Regla de tres
8
PKAHB FK VPKY 2) COVPNF[IICÙO.- JBAOCV[FKY \PN\NPICNOBHKY 2.2) JBAOCV[FKY FCPKIVBJKOVK \PN\NPICNOBHKY.- Fns jbaoctufks (prnpckfbf eêscib quk pukfk skr jkfcfb) sno fcrkitbjkotk prnpnricnobhks (F\) iubofn bh bujkotbr n fcsjcoucr kh vbhnr fk uob fk khhbs, kotnoiks kh vbhnr inrrkspnofckotk b hb ntrb buj kotbrâ n fcsj c oucrâ rkspk itcv bjk otk ko h b jc sjb p rnpn ricùo. Kdkj phn4 [ob pkrs nob rkin rrk 6< j ktrns ko ; skauo fns. (Kspbicn vs. Vc kjpn) Jbaoc tuf Ubh nrks inrrk spnofckotks B4 Kspbic n (j ktrns) 6< =< 20< 25< 0<< @4 Vc kjpn (skauo fns ) ; 2< 2; 0< 0; Bh fcvcfcr sus vbhnrks inrrkspnofckotks kh inickotk ks sckjprk inostbotk, ks fkicr, sc fns jbaoctufks B y @ sno fcrkitbjkotk prnpnricnobhks, sk fkontb4 B (F\) @ n B @, kotnoiks G @ B 2.0) JBAOCV[FKY COUKPYBJKOVK \PN\NPICNOBHKY.- Fns jbaoctufks sno covkrsbjkotk prnpnricnobhks (C\) iubofn bh bujkotbr n fcsjcoucr kh vbhnr fk uob fk khhbs kotnoiks kh v bhnr fk h b ntrb fcsj coucrâ n buj kotbrâ rksp kitcv bjk otk ko h b jc sjb prnp nricùo. Kdkj phn4 [ob pkr snob rkinrrk 25< gj (Ukhnic fbf vs. V c kjpn) Jbaoc tuf Ubh nrks inrrkspnofckotks B4 Ukh nicfbf (gj/m ) ; 2< 0< 6< =< @4 Vc kjpn (m) 90 25 = 6 0 Bh juhtcphcibr sus vbhnrks inrrkspnofckotks kh prnfuitn ks sckjprk inostbotk, ks fkicr, sc fns jbaoctufks B y @ sno covkrsbjkotk prnpnricnobhks, sk fkontb4 B (C\) @ n B 2 @, kotnoiks B @: G Ontb4 Yc cotkrvckoko 9 n jâs jbaoctufks tnfbs khhbs hbs pnfkjns inhnibr ko uob jcsjb kxprkscùo. Kdkjphn 4 Yc B @ y B 2 I, sk pukfk kxprksbr bsê4 G @ I B
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Transcript of Regla de tres
5/8/2018 Regla de tres - slidepdf.com
http://slidepdf.com/reader/full/regla-de-tres-559abe7b719e0 1/8
WAIFK EA UWA]
;) HJUWBEQMMHÝJ.- DKIJHUQEA] SWBSBWMHBJKFA]
;.;) DKIJHUQEA] EHWAMUKDAJUA SWBSBWMHBJKFA].- Ebs dkijhtueas(prbphaeke `äshmk qua puaea sar daehek) sbj ehramtkdajta prbpbrmhbjkfas (ES) mukjeb kf
kudajtkr b ehsdhjuhr af vkfbr ea ujk ea affks, ajtbjmas af vkfbr mbrraspbjehajta k fk btrkkudajtkrë b ehsdhjuhrë raspamthvkdajta aj fk dhsdk prbpbrmhýj.
Anadpfb> Qjk parsbjk rambrra 53 datrbs aj 1 saiujebs. (Aspkmhb vs. Uhadpb)
Dkijhtue Pkfbras mbrraspbjehajtasK> Aspkmhb (datrbs) 53 <3 ;73 ;03 733G> Uhadpb (saiujebs) 1 ;3 ;1 73 71
Kf ehvhehr sus vkfbras mbrraspbjehajtas af mbmhajta as shadpra mbjstkjta, as eamhr, sh ebsdkijhtueas K y G sbj ehramtkdajta prbpbrmhbjkfas, sa eajbtk> K (ES) G b K G, ajtbjmas
O G
K
;.7) DKIJHUQEA] HJPAW]KDAJUA SWBSBWMHBJKFA].- Ebs dkijhtueas sbjhjvarskdajta prbpbrmhbjkfas (HS) mukjeb kf kudajtkr b ehsdhjuhr af vkfbr ea ujk ea affks ajtbjmasaf vkfbr ea fk btrk ehsdhjuhrë b kudajtkrë raspamthvkdajta aj fk dhsdk prbpbrmhýj.
Anadpfb> Qjk parsbjk rambrra ;03 od (Pafbmheke vs. Uhadpb)
Dkijhtue Pkfbras mbrraspbjehajtasK> Pafbmheke (od/l) 1 ;3 73 53 <3G> Uhadpb (l) =7 ;0 < 5 7
Kf dufthpfhmkr sus vkfbras mbrraspbjehajtas af prbeumtb as shadpra mbjstkjta, as eamhr, sh ebs
dkijhtueas K y G sbj hjvarskdajta prbpbrmhbjkfas, sa eajbtk> K (HS) G b K
; G, ajtbjmas
KG4 O
Jbtk> ]h hjtarvhajaj = b dës dkijhtueas tbeks affks fks pbeadbs mbfbmkr aj ujk dhsdk axprashýj.
Anadpfb> ]h K G y K
; M, sa puaea axpraskr ksä> O
G
M K
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7) WAIFK EA UWA] ]HDSFA EHWAMUK
Mbjshsta aj qua ekebs = vkfbras mbrraspbjehajtas k 7 ebs dkijhtueas ehramtkdajta prbpbrmhbjkfassa eaga ajmbjtrkr uj mukrtb vkfbr.
Anadpfb> Qj mhmfhstk rambrra ;7 od aj ;0 dhjutbs. ²[uè ehstkjmhk rambrrarë aj ujk lbrk2
]bfumhýj> K dkybr aspkmhb rambrrheb adpfakrë dkybr thadpb, ajtbjmas af aspkmhb y thadpb sbjdkijhtueas ehramtkdajta prbpbrmhbjkfas
Dkijhtue Pkfbrasmbrraspbjehajtas
K> Aspkmhb (od) ;7 x
G> Uhadpb (dhj) ;0 03
k) Sfkjtab>
;7 od ;0 dhj
\ 03 dhj
g) Waifk> Dufthpfhmkjeb aj Kspk (Dètbeb> Kspk)
x ∘ ;0 dhj 4 ;7 od ∘ 03 dhj
x 4;7 od ∘ 03 dhj
;0 dhj4 51 od
m) Mbdprbgkmhýj> ]h K G, ajtbjmas>
K
G4 O ⇗
4
4 ⇗;7
;04
03
Wadpfkzkjeb fk raspuastk bgtajhek>
;7
;0 4
51
03 ⇗
=
5 4
=
5 Fb qua sa quaräk mbdprbgkr
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=) WAIFK EA = ]HDSFA HJPAW]K
Mbjshsta aj qua ekebs = vkfbras mbrraspbjehajtas k 7 dkijhtueas hjvarskdajta prbpbrmhbjkfas saeaga ajmbjtrkr uj mukrtb vkfbr.
Anadpfb> = bgrarbs puaeaj lkmar ujk bgrk aj 75 eäks ²Aj muëjtb thadpb lkrëj fk dhsdk bgrk 7bgrarbs2
]bfumhýj> Mbj dajbs bgrarbs fk bgrk sa mbjstruhrë aj dës eäks, ajtbjmas af jþdarb ea bgrarbs yaf thadpb sbj dkijhtueas hjvarskdajta prbpbrmhbjkfas.
Dkijhtue Pkfbrasmbrraspbjehajtas
K> Bgrarbs = 7G> Uhadpb (eäks) 75 x
k) Sfkjtab> Mbdb ; lbrk 4 03 dhjutbs
= bgrarbs 75 eäks
7 bgrarbs x
g) Waifk> Dufthpfhmkjeb aj Skrkfafb (Dètbeb> Skrkfafks)
= bgrarbs 75 eäks 4 7 bgrarbs x
x 4= bgrarbs ∘ 75 eäks
7 bgrarbs4 =0 eäks
m) Mbdprbgkmhýj>
⇗ ∘ 4 ⇗ ∘ 4 ∘ 4
∘ 4
Wadpfkzkjeb af vkfbr mkfmufkeb>= ∘ 75 4 7 ∘ =0 ⇗ 97 4 97 Fb qua sa quaräk mbdprbgkr.
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5) WAIFK EA UWA] MBDSQA]UK
As kquaffk aj fk qua fks dkijhtueas qua sa mbdpkrkj sbj = b dës.
Dètbeb ea fks Wkyks> Fk raifk ea = mbdpuastk thaja = pkrtas>
k) Mkusk> Wakfhzkebras ea fk bgrk b kmmhýj y sus mbjehmhbjas
g) Mhrmujstkjmhk> Dkijhtueas rafkmhbjkeks mbj af thadpb
m) A`amtb> Fb rakfhzkeb, fk bgrk, sus daeheks, su eh hmuftke
Anadpfb> Skrk lkmar ujk zkjnk ea =3 datrbs ea fkrib pbr ;3 ea kjmlb, ;1 bgrarbs lkj trkgknkeb 0eäks k rkzýj ea ;7 lbrks ehkrhks. ²Muëjtbs eäks trkgknkrëj ;< bgrarbs k 8 lbrks ehkrhks aj lkmar ujkzkjnk ea 51 datrbs ea fkrib pbr 73 ea kjmlb2
]bfumhýj> K dës bgrarbs (K) fk bgrk sa lkrë aj dajbs eäks (G), pbr fb tkjtb K
; G. K dajbs
lbrks ehkrhks ea trkgknb (M) fk bgrk sa lkrë aj dës eäks (G), pbr fb tkjtb G
;M. K dës datrbs ea
fkrib (E) fk bgrk sa lkrë aj dës eäks (G), pbr fb tkjtb G E. X k dës datrbs ea kjmlb (A)
Fk bgrk sa lkrë aj dës thadpb, pbr fb tkjtb G A.
Dkijhtue Pkfbrasmbrraspbjehajtas
K> Bgrarbs ;1 ;<G> Uhadpb (eäks) 0 x
M> Uhadpb (lbrks ehkrhks) ;7 8E> Datrbs ea fkrib =3 51A> Datrbs ea kjmlb ;3 73
k) Sfkjtab>
Mkusk Mhrmujstkjmhk A`amtbBgrarbs Eäks Lbrks ehkrhks Fkrib Kjmlb
;1;<
0x
;78
=3 ;351 73
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g) Waifk> Dètbeb ea fks rkyks
;< ∘ x ∘ 8 ∘ =3 ∘ ;3 4 ;1 ∘ 0 ∘ ;7 ∘ 51 ∘ 73 ⇗ x 4; 1 ∘ 0 ∘ ; 7 ∘ 5 1 ∘ 7 3
; < ∘ 8 ∘ = 3 ∘ ; 34 73 eäks
m) Mbdprbgkmhýj> Ea kmuareb k fbs ektbs sa thaja qua>
4 ⇗
∘ ∘
∘
4 ∘ ∘
∘
4
; 1 ∘ 0 ∘ ; 7
=3 ∘ ;34
; < ∘ ∘ 8
51 ∘ 73⇗
;<
14
;<
1
Ukf mbdb sa quaräk mbdprbgkr.
1) DH]MAFËJAK EA SWBGFADK]
Jbtk> Fbs prbgfadks qua sa prasajtkj k mbjthjukmhýj jb lkj sheb rasuaftbs aj af ;33%, pbr fb quafk sbfumhýj mbdpfatk quaek mbdb tkrak pkrk ustaeas asthdkebs famtbras.
;) Gartlk Hgunès, ujk kdk ea mksk, fkvk pbr mkek =7 dhjutbs ;3 pkjtkfbjas. ²Muëjtbs pkjtkfbjasfkvkrë aj ;l 73 dhjutbs2
x ∘ =7 dhj 4 ;3 pkjtkfbjas ∘ <3 dhj ⇗ x 4;3 pkjtkfbjas ∘ <3 dhj
=7 dhj4 71 pkjtkfbjas
7) ;3 bgrarbs puaeaj lkmar ujk bgrk aj 75 eäks ²Aj muëjtb thadpb lkrëj fk dhsdk bgrk < bgrarbs2
Bgrarbs Eäks;3 75
< x
x ∘ < bgrarbs 4 ;3 bgrarbs∘ 75 eäks ⇗ x 4;3 bgrarbs ∘ 75 eäks
< bgrarbs4 =3 eäks
Skjtkfbjas Uhadpb;3 =7 dhj
x <3 dhj
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=) 0 mkgkffbs thajaj rkmhýj pkrk ;1 eäks, sh sa kudajtkj = mkgkffbs dës. ²Skrk muëjtbs eäks kfmkjzkrëfk rkmhýj kjtarhbr2
x ∘ 8 mkgkffbs 4 0 mkgkffbs ∘ ;1 eäks ⇗ x 40 mkgkffbs ∘ ;1 eäks
8 mkgkffbs4 ;3 eäks
5) Dkrhb ]uëraz trkgknk aj uj mbfaihb ea 933 astuehkjtas, aj af muëf raprbgkrbj af kûb af 1%.²Muëjtbs astuehkjtas jb `uarbj prbdbvhebs aj af mbfaihb ea Dkrhb2
Astuehkjtas Sbrmajtkna933 ;33%
x 1%
x ∘ ;33% 4 933 astuehkjtas ∘ 1% ⇗ x 4933 astuehkjtas ∘ 1%
;33%4 =1
1) ²Eykjhtk Whvark fa praiujtk k su lhnk Adhfy ]uëraz ²Ea què mkjtheke as $ 873 af 73 %2. ²Muëfas fk raspuastk2
x ∘ 73% 4 $ 873 ∘ ;33% ⇗ x 4$ 873 ∘ ;33%
73%4 $ 5033
0) Aj uj ajirkjkna, af phûýj dkybr thaja 53 ehajtas y af dajbr thaja 71 ehajtas. ]h af phûýj dkybrek 733 vuaftks. ²Muëjtks vuaftks ek af dajbr2
x ∘ 71 ehajtas 4 53 ehajtas ∘ 733 vuaftks ⇗ x 453 ehajtas ∘ 733 vuaftks
71 ehajtas4 =73 vuaftks
Mkgkffbs Eäks0 ;1
8 x
Mkjtheke Sbrmajtknax ;33%
873 73%
Ehajtas Puaftks53 733
71 x
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9) Qjk iukrjhmhýj ea ;=33 lbdgras thajaj vävaras pkrk ;73 eäks. ]h sa easak qua fbs vävaras euraj;3 eäks dës. ²Muëjtbs lbdgras lkgräk qua rathrkr ea fk iukrjhmhýj2
Lbdgras Eäks;=33 ;73
x ;=3
x ∘ ;=3 eäks 4 ;=33 lbdgras∘ ;73 eäks ⇗ x 4;=33 lbdgras ∘ ;73 eäks
;=3 eäks4 ;733 lbdgras
;=33 lbdgras ” ;733 lbdgras 4 ;33 lbdgras
<) K uj paýj sa fa b`rama uj suafeb ea $ ;833 kjukfas y uj mkgkffb. Kf mkgb ea < dasas as easpaeheb
ramhghajeb uj tbtkf ea $ ;733 y af mkgkffb. ²Muëf as af vkfbr eaf mkgkffb2m 4 mkgkffb
]uafeb Dasas;833 + m ;7
;733 + m <
< ∘ ($;833+m) 4 ;7 ∘ ($;733 + m) ⇗ $;1733 + <m 4 $;5533 + ;7m
$;1733 ∗ $;5533 4 ;7m ∗ <m ⇗ $<33 4 5m ⇗ m 4
$<33
5 ⇗ 4 $733
8) ]aiujeb ]uëraz, uj krtaskjb, pajsý lkmar 73 `hiurks ea dkeark aj ;1 eäks, parb tkreý 0 eäksdës pbr trkgknkr 7 lbrks dajbs mkek eäk. ²Muëjtks lbrks trkgkný ehkrhkdajta2
; ∘ ; 1 ∘ ∘ 7 3 4 ; ∘ 7 ; ∘ ( ∗ 7) ∘ 73 ⇗ =33 4 573 ∗ <53
<53 4 573 ∗ =33 ⇗ <53 4 ;73 ⇗ 4<53
;73⇗ 4 9
> ∗ 7 4 9 ∗ 7 4 1
Mkusk Mhrmujstkjmhk A amtbKrtaskjb Eäks Lbrks ehkrhks @hiurks
;;
;17;
xx-7
7373
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;3) Dktläks ]uëraz mbjtrktk k 75 bgrarbs, fbs mukfas sa mbdprbdataj k mkvkr ujk zkjnk ea 13 d eafkrib, <d ea kjmlb y 7 d ea prb`ujeheke aj ;3 eäks. Dktläks eamhea kudajtkr tbeks fksehdajshbjas ea fk zkjnk aj uj 13%. ²Muëjtbs bgrarbs sa jamashtkj pkrk tardhjkr af mbjtrktb aj fkdhtke eaf pfkzb `hnkeb sh kudajtkj su a`hmhajmhk aj uj 13%2
Mkusk Mhrmujstkjmhk A amtbBgrarbs Eäks A hmhajmhk Fkrib Kjmlb Srb`ujeheke
75x
;31
;;,1
13 < 791 ;7 =
∘ 1 ∘ ;,1 ∘ 13 ∘ < ∘ 7 4 75 ∘ ;3 ∘ ; ∘ 91 ∘ ;7 ∘ = ⇗ 47 5 ∘ ; 3 ∘ ; ∘ 9 1 ∘ ; 7 ∘ =
1 ∘ ; , 1 ∘ 1 3 ∘ < ∘ 74 ;3<
WA@AWAJMHK] GHGFHBIWË@HMK]
KXKFK, Brfkjeb, (7330), Dktadëthmk Wamrakthvk, D & P IWË@HM. Hgkrrk, Amukebr]QËWA^, Dkrhb
]QËWA^, Dkrhb, (7335), Hjtarkprajehzkna Lbfästhmb ea Dktadëthmk, Ae. Irë`hmks Sfkjatk,Hgkrrk, Amukebr.
]QËWA^, Dkrhb, (7335), Lkmhk uj Hjtarkprajehzkna Lbfästhmb ea Ëfiagrk y Iabdaträk, Ae.Irë`hmks Sfkjatk, Hgkrrk, Amukebr.
Fhgrbs y krtämufbs sbgra Krhtdèthmk, Ëfiagrk, Iabdaträk, Urhibjbdaträk, Fýihmk Dktadëthmk,Srbgkghfhekeas, Astkeästhmk Easmrhpthvk, Astkeästhmk Hj`arajmhkf, Mëfmufb Eh arajmhkf, MëfmufbHjtairkf, y Sfkjh`hmkmhbjas Eheëmthmks sa ajmuajtrkj pugfhmkebs aj>lttp>//as.smrhge.mbd/dkrhbsukrazhgunas lttp>//www.dbjbirk`hks.mbd/usukrhb/par`hfas/dkrhbRsukrazR9/dbjbirk`hkslttp>//rapbshtbrhb.utj.aeu.am/lkjefa/;7=5109<8/903
lttp>//www.ebmajtashjjbvkebras.jat/Qsukrhbs/Par/7818; lttp>//krthmufbsdktadkthmk.gfbispbt.mbd
