priokrik. Afof skghofs quh bks fphrkaifehs gësiaks, suok, rhstk, oubtipbiakaiñe y nivisiñe, sfe afetheinfs abkvh he bk htkpk nh priokrik, th ieniakofs hb prfahsf nh kprhenizkch. ]krk lkahrbf, heafetrkrës bfs siduiheths iafefs he bks kativinknhs, shûkbkenf bfs siduiheths ofohetfs, quh sfe sihoprh kauoubktivfs3
1
W h a f e f a h b f s o f o h e t f s n h k p r h e n i z k c h
Afoprhesiñe
Ietrfnuaaiñe
]rëatiak
Afesfbinkaiñe
nhb afeahptf
nhb kbdfritof
nhb kbdfritof
nhb kbdfritof
Kativinknhs quh phroithe afefahr h iethrifrizkr hb afeahptf.
Kativinknhs he`faknks k nhsaugrir hb kbdfritof y añof utibizkrbf.
Kativinknhs pkrk prkatiakr hb usf nhb kbdfritof, nh okehrk prfnuativk f sisthoëtiak.
Kativinknhs niridinks k utibizkr hb kbdfritof he nivhrsinkn nh situkaifehs pkrk kkezkr.
¶[ué puhnhs lkahr afe hstk ie`frokaiñe6 •
Qhduir bk dbfgkbinkn nhb prfahsf nh kprhenizkch nh bks fphrkaifehs gësiaks.
•
Nhthatkr he qué ofohetf sh heauhetrk aknk kbuoef, pkrk f`rhahrbh bks kativinknhs quh ehahsitk.
•
]rifrizk r, nhetrf nh bk kativinkn, hb fgchtivf rhbkaifeknf ]rifrizkr afe hb ofohetf nh kprhenizkch.
h c k z i n e h r p k h n s f t e h o f o s f b h a f e f a h W
Fgchtivfs nh kprhenizkch Keths nh prf`uenizkr he aknk uef nh bfs nïks, afopkrtiofs bfs fgchtivfs nh kprhenizkch nh tfnf hb aursf pkrk thehr uek visiñe afopbhtk. Bfs fgchtivfs rhskbtknfs sfe bfs quh sh trkgkcke afe okyfr iethesinkn k bf bkrdf nh aknk ueinkn.
XEINKN ;
XEINKN 7
XEINKN 1
• Inhetiakr hb vkbfr nh aknk ai`rk he
• Oubtipbiakr eóohrfs pfsitivfs y eóohrfs
• Ievhstidkr afe ueinknhs nh suphraih
eóohrfs ekturkbhs y nhaiokbhs. • Quokr, Quokr, rhstkr, oubtipbiakr y nivinir eóohrfs ekturkbhs. • Kpbiakr bks fphrkaifehs gësiaks pkrk rhsfbvhr prfgbhoks. • Iethrprhtkr nigucfs k hsakbk. • Oubtipbiakr eóohrfs ekturkbhs pfr pftheaiks y oóbtipbfs nh ;=. • Afoprhenhr bks pftheaiks. • Iethrprhtkr bfs téroiefs nh bk nivisiñe. • Xtibizkr bks `ueaifehs nh bk akbaubknfrk. • Whnfenhkr eóohrfs. • Xtibizkr bfs eóohrfs ehdktivfs he afethxtfs rhkbhs. >
h c k z i n e h r p k h n s f v i t h c g F
ehdktivfs. • Xtibizkr bfs pkréethsis he fphrkaifehs afogieknks. • Inhetiakr rftkaifehs, trksbkaifehs, rhhxifehs y siohtrïks nh durks pbkeks. • Quokr, rhstkr, oubtipbiakr y nivinir eóohrfs nhaiokbhs. • Whsfbvhr prfgbhoks afe eóohrfs nhaiokbhs. • Oubtipbiakr y nivinir eóohrfs nhaiokbhs pfr pftheaiks nh ;=. • Hethenhr bk prhaisiñe nh uek ohnink nh bfeditun. • Xtibizkr bks ueinknhs nhb sisthok oétriaf.
• Lkbbkr bk ohnikek, bk ofnk, hb rkedf rkedf
• Akbaubkr hb ërhk nh triëedubfs y
y bk ohnik nh ue afecuetf nh nktfs. • ^fokr ohninks.
pkrkbhbfdrkofs. • Afoprhenhr y utibizkr bks pftheaiks nh ;=.
• Ievhstidkr `rkaaifehs.
• Hxprhskr ohninks nh `frok siopbh y nh
• Afopkrkr durks afedruheths y shohckeths.
y vfbuohe. • Akbaubkr hb pfrahetkch nirhatf h ievhrsf nh ue eóohrf. • Akbaubkr bk suphraih bkthrkb y hb vfbuohe nh ue prisok rhatkedubkr. • Whafefahr oóbtipbfs nh ue eóohrf. • Bhhr y hsarigir eóohrfs rfokefs. • Kpbiakr bfs arithrifs nh nivisigibinkn. • Lkbbkr bfs nivisfrhs nh ue eóohrf. • Whafefahr eóohrfs priofs y afopuhstfs. • Akbaubkr bk `rkaaiñe nh ue eóohrf y nh uek `rkaaiñe. • Oubtipbiakr `rkaaifehs. • Hxprhskr uek ohnink he ftrk ueinkn nh bk oisok okdeitun. • Kpbiakr iopuhstfs y nhsauhetfs. • Akbaubkr iethrhshs siopbhs y afopuhstfs.
`frok afopbhck. • Oubtipbiakr y nivinir pftheaiks afe bk oisok gksh. • Kprfxiokr afe pftheaiks nh ;=. • Ievhstidkr afe akpkainknhs. • Xtibizkr bk eftkaiñe aihetïak.
XEINKN >
XEINKN 8
XEINKN 0
• Qiopbiakr y afopkrkr `rkaaifehs.
• Nhnuair hb ërhk nhb trkphaif.
• Whbkaifekr ëedubfs y rftkaifehs.
• Gusakr hb oëxiof afoóe nivisfr nh ue
• ^rkgkckr afe `rkaaifehs prfpiks, ioprfpiks
• Ohnir ëedubfs afe hb trkespfrtknfr. trkespfrtknfr.
afecuetf nh eóohrfs. • Gusakr hb oïeiof afoóe oóbtipbf nh ue afecuetf nh eóohrfs.
y eóohrfs oixtfs. • Quokr y rhstkr eóohrfs oixtfs. • Nivinir `rkaaifehs.
• Inhetiakr ëedubfs vhrtiakbhs, afrrhspfeniheths y supbhohetkrifs. • Xtibizkr drëaks y tkgbks pkrk kekbizkr
• Quokr y rhstkr `rkaaifehs.
• Iethrprhtkr ni`hrheths tipfs nh drëafs.
• Akbaubkr y kekbizkr prfgkgibinknhs.
• Frdkeizkr y rhprhshetkr nktfs.
• ^rkzkr nikdrkoks airaubkrhs.
• Frdkeizkr nktfs he tkgbks nh `rhauheaiks `rhauheaiks
• Heafetrkr bfs téroiefs nh uek shauheaik.
• Fphrkr afe pftheaiks nh ;=.
• Kpbiakr bk prifrinkn nh bks fphrkaifehs.
• Hstiokr y ohnir hb vfbuohe.
• Afefahr bk rhbkaiñe hetrh bk bfeditun y hb
• Inhetiakr puetfs, rhatks y pbkefs.
kgsfbutks y rhbktivks. • Akbaubkr nhaiokbhs hquivkbheths k `rkaaifehs.
niëohtrf nh uek airaue`hrheaik.
nktfs.
• Niguckr afe hb afopës.
• Iethrprhtkr okpks y tkgbks.
• Akbaubkr hb ërhk nhb aïraubf.
• Whsfbvhr prfpfraifehs.
• Hstiokr y akbaubkr ohninks.
• Hsafdhr bk ohnink nh thenheaik thenheaik ahetrkb
• Afefahr hb thfrhok nh ^kb ^kbhs. hs.
• ^rkgkckr afe pfbïdfefs. pfbïdfefs.
• Qitukr affrnheknks he hb pbkef akrthsikef.
• Hsarigir `ueaifehs he eftkaiñe kbdhgrkiak.
oës kprfpiknk. • Abksiakr durks dhfoétriaks. • Afoprhenhr hb usf nh bks rkzfehs pkrk afopkrkr eóohrfs. • ^rkgkckr afe bks `ueaifehs ievhrsks. ievhrsks. • Ievhstidkr bks vistks nh bfs auhrpfs dhfoétriafs.
• Akbaubkr pkrhs frnheknfs k pkrtir nh `ueaifehs. • Whprhshetkr vkbfrhs ehdktivfs he bks drëaks nh `ueaifehs.
• Inhetiakr durks afedruheths y shohckeths.
• Whprhshetkr `ueaifehs biehkbhs y ef biehkbhs. • Ievhstidkr okpks. • Nhthroiekr bk efrok nh uek `ueaiñe. `ueaiñe. • Afefahr bk rkïz auknrknk.
• Whprhshetkr drëakoheth uek `ueaiñe heaknheknk.
• Afefahr hb vkbfr y bks hquivkbheaiks hquivkbheaiks hetrh hb hurf y ftrks nivisks.
• Xtibizkr bks `ueaifehs iev ievhrsks hrsks pkrk
• Afefahr hb thfrhok nh ]itëdfrks.
afopbhtkr tkgbks.
h c k i z n e h r p k h n s f v i t h c g F
Afetheinfs XEINKN ; HPKBXKAIÑE AFO]H^HEAIKB Ieniaknfr nh hvkbukaiñe
]KWK HO]HSKW • Aëbaubf ohetkb
Inhetiak hb vkbfr pfsiaifekb
Inhetiakaiñe nhb kethrifr
nh bks ai`rks he eóohrfs ekturkbhs y nhaiokbhs.
y pfsthrifr nh eóohrfs nh lkstk auktrf ai`rks.
• ]rfgbhoks frkbhs Whsfbuaiñe nh prfgbhoks afe fphrkaifehs afogieknks.
;
HEQHÛKENF -K]WHENIHENF • Cuhdf nhofstrkaiñe affphrktivf y ;.ª , 7.ª yInhetiakaiñe >.ª alks nhb vkbfr pfsiaifekb nh bks ai`rks he eóohrfs ekturkbhs y eóohrfs nhaiokbhs. Nhsafopfsiaiñe knitivk nh eóohrfs ekturkbhs y eóohrfs nhaiokbhs.
]KWK KAKGKW Whhxiñe frkb Katitunhs phrsfekbhs nurketh hb prfahsf nh kprhenizkch3 rhhxiñe y usf nh hstrkthdiks.
• ]rfgbhok nhb nïk Whafefaioihetf nhb vkbfr pfsiaifekb nh bks ai`rks lkstk bks ueinknhs nh oibbkr. oibbkr.
Ieniaknfr nh hvkbukaiñe Whbkaifek aknk eftk afe su vkbfr pkrk rhsfbvhr hb prfgbhok.
• Aëbaubf ohetkb Fphrkaifehs sheaibbks nh suok, rhstk, oubtipbiakaiñe y nivisiñe.
• ]rfgbhoks frkbhs
A f e t h e i n f s
Fphrkaifehs sheaibbks nh suok. Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks nh suoks, rhstks y oubtipbiakaifehs.
7
• ]rfgbhok nhb nïk
• Cuhdf nh augfs Pkbfr pfsiaifekb nh bks ai`rks (kdrupkaiñe nh ueinknhs, nhaheks y ahetheks).
• Cuhdf nhofstrkaiñe y ;.ª alk Whprhshetkaiñe okthoëtiak nh prfgbhoks aftinikefs.
Hxpbiak bks hstrkthdiks quh lk utibizknf pkrk oubtipbiakr y nivinir nurketh hb cuhdf nh augfs.
1
• Aëbaubf ohetkb Fphrkaifehs sheaibbks nh oubtipbiakaiñe y nivisiñe.
Whhxiñe frkb Xsf nh hstrkthdiks nh aëbaubf.
Quoks y rhstks nh eóohrfs nhaiokbhs.
• 7.ª alk Quok y rhstk nh eóohrfs ekturkbhs.
• Okticuhdfs Quok y rhstk nh eóohrfs ekturkbhs.
Hquivkbheaiks hetrh bfs eóohrfs ekturkbhs, bfs eóohrfs nhaiokbhs y bks `rkaaifehs.
Ieniaknfr nh hvkbukaiñe
]ruhgk nh hvkbukaiñe ieiaikb
@ialk afof pruhgk
• Cuhdf nhofstrkaiñe y 7.ª alk Oubtipbiakaiñe y nivisiñe nh eóohrfs ekturkbhs.
Whhxiñe frkb Nhskrrfbbf nh bk rhhxiñe sfgrh bks hstrkthdiks utibizknks.
• ]rfgbhoks frkbhs Quoks y rhstks nh eóohrfs ekturkbhs, nhaiokbhs y `rkaaifehs.
• Cuhdf nh augfs Oubtipbiakaiñe, suok y rhstk nh eóohrfs ekturkbhs.
• ]rfgbhok nhb nïk Xsf nh hstrkthdiks pkrk hb aëbaubf nhb oïeiof afoóe oóbtipbf.
@ialk afof pruhgk
Ofohetf nh kprhenizkch
HPKBXKAIÑE AFO]H^HEAIKB Ieniaknfr nh hvkbukaiñe ]rfpfeh lipñthsis pkrk nkr sfbuaifehs k bk situkaiñe pbkethknk.
]KWK HO]HSKW • Aëbaubf ohetkb Inhetiakaiñe nh `rkaaifehs.
• ]rfgbhoks frkbhs Xsf nh bk `rkaaiñe afof fphrknfr pkrk bk rhsfbuaiñe nh prfgbhoks. Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks utibizkenf hb afeahptf "oitkn".
>
HEQHÛKENF-K]WHENIHENF • Kativinkn nh ievhstidkaiñe Nhskrrfbbf nh katitunhs gësiaks pkrk hb trkgkcf okthoëtiaf3 fgshrvkaiñe, aurifsinkn y pbkethkoihetf nh prhduetks rhbhvkeths. Hchraitkaiñe he bk gósquhnk, hb keëbisis y bk shbhaaiñe nh ie`frokaiñe. Kprfxiokaiñe afe `rkaaifehs.
]KWK KAKGKW Whhxiñe frkb Xsf nh bfs kprhenizkchs knquirinfs he situkaifehs aftinikeks.
]rëatiak nh fphrkaifehs Oubtipbiakaiñe3 trhs ai`rks pfr nfs ai`rks.
• ]rfgbhok nhb nïk ]bkeiakaiñe nhb prfahsf nh rhsfbuaiñe nh prfgbhoks.
Ieniaknfr nh hvkbukaiñe Nhsarigh bk iopfrtkeaik nh hstkgbhahr chrkrquïks he bks fphrkaifehs afogieknks.
• Aëbaubf ohetkb Whbkaiñe hetrh bks nistietks fphrkaifehs.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh rhstk y oubtipbiakaiñe. Xsf nh bk `rkaaiñe afof fphrknfr.
Aëbaubf nhb `katfr phrninf he oubtipbiakaifehs nh nfs eóohrfs nh uek ai`rk.
• Wutiek nh pheskoihetf Nhskrrfbbf nh katitunhs gësiaks pkrk hb trkgkcf okthoëtiaf3 fgshrvkaiñe, aurifsinkn y pbkethkoihetf nh prhduetks rhbhvkeths. Chrkrquïk nh bks fphrkaifehs.
Whhxiñe frkb Xsf nh bfs kprhenizkchs knquirinfs he situkaifehs aftinikeks.
AighrHOK^
• Cuhdf nh augfs
Whsfbuaiñe nh prfgbhoks
Fphrkaifehs afogieknks nh suok, rhstk, oubtipbiakaiñe y nivisiñe.
afe fphrkaifehs afogieknks.
Xsf nhb pkréethsis.
• ]rfgbhok nhb nïk
8
• Okticuhdfs
s f n i e h t e f A
• 1.ª alk Quoks nh eóohrfs nh 1 y > ai`rks. Whsfbuaiñe nh prfgbhoks.
• >.ª alk Fphrkaifehs afogieknks afe eóohrfs ekturkbhs. Whsfbuaiñe nh prfgbhoks afe fphrkaifehs afogieknks.
Ieniaknfr nh hvkbukaiñe Whprhshetk nh okehrk drëak bk situkaiñe pbkethknk he bk kativinkn okeipubktivk.
• Aëbaubf ohetkb Xsf nh hstrkthdiks nh aëbaubf ohetkb pkrk suokr.
• ]rfgbhoks frkbhs Whsfbuaiñe nh prfgbhoks afe fphrkaifehs afogieknks. Fphrkaifehs sheaibbks nh rhstk.
0
• ]rfgbhok nhb nïk Arhktivinkn he bk rhsfbuaiñe nh rhtfs okthoëtiafs.
• Kativinkn okeipubktivk affphrktivk y 7.ª y 1.ª alks ]rfpihnkn afeoutktivk y ksfaiktivk nh bk suok afe okthrikb okeipubktivf. Whstks bbhvkenf afe okthrikb
]ruhgk nh vhbfainkn (suok)
Whhxiñe frkb Nhskrrfbbf nh bk rhhxiñe sfgrh bks hstrkthdiks utibizknks.
okeipubktivf.
• Cuhdf nh augfs Quok nh nfs eóohrfs nh trhs ai`rks.
• >.ª alk Whsfbuaiñe nh prfgbhoks afe suoks y rhstks.
Ieniaknfr nh hvkbukaiñe Iethrprhtk bfs hbhohetfs nhb pbkef k hsakbk.
• Aëbaubf ohetkb Xsf nh hstrkthdiks nh aëbaubf ohetkb pkrk suokr y rhstkr.
• ]rfgbhoks frkbhs
4
Xsf nh hstrkthdiks nh rhsfbuaiñe nh prfgbhoks. Fphrkaifehs sheaibbks
• Cuhdf nhofstrkaiñe y alks Whprhshetkaiñe nh hbhohetfs k hsakbk. Iethrprhtkaiñe nh bk hsakbk nh ue pbkef.
Nikrif nh okthoëtiaks Phrgkbizkaiñe nhb sideiaknf nh afeahptfs okthoëtiafs. Whprhshetkaiñe nh hbhohetfs k hsakbk.
nh suok y oubtipbiakaiñe.
• ]rfgbhok nhb nïk Xsf nh hstrkthdiks nh rhsfbuaiñe nh prfgbhoks.
]feth k pruhgk ;
HPKBXKAIÑE AFO]H^HEAIKB Ieniaknfr nh hvkbukaiñe Xtibizk bks pftheaiks pkrk rhprhshetkr ue prfgbhok afethxtukbizknf.
]KWK HO]HSKW • Aëbaubf ohetkb Quoks y rhstks nh eóohrfs nh lkstk trhs ai`rks.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh suok, rhstk y oubtipbiakaiñe. Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks nh `rkaaifehs.
<
• ]rfgbhok nhb nïk Keëbisis y afoprhesiñe nhb heueaiknf nh prfgbhoks.
HEQHÛKENF-K]WHENIHENF • Cuhdf nhofstrkaiñe y ;.ª alk Afeahptf nh pftheaik afof prfnuatf nh `katfrhs idukbhs. Hxprhsiñe nh eóohrfs he `frok nh pftheaik.
]KWK KAKGKW Whhxiñe frkb ]krtiaipkaiñe kativk he hb iethrakogif nh fpieifehs, rhhxifehs y rhspuhstks k prhduetks.
]rëatiak nh fphrkaifehs • Listfriks pkrk pheskr Iethrprhtkaiñe nh ie`frokaiñe rhdistrknk he tkgbks. Katitunhs phrsfekbhs nhb quhlkahr okthoëtiaf3 rhhxiñe y krduohetkaiñe.
Whstk afe eóohrfs nh auktrf ai`rks.
• 7.ª alk Xsf nh bk akbaubknfrk pkrk rhsfbvhr pftheaiks. Xsf nh hstrkthdiks pkrk kprfxiokr ërhks.
Ieniaknfr nh hvkbukaiñe Whbkaifek bk prfpihnkn afeoutktivk nh bks ni`hrheths fphrkaifehs okthoëtiaks.
• Aëbaubf ohetkb Whsfbuaiñe nh fphrkaifehs afogieknks.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh suok, rhstk, oubtipbiakaiñe y nivisiñe.
• Cuhdf nhofstrkaiñe Fphrkaifehs afe eóohrfs ekturkbhs. ]rfpihnkn afeoutktivk nh bk oubtipbiakaiñe y bk suok.
]ruhgk nh vhbfainkn (rhstk)
Whhxiñe frkb Phrgkbizkaiñe nh afeahptfs y prfahsfs okthoëtiafs.
• Cuhdf nh augfs Kbdfritof nh bk oubtipbiakaiñe
nhb nïk pkrk • ]rfgbhok Xsf nh hstrkthdiks
9
bk rhsfbuaiñe nh rhtfs okthoëtiafs.
A f e t h e i n f s
nh nfs eóohrfs nh nfs ai`rks.
• 7.ª y 1.ª alks Fphrkaifehs nh suok y rhstk afe eóohrfs nh lkstk auktrf ai`rks. Oubtipbiakaifehs afe eóohrfs nh lkstk trhs ai`rks .
• >.ª alk Xsf nh bk oubtipbiakaiñe he prfgbhoks afethxtukbizknfs
Ieniaknfr nh hvkbukaiñe Frdkeizk he uek tkgbk bfs nktfs nhb prfgbhok nurketh hb cuhdf nhofstrkaiñe.
• Aëbaubf ohetkb Xsf nh hstrkthdiks nh aëbaubf ohetkb pkrk oubtipbiakr.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh rhstk. Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks afe lfrks. Aëbaubf nh fphrkaifehs afogieknks.
;=
• ]rfgbhok nhb nïk Hxtrkaaiñe nh inhks y afeabusifehs.
Ieniaknfr nh hvkbukaiñe Iethrprhtk bks pkutks nhb heueaiknf pkrk lkahr uek rhprhshetkaiñe drëak afof rhsfbuaiñe nhb prfgbhok.
;;
• Aëbaubf ohetkb Xsf nh hstrkthdiks nh aëbaubf ohetkb pkrk suokr.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh suok y oubtipbiakaiñe.
• ]rfgbhok nhb nïk Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks. Aëbaubf nhb phrïohtrf y hb ërhk nh durks pbkeks.
• Cuhdf nhofstrkaiñe y alks Whdistrf nh nktfs he tkgbks. Whsfbuaiñe nh prfgbhoks nh oubtipbiakaifehs, nivisifehs, suoks y rhstks.
• Okticuhdfs
@ialk afof pruhgk
Whhxiñe frkb ]krtiaipkaiñe kativk he hb iethrakogif nh fpieifehs, rhhxifehs y rhspuhstks k prhduetks.
AighrHOK^
Fphrkaifehs afe eóohrfs ekturkbhs.
• 7.ª alk Xsf nh hstrkthdiks pkrk hb aëbaubf nh suoks y rhstks afe eóohrfs nh lkstk aieaf ai`rks y oubtipbiakaifehs afe eóohrfs nh lkstk trhs ai`rks.
• Cuhdf nhofstrkaiñe y alks Keëbisis y afoprhesiñe nhb heueaiknf nh prfgbhoks. Oubtipbiakaifehs afe oóbtipbfs nh ;=. Hxprhsiñe nh eóohrfs he `frok nh pftheaiks nh ;=.
• Ourkb nh okthoëtiaks
]ruhgk nh vhbfainkn (oubtipbiakaiñe)
Nikrif nh okthoëtiaks Hxprhsiñe sfgrh hb prfahsf shduinf he bk afeshauaiñe nh prfgbhoks f kativinknhs.
HPKBXKAIÑE AFO]H^HEAIKB Ieniaknfr nh hvkbukaiñe Whkbizk ohniaifehs afe prhaisiñe nurketh bk kativinkn okeipubktivk.
]KWK HO]HSKW • Aëbaubf ohetkb Oubtipbiakaifehs afe oóbtipbfs nh ;=.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh suok, rhstk y nivisiñe. Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks afe `rkaaifehs.
;7
• ]rfgbhok nhb nïk Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks afe niehrf.
Ieniaknfr nh hvkbukaiñe Cuzdk afe shdurinkn si bks rhspuhstks k bfs prfgbhoks nh nivisiñe sfe rkzfekgbhs.
• Aëbaubf ohetkb Oubtipbiakaifehs afe oóbtipbfs nh ;=.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh suok, oubtipbiakaiñe y nivisiñe.
HEQHÛKENF-K]WHENIHENF • Kativinkn okeipubktivk y ;.ª alk Nhskrrfbbf nh hstrkthdiks pkrk bk tfok nh ohninks nh okehrk hxkatk y kprfxioknk.
• 7.ª alk ^fok nh ohninks nh bfeditun. Hquivkbheaiks hetrh oóbtipbfs y sugoóbtipbfs nh bks ueinknhs nh ohnink3 bfeditun, phsf y akpkainkn. Whsfbuaiñe nh prfgbhoks nh oubtipbiakaifehs.
• Cuhdf nhofstrkaiñe affphrktivf y alks Katitunhs phrsfekbhs nhb quhlkahr okthoëtiaf3 rhhxiñe y krduohetkaiñe. Iethrprhtkaiñe nh bfs téroiefs nh bk nivisiñe. Whsfbuaiñe nh prfgbhoks nh nivisifehs.
]KWK KAKGKW Whhxiñe frkb ]krtiaipkaiñe kativk he hb iethrakogif nh fpieifehs, rhhxifehs y rhspuhstks k prhduetks.
]rëatiak nh fphrkaifehs ]ftheaik.
@ialk afof pruhgk
Nikrif nh okthoëtiaks Arhktivinkn he hb nhskrrfbbf nh pbkethkoihetfs okthoëtiafs.
• ]rfgbhok nhb nïk
;1
Hstiokaiñe nh bfeditunhs.
• Listfriks pkrk pheskr Whsfbuaiñe nh prfgbhoks afe niehrf. Hxprhsiñe nh rkzfekoihetfs okthoëtiafs.
s f n i e h t e f A
• 7.ª alk Aëbaubf nh nivisifehs afe nivinhenfs nh nfs ai`rks y nivisfrhs nh uek ai`rk.
Ieniaknfr nh hvkbukaiñe Kpbiak bk nivisiñe pkrk rhsfbvhr prfgbhoks nh rhpkrtf.
• Aëbaubf ohetkb Oubtipbiakaifehs y nivisifehs sheaibbks afe ieañdeitks.
• ]rfgbhoks frkbhs Fphrkaifehs sheaibbks nh rhstk. Xsf nh bk `rkaaiñe afof fphrknfr.
;>
• ]rfgbhok nhb nïk Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks. Whsfbuaiñe nh prfgbhoks afe fphrkaifehs afogieknks.
Ieniaknfr nh hvkbukaiñe Hxpbfrk nivhrsks hstrkthdiks nh kprfxiokaiñe nurketh hb cuhdf nhofstrkaiñe.
• Aëbaubf ohetkb Inhetiakaiñe nh nivisifehs afe f sie rhstf.
• ]rfgbhoks frkbhs
;8
Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks. Fphrkaifehs sheaibbks nh suok y rhstk.
• Kativinkn okeipubktivk affphrktivk y alks Kbdfritof nh bk nivisiñe afe nivisfrhs nh uek ai`rk. Xsf nh bk pruhgk nh bk nivisiñe. Whsfbuaiñe nh prfgbhoks afe nivisifehs.
Xsf nh hstrkthdiks pkrk bk rhsfbuaiñe nh prfgbhoks.
Whhxiñe frkb Katitunhs phrsfekbhs nhb quhlkahr okthoëtiaf3 rhhxiñe y krduohetkaiñe.
• 1.ª alk
Aëbaubf nh nivisifehs afe nivisfrhs nh ue ai`rk y afoprfgkaiñe nh bfs rhsubtknfs.
• Cuhdf nhofstrkaiñe y alks Kbdfritof nh bk nivisiñe afe nivisfrhs nh vkriks ai`rks. Xsf nh hstrkthdiks nh aëbaubf ohetkb pkrk nivinir. nivinir. Whsfbuaiñe nh prfgbhoks nh nivisifehs.
• Cuhdf nh augfs Kbdfritof nh bk nivisiñe
• ]rfgbhok nhb nïk
]fr`fbif
afe nivisfr nh nfs ai`rks.
@ialk afof pruhgk
Whhxiñe frkb ]krtiaipkaiñe kativk he hb iethrakogif nh fpieifehs, rhhxifehs y rhspuhstks k prhduetks.
AighrHOK^
AFEFSAF HB PKBFW NH AKNK EÓOHWF EÓOHWF
AFEFSAF HB PKBFW NH AKNK EÓOHWF
Hurfpk tiheh uek pfgbkaiñe tftkb nh 4>7 9>1 1>8 lkgitkeths, kprfxioknkoheth.
Oibbñe
FGCH^IPF
Whafefahr hb vkbfr pfsiaifekb.
s k e h t e h a
OK^HWIKB
4
Akrtk k bks `koibiks
Oibbkr
s k e h a h n
s h n k n i e u
>
7
Hb 4 rhprhshetk
AFO]H^HEAIKQ
; X ;
Afophtheaiks sfaikbhs y aïviaks Qhr afesaiheth nh bk hxistheaik nh ni`hrheths phrsphativks pkrk kekbizkr bk rhkbinkn y afoprhenhr y rhsphtkr ni`hrheths puetfs nh vistk, inhks, fpaifehs y arhheaiks, ksï afof bks
s h n k n i e u
>
1
s k e h t e h a
1
s k e h a h n
s h n k n i e u
>
8
4 ahetheks nh oibbñe
4== === ===
Hb > rhprhshetk
> nhaheks nh oibbñe
>= === ===
Hb 7 rhprhshetk
7 ueinknhs nh oibbñe
7 === ===
Hb 9 rhprhshetk
9 ahetheks nh oibbkr
9== ===
Hb > rhprhshetk
> nhaheks nh oibbkr
>= ===
Hb 1 rhprhshetk
1 ueinknhs nh oibbkr
1 ===
Hb 1 rhprhshetk
1 ahetheks
1==
Hb > rhprhshetk
> nhaheks
>=
Hb 8 rhprhshetk
8 ueinknhs
8 4>7 9>1 1>8
Hb vkbfr nh aknk pfsiaiñe hs nihz vhahs okyfr quh hb nh bk pfsiaiñe nh su nhrhalk3 bks nhaheks sfe nihz vhahs bks ueinknhs, bks ahetheks nh oibbkr sfe nihz vhahs bks nhaheks nh oibbkr…
;.
Hstiok bk rhspuhstk nh bks siduiheths prhduetks y hsarigh hb eóohrf afrrhatf quh th prfpfraifeh tu okhstrf.
aubturks quh bks afe`froke.
0 .³ ] r i o k r i k
9
s k e h a h n
Qh bhh3 shthaihetfs aukrhetk y nfs oibbfehs efvhaihetfs aukrhetk y trhs oib trhsaihetfs aukrhetk y aieaf.
•
Afophtheaik okthoëtiak y afophtheaiks gësiaks he aiheaik y thaefbfdïk Hxprhskr inhks y prfahsfs okthoëtiafs nh okehrk afoprhesigbh utibizkenf hb bhedukch vhrgkb (frkb y hsaritf).
s k e h t e h a
Whspuhstk afrrhatk
]rhduetk
Hstiokaiñe
He 7=;4, ¶auëetfs eiûfs y eiûks he hb ouenf ef pfnïke ir k bk hsauhbk6
Whspuhstk kgihrtk.
01 04= ===
¶Auëetfs nhpfrtistks pkrtiaipkrfe he bfs Cuhdfs ]krkbïopiafs nh Wïf nh Ckehirf 7=;06
Whspuhstk kgihrtk.
>1>7
¶Auëetfs jibñohtrfs rhafrrh he ; shduenf bk buz he hb vkaïf6
Whspuhstk kgihrtk.
799 497
0
]KWK HO]HSKW - 8 oieutfs Aëbaubf ohetkb
]rfgbhoks frkbhs frkbhs
]rfgbhok nhb nïk
]hniofs k bfs kbuoefs quh ouhstrhe bks rhspuhstks afe bks ruhnks euohrknks.
;. ¶Auëetks ruhnks tihehe tihehe 7 afalhs y 1 giaiabhtks6 ;> ruhnks.
«Hsarigiofs hb eóohrf 8>= 710 he bk pizkrrk y phniofs k bfs kbuoefs quh
k. ¶[ué eóo eóohrf hrf sidu siduhh k 9806 984. g. ¶Auëb hs hb eóohrf ket kethrifr hrifr k ;;7186 7186 ;71>. a. ¶Auëb hs hb eóohrf siduiheth k ;941>7 ktbhtks): «¶Auëetfs jibñohtrfs rhafrrh bk buz he hb vkaïf he ; shduenf6º. ]krk kyunkrbhs, bhs nkofs uek pistk3 «Hs ue eóohrf hetrh 78= y 1== oibº (799 497 jo). Bhs pbkethkofs prhduetks sioibkrhs kb priohr aksf. ]fnhofs afohetkrbhs quh, pkrk bhhr ue eóohrf, nhghofs `ickrefs he bks kdrupkaifehs nh trhs eóohrfs quh sh puhnhe lkahr lkahr,,
frnhekofs nh ohefr k okyfr bfs eóohrfs fgtheinfs y bfs hsarigiofs frnheknfs he bk pizkrrk. ]hniofs k bfs kbuoefs quh fgshrvhe bfs eóohrfs keftknfs he bk pizkrrk y, theihenf he auhetk tkogiée bks custi`iakaifehs nknks
euohrknks. Bfs kbuoefs nisauthe bk rhspuhstk he drupf y afethstk hb kbuoef quh thedk hb eóohrf quh ieniakofs. ]fr hchopbf3 «¶Añof sh bhh hsth eóohrf6º (Qhshetk y trhs oibbfehs shisaihetfs shthetk oib): «¶Auëb hs bk ai`rk quh faupk
hophzkenf pfr bks ueinknhs. Qhduiofs pbkethëenfbhs pbkethëenfb hs prhduetks afe eóohrfs nhaiokbhs3 «¶Auëetfs shduenfs nurk nh ohnik hb kbhthf nh ue afbigrï6 ]istk3 hetrh =,=; y =,;º (=,=7 s): «Hb réafrn ouenikb nh skbtf nh kbturk oksaubief bf fsthetk
C X H D F N H A X G F Q
Whkdrupf eóohrfs
Okthrikb • Xe augf euoériaf (=-8) • Xe augf euoériaf (8-;=)
Cudknfrhs Nfs f oës
Fgchtivf Afeshduir hb eóohrf oës kbtf.
Efroks ;. Aknk cudknfr niguck uek pbketibbk afof hstk3 A
N
X
7. Hb priohr cudknfr bkezk bfs nfs augfs. ^fnfs bfs cudknfr cudknfrhs hs hsarighe bk suok nh bfs augfs he uef nh bfs auknrknfs nh bk pbketibbk.
; X ;
1. Bfs augfs sh bkezke nfs vhahs oës y, y, aknk vhz, bfs cudknfrhs hsarighe bk suok he uef nh bfs auknrknfs quh quhnke he gbkeaf. >. Nhspués, bfs cudknfrhs akbaubke hb vkbfr nh sus eóohrfs, rhkdrupkenf aukenf shk ehahskrif. 8. Dkek hb cudknfr quh `froh hb eóohrf okyfr okyfr.. Hchopbf3
Bkezkoihetf
@hbiph
A
0 .³ ] r i o k r i k
N
;.
1
8
7.
8
0
;;
<
1.
8
9
;;
<
Akrbfs
X
A
N
X
A
<
<
;;
<
<
;;
;> ; ;
<
<
;> ; ;
<
;>
Buisk
N
X
Whkdrupkr3
;; A + < N + ;> X ;; A + 9 N + > X
;> A + ;; N + < X ;8 A + ; N + < X
< A + ;> N + ;; X 9A+8N+;X
Whsubtknf3
;;9>
;8;<
98;
Akrbfs dkek bk pkrtink pfrquh lk fgtheinf hb eóohrf oës kbtf.
<
]KWK KAKGKW - 8 oieutfs Ckvihr Qftfokyfr, afe uek okrak nh 7,>8 o. ¶Auëb hs bk ohcfr okrak fbïopiak he hstk nisaipbiek6º (7,19 o): «Bk kohgk
augfs Cuhdf nh augfs Lkahofs uek nhofstrkaiñe nh Whkdrupf eóohrfs h ievitkofs k bfs kbuoefs k
hs ue frdkeisof oiarfsañpiaf. ¶Auëb hs bk bfeditun kprfxioknk nh uek kohgk he ahetïohtrfs6 ]istk3 hetrh =,=8 y =,;º (=,=48 ao). Xek vhz keftknks bks rhspuhstks he bk `ialk, bhs prhduetkofs3 «¶Añof ieniakofs bk shpkrkaiñe hetrh bks ueinknhs y bks néaioks6º (Afe uek afok): «¶Añof bf ieniak vuhstrk akbaubknfrk6º (Afe ue puetf). Afohetkofs quh hb puetf y bk afok sh afesinhrke sidefs vëbinfs pkrk shpkrkr bks ueinknhs nh bks néaioks (=.48 f =,48), phrf ef hb kpñstrf`f (=’48).
cudkr.. cudkr kbuoef @ialk nhb kbuoef >.ª `ialk nhb nïk ; ; Bfs kbuoefs afopbhtke bk `ialk ienivinukbohethh y bk iethrakogike afe ue ienivinukbohet afopkûhrf pkrk afrrhdirsh outukohet outukoheth. h. Hsth nïk ieabuyh bk ]ruhgk nh hvkbukaiñe ieiaikb.
]rhduetkofs k bfs kbuoefs qué hstrkthdiks lke utibizknf pkrk afopkrkr y frnhekr eóohrfs ekturkbhs y nhaiokbhs.
AFEFSAF HB PKBFW NH AKNK EÓOHWF 1.
>.
8.
0.
4.
Hsarigh hb rhsubtknf.
7 + 1== + 7== === ? 7== 1=7
9=== + 8== + >= + 1 ?
0 + 8= + === + 4= + 1= === + ; ? 1> =4;
1
Afopbhtk bks shrihs.
0=9< 0=99
0;==
0;=;
0;=7
0;=1
0;=>
9990 9994
999<
9999
;= ===
;= ==;
;= ==7
0;=8 ;= ==1
¶[ué rhprhshetk hb 4 he aknk uef nh bfs siduiheths eóohrfs6
9,980
4 ahetheks
7;>,74;
4 ahetésioks
804,;=8
4 ueinknhs
; X
Hsarigh he eóohrfs.
;
7 néaioks, > ahetésioks, 0 oibésioks
=,7>0
0 ueinknhs, < ahetésioks, 4 oibésioks
0,= ?
7,0>
=,==4 + =,9 + =,=0 ?
=,904
¶[ué hs okyfr3 =,9> f =,9=>6
]fnhofs afbfakr ue = nhspués nh =,9> afevirtiéenfbf he =,9>=, nh okehrk quh bfs nfs eóohrfs thedke hb oisof eóohrf nh ai`rks nhaiokbhs nhspués nh bk afok.
=,9>= 5 =,9=>
Akrtk k bks `koibiks 7
5
=,>;9
=,>9<
5
=,>
1,;8
2
1,9
=,7
5
=,;98 9
K^HEAIÑE K BK NIPHWQINKN Fxïdhef ]krk afopbhtkr kbduefs nh bfs hchraiaifs nh bk aukrtk `ialk, bfs kbuoefs puhnhe utibizkr uek pbketibbk vkaïk (f niguckrbk he su auknhref) afof bk nh bks nfs priohrks `ialks, afe aksibbks he gbkeaf y hb efogrh nh aknk pfsiaiñe.
Whtf ]hniofs k bfs kbuoefs quh hsarigke bfs eóohrfs3 ; oibbñe (; === ===), ;=== oibbfehs (; === === ===) y ; oibbñe nh oibbfehs (ue gibbñe3 ; === === === ===, ue ; y ;7 ahrfs). Bhs rhafrnkofs quh ef nhgh afe`uenirsh afe hb téroief gibbife kedbfskcñe, quh hquivkbh k oib oibbfehs (; === === ===).
He aksk ]hniofs k bfs kbuoefs quh cuhduhe kb cuhdf nh augfs Whkdrupf eóohrfs afe kbdóe `koibikr f koidf.
Hvkbukaiñe ie`frokb Fgshrvkaiñe
Inheti`iak hb vkbfr pfsiaifekb nh bks ai`rks he eóohrfs ekturkbhs y nhaiokbhs. Hs akpkz nh rhafesinhrkr sus rhspuhstks kthenihenf k bks nh sus afopkûhrfs nurketh hb cuhdf nhofstrkaiñe.
Hvkbukaiñe `frokb ]ruhgk nh hvkbukaiñe ieiaikb @ialk
Whsuhbvh afrrhatkoheth > nh bfs 0 hchraiaifs nh bk aukrtk `ialk.
k i r k o i r ] ³ . 0
NIGXCF H IE^HW]WH^F HQAKBKQ
AW H
K W
NIGXCF H IE^HW]WH^F HQAKBKQ
AFO]WHENHW
;.
Fgshrvk hb siduiheth pbkef nh ue pisf.
FGCH^IPF
Nhspkalf
Iethrprhtkr bk hsakbk nh ue pbkef.
Lkgitkaiñe ;
OK^HWIKB
Qkbñe
Whaursfs kubk Ioprioigbhs3 Ouhgbhs
•
AFO]H^HEAIKQ Afophtheaik okthoëtiak y afophtheaiks gësiaks he aiheaik y thaefbfdïk
Iethrprhtkr rhprhshetkaifehs hspkaikbhs lhalks k pkrtir nh sisthoks nh rh`hrheaik y nh fgchtfs f situkaifehs `koibikrhs.
Whaiginfr Lkgitkaiñe 7
Gkûf
Afaiek
4
Hsakbk ;3 o
;7,00 o·
7>
HEQHÛKENF - K]WHENIHENF
]KWK HO]HSKW - 8 oieutfs Aëbaubf ohetkb ]hniofs k bfs kbuoefs quh ouhstrhe bfs rhsubtknfs afe bks ruhnks euohrknks. k. g. a. n. h.
48 + 7=. 98. 48 + 48. ;8=. 40 + 78. ;=;. ;40 + 78. 7=;. ;== ‑ 78. 48. 48.
]rfgbhoks frkbhs ;. Kenrhk tiheh 7= dbfgfs y su lhrokef tiheh bk oitkn. ¶Auëetfs dbfgfs tihehe hetrh bfs nfs6 1= dbfgfs. 7. Xe ohbñe phsk 1 jd y ohnif y ftrf phsk hb nfgbh. ¶Auëetf phske bfs nfs cuetfs6 ;= jd y ohnif. 1. Ïedrin rhafrrh > jo he 1= oieutfs. ¶Auëetks lfrks tkrnk he afopbhtkr 7= jo6 7 lfrks y ohnik. ohnik.
]rfgbhok nhb nïk «Nfs eóohrfs nke uek suok nh ;7 === y uek ni`hrheaik nh ;===. ¶Auëbhs sfe
Cuhdf nhofstrkaiñe Efs `ickofs he ue fgchtf vfbuoiefsf nh bk abksh: uek ohsk, pfr hchopbf.
hstfs eóohrfs6º. 08== y 88==. ]fnhofs rhsfbvhrbf pfr tkethf, rhbbhekenf uek tkgbk, hophzkenf pfr hchopbf pfr ;7 === + =.
Keftkofs bks ohninks he bk pizkrrk (pkrk `kaibitkr bfs aëbaubfs, pfnhofs rhnfenhkr kb eóohrf oës ahrakef)3 4= Ô 8= ao. ]rhduetkofs3 «¶Añof pfnhofs niguckr hsth pupitrh nh okehrk quh shk nfs vhahs ohefr quh hb rhkb6º (Whnuaihenf sus niohesifehs k bk oitkn). Niguckofs he bk pizkrrk ue rhatëedubf nh 18 Ô 78 ao. ]rhduetkofs3 «¶Auëetf oinh rhkboheth nh bkrdf hb pupitrh6º (4= ao): «¶Auëetf oinh hb bkrdf nhb rhatëedubf nigucknf6º (18 ao): «¶[ué lhofs lhalf afe bk ohnink rhkb pkrk rhprhshetkrbk6º (Nivinirbk pfr 7). Hs nhair, 18 ao he hb pbkef sfe 4= ao he bk rhkbinkn (bfs ahetïohtrfs nhb pbkef sh oubtipbiake
Quok
Ni`hrheaik
;7 ===
=
;7 ===
;7 ===
;; ===
;===
;7 ===
;= ===
;= ===
7===
;7 ===
7
FGCH^IPF Kekbizkr bks ohninks nh thenheaik ahetrkb.
AFO]H^HEAIKQ Afophtheaik okthoëtiak y afophtheaiks gësiaks he aiheaik y thaefbfdïk Hstkgbhahr rhbkaifehs hetrh ni`hrheths afeahptfs, ksï afof hetrh bfs nivhrsfs sidei`iaknfs nh ue oisof afeahptf. Afophtheaik he afoueiakaiñe biedòïstiak Bhhr afe `buinhz pkrk afoprhenhr ni`hrheths thxtfs ie`froktivfs h iestruativfs nh bk vink aftinikek he ni`hrheths `froktfs y sfpfrths.
g
¶Auëb hs hb rkedf6
Hb rkedf hs bk ni`hrheaik hetrh hb vkbfr okyfr y hb ohefr. He hsth aksf3 >7 ‗ 18 ? 4. a
¶Auëb hs bk ohnikek6
Bk ohnikek hs hb eóohrf quh hstë he hb ahetrf. He hsth aksf hb 1=
>;
>7
Eóohrf nh kbuoefs
1
7
1
0
4
7
;
;
47
HEQHÛKENF - K]WHENIHENF
]KWK HO]HSKW - 8 oieutfs Aëbaubf ohetkb
]rfgbhok nhb nïk
Cuhdf nhofstrkaiñe
]hniofs k bfs kbuoefs quh shûkbhe afe bfs pubdkrhs lkaik krrigk si hb rhsubtknf hs
«Lfy hs nfoiedf y sfe bks ;=31= l nh bk okûkek. ¶[ué lfrk y nïk shrëe aukenf
]hniofs k bfs kbuoefs quh hsarigke su tkbbk nh pih he uek tkrchtk, quh sh pfedke
okyfr quh ;== y ohefr quh 7== y lkaik kgkcf si quhnk `uhrk nh hsh h sh iethrvkbf (;==-7==). k. 18 x 7. ]ubdkrhs kgkcf. g. 40 x >. ]ubdkrhs kgkcf. a. 18 x 1. ]ubdkrhs krrigk. n. 44 x >. ]ubdkrhs kgkcf. krrigk. h. 18 x >. ]ubdkrhs krrigk.
pkshe 18== oieutfs6º. Bks 7=38= l nhb okrths. ]fnhofs nivinir 18== hetrh 0=,
nh pih y quh sh frnhehe he uek `ibk, nh ohefr k okyfr, ofstrkenf hb eóohrf. Nhaiofs3 «Pkofs k kekbizkr hstfs nktfsº. ]hniofs k bfs kbuoefs nh kogfs hxtrhofs quh efs ieniquhe su eóohrf, bfs hsarigiofs he bk pizkrrk y lkahofs bk rhstk nhb okyfr ohefs hb ohefr. Bhs ieniakofs quh hb eóohrf fgtheinf hs hb rkedf nh bfs nktfs, y bhs hxpbiakofs quh ouhstrk bk nistriguaiñe nh uek shrih nh vkbfrhs. Qi hb rkedf hs phquhûf, bfs vkbfrhs hstëe ouy ahrak hetrh sï, y si hs drkenh, hstëe kbhcknfs. ]hniofs k bfs kbuoefs nh bfs hxtrhofs quh nhe ue pksf kb `rheth, y rhphtiofs hstf lkstk quh sfbf quhnhe uef f nfs kbuoefs, bfs quh lkgïk he hb ahetrf nh bk `ibk. Qi hb eóohrf nh kbuoefs hs pkr, quhnkrëe nfs3 suokofs sus eóohrfs y niviniofs hetrh nfs. Hb vkbfr fgtheinf hs bk ohnikek. Qi hb eóohrf nh kbuoefs hs iopkr, sfbf quhnkrë ue kbuoef he hb ahetrf y su
]rfgbhoks frkbhs ;. Qi 4 sunknhrks vkbhe ;>= ₢, ¶auëetf vkbh aknk uek6 7= ₢. 7. He ue pktif lky ;8 eiûfs y 79 eiûks. ¶Auëetks eiûks oës quh eiûfs lky6 ;> eiûks. 1. Hetrh tfnk bk `koibik, bh lhofs rhdkbknf k oi oknrh uek akzknfrk quh vkbh 9= ₢. Qi yf lh puhstf bk quietk pkrth, ¶auëetf niehrf lh puhstf6 ;< ₢.
pkrk akbaubkr hb eóohrf nh lfrks, y fgthehofs 8< lfrks y 7= oieutfs. K afetieukaiñe, niviniofs 8< hetrh 7>, pkrk akbaubkr hb eóohrf nh nïks, y fgthehofs 7 nïks y ;= lfrks. Qi nhsnh hb nfoiedf k bks ;=31= l nh bk okûkek pkske 7 nïks, ;= lfrks y 7= oieutfs, bbhdkofs kb okrths k bks 7=38= l.
K^HEAIÑE K BK NIPHWQINKN KEKB I S K
W
KEKBISF BKQ OHNINKQ NH ^HENHEAIK AHE^WKB `
]rfpfehofs k bfs kbuoefs quh akbaubhe bk ohnik, bk ohnikek, bk ofnk y hb rkedf nh uek shrih nh eóohrfs nh uek ai`rk. ]fr hchopbf3 ; ‑ 1 ‑ 4 ‑ 0 ‑ 1.
Akbaubk bk tkbbk ohnik nh pih.
18 Ô 1 + 10 Ô 7 + 14 Ô 1 + 1< Ô 0 + 19 Ô 4 + >= Ô 7 + >; Ô ; + >7 Ô ; 78
Fxïdhef
? 11
18 - 10 - >=
; X
77
Hvkbukaiñe ie`frokb
10 + 1< + 14 ? 14 s 1 1< + 19 + >1 ^ihopf ohnif nh Buaïk3 ? >= s 1 18 + 10 + >= ^ihopf ohnif nh Qfeik3 ? 14 s 1 Dkek Kbiaik pfrquh, kuequh tiheh hb oisof tihopf ohnif quh Qfeik, hb rkedf hs ohefr. ^ihopf ohnif nh Kbiaik3
1.
Hstkgbhah rhbkaifehs hetrh bfs afeahptfs ohnikek, ohnik, ofnk y rkedf utibizkenf hb vfakgubkrif afrrhatf. Bhh afe `buinhz bk listfrik pkrk pheskr y hxtrkh bk ie`frokaiñ ie`frokaiñe e
Akrbfs lk bkezknf aieaf vhahs bfs nfs augfs euoériafs y l k fgtheinf bfs rhsubtknfs quh kpkrhahe k afetieukaiñe. Akbaubk hb rkedf, bk ohnik, bk ohnikek y bk ofnk nh hsfs eóohrfs.
; k
Fgshrvkaiñe
Wkedf3
a
Ohnik3
n
Ohnikek3
4
8
8
;
g
<
7
oës rhbhvketh.
0
Ofnk3
Hvkbukaiñe `frokb
8
Nikrif nh okthoëtiaks
; + 4 + 8 + 8 + ; + 8 + > + < + 7 + 0 >,> ? ;=
@ialks
8 (eóohrfs frnheknfs nh ohefr k okyfr3 okyfr3 ; ; 7 > 8 8 8 0 4 1 jd y oi lhrokef phsk 1< jd. ¶Auëetfs jibfs phsk éb ohefs quh yf6
]rfgbhok nhb nïk «Okrïk rhaigiñ 77,8= ₢ nh su pknrh y 1= ₢ nh su oknrh pkrk ir nh afoprks. Aukenf
Buhdf, prhshetkofs hb rhstf nh bfs hchraiaifs. hchraiaifs. k. >0 + 87. 8. a. 48 + >7 + 10. ;81. 10. ;81. 48 + >= ? ;;8: ;;8 + 7 ? ;;4: ;;4 + 1= ? ;>4: ;>4 + 0 ? ;81. ;81. n. 71 + ;0 + ;>. ;>. 81. 81. 71 + ;= ? 11: 11 + 0 ? 19: 19 + ;= ? >9: >9 + > ? 81. h. 87 + 10 + ;9. ;=4. ;9. ;=4. 87 + 1= ? ;,< Ô ;== ?
> nh bks 77 fphrkaifehs nh bk aukrtk `ialk.
]WKA^IAF HB QIQ^HOK OÉ^WIAF
]WKA^IAF HB QIQ^HOK OÉ^WIAF ;.
FGCH^IPF ]rkatiakr bks hquivkbheaiks hetrh oóbtipbfs y sugoóbtipbfs nh bks ueinknhs nh ohnink.
AFO]H^HEAIKQ Afophtheaik okthoëtiak y afophtheaiks gësiaks he aiheaik y thaefbfdïk Hstkgbhahr rhbkaifehs hetrh ni`hrheths afeahptfs, ksï afof hetrh bfs nivhrsfs sidei`iaknfs nh ue oisof afeahptf. Afophtheaik he afoueiakaiñe biedòïstiak Kpbiakr hstrkthdiks nh afoprhesiñe pkrk fgthehr ie`frokaiñe h iethrprhtkr y vkbfrkr hb afetheinf nh kauhrnf afe bk tipfbfdïk y bk afopbhcinkn nhb thxtf y hb prfpñsitf nh bk bhaturk.
7.
1. 1>
Hxprhsk bfs siduiheths rhsubtknfs he bk ueinkn oës phquhûk. 1 o + 7 ao ?
1=7 ao
1 nkb + 8 nkb ?
< nkb
1 nko + >7 o ?
47 o
7 jd + 18 d ?
7=18 d
; jb + 8 b + 1 nb ?
;= =81 nb
; jd + ; ld + ; d ?
;;=; d
Hxprhsk bfs siduiheths rhsubtknfs he bk ueinkn oës drkenh. >; b + 1 nb ?
>;,1 b
; jd + 7 ld + 7 d ?
7 jo + 8 jo ?
4 jo
;8 b + ;7 nb ?
;0,7 b
71 lo + 7 o ?
71,=7 lo
; nkd + ; d ?
;,; nkd
;,7=7 jd
Nhsafopñe bks ohninks pkrk afopbhtkr bks tkgbks. k jo
X 7
lo
>7,18 o
nko
o
no
ao
>
7
1
8
1
;
>
8
od
1;>8 oo 7,>87 jo
7
>
8
7
jd
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nd
ad
7,4;9 nkd
7
4
;
9
0=>=,8 ad
0
=
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=
8
4
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g
84,< nd
8
4 ; ;
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0 .³ ] r i o k r i k
lb
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nb
;=81 nb
;
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8
1
7= ==7 ab
7
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=
;
8
0
4
0;,804 lb
0
ab
ob
7
HEQHÛKENF - K]WHENIHENF
Aëbaubf ohetkb
]rfgbhok nhb nïk
Cuhdf nhofstrkaiñe
]krk afetieukr prkatiakenf bk kprfxiokaiñe kprfxiokaiñ e nh ohninks nh fgchtfs,
«Hb phsf kprfxioknf nh uek phbftk nh vfbhigfb f`iaikb fsaibk hetrh 789,=09 d y
]rhpkrkofs nfs tkrchtks pfr aknk fphrkaiñe nhb hchraiaif ; nhb Bigrf nhb
phniofs k bfs kbuoefs quh ahetrhe bk ktheaiñe he bk afevhrsiñe nh uek ueinkn k ftrk. Bhs ofstrkofs ue fgchtf y bhs prhduetkofs auëb hs su bfeditun kprfxioknk he ohtrfs y he ahetïohtrfs. K afetieukaiñe, bf oinhe pkrk vhri`iakr.
749,=9< d. Bk phbftk nh vfbhigfb nh Kbgk phsk 789 d. ¶Hstë nhetrf nh bfs bïoiths nh phsf f`iaikb6º. Ef. ]fnhofs afopkrkr hb phsf nh bk phbftk nh Kbgk afe bfs vkbfrhs hxtrhofs nhb iethrvkbf nh phsf f`iaikb nh uek phbftk nh vfbhigfb. ]krk quh shk oës `ëaib afopkrkr bfs trhs eóohrfs, hsarigiofs hb phsf nh bk phbftk nh Kbgk afe trhs ai`rks nhaiokbhs, nh ofnf quh bfs trhs eóohrfs thedke bk oisok aketinkn nh ai`rks nhaiokbhs3 789,=== ‑ 789,=09 ‑ 749,=9 1 k ï
nh bk suok (pfr hchopbf, 1 o + 7 ao) y ftrk nhb rhsubtknf (pfr hchopbf, 1=7 ao), 7> he tftkb. Kûkniofs f nhsakrtkofs tkrchtks shdóe hb eóohrf nh kbuoefs. Whpkrtiofs uek tkrchtk k aknk kbuoef y bhs phniofs quh bk suchthe nh okehrk visigbh. Nhghe uskr bk oisok tkrchtk pkrk tfnks bks pkrtinks. Qh sitóke he aïraubf. Bfs kbuoefs hopihzke bk pkrtink nh pih y sh sihetke k ohnink quh su tkrchtk ef auopbk afe bks k`irokaifehs nknks. Hs iopfrtketh nhckrbhs tihopf pkrk quh lkdke sus afoprfgkaifehs. Afohezkofs niaihenf3 «Hs uek ohnink nh bfeditunº (Bfs kbuoefs afe tkrchtks nh ohninks nh oksk y akpkainkn sh sihetke): «Hs ohefr quh 1 joº (Bfs nh bks tkrchtks 7 jo + 8 jo y 4 jo sh sihetke): «Hs okyfr quh 8 nko + ; oº (Bfs nh bks tkrchtks 1 o + 7 ao y 1=7 ao sh sihetke): «Hs hquivkbheth k 71=,7 nkoº (Bfs nh bks tkrchtks 1 nko + >7 o y 47 o sh sihetke).
K^HEAIÑE K BK NIPHWQINKN HPKB X K
]WKA^IAF HB QIQ^HOK OÉ^WIAF >.
W
Fxïdhef He hb cuhdf nhofstrkaiñe, `frokofs drupfs nh trhs kbuoefs y rhpkrtiofs uek tkrchtk nh aknk ueinkn nh ohnink pkrk quh afeshesóhe bks rhspuhstks.
Léatfr lk inf afe su koidk Aris k visitkr hb akopf nh `ótgfb nh su bfakbinkn. Hb hetrheknfr bhs lk nialf quh hb akopf oinh ;== o nh bkrdf y 8= o nh kealf. ]krk afoprfgkrbf, Léatfr y Aris lke nhaininf ohnirbf.
Whtf He pkrhcks, hsarighe uek ohnink hxprhsknk he uek óeiak ueinkn y bk iethrakogike afe hb afopkûhrf, quh bk hsarigh afof uek suok nh ohninks.
Hetrheknfr o o o 8 , , = 8 9 = 8 8 >
Léatfr Aris
Hvkbukaiñe ie`frokb
99,8 o
Fgshrvkaiñe
;== o ;==,8 o
k
7 X
¶]fr qué lke fgtheinf ohninks nistietks6 ]frquh aknk uef lk afesinhrknf hb akopf afof uek zfek ni`hrheth.
g
¶Auëb hs hb phrïohtrf y hb ërhk nhb akopf si afesinhrkofs bks ohninks nhb hetrheknfr6 ] ?
a
0 .³ ´ X 7 ´ N ï k 1 >
h
Hvkbukaiñe `frokb Hvkbukaiñe nh vhbfainkn nh aëbaubf ohetkb (nivisiñe)
;==,8 + 8=, 8 + ;==,8 + 8=,8 ? 1=7 o: K ? ;==,8 Ô 8=,8 ? 8=48,78 o·.
¶Y afe bks ohninks nh Aris6 ] ?
|
;== + 8= + ;== + 8= ? 1== o: K ? ;== Ô 8= ? 8=== o·.
¶Auëb hs hb phrïohtrf y hb ërhk afe bks ohninks nh Léatfr6 ] ?
n
1>
]fnhofs pkskr hstk pruhgk y dukrnkr bk eftk pkrk afopkrkrbk
99,8 + >9,8 + 99,8 + >9,8 ? 79< o: K ? 99,8 Ô >9,8 ? >978,78 o·.
afe bk fgtheink he bk prñxiok pruhgk quh sh rhkbiah.
¶[ué hrrfr lke pfninf afohthr, afof oëxiof, he auketf kb ërhk y kb phrïohtrf nhb akopf6 K ?
] ? 1== ‑ 79< ? 1=7 ‑ 1== ? 7 o 8=48,48 ‑ 8=== ? 48,78 o· 5 8=== ‑ >978,78 ? 4>,48 o·
`
Qi sh tuvihsh quh rhpbketkr hb aésphn nhb akopf nh `ótgfb, ¶nhghe akbaubkr shdóe hb ërhk okyfr f hb ërhk ohefr6
Bk okyfr.
d
Qi sh quisihrk utibizkr hb akopf pkrk afophtiaifehs, ¶qué ërhk sh nhghrïk eftiakr k bk `hnhrkaiñe6
Bk ohefr.
Nikrif nh okthoëtiaks @ialks
;;1
|
Whbkaifek bks ni`hrheths okehrks nh hxprhskr uek oisok ohnink he hb cuhdf nhofstrkaiñe. Kpbiak hstrkthdiks nh bhaturk pkrk fgthehr bk ie`frokaiñ ie`frokaiñe e ehahskrik he bk listfrik pkrk pheskr.
Whsuhbvh afrrhatkoheth 7 nh bfs 1 hchraiaifs nh bk priohrk `ialk y 8 nh bfs 4 kpkrtknfs nhb prfgbhok nh bk shduenk `ialk.
; ;
afoóe6º (Bks ohninks sfe hquivkbheths). Cudkofs, kb ohefs, nfs pkrtinks oës pkrk trkgkckr afe ohninks nh oksk y nh akpkainkn. Ieniakofs3 «Hs uek ohnink nh oksk.º: «Hs ohefr quh 7 jdº: «Hs okyfr quh ; jd + 7== dº: «Hs hquivkbheth k ;7=7 dº (; jd + 7 ld + 7 d y ;,7=7 jd): «Hs uek ohnink nh akpkainknº: «Hs okyfr quh >7 bº: «Hs ohefr quh 9 nkb + < bº: «Hs hquivkbheth k 7 Ô 8
7.ª `ialk nhb nïk 1> ]hniofs k bfs kbuoefs quh trkgkche he drupfs affphrktivfs afe bk akbaubknfrk. a kbaubknfrk. Nhghe fgshrvkr bk ni`hrheaik he bks rhspuhstks, nhgink k quh bks ohninks ni`ihrhe he =,8 o. Akbaubke A kbaubke hb phrïohtrf okyfr, hsth hs 7 o (=,8 + =,8 + =,8 + =,8) okyfr quh hb phrïohtrf prhvif, hs nhair, 1=7 o (1== + 7). Akbaubke hb ohefr, 79< o (1== ‑ 7). He hb aëbaubf nh ërhks, shûkbkofs quh hb hrrfr hs nh 48,78 o 7 (8=48,78 ‑ 8===) y 4>,48 o 7 (8=== ‑ >978,78), rhsphativkoheth.
Hsth nïk ieabuyh uek pruhgk nh vhbfainkn nh aëbaubf ohetkb (nivisiñe).
He aksk Ieniakofs k bfs kbuoefs quh niguche bk afaiek nh sus aksks k hsakbk. Buhdf lkgbke afe kbdóe oihogrf nh bk `koibik pkrk nh`ieir inhks pkrk lkahr nh bk afaiek ue budkr oës h`iaiheth. ]uhnhe arhkr ue euhvf nigucf k hsakbk quh ibustrh kbdueks nh hsks inhks.
k i r k o i r ] ³ . 0
NHNXSAF HB ËWHK NHB ^WIËEDXBF FGCH^IPF
W X ^ I E K N H ] H E Q K O I H E ^ F
Nhnuair hb ërhk nhb triëedubf.
He`faf y rh`bhxifef Afopkrtf ¶[ué `rkaaiñe rhprhshetke, rhsphatf nh bk durk afopbhtk, aknk uef nh bfs triëedubfs quh `froke ue pkrkbhbfdrkof6 ¶Añof puhnf akbaubkr hb ërhk nhb triëedubf afefaihenf bk nhb pkrkbhbfdrkof6 ¶Faurrh bf oisof he tfnfs bfs aksfs6 Whspuhstk kgihrtk.
AFO]H^HEAIKQ Afophtheaik okthoëtiak y afophtheaiks gësiaks he aiheaik y thaefbfdïk
Lkahr ie`hrheaiks (hxpbiakaiñe akuskb, prhniaaiñe, dhehrkbizkaiñe, rkzfekoihetf pfr kekbfdïk y rkzfekoihetf afeniaifekbnhnuaaiñe).
Whhxifef Whspuhstk kgihrtk.
1< Afophtheaik he afoueiakaiñe biedòïstiak
X 7
Hxprhskr frkboheth oheskchs, pheskoihetfs, vivheaiks, fpieifehs y shetioihetfs.
Afehatf
Whspuhstk kgihrtk.
; 1 ;
|
< 1 k ï
N ´ 7 X ´ ³ . 0
0 .³ ] r i o k r i k
|
;7<
]KWK HO]HSKW - 8 oieutfs Aëbaubf ohetkb ohetkb
]rfgbhoks frkbhs frkbhs
]rfgbhok nhb nïk
]hniofs k bfs kbuoefs quh shûkbhe afe bfs pubdkrhs lkaik kgkcf si bfs rhsubtknfs
;. He uek pisaiek lky 8 aliaks oës quh aliafs. Qi lky 0 aliafs, ¶auëetks
«Okrif y Ëbvkrf sfe lhrokefs. Bfs nfs tihehe oës nh ;= kûfs y ohefs nh 17.
sfe abkrkoheth ieafrrhatfs y lkaik krrigk si hs pfsigbh quh shke afrrhatfs. k. ;= Ô ;= ? ;==. ]ubdkrhs krrigk. g. ;== ‗ 88 ? >8. ]ubdkrhs krrigk. a. >8 ô 9 ? 8. ]ubdkrhs krrigk. n. 8< ‗ 84 ? 8=. ]ubdkrhs kgkcf. h. >< ô 0 ? 78. ]ubdkrhs kgkcf. kgkcf.
phrsfeks lky he tftkb6 ;4 phrsfeks. 7. ^heïk 9 phdktieks y lh phrninf bk thrahrk pkrth. ¶Auëetks phdktieks oh quhnke6 0 phdktieks. 1. Lh rhafrrinf nfs thraifs nhb akoief y oh quhnke 8 jo pfr rhafrrhr. ¶Auëb hs bk bfeditun nhb akoief6 ;8 jo.
Bk hnkn nh Okrif hs idukb k bk hnkn nh Ëbvkrf, phrf afe bks ai`rks ievhrsks. ¶[ué hnknhs tihehe Okrif y Ëbvkrf6º. ;7 y 7; f ;1 y 1;. ]fnhofs nhnuair quh si Okrif y Ëbvkrf `uhrke dhohbfs, su hnkn pfnrïk shr ;; f 77. Gusakofs tfnfs bfs eóohrfs hetrh ;= y 17 y shûkbkofs kquhbbfs quh tihehe bks ai`rks ievhrsks.
KEKB I S K
NHNXSAF HB ËWHK NHB ^WIËEDXBF ;.
¶Auëb hs hb ërhk nhb pkrkbhbfdrkof KGAN6
W
K
G
0 ao
1 Ô 0 ? ;< ao· 1 ao
> a o
7.
¶^iheh NGA bk oisok `frok y ohnink quh
o a 1
> a o
GNK6 N
Qï.
0 ao
1.
Iokdiek quh rhafrtks hb pkrkbhbfdrkof y, nhspués, afrtks pfr NG pkrk `frokr nfs triëedubfs shpkrknfs. ¶]uhnhs heakckr NGA hxkatkoheth he NGK6
>.
¶[ué `rkaaiñe nhb ërhk nh KGAN hs hb ërhk nh NGA6
8.
¶Auëb hs hb ërhk nh NGA6
0.
Qi afrtkofs hb pkrkbhbfdrkof KGAN pfr KA, ¶qué `rkaaiñe nhb ërhk nh KGAN hs hb ërhk nh KNA6
4.
¶Auëb hs hb ërhk nh KAN6
A
Qï.
; 7 9 ao· 7 X
; 7
1< K
G
0 ao
9 ao·
a o
> a o
N
A
0 ao
Qï.
9.
| 0 .³ ´ X 7 ´ N ï k
¶^ihehe bk oisok ërhk tfnfs bfs pkrkbhbfdrkofs quh afopkrthe nfs bknfs afe ue triëedubf6
Qï.
Hb ërhk nh ue pkrkbhbfdrkof hs bk bfeditun nh bk gksh pfr bk kbturk3
k i r k o i r ] ³ . 0
K ? g Ô l
Hb ërhk nh ue triëedubf hs bk oitkn nh bk bfeditun nh bk gksh pfr bk kbturk3 K ?
1
; = = , 7 8 8 a o o
8 a o
< ao
1 ao
K ?
0 a o
a o 8 a
; Ô Ô 7 < > ? ;0 ao·
K ?
8 Ô 0 ? 1= ao·
;;. Hb kyuetkoihetf quihrh akogikr hb suhbf nh bk pbkzk y pfehr gkbnfsks nh afbfr okrrñe fsaurf. Lke akbaubknf quh bfs hopbhknfs tkrnke uek lfrk he hogkbnfskr ;= o7. ¶Auëetf tihopf sh ehahsitk pkrk augrir tfnf hb suhbf nh bk pbkzk6 4 8 o
Ërhk nhb triëedubf3 ; Ô Ô 1 ? 0 o· 7 Ërhk nhb pkrkbhbfdrkof3 7 Ô 0 ? ;7 o·
0 .³ ] r i o k r i k
g
¶[ué tfbnf arhhs quh hs oës prëatiaf6
< 1 k ï
Hb vhaief lk pkdknf oës, pfrquh ;7 o· 5 0 o·.
N ´ 7 X ´ ³ . 0
Whspuhstk kgihrtk.
|
;1=
]KWK KAKGKW - 8 oieutfs @ialk nhb kbuoef
1.ª `ialk nhb nïk 1<
7.ª `ialk nhb nïk 1
o a 7
7 ao o a >
< ao
k
Akbaubk hb ërhk nhb auknrknf.
Akbaubk hb ërhk nhb pkrkbhbfdrkof. pkrkbhbfdrkof.
g
7 Ô 7 ? > ao·
7 X
< Ô > ? 17 ao·
1<
Akbaubk hb ërhk nhb triëedubf.
a
Akbaubk hb ërhk nh tfnk bk durk.
n
; Ô 7 Ô > ? > ao· 7
> + > + 17 ? >= ao·
;>. Nhthroiek hb ërhk nh aknk durk. ]krk lkahrbf, tihehs quh nivinirb nivinirbks ks he triëedubfs, pkrkbhbfdrkofs f rhatëedubfs y akbaubkr bk suok nh tfnks bks ërhks. k
a o 0 7,
o a 7
0 ao
g
7 , 0 a o
o a 8
1,> ao 1 , > a o
> a o
o a >
1 ao
1 ao ; ao
|
1,> ao ; ao
0 .³ ´ X 7 ´ N ï k
Ërhk auknrknf3 1,> Ô 1,> ? ;;,80 ao· K ?
k i r k o i r ] ³ . 0
Ërhk rhatëedubf3 0 Ô > ? 7> ao· Ërhk triëedubf3 ; Ô 1 Ô > ? 0 ao· 7 Ërhk auknrknfs3 ; Ô ; Ô 7 ? 7 ao·
Ërhk triëedubf3 ; Ô 1,> Ô 7 ? 1,> ao· 7
1 + ;;,80 ? ;>,90 ao·
K ? 7> + 0 + 7 ? 17 ao·
;1;
| ; 1 >
K^HEAIÑE K BK NIPHWQINKN Fxïdhef Hvkbukaiñe ie`frokb
]fnhofs rh`frzkr bfs afetheinfs afe bk `ialk nhb nïk 1< nh OyWFFO.
Fgshrvkaiñe
Whtf ]fnhofs kopbikr bfs afetheinfs afe bk `ialk nhb nïk 1< nh OyWFFO.
AighrHOK^ - Qhsiñe < Aëbaubf nhb ërhk nhb triëedubf rhatëedubf. Xeinknhs nh ohnink nhb sisthok oétriaf. Whsfbuaiñe nh prfgbhoks afe eóohrfs nhaiokbhs. ^rksbkaiñe, rftkaiñe, rh`bhxiñe y siohtrïk. Aëbaubf nhb ërhk nhb pkrkbhbfdrkof. Aëbaubf nhb ërhk nhb triëedubf.
•
•
•
•
•
•
Nhnuah añof akbaubkr hb ërhk nh ue triëedubf k pkrtir nh bk nh ue pkrkbhbfdrkof. Hs akpkz nh hxpbiakr bfs pksfs shduinfs pkrk akbaubkr hb ërhk nh ue triëedubf.
Hvkbukaiñe `frokb ]fr`fbif
Hb kbuoef puhnh dukrnkr he su pfr`fbif nh okthoëtiaks hb hsquhok quh lk lhalf he aksk. @ialks Whsuhbvh afrrhatkoheth 1 nh bfs 8 hchraiaifs nh bk thrahrk `ialk y bk aukrtk `ialk.
AFEFSAF BFQ NIPIQFWHQ
AW H H
K W
;.
AFEFSAF BFQ NIPIQFWHQ
Fgshrvk hstks pihzks. Whprhshetke bfs eóohrfs 7, 1, 8 y 4. Afogieëenfbks puhnhs rhprhshetkr ftrfs eóohrfs.
7
FGCH^IPF
8
4
¶[ué eóohrfs rhprhshetke bfs siduiheths gbfquhs6 @ïckth he hb hchopbf.
k
Lkbbkr bfs nivisfrhs nh ue eóohrf.
1
OK^HWIKB ]ihzks nh afbfrhs nh ue cuhdf
•
7Ô7?>
7Ô1?0
nh afestruaaiñe
Afestruyh bfs eóohrfs 7;, ;7 y ;< afe bks pihzks quh afrrhspfenke.
g
7; ? 1 Ô 4
AFO]H^HEAIKQ Afophtheaik okthoëtiak y afophtheaiks gësiaks he aiheaik y thaefbfdïk Hxprhskr inhks y prfahsfs okthoëtiafs nh okehrk afoprhesigbh utibizkenf hb bhedukch vhrgkb (frkb y hsaritf).
7 Ô 7 Ô 7 Ô 1 Ô 1 ? 47
;7 ? 7 Ô 7 Ô 1
;< ? 7 Ô 1 Ô 1
¶Añof pfnhofs lkbbkr bfs nivisfrhs siopbhs nh >76 Kpbiak bfs arithrifs nh nivisigibinkn pkrk heafetrkrbfs.
a
Ni vi visfr
04 X 1
Ari th thrif nh ni vi visi gi gibi nk nkn
>7
7
Nivisigibinkn pfr 7.
7;
1
Nivisigibinkn pfr 1.
4
4
Nivisigibinkn pfr 4.
;
Qhetinf nh bk ieiaiktivk y hspïritu hoprhenhnfr Nhskrrfbbkr lkgibinknhs pkrk lkahr `rheth k bfs akogifs y bks ni`iaubtknhs afe kutfhstiok y hspïritu nh suphrkaiñe.
Whprhshetk he tu auknhref bks afogiekaifehs nh bfs nivisfrhs siopbhs p krk `frokr tfnfs bfs nivisfrhs nh >7. @ïckth he hb hchopbf.
n
;
7
1
0
4
;>
7;
>7
8 = 7
|
0Ô4 `katfr f nivisfr nh Xe `katfr f nivisfr nh ue eóohrf hs kquhb vkbfr quh nivinh kb eóohrf he pkrths hxkatks. Hb ; hs nivisfr n h tfnfs bfs eóohrfs. Qi >7 ô ;> ? 1 nhaiofs quh3 >7 hs nivisigbh nivisigbh pfr pfr ;> pfrquh hb rhstf nh bk nivisiñe hs =. ;> hs nivisfr nivisfr f f `katfr `katfr nh nh >7. oóbtipbf nh >7 hs oóbtipbf nh ;>.
0 .³ ] r i o k r i k
|
7;0
HEQHÛKENF - K]WHENIHENF
]KWK HO]HSKW - 8 oieutfs Aëbaubf ohetkb
]rfgbhok nhb nïk
Cuhdf nhofstrkaiñe
Ofstrkofs k bfs kbuoefs aieaf fgchtfs nistietfs nh bk abksh y bhs phniofs quh
«Bk pkaiheaik tiheh rhafophesk pkrk bfs abiheths nh Ckjjk. Aukenf uek alkquhtk
Afopfehofs y nhsafopfehofs eóohrfs afe pihzks nh afestruaaiñe,
kprfxiohe sus ohninks. Nhghofs iethetkr quh bks ueinknhs shke bks oisoks pkrk tfnfs bfs fgchtfs. Nhspués, ue vfbuetkrif lkah bks ohniaifehs.
hstë he bk tihenk nurketh uek shokek, hb prhaif sh rhgkck ue ;= %. Nhspués nh ftrk shokek, hb prhaif vuhbvh k rhgkckrsh ue 7= %. Bk thrahrk shokek, hb prhaif nh bk alkquhtk sh rhgkck ue 8= %. @rkeaisaf afoprñ uek alkquhtk quh bbhvkgk 7> nïks he bk tihenk. ]kdñ 47 ₢. ¶Auëb hrk su prhaif fridiekb6º. 7== ₢. Nknf quh lke pksknf oës nh trhs shokeks, bh lke kpbiaknf bfs 1 nhsauhetfs. Akrdkofs hb 8= % kb prhaif `iekb3 47 Ô 7 ? ;>>: ;>> hs hb 7 bfs arithrifs nh nivisigibinkn nivisigibinkn,, uef k uef3 «¶>7 hs nivisigbh pfr 76º (Qï): «¶]fr qué6º (Hs pkr.): «¶Auëb hs hb afaiheth6º (7;): y hsarigiofs bk nhsafopfsiaiñe he bk pizkrrk. «¶7; hs
]rfgbhoks frkbhs ;. Kek lizf ;; `ftfs, phrf nurketh hb nïk gfrrñ 1. ¶Auëetks `ftfs tiheh6 < `ftfs. 7. Nh 1= pistkalfs quh theïk, oh lh afoinf bk thrahrk pkrth. ¶Auëetfs oh quhnke6 7= pistkalfs. 1. ¶Auëetfs bknfs tiheh ue lhptëdfe lhptëdfef6 f6 4 bknfs.
4 0 k ï N ´ 1 X ´ ³ . 0
K^HEAIÑE K BK NIPHWQINKN Fxïdhef
AFEFSAF BFQ NIPIQFWHQ 7.
]krk rhsfbvhr bfs hchraiaifs nh bks `ialks, bfs kbuoefs puhnhe uskr pihzks nh afestruaaiñe.
Lkbbk bfs nivisfrhs nh >8, pksf k pksf. k
Ieniak qué arithrifs nh nivisigibinkn uskrïks pkrk lkbbkr bfs nivisfrhs nh >8. nivisigibinkn pfr ;
g
nivisigibinkn pfr 7
nivisigibinkn pfr 1
nivisigibinkn pfr 8
Whtf
nivisigibinkn pfr 4
Afefainfs bfs nivisfrhs nh ;==, ¶añof pfnhofs akbaubkr bfs nivisfrhs nh ;===6
¶Afe qué afogiekaifehs puhnhs `frokr hb eóohrf >86
;
1
8
9
>8 ô 8 ?
9
>8 ô 1 ?
;8
>8 ô ; ?
>8
>8
;8
1 X
a
¶Auëbhs sfe bfs nivisfrhs nh >86 N(>8) ?
;, 1, 8, 9, ;8, >8 04
1.
Afbfak aknk nivisfr he su budkr afrrhspfeniheth. @ïckth he hb hchopbf.
;
7
1
>
0
9
<
;7
;<
74
7>
Hvkbukaiñe ie`frokb
10
Fgshrvkaiñe
; 10
7
1
; 1
;<
>
;7 9 | 0 .³ ´ X 1 ´ N ï k 0 4
>.
9
74
0
Hxpfeh hb prfahsf quh lk shduinf pkrk lkbbkr bfs nivisfrhs nh ue eóohrf he su Nikrif nh okthoëtiaks. Inheti`iak hb fgchtivf nh bk tkrhk y
7
7>
74
10
;
1
7>
;7
> <
0
pbkei`iak bfs pksfs k rhkbizkr he bk rhsfbuaiñe nh bk `ialk he pkrhcks.
Hsarigh tfnfs bfs nivisfrhs nh aknk eóohrf.
;, 7, 4, ;>
N(18) ?
;, 8, 4, 18
N(70) ?
;, 7, ;1, 70
N(91) ?
;, 1, 1;, 91
N(1=) ?
;, 7, 1, 8, 0, ;=, ;8, 1=
N(;==) ?
;, 7, >, 8, ;=, 7=, 78, 8=, ;==
N(;>) ?
Hvkbukaiñe `frokb Nikrif nh okthoëtiaks @ialks
| 7 = 0
7;4
Whsuhbvh afrrhatkoheth 7 nh bfs > hchraiaifs nh bks `ialks.
]KWK KAKGKW - 8 oieutfs nivisigbh pfr 76º (Ef): «¶7; hs nivisigbh pfr 16º (Qï). Y, fgthehofs ksï bfs `katfrhs siopbhs (>7 ? 7 Ô 1 Ô 4). ]krk afeshduir
@ialk nhb kbuoef 7.ª `ialk nhb nïk 04
tfnfs bfs `katfrhs f nivisfrhs nh >7, bf rhprhshetkofs afe bks pihzks (kokribbk (kokribbk,, ekrkeck y vhrnh) y quitkofs y pfehofs pihzks lkstk `frokr tfnks bks afogiekaifehs pfsigbhs. Bfs kbuoefs puhnhe ir afopbhtkenf bk priohrk `ialk nhb Bigrf nhb kbuoef. Qhûkbkofs quh hb ; hs nivisfr nh tfnfs bfs eóohrfs y afoprfgkofs quh bfs nivisfrhs nh >7 hstëe rhbkaifeknfs nfs k nfs. ]krk kakgkr, bhhofs bk nh`ieiaiñe nh bk `ialk y bk afohetkofs hetrh tfnfs. Whphtiofs hb prfahsf he pkrhcks afe ftrfs eóohrfs. ]hniofs k aknk pkrhck quh hbick ue eóohrf pkrk quh ftrk pkrhck afestruyk bfs gbfquhs y akbaubh tfnfs bfs nivisfrhs nh hsh eóohrf.
7 y 1 nh bk `ialk nh `frok ienivinukb y hb >, he pkrhcks.
Bfs kbuoefs puhnhe rhkbizkr bfs hchraiaifs
Nikrif nh okthoëtiaks ]hniofs k bfs kbuoefs quh hxpbiquhe he hb Nikrif nh okthoëtiaks añof lke heafetrknf bfs nivisfrhs nhb eóohrf ;==.
He aksk ]hniofs k bfs kbuoefs quh afestruyke he aksk bfs eóohrfs >< y 8= afe pihzks siopbhs (7, 1, 8 y 4).
k i r k o i r ] ³ . 0
Okthoëtiaks rhkbhs y okeipubktivks Knhoës, thenrës tfnf hb okthrikb ehahskrif pkrk quh tus kbuoefs kprhenke okeipubkenf3 cuhdfs nh ohsk, tkrchtks, rhatks euoériaks, ue hstualh pkrk aknk kbuoef afe alks, augfs, tkgbks nh oubtipbiakr...
¡pkrk kprhenhr lkaihenf y nis`rutkenf!
Nhsaugrh oës he www.thjokehnuaktife.afo
Kafopkûkoihetf phrsfekbizknf Heshûkr afe bfs prfdrkoks thjoke hs uek kutéetiak kpuhstk pfr bk ieefvkaiñe hnuaktivk y pfr hb afoprfoisf afe tus kbuoefs. Xe nhsk`ïf hofaifeketh h iespirknfr quh kgfrnkofs cuetf k ti, afe ibusiñe y ridfr. ]krk hbbf, pfehofs k tu nispfsiaiñe rhaursfs, `frokaifehs y ue pbke nh kafopkûkoihetf phrsfekbizknf nurketh tfnf hb aursf. Heafetrkrës tfnfs hstfs rhaursfs y shrviaifs sihoprh he
oyrffo, tu pbktk`frok febieh nfaheth.
tjbhkreied
Thgiekrs
]bktk`frok `froktivk afe tfnf bf ehahskrif pkrk hsphaikbizkrth he euhstrfs prfdrkoks.
Afevhrskaifehs y tkbbhrhs Afevhrskaifehs afe rh`hrheths y hxphrtfs he hnuakaiñe.
Kafopkûkoihetf he hb kubk
Whueifehs phnkdñdiaks
^h kafopkûkofs nhsnh bk pbkeiakaiñe nh bk shsiñe lkstk bk rhkbizkaiñe he hb kubk.
Whsuhbvh tus nunks
Bkgs
Ahetrf nh kyunk
Heauhetrfs `froktivfs y hxphriheaikbhs afe ftrfs nfaheths afof tó.
Xek gksh nh afefaioihet afefaioihetf f pkrk rhsfbvhr tus afesubtks nh okehrk ieohniktk.
afe ue phnkdfdf sihoprh k tu nispfsiaiñe nispfsiaiñe..
Hxphriohetkr, kekbizkr, hvkbukr, arhkr. Gkcf hstks prhoisks y nhsnh bks iethbidheaiks oóbtipbhs, HOK^ prfpfeh k bfs kbuoefs ue kprhenizkch iethdrkb nh bks okthoëtiaks. Afesaiheth nh bk ehahsinkn nh skghr trkgkckr nh `frok affphrktivk y bk iopfrtkeaik nhb cuhdf he hb kprhenizkch, HOK^ frdkeizk sus afetheinfs pkrk quh bfs kbuoefs puhnke he`rhetkrsh y knkptkrsh k nistietfs afethxtfs nh bk vink nikrik. Afe HOK^ bks okthoëtiaks sh kprhenhe y sh nis`rutke.
= = 7 = = = O J ^
; > ; = = ; = ; = > < ; 7 I \ \
bks euhvks okths
0.³ ]riokrik / ueinknhs ;-7-1
Bigrf nh ouhstrk
HOK^ hs oës quh ue bigrf He HOK^ sh kprhenh k trkvés nh uek drke nivhrsinkn nh hxphriheaiks okeipubktivks, bóniaks y afethxtukbizknks quh kshdurke hb nhskrrfbbf nh bk afophthe afophtheaik aik okthoëtiak. Bk shsiñe he hb kubk sh hstruaturk he trhs ofohetfs abkvh. Bks alks nh hsth bigrf sfe sfbf uek pkrth nhb prfahsf nh kprhenizkch nh HOK^. HOK^.
]krk hophzkr @fohetkofs bk kdibinkn ohetkb, bk hsaualk kativk y hb rkzfekoihetf bñdiaf. Hs hb ofohetf pkrk hb aëbaubf ohetkb, bfs prfgbhoks frkbhs y bfs prfgbhoks nhb nïk.
]WFGBHOK NHB NÏK
]WFGBHOKQ FWKBHQ
AËBAXBF OHE^KB
r k h
] k
NIKWIF OK^HOË^IAF
ophzk r r
OK^ICXHDFQ
r k g k
]GB
a
WH@BH\IFEHQ FWKBHQ
k k r k
]
LIQ^FWIKQ ]KWK ]HEQKW AIGHWHOK^
f
n
e i h
@IALKQ
n
CXHDFQ NH AXGFQ
H esh û k e n f
p
k
-
KA^IPINKNHQ OKEI]XBK^IPKQ
]krk kakgkr Whhxifekofs sfgrh bf kprheninf y bbhvkofs k akgf nieëoiaks quh phroithe k bfs kbuoefs kkezkr bfs kprhenizkchs.
e r h
CXHDFQ NHOFQ^WKAIÑE HQ^WK^HDIKQ Y WX^IEKQ NH ]HEQKOIHE^F
Heshûkenf-kprhenihenf He bk pkrth ahetrkb nh aknk shsiñe kprhenhofs bfs afetheinfs okthoëtiafs afogiekenf kbdueks nh hstks kativinknhs hxphriheaikbhs y okeipubktivks.
Xek drke nivhrsinkn nh hxphriheaiks HOK^ f`rhah kativinknhs pkrk kprhenhr bfs afetheinfs nhsnh tfnks bks iethbidheaiks, pkrk quh tfnfs bfs kbuoefs afehathe afe bks okthoëtiaks.
Bñdiaf-okthoëtiak
Biedòïstiaf-vhrgkb
Afrpfrkb-aiehstésiak
Ekturkbistk
Ietrkphrsfekb
Pisukb-hspkaikb
Ousiakb
Iethrphrsfekb
Kativinknhs pkrk nhskrrfbbkr bk afophtheaik Bk ^kxfefoïk ^kxfefoïk nh Gbffo abksiak abksia k bfs eivhbhs nh pheskoihetf quh sh pfehe he prëatiak he bfs prfahsfs nh kprhenizkch. Xe kbuoef afophtheth hs kquhb akpkz nh utibizkr bfs eivhbhs nh n h pheskoihetf suphrifr. suphrifr. ]fr hbbf, he HOK^ sh shauheaike kativinknhs nh kprhenizkch nhnuativf quh phroithe kpbiakr, kekbizkr, hvkbukr y arhkr, pkrk kprhenhr k trkes`hrir Bfs kprhenizkchs k situkaifehs nhb nïk k nïk.
He HOK^ sh `fohetke bfs eivhbhs nh pheskoihetf nh frnhe suphrifr. B I S
W
´
E K
KW
´
H P K
B X K
K
W
K
A
A
´
W
I B
H
]
K
W
K
W H N
W H
A F
W N K K W
´
H E
A F O ] W
Q H ^ K O Q K P H X E Q K B H A F E F A
1
AFEFSAF HB PKBFW NH AKNK EÓOHWF
Hurfpk tiheh uek pfgbkaiñe tftkb nh 4>7 9>1 1>8 lkgitkeths, kprfxioknkoheth.
Oibbñe s k e h t e h a
4
s k e h a h n
>
Oibbkr s h n k n i e u
7
s k e h t e h a
9
s k e h a h n
>
s h n k n i e u
1
s k e h t e h a
1
s h n k n i e u
s k e h a h n
>
8
Qh bhh3 shthaihetfs aukrhetk y nfs oibbfehs efvhaihetfs aukrhetk y trhs oib trhsaihetfs aukrhetk y aieaf.
; X ;
Hb 4 rhprhshetk
4 ahetheks nh oibbñe
4== === ===
Hb > rhprhshetk
> nhaheks nh oibbñe
>= === ===
Hb 7 rhprhshetk
7 ueinknhs nh oibbñe
7 === ===
Hb 9 rhprhshetk
9 ahetheks nh oibbkr
9== ===
Hb > rhprhshetk
> nhaheks nh oibbkr
>= ===
Hb 1 rhprhshetk
1 ueinknhs nh oibbkr
1 ===
Hb 1 rhprhshetk
1 ahetheks
1==
Hb > rhprhshetk
> nhaheks
>=
Hb 8 rhprhshetk
8 ueinknhs
8 4>7 9>1 1>8
Hb vkbfr nh aknk pfsiaiñe hs nihz vhahs okyfr quh hb nh bk pfsiaiñe nh su nhrhalk3 bks nhaheks sfe nihz vhahs bks ueinknhs, bks ahetheks nh oibbkr sfe nihz vhahs bks nhaheks nh oibbkr…
;.
Hstiok bk rhspuhstk nh bks siduiheths prhduetks y hsarigh hb eóohrf afrrhatf quh th prfpfraifeh tu okhstrf. ]rhduetk
He 7=;4, ¶auëetfs eiûfs y eiûks he hb ouenf ef pfnïke ir k bk hsauhbk6 ¶Auëetfs nhpfrtistks pkrtiaipkrfe he bfs Cuhdfs ]krkbïopiafs nh Wïf nh Ckehirf 7=;06 ¶Auëetfs jibñohtrfs rhafrrh he ; shduenf bk buz he hb vkaïf6
Hstiokaiñe
Whspuhstk afrrhatk
0
AFEFSAF HB PKBFW NH AKNK EÓOHWF
He bfs Cuhdfs Fbïopiafs nh Wïf nh Ckehirf 7=;0, bk eknknfrk Oirhik Ghbofeth dkeñ hb grfeah he bfs >== o hstibfs afe ue tihopf nh 747,19 s. s k e h t e h a
s k e h a h n
s h n k n i e u
7
4
7
s k o i a é n ,
1
s k o i s é t e h a
k s o i s é b i o
9
=
Qh bhh3 nfsaihetfs shthetk y nfs afok trhsaihetfs efvhetk f nfs sihth nfs afok trhs euhvh ahrf. Hb 7 rhprhshetk
7 ahetheks
7==
Hb 4 rhprhshetk
4 nhaheks
4=
Hb 7 rhprhshetk
7 ueinknhs
7
Hb 1 rhprhshetk
1 néaioks
=, 1
Hb 9 rhprhshetk
9 ahetésioks
=,=9
Hb = rhprhshetk
= oibésioks
=,===
; X
747,19= Bk afok sihoprh hstë situknk hetrh bks ueinknhs y bks néaioks. K kogfs bknfs nh bk afok, aknk pfsiaiñe p fsiaiñe tiheh ue vkbfr nh nihz vhahs hb vkbfr nh bk pfsiaiñe nh su nhrhalk.
7.
Hstiok bk rhspuhstk nh bks siduiheths prhduetks y hsarigh hb eóohrf afrrhatf quh th prfpfraifeh tu okhstrf. ]rhduetk
¶Auëetfs shduenfs nurk, nh ohnik, hb kbhthf nh ue afbigrï6 ¶Auëb hs bk ohcfr okrak fbïopiak, he ohtrfs, he bk ofnkbinkn skbtf nh kbturk oksaubief6 ¶Auëb hs bk bfeditun kprfxioknk, kprfxioknk, he ahetïohtrfs, nh uek kohgk6
Hstiokaiñe
Whspuhstk afrrhatk
;
4
C X H D F N H A X G F Q
Whkdrupf eóohrfs
Cudknfrhs Nfs f oës
Okthrikb • Xe augf euoériaf (=-8) • Xe augf euoériaf (8-;=)
Fgchtivf Afeshduir hb eóohrf oës kbtf.
Efroks ;. Aknk ccudknfr udknfr niguck uek pbketibbk afof hstk3 A
N
X
7. Hb priohr cudk cudknfr nfr bkezk bfs nfs augfs. ^^fnfs fnfs bfs cudknfrhs hsarighe bbkk suok nh bfs augfs he uef nh bfs auknrknfs nh bk pbketibbk.
; X ;
1. Bfs augfs sh bkezke nfs vhahs oës y, aknk vhz, bbfs fs cudknfrhs hsarighe bk suok he uef nh bfs auknrknfs quh quhnke he gbkeaf. >. Nhspués, bfs cudknfrhs akbaubke hb vkbfr nh sus eóohrfs, rhkdrupkenf aukenf shk ehahskri ehahskrif. f. 8. Dkek hb cudknfr quh `froh hb eóohrf okyfr okyfr.. Hchopbf3
@hbiph
Bkezkoihetf
A
N
Akrbfs
X
A
N
X
A
<
<
;;
<
<
;;
;> ;;
<
<
;> ;;
<
;.
1
8
7.
8
0
;;
<
1.
8
9
;;
<
;>
Buisk
N
X
Whkdrupkr3
;; A + < N + ;> X ;; A + 9 N + > X
;> A + ;; N + < X ;8 A + ; N + < X
< A + ;> N + ;; X 9A+8N+ ;X
Whsubtknf3
;;9>
;8;<
98;
Akrbfs dkek bk pkrtink pfrquh lk fgtheinf hb eóohrf oës kbtf.
<
AFEFSAF HB PKBFW NH AKNK EÓOHWF 1.
>.
8.
0.
Hsarigh hb rhsubtknf.
7 + 1== + 7== === ?
9=== + 8== + >= + 1 ?
0 + 8= + === + 4= + 1= === + ; ?
Afopbhtk bks shrihs.
0=9< 0=99
0;=8
9990 9994
;= ==1
¶[ué rhprhshetk hb 4 he aknk uef nh n h bfs siduiheths eóohrfs6
9,980
7;>,74;
804,;=8
; X
Hsarigh he eóohrfs.
;
7 néaioks, > ahetésioks, 0 oibésioks 0 ueinknhs, < ahetésioks, 4 oibésioks
4.
Hsarigh hb rhsubtknf.
=,==9 + =,=7 + =,8 ?
=,0 + =,=1 + =,==; ?
7 + =,0 + =,=> ?
=,==4 + =,9 + =,=0 ?
¶[ué hs okyfr3 =,9> f =,9=>6
]fnhofs afbfakr ue = nhspués nh =,9> = ,9> afevirtiéenfbf he =,9>=, nh okehrk quh bfs nfs eóohrfs thedke hb oisof eóohrf nh ai`rks nhaiokbhs nhspués nh bk afok.
=,9>= 5 =,9=> 7
=,>;9
=,>9<
=,>
1,;8
1,9
=,7
=,;98
9
AW H H
K W
NIGXCF H IE^HW]WH^F HQAKBKQ
AFO]WHENHW
;.
Fgshrvk hb siduiheth pbkef nh ue pisf.
Nhspkalf Lkgitkaiñe ;
Qkbñe
Whaiginfr Lkgitkaiñe 7
Gkûf
Afaiek
4
Hsakbk ;3
AW H H
NIGXCF H IE^HW]WH^F HQAKBKQ 7.
K W
^h nispfehs k nhafrkr hb pisf. Whafrtk bfs ouhgbhs quh th prfpfraifeh hb okhstrf, nisauth su afbfakaiñe cuetf afe tus afopkûhrfs y pédkbfs he hb budkr quh afesinhrhs oës knhauknf.. K afetieukaiñe, rhspfenh k bks prhduetks. knhauknf
k
¶Auëetf oinh nh bkrdf bk akok ienivinukb6
; X
4
1.
g
Nishûk y niguck ue ouhgbh quh quihrks afbfakr he hb pisf. ¶Auëbhs sfe sus niohesifehs rhkbhs6
a
¶Akgh, he hb rhaiginfr, ue ouhgbh nh 7 o nh bkrdf6
Ieniak, nh nfs okehrks nistietks, uek hsakbk he bk quh aknk ahetïohtrf nhb pbkef sh afrrhspfenk afe ; o he bk rhkbinkn.
78
KEKB I S K W
;.
KEKBISF BKQ OHNINKQ NH ^HENHEAIK AHE^WKB
Pkofs k lkahr ue hstunif hstknïstiaf nh bk tkbbk nh pih nh tfnfs bfs kbuoefs nh bk abksh. Afethstk k bks prhduetks.
k
Hsarigh bfs eóohrfs quh ieniake bk tkbbk nh pih nh tfnfs tu tuss afopkûhrfs, ieabuink bk tuyk, y frnéekbfs nh ohefr k okyfr.
g
¶Auëb hs hb rkedf6
a
¶Auëb hs bk ohnikek6
n
¶Auëb hs bk ofnk6
77 X ;
Hb rkedf nh ue afecuetf nh eóohrfs hs bk ni`hrheaik hetrh hb vkbfr oës drkenh y hb oës phquhûf. Efs ouhstrk bk nisphrsiñe nh bfs vkbfrhs he ue afecuetf nh nktfs. Bk ohnikek nh ue afecuetf nh eóohrfs hs hb eóohrf quh hstë he ohnif aukenf bfs eóohrfs hstëe frnheknfs nh ohefr k okyfr. Bk ofnk hs hb téroief quh kpkrhah afe okyfr `rhauheaik he ue afecuetf.
h
Afopbhtk bk tkgbk nh `rhauheaiks afe bfs nktfs fgtheinfs.
^kbbk Eóohrf nh kbuoefs
47
KEKB I S K W
KEKBISF BKQ OHNINKQ NH ^HENHEAIK AHE^WKB `
d
Akbaubk bk tkbbk ohnik nh pih.
¶Auëetfs kbuoefs tihehe uek tkbbk suphrifr k bk ohnik6
Bk ohnik hs hb eóohrf quh sh fgtiheh kb suokr ue drupf nh eóohrfs y nivinir hb rhsubtknf pfr bk aketinkn nh eóohrfs quh lky.
7.
He bk ekb `hoheiek nh ektkaiñe nh 8= o hstibf bigrh, dkek bk kbuoek quh afesiduh bk ohnik oës gkck y, he aksf nh hopkth, bk quh tiheh ohefr rkedf he bfs tihopfs. ¶[uiée dkek bk ekb6
^ihopf (s)
1.
Kbiaik
Buaïk
Qfeik
10 - 1< - 14
1< - 19 - >1
18 - 10 - >=
Akrbfs lk bkezknf aieaf vhahs bfs nfs augfs euoériafs y lk fgtheinf bfs rhsubtknfs quh kpkrhahe k afetieukaiñe. Akbaubk hb rkedf, bk ohnik, bk ohnikek y bk ofnk nh hsfs eóohrfs.
; k
Wkedf3
a
Ohnik3
n
Ohnikek3
4
8
8
;
8
> g
< Ofnk3
7
0
; X
77
41
C X H D F N H A X G F Q
Lkstk 78
Cudknfrhs Nfs f oës
Okthrikbhs • Nfs augfs euoériafs (=(=-8) 8) • Nfs augfs euoériafs ((8-;=) 8-;=)
Fgchtivf Afeshduir hb prfnuatf oës ahrakef k 78.
Efroks ;. Bfs cudknfrhs sh tureke pkrk bkezkr bfs auktrf augfs. Qi skbh ue ;=, nhgh vfbvhr k bkezkrsh hsh augf. 7. hethrfs Afe bfs eóohr eóohrfs fs quhauyf sh lke fgtheinf, cudknfr ai`rks, rks, f nhaiokbhs, prfnuatf shkaknk ahrakef k 78.nhgh `frokr nfs eóohrfs nh nfs ai` 1. Hb cudknfr quh fgthedk hb pr prfnuatf fnuatf oës ahrakef k 78 dkek. 11 X 7
>. Nhgh utibizkrsh uek akbaubk akbaubknfrk nfrk f pk pkphb phb y bëpiz pkrk vhriakr bbfs fs prfnuatfs sfbf si ef sh puhnh ieniakr pfr kprfxiokaiñe qué rhsubtknf sh kahrak oës k 78. Hchopbf3
Kbiaik
Bkezk
=
;
8
Cuke
4
;
8
8
Oubtipbiak
8, 8,;; Ô 4, 4,= =
8,; 8,; Ô 8,7 8,7
Kprfxiok
18
78
Cuke dkek bk pkrtink pfrquh su rhsubtknf sh kahrak oës k 78.
7
;=<
WHQXHBPF ]WFGBHOKQ AFE NHAIOKBHQ ;.
Ievhetk ue prfgbhok. Keths nh hsarigirbf, rhspfenh k bks prhduetks nhb frdkeizknfr drëaf afe tus afopkûhrfs.
¶[ué nktfs nkré6
¶[ué pkskrë6
]rfgbhok ¶[ué lkgrë quh lkahr pkrk sfbuaifekrbf6
¶Auëb shrë bk prhduetk ekb6
7 X
11
7.
Hsarigh hb prfgbhok quh lks ievhetknf cuetf k tus afopkûhrfs.
;=9
WHQXHBPF ]WFGBHOKQ AFE NHAIOKBHQ 1.
Wfghrtf quihrh augrir afe ofquhtk hb nfroitfrif. Bk lkgitkaiñe oinh 1,0 o nh kealf pfr 0,1 o nh bkrdf. Bk ofquhtk quh bh dustk oinh > o nh kealf y auhstk auhst k 7;,98 ₢ hb ohtrf nh bkrdf. ^iheh quh afoprkr uek pihzk nh > o nh kealf, kuequh hb nfroitfrif hs oës hstrhalf y sfgrkrë ofquhtk. Whspfenh k bks prhduetks. k g
>.
¶Auëetfs ohtrfs nh bkrdf tiheh quh afoprkr Wfghrtf6 ¶Auëetf tiheh quh pkdkr6
Hb vhenhnfr vhenhnfr bh hxpbiak quh puhnh iestkbkrbh bk ofquhtk k 1,78 ₢ hb ohtrf au auknrknf. knrknf. Hsth shrviaif ieabuyh afrtkr bk ofquhtk y heafbkrbk. Whspfenh k bks prhduetks.
k
¶Auëetfs ohtrfs auknrknfs tiheh hb nfroitfrif6
g
¶Auëetf bh afstkrë k Wfghrtf bk iestkbkaiñe nh bk ofquhtk6
a
¶Auëetf bh afstkrë k Wfghrtf bk ofquhtk y hb shrviaif nh iestkbkaiñe6
11 X 7
8.
Ftrk tihenk f`rhah uek biquinkaiñe nh skbnfs afe trfzfs nh ofquhtk quh yk sh lke afrtknf. Phenhe ue trfzf nh ofquhtk quh oinh >,= o nh kealf y 0,4 o nh bkrdf pfr ;9,98 ₢ hb ohtrf nh bkrdf. ¶Auëetf bh afstkrë k Wfghrtf hb trfzf nh ofquhtk he hstk tihenk6
;;=
WHQXHBPF ]WFGBHOKQ AFE NHAIOKBHQ 0.
Bk tihenk afgrk 1,8= ₢ pfr augrir afe ofquhtk ue ohtrf auknrknf. Whspfenh k bks prhduetks.
k
¶Auëetf afstkrë bk iestkbkaiñe nh bk ofquhtk6
g
¶Auëetf bh afstkrë k Wfghrtf augrir su lkgitkaiñe afe ofquhtk si bf lkah he hstk tihenk6
4.
¶Auëb nh bks nfs tihenks hs oës hafeñoiak6
Ô 7 ?
7Ô1?
9,> Ô =,7 ?
7; Ô 1; ?
9,> Ô =,=7 ?
7,; Ô 1,; ?
9,> Ô ;,=7 ?
7,=; Ô 1,; ?
=,9> Ô ;,=7 ?
7,=; Ô 1,=; ?
=,9> Ô ;,==7 ?
7,=; Ô 1,==; ?
;=. Whsuhbvh bks fphrkaifehs ohetkboheth. @ïckth he bfs sidefs.
;,8 ô ;= ?
;,8 ô ;== ?
=,=8 Ô ;== ?
08= ô ;=== ?
>,< Ô ;== ?
;,8 Ô ;=== ?
47 Ô ;= ?
47 ô ;== ?
; ô ;= ?
8 ô ;== ?
;;;
]WKA^IAF HB QIQ^HOK OÉ^WIAF ;.
7.
1. 1>
Hxprhsk bfs siduiheths rhsubtknfs he bk ueinkn oës phquhûk. p hquhûk. 1 o + 7 ao ?
; jd + ; ld + ; d ?
1 nkb + 8 nkb ?
1 nko + >7 o ?
7 jd + 18 d ?
; jb + 8 b + 1 nb ?
Hxprhsk bfs siduiheths rhsubtknfs he bk ueinkn oës drkenh. >; b + 1 nb ?
; jd + 7 ld + 7 d ?
7 jo + 8 jo ?
;8 b + ;7 nb ?
71 lo + 7 o ?
; nkd + ; d ?
Nhsafopñe bks ohninks pkrk afopbhtkr bks tkgbks. k
X 7
jo
lo
nko
o
no
ao
oo
jd
ld
nkd
d
nd
ad
od
jb
lb
nkb
b
nb
ab
ob
>7,18 o 1;>8 oo 7,>87 jo
g
7,4;9 nkd 0=>=,8 ad 84,< nd a
;=81 nb 7= ==7 ab 0;,804 lb
;;7
HPKB X K
]WKA^IAF HB QIQ^HOK OÉ^WIAF >.
W
Léatfr lk inf afe su koidk Aris k visitkr hb akopf nh `ótgfb nh su bfakbinkn. Hb hetrheknfr bhs lk nialf quh hb akopf a kopf oinh ;== o nh bkrdf y 8= o nh kealf. ]krk afoprfgkrbf, Léatfr y Aris lke nhaininf ohnirbf.
Hetrheknfr o o o 8 8 , , 9 = = 8 8 >
Léatfr Aris
99,8 o ;== o ;==,8 o
k
¶]fr qué lke fgtheinf ohninks nistietks6
7 X
1>
g
¶Auëb hs hb phrïohtrf y hb ërhk nhb akopf si afesinhrkofs bks ohninks nhb hetrheknfr6
a
¶Auëb hs hb phrïohtrf y hb ërhk afe bks ohninks nh Léatfr6
n
¶Y afe bks ohninks nh Aris6
h
¶[ué hrrfr lke pfninf afohthr, afof oëxiof, he auketf kb ërhk y kb phrïohtrf nhb akopf6
`
Qi sh tuvihsh quh rhpbketkr hb aésphn nhb akopf nh `ótgfb, ¶nhghe akbaubkr shdóe hb ërhk okyfr f hb ërhk ohefr6
d
Qi sh quisihrk utibizkr hb akopf pkrk afophtiaifehs, ¶qué ërhk sh nhghrïk eftiakr k bk `hnhrkaiñe6
;;1
L I Q ^ F W I K Q
1> ] K W K ] H E Q K W
Inhks
dkbëatiaks (II)
Bhofe trkgkckgk aknk nïk he bk rhpkrkaiñe nh bk Bhofewkdhe. „Oh dustk oualf rhpkrkr oi ekvh, bf quh phfr bbhvf hs quh sh oh akeske oualf bks pihreks yhenf nh ue bknf pkrk hb ftrf „bhs nicf k sus koidfs. K Dkbk y Duibbh bhs dustkgk oualf trkgkckr he euhvks inhks, ksï quh sh pusihrfe k pheskr he sfbuaifehs.
N H K N QK O H Q F E H Q I F A K WK W K ] ]K W H
K ^K ] X H W ^ K NK W ^ E H H H H N H N H K N QK O H Q G XC F N I G
Duibbh nigucñ ue pbkef k hsakbk nh bk ekvh. Qu pbkef hrk ksï3 H N H AKCK N K P H Q BK A B
N H K N QK O H Q OK E N F Q
K BK B B ^ WK O ] I B N H B E K B OK A É
; o 8 ao ? ; ;, 8 k ; saa k b k H s
H N H K N QK O H Q Q F B NK W
;;>
Duibbh hstuvf fgshrvkenf kb phquhûf hxtrkthrrhstrh oihetrks trkgkckgk pfr bk ekvh y tfoñ eftks ouy prhaisks. Dhehrkboheth bf quh lkaïk Bhofe hrk3 ;. Hophzkgk hb n nïk ïk trks bk ohsk nh okenf okenfs, s, prhduetkenf k Oirt si lkgïk eftia eftiaiks iks nh su pbkehtk. 7. Igk kb kbokaée k gusakr okthrikb. 1. Nhniakgk ue ttihopf ihopf kb ofet ofetkch kch y nhsofet nhsofetkch kch nh pihzk pihzkss he bk ohsk nh rhpkrkai rhpkrkaifehs. fehs. >. Bbhvkgk hb air airauitf auitf k bk ohsk nh nigucf, lkaïk u uefs efs gfahtfs y sh bf bfss hevikgk k O Oirt. irt. 8. Whpkrkgk pihzks he bk ohsk n nhh sfbnkr sfbnkr.. 0. Whviskgk hb pkehb nh afetr afetrfb fb he bk ohsk nh okenfs. 4. Igk k bk akck nh abkv abkvhs hs y f fgtheïk gtheïk hb añnidf nh krrkequh.
Q K I W F ^ Q I L
;;8
W X ^ I E K N H ] H E Q K O I H E ^ F
He`faf y rh`bhxifef Afopkrtf ¶[ué `rkaaiñe rhprhshetke, rhsphatf nh bk durk afopbhtk, aknk uef nh bfs triëedubfs quh `froke ue pkrkbhbfdrkof6 ¶Añof puhnf akbaubkr hb ërhk nhb triëedubf afefaihenf afefaih enf bk nhb pkrkbhbfdrkof6 ¶Faurrh bf oisof he tfnfs bfs aksfs6
Whhxifef
1< X 7
Afehatf
;7<
KEKB I S K W
NHNXSAF HB ËWHK NHB ^WIËEDXBF ;.
¶Auëb hs hb ërhk nhb pkrkbhbfdrkof KGAN6
K
1 ao
> a o
7.
0 ao
1.
Iokdiek quh rhafrtks hb pkrkbhbfdrkof y, nhspués, afrtks pfr NG pkrk `frokr nfs triëedubfs shpkrknfs. ¶]uhnhs heakckr NGA hxkatkoheth he NGK6
>.
¶[ué `rkaaiñe nhb ërhk nh KGAN hs hb ërhk nh NGA6
8.
¶Auëb hs hb ërhk nh NGA6
0.
Qi afrtkofs hb pkrkbhbfdrkof KGAN pfr KA, ¶qué `rkaaiñe nhb ërhk nh KGAN hs hb ërhk nh KNA6
a o
> a o
N
9.
o a 1
> a o
¶^iheh NGA bk oisok `frok y ohnink quh GNK6 N
4.
G
0 ao
0 ao
¶^ihehe bk oisok ërhk tfnfs bfs pkrkbhbfdrkofs quh afopkrthe nfs bknfs afe ue triëedubf6
Hb ërhk nh ue pkrkbhbfdrkof hs bk bfeditun nh bk gksh pfr bk kbturk3 K ? g Ô l
Hb ërhk nh ue triëedubf hs bk oitkn nh bk bfeditun nh bk gksh pfr bk kbturk3 K ?
; g Ô l 7
A
;79
NHNXSAF HB ËWHK NHB ^WIËEDXBF ;=. Akbaubk hb ërhk nh bks siduiheths durks. 8,8 ao
k
g
o a >
; = = ,7 8 a o o
8 a o
0 a o
a o 8 a
< ao
1 ao
;;. Hb kyuetkoihetf quihrh akogikr hb suhbf nh bk pbkzk y pfehr gkbnfsks nh afbfr okrrñe fsaurf. Lke akbaubknf quh bfs hopbhknfs tkrnke uek lfrk he hogkbnfskr ;= o 7. ¶Auëetf tihopf sh ehahsitk pkrk augrir tfnf hb suhbf nh bk pbkzk6 4 8 o
1< X 7
o
o 1
k
g
0o
o 7
Qi bfs nfs lke utibizknf uek thbk quh vkbh 0 ₢ pfr ohtrf auknrknf, ¶quiée lk pkdknf oës pfr hb tfbnf6
¶[ué tfbnf arhhs quh hs oës prëatiaf6
;1=
NHNXSAF HB ËWHK NHB ^WIËEDXBF ;1. ]krk akbaubkr hb ërhk nh uek durk afopbiaknk, pfnhofs nhsafopfehrbk he pkrths oës phquhûks. ]fr hchopbf, pfnhofs nhsafopfehr bk siduiheth durk he ue auknrknf (rfsk), ue triëedubf (vhrnh) y ue pkrkbhbfdrkof (kzub).
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Akbaubk hb ërhk nhb auknrknf.
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Akbaubk hb ërhk nhb triëedubf.
n
Akbaubk hb ërhk nhb pkrkbhbfdrkof.
7 X
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Akbaubk hb ërhk nh tfnk bk durk.
;>. Nhthroiek hb ërhk nh aknk durk. ]krk lkahrbf, tihehs quh nivinirbks he triëedubfs, pkrkbhbfdrkofs f rhatëedubfs y akbaubkr bk suok nh tfnks bks ërhks. k
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AFEFSAF BFQ NIPIQFWHQ
Fgshrvk hstks pihzks. Whprhshetke bfs eóohrfs 7, 1, 8 y 4. Afogieëenfbks puhnhs rhprhshetkr ftrfs eóohrfs.
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¶[ué eóohrfs rhprhshetke bfs siduiheths gbfquhs6 @ïckth he hb hchopbf.
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Afestruyh bfs eóohrfs 7;, ;7 y ;< afe bks pihzks quh afrrhspfenke.
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¶Añof pfnhofs lkbbkr bfs nivisfrhs siopbhs nh >76 Kpbiak bfs arithrifs nh nivisigibinkn pkrk heafetrkrbfs.
Nivisfr
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Arithrif nh nivisigibinkn
>7
X 1
7;
Whprhshetk he tu auknhref bks afogiekaifehs nh bfs nivisfrhs siopbhs pkrk `frokr tfnfs bfs nivisfrhs nh >7. @ïckth he hb hchopbf.
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0Ô4 `katfr f nivisfr nh Xe `katfr f nivisfr nh ue eóohrf hs kquhb vkbfr quh nivinh kb eóohrf he pkrths hxkatks. Hb ; hs nivisfr nh tfnfs bfs eóohrfs. Qi >7 ô ;> ? 1 nhaiofs quh3 >7 hs nivisigbh nivisigbh pfr pfr ;> pfrquh hb rhstf nh bk nivisiñe hs =. ;> hs nivisfr nivisfr f f `katfr `katfr nh nh >7. >7 hs oóbtipbf oóbtipbf nh nh ;>.
>7
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AFEFSAF BFQ NIPIQFWHQ 7.
Lkbbk bfs nivisfrhs nh >8, pksf k pksf. k
Ieniak qué arithrifs nh nivisigibinkn uskrïks pkrk lkbbkr bfs nivisfrhs nh >8. nivisigibinkn pfr ;
g
nivisigibinkn pfr 7
nivisigibinkn pfr 1
nivisigibinkn pfr 8
nivisigibinkn pfr 4
¶Afe qué afogiekaifehs puhnhs `frokr hb eóohrf >86
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8
>8
>8 ô 8 ? >8 ô 1 ? >8 ô ; ? 1 X
¶Auëbhs sfe bfs nivisfrhs nh >86 N(>8) ?
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Afbfak aknk nivisfr he su budkr afrrhspfeniheth. @ïckth he hb hchopbf.
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Hsarigh tfnfs bfs nivisfrhs nh aknk a knk eóohrf. N(;>) ?
N(18) ?
N(70) ?
N(91) ?
N(1=) ?
N(;==) ?
10
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n H h x b p p r h r f s g f b b h k o s k f b u a i ñ e
r h y K p s / b f f i a b v f f p h h b r r k h k s b a h i s p f r r f e t h k g s t b h h p d o k i k k r k s
r h Q h f s h s p t b r f h r k h a b v k t a h h a i i d f r f i e h e k f b h s p s y k b r p / s f f g k r b k h o k
h I e b t p h r r f p g r b h h o t f k
i e E t h h a r h p s r i t h t f k r k y h u b n r k h s p u k b r t k k n f .
p k r k s h d u i r s u s p k s f s .
p H h i b r c f f e u h e a k h h s i s t t f r k k h y t u d n i k k ,
a p p I n f k h h e k r r e h s f e t i b b k h f g a a s h f . r h s b i f q t u f s é k n y k l u k n t f a s h k , r
p p B k h h f r f h k r a e b f h o h a e u p h s e r i a h t f i e n k k n y f h u r , b f n . k
h N s f a y r i k b g i r s f b k b s u u a i e ñ i e n k s n i e h s .
q n Q i u h d h k b f l h b f h h t s s r p b k h k d t s h i f n d s f k . i
p p H k h b i r r c f f k n e u s h h k e k a h h r s s r t i t f f r b b k k k r y t h b u d k i . n k k ,
i e h A n b f h h a h o e h e t p s u i r a e t i a e k f i h k n r k y n f b f u f n s , p n k h k p r t f k r f s k .
I e i a i k n f
a a N f f f r y r e h b b k s s k p s f u f e e u b n n i a i k i h e n ñ t h e h s s .
a q n Q f u h d i r h k b f r h u b a t h f t s i s f i b s z t r p . f k k t s b h f f s d i s n k k y r f t s h v i s f
y H s b i c é f a u ñ e o k f h n s h t r s k k t r r h i d f b b k k r b k .
p h A r h h i f b n o k r f h a p e i f e r e f t h i e k s r é a n f b f f a b s h f . ñ o s b f n h e u t k f e a s , k i n f
K v k e z k n f
N s i a f f b r k r y h b r s k h p s s p f f u e b h n u s i a i t h e ñ k t e h h s s a b y f e ñ d a k b f s i a o k u . r p n e i u h k g n f h s
b n a Q f f d i s h c r f r n f k e h b a f t s f i e t s d f s p a u y k f e r s r f h f r v s h , a i f a y s t f f q u q e s h b . u f u h s t e n i b f k i t f f z o s h
k v s H b k é b i b n f p f c r h r f k s u g r k e b s r k h i r o r f h b s k h b t s k . p r r b k f k h e y t n p d i h u k r , ï h k n f
b y I k e p t r h u h s h r p p n r u f h h i t s o f t k h k b h d p i r s e p k f h r g r b k h n o k k .
] r i e a i p i k e t h
H x p h r t f
W ó g r i a k n h
h r s f b u a i ñ e n h p r f g b h o k s
^haefbfdïk kb shrviaif nhb kprhenizkch AighrHOK^ hs bk kpbiakaiñe pkrk bk prëatiak shokekb nh HOK^ nh okehrk kutñefok y phrsfekbizknk. AighrHOK^ phroith ue kprhenizkch knkptktivf, afe kativinknhs quh sh kcustke kb prfdrhsf nhb kbuoef.
Afe `hhngkaj ieohniktf pkrk `kaibitkr bk kutfefoïk.
Hxphriohetkr, kekbizkr, hvkbukr, arhkr. Gkcf hstks prhoisks y nhsnh bks iethbidheaiks oóbtipbhs, HOK^ prfpfeh k bfs kbuoefs ue kprhenizkch iethdrkb nh bks okthoëtiaks. Afesaiheth nh bk ehahsinkn nh skghr trkgkckr nh `frok affphrktivk y bk iopfrtkeaik nhb cuhdf he hb kprhenizkch, HOK^ frdkeizk sus afetheinfs pkrk quh bfs kbuoefs puhnke he`rhetkrsh y knkptkrsh k nistietfs afethxtfs nh bk vink nikrik. Afe HOK^ bks okthoëtiaks sh kprhenhe y sh nis`rutke.
= = 7 = = = O J ^
; > ; = = ; = ; = > < ; 7 I \ \
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