MAKALAH BILANGAN PECAHAN 1

! !  !  !#%! f°f°½nff°¯½ff°f°f°f°¯¯½°f©¯ff°ff f@f½¯f°f°½°9¯f°¯½ff° f°f°f°ff°f°½°¯½ff°f°f°½¯f°¾ ©°¾f°f°½nff°fff½nff°f¾f½nff°nf¯½f°½nff°¾¯f ½¾°f°½¯

 

,3,350.,,3,/,,-,3,3,3/,5,9/3,9,,3/,,2-039: /03,3 ,--,3,3-:,9-/,3--:,31,947/,7, 8,3, 8,3,,2: ,2:202 20280-: 80-:,,50 ,,5002 02:/,3 :/,3,5090 ,5090780-: 780-:9/-, 9/-,203 203,/ ,/ /:,-,,38,2,-08,7$09,58,9:-,,3,5090780-:9/3,2,,38,9:507/:,

 

,9,:80903,/,3/349,8,3 02:/,3,5,-,809,5-,,3,5090780-:9 /-,02-,203,//:,-,,38,2,-08,72,,809,5-,,3,5090780-:9

 

 

 

/3,2,,38,9:507025,9,9,:80507025,9/,3/349,8,3 ,3,3 /,3 90780-:9/3,2,,3-,3,350.,,3,3,3,390709,/,9,8/3,2,,3 502-,3 /,5:3-,3,3,390709,/-,,/3,2,,3 /,5:3-,3,3,390709,/-,,/3,2,,3 5030-:9   %  ,3,,/,39,7,-,3,3-,3,3-07:9,3207:5,,350.,,3 ,

   -.

 %039:,350-,3/,35030-:950.,,350.,,3-07:9 ,

-  .   

 !,3,38054943,:,/,,.2%039:,35,3,3/,7 ,

$0507025,9,:90780-:9

- %,5072,,:90780-:9 !03008,,3

   - 207:5,,350.,,3,703,808:,/03,3/013850.,,3   . -:,350.,,3,703,207:5,,31,947/,7 

 , 207:5,,350.,,3,703,808:,/03,3/013850.,,3



   -502-,350.,,3 ,/,,/,35030-:93,   .!02-,350.,,3 ,/,,/,35030-:93,,/,,   ,!,3,3/,780507025,9,:90780-:9,/,, .2   -!,3,3/,79,5072,,:90780-:9,/,, .2 

 ,!02-,350.,,3 ,/,,/,35030-:93,,/,,





$ $!

 !0.,,3:73 !0.,,32:73,/,,50.,,3,3502-,33,0-0./,75,/,

   

 

5030-:93,4394.4394/,750.,,32:73,39,7,,3  /,3   !0.,,3%/,:73,/,,50.,,3,35030-:93,0-0./,75,/,

   

 

502-,33,4394.4394/,750.,,39/,2:73,39,7,,3  /,3  !0.,,3,25:7,3

!0.,,3.,25:7,3,/,,50.,,3,3907/7,9,8-,3,3-:,9,-/,3.

 

 

     50.,,3.,25:7,3,39,7,,3  /,3    

,3-0781,9, , /03,3 ,/,,50.,,32:734394.4394/,7

!0.,,3.,25:7,3/,5,9/50740/,750.,,39/,2:7309:5:, !0.,,3.,25:7,3/,5,9/50740/,7 50.,,39/,2:7309:5:, 80-,3,50.,,39/,2:73/,5,9/50740/,750.,,3.,25:7,3  03:-,!0.,,3%/,:7303,/!0.,,3.,25:7,3 ,7,:39:203:-,50.,,39/,2:73203,/50.,,3.,25:7,3,/,, /03,320,:,3502-,,3,39,7,502-,3/,35030-:93, 4394 &-,,503:8,350.,,39/,2:73-07:9/,,2-039:50.,,3.,25:7,3   

     

!03008,,3  ,:,34507,8502-,,35,/,50.,,390780-:9



   -502-,350.,,3 ,/,,/,35030-:93,   .!02-,350.,,3 ,/,,/,35030-:93,,/,,   ,!,3,3/,780507025,9,:90780-:9,/,, .2   -!,3,3/,79,5072,,:90780-:9,/,, .2 

 ,!02-,350.,,3 ,/,,/,35030-:93,,/,,





$ $!

 !0.,,3:73 !0.,,32:73,/,,50.,,3,3502-,33,0-0./,75,/,

   

 

5030-:93,4394.4394/,750.,,32:73,39,7,,3  /,3   !0.,,3%/,:73,/,,50.,,3,35030-:93,0-0./,75,/,

   

 

502-,33,4394.4394/,750.,,39/,2:73,39,7,,3  /,3  !0.,,3,25:7,3

!0.,,3.,25:7,3,/,,50.,,3,3907/7,9,8-,3,3-:,9,-/,3.

 

 

     50.,,3.,25:7,3,39,7,,3  /,3    

,3-0781,9, , /03,3 ,/,,50.,,32:734394.4394/,7

!0.,,3.,25:7,3/,5,9/50740/,750.,,39/,2:7309:5:, !0.,,3.,25:7,3/,5,9/50740/,7 50.,,39/,2:7309:5:, 80-,3,50.,,39/,2:73/,5,9/50740/,750.,,3.,25:7,3  03:-,!0.,,3%/,:7303,/!0.,,3.,25:7,3 ,7,:39:203:-,50.,,39/,2:73203,/50.,,3.,25:7,3,/,, /03,320,:,3502-,,3,39,7,502-,3/,35030-:93, 4394 &-,,503:8,350.,,39/,2:73-07:9/,,2-039:50.,,3.,25:7,3   

     

!03008,,3  ,:,34507,8502-,,35,/,50.,,390780-:9



     ,:,34507,8502-,,35,/,50.,,390780-:9

     ,:,34507,8502-,,35,/,50.,,390780-:9

     03:-,!0.,,3,25:7,303,/!0.,,3%/,:73 &39:203:-,50.,,3.,25:7,3203,/50.,,39/,2:73/,5,9 203:3,,37:2:8-07:9

I   { /03,3. 4394 %:8,350.,,3.,25:7,3203,/50.,,39/,2:73   

 

   

!03008,,3 

  { 

       {          {        







 !$ !0.,,3803,,/,,50.,,350.,,3,32025:3,09,,38,2,5,/,,78 -,3,3

              !0.,,3 803,/03,3 /,3 /9:8              !0.,,3 803,/03,3 /9:8       !0.,,3 803,/03,3 /9:8  

,3,3,3202-,502-,3/,35030-:98:,9:50.,,3:39: 203/,5,9,350.,,3803,,/,,1,94750780:9:,3/,7502-,3/,3 5030-:93, ,7,:39:203/,5,9,350.,,350.,,-803,,/,,/03,3203,,9,: 202-,502-,3/,35030-:950.,,390780-:9/03,3-,3,3,39/, 4394 %:8,3/:,50.,,3,3803,/03,350.,,350.,,3-07:9    

       

!03008,,3

 

 ,,3 /03,38:,9:-,3,3,39/,28,3,/,3

803,/03,3    803,/03,3       

 

 

03,3/02,3/:,50.,,3,3803,/03,3 ,/,, /,3 

 

 ,,3 /03,38:,9:-,3,3,39/,28,3,/,3

803,/03,3      803,/03,3     



 

 

 

03,3/02,3/:,50.,,3,3803,/03,3 ,/,, /,3 

 

 -,,3 /03,38:,9:-,3,3,39/,/,3207:5,,31,947 50780:9:,3/,7/,328,3,/,3

   803,/03,3    803,/03,3  

 

 

03,3/02,3/:,50.,,3,3803,/03,3 ,/,, /,3 

 

 

 ,,3 /03,38:,9:-,3,3,39/,,9,:-,,3, /03,31,947 50780:9:,3/,7/,3

   803,/03,3    803,/03,3  

 

 

03,3/02,3/:,50.,,3,3803,/03,3 ,/,, /,3  !0.,,3803,-,8,3,/80-:9:,50.,,30:;,03&39:203039:,3 50.,,3,3803,/,5,9/,:,3/03,3.,7,80-,,-07:9  !07,,,3/03,3-03/,43709

     

9,,,3203:3:,3.4394-,,   /03,3203:3,,302-,7 079,8,3-07-039:507805,3,33,58002-,7079,89:80-,, -,,3:9:$,9:02-,7079,8/5,9203,//:,-,,3,38,2,803,

 

/50740 02:/,302-,7,3,3/5,9203,/-,,3,38,2,

 

02:/,3/5,9,203,/803,/50740   !07,,,3/03,3,78-,3,3 !0.,,3803,/,5,95:,/9:3:,3/03,3203:3,,3,,9507,,,78 -,3,3

        

               /,380907:83,     

 03,3202507:,850.,,3



 

!0.,,3,3803,/03,3 /,5,9/50740/03,3,3202507:,8/,7

 

   

50.,,3 203,/  /,380907:83,/03,3203:3,,3,,9507,,9,-0 50.,,3803,,3/50740/,79,-0507,,3  #! 030/07,3,,350.,,3,/,,203:-,8:,9:50.,,3203,/50.,,3,3 ,3803,,3502-,3/,35030-:93,9/,,2021,94750780:9:,3 8,3 ,7,:39:2030/07,3,3,8:,9:50.,,3,9,:203/,5,9,350.,,3803,,3 5,380/07,3,,/,,/03,3202-,502-,3/,35030-:9/03,3!/,7 502-,3/,35030-:990780-:9 ,7,3,,9:/03,3202-,502-,3/,35030-:93,/03,3!/,7 0/:,3,

 

8,3,039:80/07,3,/,7

,947572,/,7 ,947572,/,7 !/,7/,3,/,, $03,-039:80/07,3,3,/03,3202-,502-,3/,35030-:93,/03,3 

    4394 %:8,350.,,350.,,3-07:9/,,2-039:,35,380/07,3,    

       

!03008,,3  ,94750780:9:,3907-08,7!/,7/,3,/,,



 

&39:203/,5,9,3-039:50.,,3,35,380/07,3,/,7 -,, 502-,3/,35030-:9/03,3

     

50740 

 

 

03,3/02,3-039:50.,,3,35,380/07,3,/,7 ,/,,   ,94750780:9:,3907-08,7!/,7/,3,/,,

 

!0.,,3,35,380/07,3,/,7 ,/,,

  

 ,94750780:9:,3907-08,7!/,7/,3,/,,

 

!0.,,3,35,380/07,3,/,7 ,/,,

  

 ,94750780:9:,3907-08,7!/,7/,3,/,,

 

!0.,,3,35,380/07,3,/,7 ,/,,

  

 &#&%! ,

02-,3/3,3!0.,,3

 

 

8,3,,2:/-07/:,50.,,3,9: /,3 ,7,:39:202-,3/3,33, ,/,,/03,3203,2-,7 ,7,,3:39:202-,3/3,3/:,50.,,3,3-075030-:98,2,,/,, 202-,3/3,3502-,33,,3909,5,50.,,350.,,3,3,7:8,2: -,3/3,390780-:92025020-:9,3-07-0/,2,,5030-:9/,750.,,3 50.,,390780-:9,7:8/8,2,,39070-/,::/03,3203.,705,9,3 5080:9:,39070.!/,35030-:95030-:99: 4394 03,550.,,3-07:9/03,39,3/,,9,:,,7203,/5073,9,,3,3 -03,7 

   !030-:90/:,50.,,390780-:990,8,2,03,3/02,3,2:.::5 202-,3/3,3502-,33,

202502-,3  202502-,3  

  

0,8-,,,/



  

05,9,350780:9:,39070.!/,7/,3,/,,

 

%039:,350.,,3803,/,7 ,32025030-:9

  

,2:50740

 

 

   

0,703, 803,/03,3 /,5,9/825:,3   

  

!/,7/,3,/,,

 

%039:,350.,,3803,/,7 ,32025030-:9

  

,2:50740

      /,5,9/825:,3   

0,703,803,  - 03:7:9,3!0.,,3

03039:,3-,3,3,30--08,7,9,:0-0./,7-0-07,5,-,3,3 /80-:9203:7:9,3-,3,3 ,,2:,,3203:7:9,350.,,3-075030-:98,2,2,,:7:9,350.,,3

50.,,390780-:9-07/,8,7,3:7:9,3502-,33,,3909,5,50.,,3 50.,,3,3,,3/:7:9,390780-:92025:3,5030-:9,3-0/,2,,,2: ,7:8203039:,350.,,350.,,3803,3,9070-/,:: 4394

   /,32:,/,7,39070.    

&7:9,3,50.,,350.,,3 

!07,9,35030-:9809,550.,,3,9:/,3 05,9,350780:9:,39070./,7/,3,/,,

803,/03,3803,/03,3      803,/03,3803,/03,3    



03,3/02,3:7:9,350.,,350.,,390780-:92:,/,7,39070.,/,,

/,3       .

03039:,309,!0.,,3!,/,,78,3,3

!0.,,32:7390709,/,39,7,-,3,3/,35,/,,78-,3,3,7,:39: 203039:,309,50.,,35,/,,78-,3,3,/,,80-,,-07:9  ,,,7,,39,7,/,3203,/-0-07,5,-,,38,2,-08,7808:,5030-:9

 

50.,,3,3,,3/9039:,309,3,8,3,:39: -07,79,7,,39,7, /,3/-,203,/-,,38,2,-08,7

   

 

 02:/,3,:,3507-,3/3,3,39,7,  /,3 

   

 ,2:50740  

 

/03,3/02,309,50.,,3 5,/,,78-,3,3,/,,80-,,-07:9

   

   4394

 

%039:,309,50.,,3 5,/,,78-,3,3 !03008,,3 ,,,7,,39,7,/,3203,/-,,38,2,-08,7

                       ,2:50740              

,:,3507-,3/3,3,39,7,       /,3 

 

09, 5,/,,78-,3,3/,5,9,2:,95,/,,78-,3,3-07:9 

 

 

 

 

 

 

 !03,3,2,343805 ,

!07,,,3/03,3203:3,,3-,3:3-,3:3042097



 



,3:3-,3:3042097/,5,9/:3,,380-,,,,9:39: 202-,3/3,3/,3203:7:9,350.,,3-,8,/,350.,,3.,25:7,3 ,,3,3/:3,,3,7:82:/,/5,9/,73,,9,:/5494354943 :39:203:7:9,3:,8,3/,7-,3:3-,3:390780-:9803,/,5,9 /,9:7:9,3/,7:,8,3-,3:3,320,:7:9,3/,7-,3,33,

    - 03,3507,,,359,,9,:053,3053,350.,,3 053,350.,,3-07:3,:39:202-,/3,350.,,3-,8,,7 507,,,3/,3,2-,788,,,3/,5,9202-,3/3,3/,380,:8 203:7:9,3-,3,3-,3,350.,,3,3/33,3 .

03,3203,2,,35030-:93,

 

 

9,-,3/3,3 /,3 /03,3.,7,203,2,,35030-:93,,9,: 203039:,350.,,3803,3,0-/::0,9,33,,3,3.,7 /,:,388,-,503,3,2,34380550.,,3803,5,/,-,,3. /5,,2/,390,/7,5,30907,25,3,40:7:,9:203039:,3

    $090,5030-:93,8,2,9,-,3/3,3502-,33,         ,703,2,,  ,/       0907,25,3,9,:903.05,9 ,

,502-,33,8,2, ,7507,,,3507,,,3:,8,32,:5:3053,350.,,3/,5,9/,9

           

-,,       $03,/,5,9/9039:,3-,,5,/, 50.,,354891-,502-,33,8,2,2,,50.,,3,30-/,7 ,/,,50.,,3,35030-:93,,3,3,-073,0-0.$0/,3,3 5,/,50.,,330,91,,380-,3, - ,5030-:93,8,2, !0.,,3,35030-:93,8,2,2:/,/-,3/3,320,:507,,,3 507,,,3:,8,32,:5:3053,3053,350.,,3

 

 

4394 /,3  !,/,50.,,354891-,5030-:93,8,2,2,,50.,,3,30-/,7 ,/,,50.,,3,3502-,33,,3,3,0-/,7,3,3 .

,502-,3/,35030-:93,9/,8,2,



,502-,3/,35030-:93,9/,8,2,2,,-8,203:3,,39,3/, 8,3

-07,79  803,9,3/,,3905,9,/,,         2,,      !$ !0.,,3/082,207:5,,3-039:,3503:8,350.,,3!0.,,3/082,,/,, 50.,,3,35030-:93,207:5,,35075,3,9,3/,7-,3,328,3,

    



,3,/-0,,342,

  %



,3,/-0,,342,

 /03,33-,3,3,,3,/-0,,342, 

5

,

03:-,039:!0.,,303,/!0.,,3082, !0.,,32:7350.,,39/,2:73/,350.,,3.,25:7,3/,5,9 /3,9,,3/,,2-039:50.,,3/082, 8,3,

  /9:8     /9:8               /9:8    039:50.,,3/3,2,,350.,,38,9:/082,039:50.,,3 /3,2,,350.,,39,/082,/,5:3-039:50.,,3/3,2,,3 50.,,3/:,/082, ,3,3/082,,3202:,9,3,-07:,328,3,/80-:9 -,3,3/082,-07:,3/,5:3-039:,9,:/3,2,,3 -,3,3/082,9/,-07:,3 4394 %:8,50.,,350.,,3-07:9/,2-039:50.,,3/082, 

 

 

 

 



 

 

 

  - 03:-,039:082,03,/039:!0.,,3 4394 80-,,8:,9:50.,,32:73/,2-039:,35,380/07,3,

     ,/50.,,3/082,/,5,9/9:8203,/

 

!0.,,3/082,/,5,9/9:8/,,2-039: 

02:/,380/07,3,,350.,,390780-:9/03,3.,7,202-,502-,3/,3 5030-:9/03,31,94750780:9:,3907-08,7/,7/,3,9:

      

,350740

03,3/02,3-039:50.,,32:73,35,380/07,3,/,7

 

,/,, 

 !#$! ,

!07803

,9,507803-07,8,/,7,9,507.039,3,793,507807,9:8!07803,/,,50.,,3 ,35030-:93,807,9:8!07803/,2-,3,3

 /,3,/-,.,,507803     ,/   -072,3,        ,/ -072,3,       -072,3, ,/  ,

4394  &-,,50.,,3-07:90/,,2-039:507803 ,

 

 

 

  -

 



.

 

 

 

 &-,,-039:507803-07:90/,,2-039:50.,,32:73 ,



   ,/,,!/,7/,3   



- 

        



- !072 !072,/,,50.,,3,35030-:93,807-:,9,:50.,,3507807-:!072 /,2-,3,3/03,3

 /,3,/-,.,,5072         8,3,     ,

!0.,,35072,39,7,,3/:3,,3:39:203,9,,38,39,8,/,7,7,2 ,7,:98,3,,/,7,7,2,:907,,/,,793,907/,5,9 7,2,7,25,/,809,57,2,7/,:907, 4394  &-,,-039:50.,,3-07:9203,/-039:5072 ,

 

   {       

-

 &-,,-039:-07:9/,,2-039:50.,,32:73 ,



   ,/,,!/,7/,3



- 

   ,/,,!/,7/,3





 !#$%&!!  !& ,,2203008,,345078,8503:2,,3,7:8202507,9,35030-:9/,7 50.,,350.,,3,3,,3/:2,,3,50.,,350.,,39:-075030-:9 8,2,.::5203:2,,3502-,33,

     /03,3. ,3909,5,5030-:90/:,50.,,3-07-0/,2,,9070-/,::/8,2,,3 /03,3203:3,,3!/,75030-:95030-:93,02:/,3:2,,3 502-,3502-,33, $1,981,9!03:2,,3  $1,9848,91 ,-.,-. 4394   $1,942:9,91 ,--, 4394 



 &38:7/0399,8907,/,5503:2,,3 ,3,34/80-:9:38:7/0399,8,9,:3097,907,/,5503:2,,3 ,, 4394   &38:73;078907,/,5503:2,,3 3;078:2,,,3/,7,,/,,, 3;078:2,,,3/,7,,/,,, ,,,, .4394           0781,99079:9:5 5,-,/:,-:,-,3,3-:,9/9,2-,,32,,,83,,/,,



-,3,3-:,9:, ,/,3- -,3,3-:,92,,,-.. -,3,3-:,9 .4394  -,3,3-:,9 4394 9:3,,8503:2,,350.,,3-07:9 





               {        {           ,/                            

 

   %        



                                       ,/           {  !0.,,3.,25:7,3, /,5,9/9:8/,,2-039:50.,,39/,2:73   



 !&#! 507,8503:7,3,35,/,50.,,3207:5,,30-,,3/,74507,8 503:2,,35,/,50.,,3&39:20,:,3503:7,3,35,/,50.,,3 -075030-:98,2,.::5203:7,3,3502-,33,

     /03,3. 5,-,5030-:93,8,2,502-,3-8,,38:3/:7,3,3 5,-,5030-:90/:,50.,,390780-:9-07-0/,2,,9070-/,:: 5030-:95030-:93,/8,2,,3/03,3203:3,,3!/,75030-:9 5030-:93,02:/,3:7,3,3502-,3502-,33, !03:7,3,350.,,3/03,35030-:9,39/,8,2,

   #:2:8       {{#:2:8         8,3,          &39:503:7,3,3/03,35030-:9,39/,8,2,5030-:93,,7:8/8,2,,3 9070-/,::/03,3/:,.,7,8,2,805079/03,3503:2,,3 /03,3203,,30/:,5030-:97:2:8 /03,3203039:,3!3,7:2:8 4394 9:3,503:7,3,350.,,3-07:9 





               {        {           ,/                      {       

 {         ,,                  

 

        %   



                  

      

,/

     

  !#!

,,2507,,3-,3,350.,,3502-,3/,,3/03,3502-,3 5030-:9/,,3/03,35030-:9 O

!07,,3-,3,350.,,3/03,3-,3,3-:,9

 

. 

 

      

#:2:8 -

    O

!07,,3-,3,350.,,3/03,3-,3,350.,,3

  ./,3/   

#:2:8  

     O

!07,,3-,3,350.,,3/03,3-,3,350.,,3.,25:7,3 

  {          

  

 

 

&39:2039:3507,,350.,,3 /,3 /03,3-/,3//,5,9 203:3,,37:2:8-07:9

    -/,3/    !,/,507,,350.,,3-07,:81,981,9-07:9  42:9,91



,--,/03,3,/,3--,3,350.,,3  848,91 ,-.,-./03,3,-/,3.-,3,350.,,3  897-:91 -.,-,./03,3,-/,3.-,3,350.,,3 4394 



                {        {           { ,/        

 

           ,/     

 !! O

!02-,,3-,3,350.,,3/03,3-,3,350.,,3

         

#:2:8    

03,/507,,3/03,3-,3,30/:,3,502-,3/,35030-:93, /9:,7

 

 

&39:2039:3502-,,350.,,3 907,/,5 /03,3-/,3//,5,9 203:3,,37:2:8-07:9

   /03,3-/,3/     4394 9:3,,84507,8502-,,3-07:9

         

 









                         {          ,/        

             

  

 !#!%!





,3,3-075,3,9/,5,9/9:8/,,2-039:

             



31,947

 



31,947

 



$1,981,9,3/2405075,3,9,3-,3,3-:,9,9:80-,,-07:9   











          /03,323 

 

    

  

4394 9:3,5075,3,9,350.,,3-07:9 





 



      



     





                  

 

 %&& 039:-,:-,8,3,/:3,,3:39:203,9,,3-,3,3,38,3,9-08,7 ,9,:8,3,90.,,7503:8,33,0-01803$0-,,.43940.05,9,3.,,,

 2/09

809,72/09/,5,9/9:8

9:7,3503:8,3-,3,3-,:,/,,80-,,-07:9  &39:-,3,3,30--08,7/,72,,503:8,3-039:-,:3,,/,,

 /03,3^,/,33-,3,3,8

,



 &39:-,3,3/,39,7,/,32,,503:8,3-039:-,:3,,/,,, /03,3^,/,33-,3,3,8 4394 %:8,3-,3,3-,3,3-07:9/,,2-039:-,:  

,/,,-,3,3,30--08,7/,70,703,9::3,,3,9:7,3,

 /03,3^,/,33-,3,3,850740,/,33 03,3/02,3-039:-,:/,7,/,,  

  ,/,,-,3,3,30--08,7/,70,703,9::3,,3

 /03,3^,/,33-,3,3,850740,/,33 03,3/02,3-039:-,:/,7,/,,  ,9:7,3,

  ,/,,-,3,3,390709,/,39,7,/,30,703,9:

 /03,3^,/,33-,3,3,850740,

:3,,3,9:7,3, /,33

 

03,3/02,3-039:-,:/,7,/,,  



,/,,-,3,3,390709,/,39,7,/,30,703,9:

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,:,3502-:,9,30,9,8 

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3,907,75,/,,/,,

O

0,703,2,,502-:,9,33,,/,,

03,3/02,3502-:,9,38,25,8,9:9025,9/082,,/,,  :,9,38,25,8,9:9025,9/082, 202/:,9025,9/082, 3,907,75,/,,/,,803,502-:,9,33,,/,, ,/502-:,9,38,25,8,9:9025,9/082,,/,,

 :,9,38,25,/:,9025,9/082, 2029,9025,9/082, 3,907,75,/,,/,,803,502-:,9,33,,/,, ,/502-:,9,38,25,/:,9025,9/082,,/,,





 !03:7,3,3,3,3:,9 ,5,-,907,/503:7,3,3-,3,3-:,954891/03,3-,3,3-:,954891 2,,  ,3,3-:,954891/:7,3/03,3-,3,3-:,954891,30-0. 2,, ,83,/,,-,3,3-:,954891 4394   ,3,3-:,954891/:7,3/03,3-,3,3-:,954891,30- -08,72,, ,83,,/,-,3,3-:,930,91 4394  -5,-,907,/503:7,3,3-,3,3-:,930,91/03,3-,3,3-:,930,91 2,,  ,3,3-:,930,91/:7,3/03,3-,3,3-:,930,91,30- 0. 2,,,83,,/,,-,3,3-:,954891 4394 3,9  ,3,3-:,930,91/:7,3/03,3-,3,3-:,930,91,30- -08,7 2,,,83,,/,,-,3,3-:,930,91 4394   ,3,3-:,930,91,3/:7,38,2,/03,3-,3,3-:,930,91 ,3 203:7,32,,,83,,/,,34 4394  .!03:7,3,3-,3,3-:,954891/03,3-,3,3-:,930,91,83,80,: -,3,3-:,954891 .4394



 /!03:7,3,3-,3,3-:,930,91/03,3-,3,3-:,954891,83,80,: -,3,3-:,930,91 .4394  0!03:7,3,3/,:,3/03,3.,7,-078:8:3 .4394  !748085079:3,3  :7,3/03,3,703,:7,3/,72,,53,25::,3/,7 ,3,/8,2533,803,203,//:7,3,83,  ,703,,3,5::,35,/,8:/,/53,22,,80,7,3 203,/,703,/:7,3/,7,3,9/,-8,2,,53,2 ,3,7,9:8,3/,77,9:8,3203,/02:/,3/:7,3 ,83,  ,703,,3,7,9:8,35,/,8:/,/53,22,,80,7,3 203,/02:/,3/:7,3/03,39/,,/,,3,/-,,3, 203,/  ,83,,/,,

!03:7,3,3/,3$1,981,93, &39:802-,7,3-,3,3-:,9-07,: ,-,- ,-,- .4394   $1,942:9,91/,3,848,919/,-07,: ,- -, ,-. ,-. 4394      



!03:7,3,3-,3,3342025:3,81,9 ,,/,3,, 0781,99079:9:5,9:-,/:,-:,-,3,3-:,9/:7,3,3 ,83,,/,,-,3,3-:,9:, ,/,3- -,3,3-:,92,,,-.. -,3,3-:,9 .4394 

 -,3,3-:,9

 !07,,3 !03:2,,3-07:,3 , !07,,3,3,3,.,  ,7,203/,9,7 50,,3/:,-,3,3/03,3,3,  50,,3-,3,3,3,/03,3-,3,3,3,  5::,3/,38,9:,3/58,,3     507,,3/:,-,3,3/03,3,3,      507,,3-,3,305,9,3805::5::,37,9:8,37-:,3 ,3/,,3,3,-,3,3,3-:,334:2,5::,33,/:2,,3 /,3 /9:8/-0,,3,83, 

,7,-078:8:3



 !748085079:3,3  ,,3/,3/,7,3,,83,9:8,3,/,3825,3  ,,3/,3/,7,3,,83,/9,2-,,3,825,3,3 ,83,/-,785079,2,,83,  ,,3/,3,83,9:8,3,/,3825,3 /-,,,3,-07080744207  ,,3/,3,83,/9,2-,,3,825,3,3 ,83, 

9,2-,,3,8/,3

- !07,,3,3,3:,9 ,8507,,3/:,-,3,3-:,954891,/,,-,3,3-:,954891  4394 ,8507,,3-,3,3-:,954891/,330,91,83,,/,,-,3,3-:,9 30,91  4394 ,8507,,3/:,-,3,3-:,930,91,83,,/,,-,3,3-:,954891  4394 . !07,,3/,3$1,981,93, $1,9848,91 ,-.,-. 4394

$1,942:9,91 ,--, 4394

$1,9/897-:91 ,-.,-,. 4394



&38:7/0399,8:39:507,,3 ,8507,,3-,3,3-:,9/03,334,83,,/,,-,3,334 , ,8507,,3-,3,3-:,9/03,3,83,,/,,-,3,3-:,99::, ,,,

0781,99079:9:5 ,/:,-,3,3-:,9/,,32,,,83,,/,,-,3,3-:,9:,

,-.,-. -,3,3-:,9  !02-,,3 !02-,,3/,3$1,981,93, ,8-,/:,-,3,3-:,954891,/,,-,3,354891  4394 ,8-,/:,-,3,3-:,930,91,/,,-,3,354891  4394 ,8-,/:,-,3,3-:,9,3-07-0/,,/,,-,3,330,91   4394  ,8-,-,3,3-:,9/03,334,/,,9/,907/0138 ,9/,907/0138= ,34 4394

=%/,907/0138  %/,-07,:81,942:9,91/,3,848,91 ,- -, ,-. ,-.



 

4394 

   0781,99/,9079:9:5 ,/:,-,3,3-:,9/-,,83,-0:29039:-,3,3-:,9:,

.4394 -,3,3-:,9

 

 -:,3-,3,3-:,9-,3,350.,,3  !02,3,9,3-,3,3-:,9

IIII

,3

$0:2,31,947 4394 

 !$#$!#$%& ! ,7,9072:/,:39:20,:,3503,87,35,/,-,3,350.,,3,/,, /03,3202-:,9,3-,3,350.,,390780-:90-,3,3-:,9,35,3/0,9 !07,9,3.4394.4394-07:9 4394 %,87,3,84507,8-,3,350.,,3-07:9 

  

 

,3,3-:,9,3907/0,9/03,3 ,/,,

 

,3,3-:,9,3907/0,9/03,3 ,/,,

 

 

03,3/02,39,87,3/,7  ,/,,

 

 

,5,9/9:8  

   

   

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

   

,5,9/9:8  

 

 

   

   ,3,3-:,9,3907/0,9/03,3 ,/,,    03,3/02,39,87,3/,7  ,/,,     ,5,9/9:8             ,3,3-:,9,3907/0,9/03,3 ,/,,   ,3,3-:,9,3907/0,9/03,3 ,/,,    03,3/02,39,87,3/,7  ,/,,     ,5,9/9:8     ,3,3-:,9,3907/0,9/03,3 ,/,,



43805/,3507,89:3,3,3 507,8/,8,7,79209,,/,,503:2,,3503:7,3,3507,,3/,3502-,,3 ,,:5:34507,84507,8,3,30-.,38050795078039,80,,7:,/7,9 502,3,9,3/,34,792,,/,3:,/2,8:,30/,,2,90473!079:3,3 /,,2,79209,/,:,3203:7:98:,9::7:9,34507,8,3203039:,34507,8 ,79209,,32,3,0-/::/,:,3 79209,-,3,3,8-,3,3-:,9-,3,37,843,/,3-,3,370,:2:23, /50,,740,3,804,,320250,,7,4792,2,3:,,79209,,2:3 /02,3-,3,47,3,30-8:,203:3,,3,,9,,9805079,:,947 425:907,9,:80254,:39:20,:,35079:3,3,79209, 507,89:3,3,3:,9 ,3,3-:,9,/,,-,3,3,3907/7/,7-,3,330,9134/,3-,3,3 54891,3,3-:,9907/7/,7-,3,3.,.,/,330,913, ,/,,8,2,/03,3/,39/,/2,8:,3,80.,7,90758,,3,3-:,9 /,5,9/9:8,39,35,4254303/082,,9,:50.,,3



5,-,/,,28:,9:84,.079,907/,5,98:,9:-,3,3,3//,::,9,:/:9,9, ,9,2:3/:79:7:3,,7:8,2,97:/-,,/5,,/239,,9,::9,32,, 2,3,3,80-,,-,3,330,914394$::/49,%44/-,,34,793, 8::/49,%44 507,8!0.,,3  !03:2,,3/,3!03:7,3,3!0.,,3 !03:2,,3/,3503:7,3,350.,,3-,8,/,350.,,3.,25:7,3 03008,,3503:2,,3/,3503:7,3,350.,,3-,8,/,5,9/,:,3 /03,3203,2,,35030-:93,/,320308:,,3502-,33,80,3:93, ,8/,7503:2,,3,9,:503:7,3,350.,,33,,/,,/03,3 203:2,,3,9,:20:7,3,3502-,3502-,33,/,35030-:9909,5 8,2,  !07,,3/,3!02-,,3!0.,,3 !07,,3/,3502-,,350.,,3-,8,/,350.,,3.,25:7,3 !07,,350.,,3.,25:7,3,7:8/:-,203,/507,,350.,,3-,8, $0,3:93,,8507,,350.,,3-,8,,/,,,8507,,3502-,3 /03,3502-,3/,35030-:9/03,35030-:9  507,8,25:7,3 03008,,34507,8.,25:7,35,/,-,3,350.,,3/,5,9203:3,,3 ,9:7,34507,8.,25:7,38050795,/,-,3,3-:,9

 %#!!#%& &! !079:3,3/03,3203:3,,350.,,3-,3,/:25,/,,20/:5,380,7 ,7 4394  !,94-,-007,80-,,502-:,9943,9&39:202-:,980-,9,3943,9

 

/507:,3,:,35,3,33, 2 ,5,94-,2025:3,,:,3 5,3,33,2-07,5,-,9,3943,9,3/,5,9/-:,9 ,,-



 

   

     3,,3202-:,9,8,3-38,30-,7,3/,759,$09,5-38,3

 

20207:,359,,35,3,33, 207,5,259,,3/507:,3:39: 202-:,9,8,3-38,3 ,,-

 

 

 

 

 

 2 <2 <2 2 2

2 

,/59,,3/507:,3

 !$!##$ $0-:,50.,,3,3203::,37,849/,8,2,/03,350.,,3,3 20,-,,3/,7080:7:,3:9:,50.,,3-8,/:3,,3:39: 203:3:,37,84,,32025:3,39075709,8,3-07-0/,/-,3/3,350.,,3 80-,,-,,3,3:9:$0-,,.4394502-,3/,780-:,50.,,380-,, 7,842:33203,9,,34-0/,,2:25:,34-00,703,9:43805 50.,,380-,,7,84,7:80,8-,,3,&39:202,,2203,5,50.,,3 207:5,,3507-,3/3,37,84/,5,9/57,3/,,289:,88050793 4394  /3/,/,3/9,202-,9,3:3,,-20304,9440439433/, /,,223:203,,94480,2,,780/,3,3/9,,75,-, /3/,90,203,,94480,2,,7-07,5,,7,/9,90,203,, 9443, #,84:39:2,8,,/,9,8,/,,80-:,5073,9,,3/,5,9/:3,,3 :39:2020.,,32,8,,9:

/03,3507,,3,,3//,5,9           3 3  3 3 3 ,//9,90,203,,9443,,7



 %3-,/,3/,7/,3/,2,832,83.2/,3.2,, 507-,3/3,393/,7/,3/,,/,,,9,:/03,32,83 2,83/-,,3/,9,,380-,,502-,3/3$03,/,5,7/,9,,3

 

-,,93/,7933/,,9,:933/,7,/,, 93/, 03,3/02,3/,5,9/825:,3-,,507-,3/3,3/,5,9/3,9,,3

 

 

80-,,50.,,3 /,3507-,3/3,3/,5,9/3,9,,380-,,50.,,3   !,3,3/,30-,78:,9:507805,3,32025:3,507-,3/3,3,:,8 507805,3,39:.22,,9039:,3::7,35,3,3/,30-,7/,750780 5,3,39: !03008,,3 09,:! :,855.2 ,,-

:,855.2 8,507-,/3,33,32,,5,3,3/,30-,7/,7507805,3,39:,/,, 33 :,8507805,3,35.2 ,/33

3 3 3

 

3

,/5,3,33.2.2 0-,73.2.2

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MAKALAH BILANGAN PECAHAN 1

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