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Gdtrcmbs

Ebhrudry =, 8>42

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^rapbrtcbs ae Gdtrcx Apbrdtca`s

(Gdtrcx Dllctca`)

4. + 7 +

8.   + + 7 + +  

=. \jbrb cs d u`cqub g x ` gdtrcx A sumj tjdt  + 7  ear d`y g x ` gdtrcx D. \jb gdtrcx

A cs mdffbl g x ` zbra gdtrcx

<. Ear bdmj g x gdtrcx D, tjbrb cs d u`cqub gx ` gdtrcx (∘) s.t.  + ∘ 7 . \jb

gdtrcx ∘ cs tjb `bidtcvb ae D.

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^rapbrtcbs ae Gdtrcx Apbrdtca`s

(Gdtrcx Guftcpfcmdtca`)

4.   7  

8.   + 7 +  

=.  + 7 +  

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^rapbrtcbs ae Gdtrcx Apbrdtca`s

(]mdfdr Guftcpfcmdtca`)

4. r 7  

8. + 7 +  

=. + 7 +  

<.   7 7  

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^rapbrtcbs ae Gdtrcx Apbrdtca`s

(\rd`spasb)

4. ()7  

8. ( + )7 +  

()

7

 <. ()7  

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4. Clb`tcey d`l trd`searg gdtrcmbs c` raw

rblumbl bmjbfa` earg

8. Lbtbrgc`b bfbgb`tdry raw apbrdtca`s

=. ]afvb systbgs ae fc`bdr bqudtca` usc`i Iduss

 ” Oarld` rblumtca` pramblurb

Ahobmtcvbs?

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Gdtrcx c` rblumbl bmjbfa` earg

Lbec`ctca`?

D`  gdtrcx cs c` rblumbl raw bmjbfa` eargwjb` ct sdtcsecbs tjb eaffawc`i?

4. Dff raws ma`scstc`i b`tcrbfy ae zbrabs, ce d`y, drbdt tjb hattag ae tjb gdtrcx

> > >

 

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Gdtrcx c` rblumbl bmjbfa` earg

Lbec`ctca`?

D`  gdtrcx cs c` rblumbl raw bmjbfa` earg

wjb` ct sdtcsecbs tjb eaffawc`i?4 . D ff r aw s ma s cs tc i b t cr bf y ae z br ab s, ce d y, dr bd t tj bh at ta g ae tj bg dt rc x

8. \jb fbdlc`i b`try ae bdmj raw cs 4 

44

> > >

 

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Gdtrcx c` rblumbl bmjbfa` earg

Lbec`ctca`?

D`  gdtrcx cs c` rblumbl raw bmjbfa` earg wjb` ctsdtcsecbs tjb eaffawc`i?4 . D ff r aw s ma s cs tc i b t cr bf y ae z br ab s, ce d y, dr bd t tj bh at ta g ae tj bg dt rc x

8. \jb fbdlc`i b`try ae bdmj raw cs 4 

=. Ce raw  d`l + 4 drb twa summbsscvb raws tjdt la `atma`scst b`tcrbfy ae zbrabs, tjb` tjb fbdlc`i b`try aeraw + 4 cs ta tjb fbet ae tjb fbdlc`i b`try ae raw  

4

> 4

> > >

 

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Gdtrcx c` rblumbl bmjbfa` earg

Lbec`ctca`?

D`  gdtrcx cs c` rblumbl raw bmjbfa` earg wjb` ctsdtcsecbs tjb eaffawc`i?4 . D ff r aw s ma s cs tc i b t cr bf y ae z br ab s, ce d y, dr bd t tj bh at ta g ae tj bg dt rc x

8. \jb fbdlc`i b`try ae bdmj raw cs 4 

=. Ce raw  d`l +4   drbtwasummbsscvbraws tjdtla `atma`scstb`tcrbfy ae zbrabs,tjb`tjb fbdlc`i b tryae raw + 4  cs tatjb fbetae tjbfbdlc`i b`tryae raw  

<. Ce d mafug` ma`tdc`s d fbdlc`i b`try ae sagb raw, tjb`dff atjbr b`trcbs c` tjdt mafug` drb zbra.

4 >

> 4

> > >

 

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Bxdgpfb 4?

  74 > >

> 4 >

> > 4

 ∘8

=

>

  74 8 >

> > 4

> > >

 >

>

4

 

74 > >

> 4 <

> > >

 ∘8

=

>

  7

4 > > = >

> > 4 > >

> > > > 4> > > > >

 

Xblumbl raw bmjbfa` earg

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Bxdgpfb 8?

  74 8 >

> > >

> > 4

 ∘8

>

∘=

  74 > =

> 8 ∘8

> > 4

 <

2

8

 

74 > =

> 4 <

> 4 >

 ∘8

=

>

  7

4 8 > = >

> 4 4 > >

> > 4 ∘8 4> > > > >

 

@at c` rblumbl raw bmjbfa` earg

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Bfbgb`tdry Xaw Apbrdtca`s

4. C`tbrmjd`ib raws ae D

8. Guftcpfy raw r ae D hyd `a` zbra ma`std`t

=. Dll l tcgbs raw r ae Dta raw s ae D

↜  

  7

4 8 >

> > >> > 4 

∘8

>∘=  

  74 8 >> > 4

> > >

 ∘8∘=

>

 

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Bfbgb`tdry Xaw Apbrdtca`s

4. C`tbrmjd`ibraws ae D

8. Guftcpfy raw r ae D hy d `a` zbra ma`std`t

=. Dll l tcgbs raw r ae D ta raw s ae D

↜  

4

8 

+  

  7

4 8 >

> 8 8> < =  

  74 8 >

> 4 4

> < =

 

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Bfbgb`tdry Xaw Apbrdtca`s

4. C`tbrmjd`ibraws ae D

8. Guftcpfy rawr ae D hy d a` zbra ma std`t

 

=. Dll l tcgbs raw r ae D ta raw s ae D ↜  

 

∘8 +  

  7

4 8 >

> 4 4> < =

 

  74 > ∘8

> 4 4

> < =

 

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Lbec`ctca`? D` g x ` gdtrcx D cs sdcl ta hb raw

bqucvdfb`t ta d` g x ` gdtrcx H ce H md` hb

ahtdc`bl hy dppfyc`i d ec`ctb sbqub`mb aebfbgb`tdry raw apbrdtca`s ta D.

Bxdgpfb =?

  7 4 8 < =8 4 = 8

4 ∘4 8 =

  7 8 < : 54 ∘4 8 =

< ∘4 9 :

 

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Bxdgpfb =?

  7

4 8 < =

8 4 = 84 ∘4 8 =

  7

8 < : 5

4 ∘4 8 =< ∘4 9 :

 

]tbp =? 8 +  

  78 < : 5

4 ∘4 8 =

< ∘4 9 :

 

Jb`mb, gdtrcx D cs raw

bqucvdfb`t ta gdtrcx H

]tbp 8? ↜  

  78 < : 5

4 ∘4 8 =

8 4 = 8

 

]tbp 4? 8 

  7 8 < : 58 4 = 8

4 ∘4 8 =

 

⟿ 

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^ramblurb c` \rd`seargc`i d gdtrcx ta

cts Xaw Bmjbfa` Earg

4. Ec`l tjb ecrst (fbet ta rcijt) mafug` c` D `at dffae wjasb b`trcbs drb zbra. \jcs mafug` csmdffbl pcvatdf mafug`.

8. Clb`tcey tjb ecrst (tap ta hattag) `a`zbrab`try c` tjb pcvatdf mafug`. \jcs b`try csmdffbl tjb pcvat.

=. C`tbrmjd`ib, ce `bmbssdry, tjb ecrst raw wctjtjb raw wjbrb tjb pcvat ammurs sa tjdt tjbpcvat cs `aw c` tjb ecrst raw.

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<. Lcvclb tjb ecrst hy tjb pcvat sa tjdt tjb b`try c`tjb ecrst raw d`l pcvatdf mafug` cs `aw 4.

2. Dll guftcpfbs ae tjb ecrst raw ta dff atjbr raws ta

gdkb dff b`trcbs c` tjb pcvatdf mafug`, bxmbpt tjbb`try wjbrb tjb pcvat cs famdtbl, bqudf ta zbra.

5. Clb`tcey H ds tjb (g ” 4) x ` suh gdtrcx ae tjb

rbsuftc`i gdtrcx, ahtdc`bl hy lbfbtc`i gb`tdffy ctsecrst raw.

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9. Dll guftcpfbs ae tjb ecrst raw ae tjb rbsuftc`i

gdtrcx ta dff atjbr raws sa tjdt dff b`trcbs c` tjb

pcvatdf mafug`, bxmbpt ear tjb pcvat, hbmagb

zbra

:.Clb`tcey M ds tjb (g -8) x ` suh gdtrcx ae tjb

rbsuftc`i gdtrcx, ahtdc`bl hy lbfbtc`i gb`tdffy

tjb ecrst raw. Xbpbdt stbps 4-9 a` tjcs gdtrcx.

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Bxdgpfb <? Xblumb tjb eaffawc`i

gdtrcmbs c`ta cts raw bmjbfa` earg

4.   74 8 =

8 ∘4 4

= > 4

 3

:

=

 

8. 7

4 4 8 ∘2 =

8 2 ∘4 ∘3 ∘=

8 4 ∘4 = ∘44

4 ∘= 8 9 ∘2

 

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+ + 8 ∘ 2 7 = 

8 + 2 ∘ ∘ 3 7 ∘= 

8 + ∘ + = 7 ∘44  ∘ = + 8 + 9 7 ∘2 

+ 8 + = 7 3 

8 ∘ + 7 : = ∘ 7 = 

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Iduss-Oarld` rblumtca` gbtjal

^ramblurb?

4. Earg duigb`tbl gdtrcx

8. \rd`searg duigb`tbl gdtrcx ta rblumbl raw

bmjbfa` earg usc`i bfbgb`tdry rawapbrdtca`s

=. \jb fc`bdr systbg tjdt marrbspa`ls ta tjb

gdtrcx c` rblumbl raw bmjbfa` earg ahtdc`blerag stbp 8 jds bxdmtfy tjb sdgb safutca`s dstjb icvb` fc`bdr systbg.

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Bxdgpfb 2? ]afvb tjb fc`bdr systbg hy

Iduss Oarld` rblumtca` gbtjal

+ 7 > 

8 ∘ + = 7=

∘ 8 ∘ 7 = 

4 8 =

8 ∘4 4

= > ∘4

3

:

=

 

4 8 =

8 ∘4 4

= > ∘4

73

:

=

 

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]afvb tjb fc`bdr systbg hy Iduss

Oarld` rblumtca` gbtjal

4. + + 8 ∘ 2 7 = 

8 + 2 ∘ ∘ 3 7 ∘= 

8 + ∘ + = 7 ∘44  ∘ = + 8 + 9 7 ∘2 

8. + + 7 >  + 7 = 

+ 7 4