matemática nb2

8/6/2019 Matemática NB2

http://slidepdf.com/reader/full/matematica-nb2 1/32

8

GLHW F 78

H g z k } k j h j f w

Oiwfy}h lhw wknvkfczfw yfgzhw cvbëykghw1

■ ¿Fc xvë cñbfyo phyzfc fwzhw yfgzhw? ###########

■ ¿G÷bo fw lh jkwzhcgkh fczyf lhw bhyghw? ###########

■ Kcjkgh fc xvë cñbfyow fwzèc vikghjow1

lh fwzyfllh ###########

fl goyhq÷c ###########

lh lvch ###########

lh mlfgdh ###########

■ Fwgykif vch H fc fl cñbfyo : { vch I fc fl ># 0

8

9

7

:

6

=

>

4

;

80

0 8 9 7 : 6 = > 4 ; 80

9

■ Jfwgykif ghjh vch jf fwzhw yfgzhw#

■ Hcozh fc ghjh vch jf fwzhw yfgzhw low cñbfyow xvf mhlzhc fc lhw bhyghw#

0 9 : = 80 89 8: 84 90

0 6 90 :6

Fwgykif low cñbfyow xvf goyyfwpocjfc h lhw bhyghw fc lhw yfgzhw cvbëykghw1

7

94 9; 79 :8

800 =00



9

G v h j f y c o j f z y h i

h a o " P f y â o j o 7 " B h z f

b è z k g h " 7 I è w k g o

:

6

=

>

Fc lh yfgzh wknvkfczf fwgykif low cñbfyow1 4, 8=, 66, 49 { 806#

Fc ghjh ghwo, gobplfzh lhw wfgvfcgkhw jf hgvfyjo hl phzy÷c# Lvfno, fc zvgvhjfyco jf bhzfbèzkgh, vikgh fwow cñbfyow fc vch yfgzh cvbëykgh#

Ghjh vch jf fwzhw yfgzhw cvbëykgh zkfcf vc fyyoy# Jfwgyâiflo#

Fwgykif cñbfyow fc fwzh yfgzh cvbëykgh jf bojo xvf pvfjhw vikghy fl 9#000#

0 80 800

800 860 960 760

660 6;0 =00

8#000 ;#000 80#000

600 690 670 660 640 =00 =90 =60 >00 >90 >70

900 700 :00 600 =00 >00 400



GLHW F 79

8


Oiwfy}h fl gvhjyo wknvkfczf { lff lhw kcwzyvggkocfw phyh gobplfzhy lh hgzk}kjhj#

■ Fwgykif fl 860#000 fc wv gvhjykzo5 fcgvfczyh ozyo cñbfyo xvf zfcnh lowbkwbow jânkzow { fwgyâiflo fc wv gvhjykzo# Pkczh hbiow goc vc bkwbo goloy#Jkyfbow xvf fllow moybhc vch —phyfah‛#

■ Fwgykif fl 7>0#000 { wv “phyfah‒ fc wvw gvhjykzow5 pkczh hbiow goc ozyo goloy#

■ Flknf ozyow zyfw cñbfyow, fcgvfczyh wvw “phyfahw‒ { pkczh low gvhjykzow#

■ ¿Gvèl fw lh phyfah jf 880#000?

■ Pkczh jf vc goloy zojow low cñbfyow “wolkzhykow‒#

■ Gobplfzh low cñbfyow xvf fwzèc fc lh pykbfyh golvbch { wvwgoyyfwpocjkfczfw “phyfahw‒#

■ Gobplfzh low jf lh golvbch jocjf fwzè fl 60#000 { wvw “phyfahw‒#

■ Jfwgykif lh vikghgk÷c jf low cñbfyow { wvw “phyfahw‒#

■ Mkchlbfczf, gobplfzh lo xvf hñc mhlzh#

80#000 90#000 70#000 :0#000 60#000 =0#000 >0#000 40#000 ;0#000

800#000 880#000

9=0#000

700#000

:90#000

6:0#000

==0#000 =>0#000

>60#000

470#000 440#000

;00#000



:




9

Gopkh low cñbfyow jf lh wknvkfczf mklh jfl gvhjyo hczfykoy { viâghlow fc lh yfgzhcvbëykgh jkivahjh h goczkcvhgk÷c1

7

Vch pyomfwoyh wolkgkzh h low fwzvjkhczfw xvf dhnhc vch pyopvfwzh phyhyfpyfwfczhy low cñbfyow 890#0005 900#0005 846#0005 8=0#000 fc vchyfgzh cvbëykgh#

Zyfw fwzvjkhczfw dkgkfyoc lhw wknvkfczfw pyopvfwzhw1

Vikgh low cñbfyow :>6#000 { fl :06#000 fc lh yfgzh cvbëykgh hczfykoy#Pvfjfw dhgfylh fc zv gvhjfyco jf bhzfbèzkgh phyh hpo{hyzf fc low gvhjyhjkzow#

■ Hchlkgfc lhw zyfw pyopvfwzhw { jfgkjhc gvèl fw lh bfaoy opgk÷c#

■ ¿Zkfcfc vch opgk÷c bfaoy hñc?

■ Vikxvfc low cñbfyow pfjkjow wfnñc lh opgk÷c fwgonkjh#

:90#000

:90#000

YkghyjoGfgklkh

[o lh dhyë jfwjf800#000 dhwzh 900#000 {xvf h}hcgf jf 8#000 fc

8#000#

[o vzklkqhyë vch yfgzhxvf }h{h jf 800#000 h900#000 { xvf h}hcgfjf 80#000 fc 80#000#

Philo

[o gocwzyv{o vch yfgzhxvf phyzh fc 890#000,xvf llfnvf h 900#000 {

xvf }h{h jf 800 fc 800#



GLHW F 77


8

Oiwfy}h fl gvhjyo wknvkfczf# Fwgykif low cñbfyow xvf }hc fc low gvhjykzow owgvyow#

■ ¿Xvë cñbfyo fwzè vikghjo fc lh powkgk÷c jf lh Gfczfch jf Bkl $GB+ jf zojowlow cñbfyow jf fwzf gvhjyo?

■ ¿Xvë zkfcfc fc gobñc low cñbfyow jf lhw mklhw bhyghjhw goc mlfgdh?

■ ¿Xvë jânkzo wf vikgh fc fl lvnhy jf lh powkgk÷c jf lhw Jfgfchw jf Bkl $JB+fc low cñbfyow jf lh mklh xvf zkfcf lh pykbfyh mlfgdh? ¿H gvèczhw vckjhjfwfxvk}hlf?

8#000 9#000 7#000 :#000 6#000 =#000 >#000 4#000 ;#000

800#000 808#000

880#000

890#000

870#000

8:0#000

860#000

8=0#000

8>0#000

840#000

8;0#000 8;;#000



=




9

7

Vikgh fc ghjh vch jf lhw yfgzhw cvbëykghw xvf fwzèc h goczkcvhgk÷c,fl cñbfyo :67#

H goczkcvhgk÷c wf dhc jkivahjo zyfw “zyoqow‒ jf gvhjyow jf cñbfyow zyhihahjowhczfykoybfczf# Gobplfzh low gvhjyow wobiyfhjow#

8=0#000 8=9#000

8>0#000

8;0#000

7:0#000

769#000

7=7#000

7>0#000

;==#000

;4>#000

;==#000

■ ¿Fc gvèl zf yfwvlz÷ bèw wfcgkllo? ¿Poy xvë?

■ ¿Fc gvèl jf fllhw fw bèw fthgzh lh vikghgk÷c jfl cñbfyo? ¿Poy xvë?

■ Gobphyzf { gobphyh lhw yfwpvfwzhw goc zv gvywo#

0 8#000

0 600

:00 600

:60 :=0



GLHW F 7:


8

Vch kcmoybhgk÷c kcjkgh xvf fl }olgèc Oaow jfl Whlhjo, fc lh myoczfyh fczyfHynfczkch { Gdklf, zkfcf vch hlzvyh jf ghwk >#000 bfzyow5 fl }olgèc Zhgoyh vikghjofc fl coyzf jf Gdklf bkjf =#000 bfzyow jf hlzvyh5 fl }olgèc Dvjwoc xvf fwzè fc flwvy jf Gdklf, bkjf vc pogo bèw jf :#000 bfzyow5 fl }olgèc Ghlivgo bkjf vc pogobèw jf 9#000 bfzyow#

Fc fl jkivao xvf wknvf fwzèc yfpyfwfczhjow fwzow gvhzyo }olghcfw#

■ Fwgykif wvw cobiyfw fc fl jkivao#

■ Gobphyh goc zv gobphøfyo o gobphøfyh fc xvë }olgèc vikghyoc low cobiyfw#■ ¿Fc xvë zf mkahwzf phyh pocfy low cobiyfw h low }olghcfw?

■ ¿Xvkëc jf low zyfw zkfcf lh yhq÷c? ############################

■ Lhw hlzvyhw jf low gvhzyo }olghcfw zkfcfc gvhzyo jânkzow# ¿Gvèl fw fl bèw hlzo?

YkghyjoGfgklkh

Co# Fwf fbpkfqh goc 9#

90#000 zhbikëc

fbpkfqh goc 9 { fwfwfyâh yf hlzo#

Philo

Fl bèw hlzo fw flGhlivgo#

] o l g è c

############################

] o l g è c

############################

] o l g è c

############################

] o l g è c

############################



4




9

Fc zv gvhjfyco jf bhzfbèzkgh, yfpyfwfczh lhw locnkzvjfw jf low yâow jf lhwknvkfczf zhilh5 wføhlh gvèl fw fl bèw lhyno#

7

Fc vc iowxvf wf oynhckq÷ vch ghyyfyh fczyf low gocfaow Phyjo, Ilhcxvkzo,Bhcgdhjo { Oyfa÷c# Fl jfwhmâo mvf gvèczow bfzyow goyyâh ghjh vco fc bfjkh doyh#

Fwzf mvf fl yfwvlzhjo1 Phyjo goyyk÷ 79#000 bfzyow5 Ilhcxvkzo 97#000 bfzyow5

Bhcgdhjo 94#000 bfzyow5 { Oyfa÷c ;#000 bfzyow#■ Yfpyfwfczh low zyhbow yfgoyykjow poy ghjh vco# ¿Gvèl goyyk÷ bèw bfzyow?

:

■ Yfpyfwfczh vc ghbkco jf 7:6 bfzyow, ozyo jf :76 bfzyow { ozyo jf 6:7bfzyow# ¿Gvèl fw fl bèw lhyno? ¿G÷bo lo whifw?

■ Hnyfnh zyfw gfyow h lh locnkzvj jf ghjh ghbkco, yfpyfwëczhlow { wføhlh gvèl fwfl bèw lhyno#

■ Oyjfch fwzow yâow jf bfcoy h bh{oy locnkzvj#

■ Gobphyh zvw yfwvlzhjow goc low jf zv gobphøfyo o gobphøfyh#

■ ¿G÷bo whifw gvèl fw fl bèw goyzo?

Cobiyf jfl yâo Locnkzvj

Hbhqochw $Iyhwkl+ >#000 eb

Jfl Coyzf $Hynfczkch+ 9#000 eb

Bkwwkwwkpk $Fwzhjow Vckjow+ =#000 eb

]âwzvlh $Polockh+ 8#000 eb

Nyhcjf $Bëtkgo+ 7#000 eb

Lokyh $Myhcgkh+ 8#000 eb

■ ¿Xvkëc zkfcf lh yhq÷c? ############################

YkghyjoGfgklkh

Fl xvf fbpkfqh poy ;#

¨Fwf goyyk÷ bèw(

¨Co( Fwf fw fl xvf

goyyk÷ bfcow#



GLHW F 76


8

Avfno vco

Fwzf fw vc avfno fc phyfahw fc xvf fl jfwhmâo fwmoybhy cñbfyow goc jow jânkzow# Nhch fl xvf moybh flcñbfyo bh{oy#

■ Jkwpocfc jf jkfq zhyafzhw5 ghjh vch zkfcf vc jânkzojfl 0 hl ;#

■ Hl kckgko jfl avfno, lhw zhyafzhw fwzèc jkwpvfwzhw

woiyf lh bfwh, iogh hihao# Poy zvyco, ghjh avnhjoywhgh jow zhyafzhw { lhw jkwpocf phyh hybhy vccñbfyo#

■ Ghjh vco ivwgh moybhy fl cñbfyo bèw nyhcjf xvfpvfjh, goc wvw jow zhyafzhw# Yfnkwzyhc fc vch zhilhlow yfwvlzhjow jf low avfnow#

■ ¿Xvë gocwfao jhyâhw phyh moybhy fl bh{oy cñbfyo?

■ ¿Ftkwzf hlnvch zhyafzh xvf zf jë lh gfyzfqh xvf }hw hnhchy? ¿Poy xvë?

Ykghyjo

Gfgklkh

Fc fl Avfno jow nhch lh avnhjoyh xvf moybh flcñbfyo bèw gdkgo, bèw}fgfw#

Fc fl Avfno zyfw nhchfl avnhjoy xvf moybh flcñbfyo bèw nyhcjf jfzyfw jânkzow#

Philo

Fc fl Avfno vco nhchfl avnhjoy xvf moybhfl cñbfyo bèw nyhcjf,

bèw }fgfw#

Avfno jow

Goc lhw bkwbhw gocjkgkocfwhczfykoyfw, whghc jow zhyafzhw phyhmoybhy fl bfcoy cñbfyo#

■ ¿Goc gvèl zhyafzh nhchw fc fwzf avfno?

Avfno zyfw

Goc lhw bkwbhw gocjkgkocfwhczfykoyfw, ghjh vco whgh zyfwzhyafzhw phyh moybhy vc cñbfyo goczyfw jânkzow#

■ ¿Goc xvë zhyafzh whifw xvfwkfbpyf }hw h nhchy hl moybhy flbh{oy cñbfyo? ¿Poy xvë?



0




7

Fwgykif zyfw cñbfyow, fc ghjh ghwo, xvf wfhc bh{oyfw xvf low wknvkfczfw1

:

Oyjfch jf bfcoy h bh{oy low wknvkfczfw cñbfyow1

9

Goczkcñhc fl zyhihao fc phyfahw# Hdoyh zkfcfc jkwpockilfw jow wfzw jf zhyafzhw5fwzo fw, zkfcfc jow zhyafzhw goc fl bkwbo jânkzo# Hbiow wfzw fwzèc jkwpvfwzowwoiyf lh bfwh, iogh hihao# Ghjh vco whgh zyfw jf fwzhw zhyafzhw# Goc fwow zyfwcñbfyow moybh vc cvf}o cñbfyo# Nhch fl xvf moybh fl cñbfyo bh{oy#

■ ¿Xvë zhyafzh zf jh lh gfyzfqh xvf wkfbpyf }hw h nhchy? ############ ¿Poy xvë?■ Wvpocnhc xvf low jow zkfcfc lh zhyafzh goc fl ;, ¿xvë ozyh zhyafzh fw cfgfwhykh

phyh nhchy? ############

■ ¿Pojyâhw nhchy wk zkfcfw lh zhyafzh goc fl 0? ############

■ ¿Wf pvfjf fbphzhy fc fwzf avfno? ############ ¿Poy xvë? Jh vc fafbplo phyhyfwphljhy zv yfwpvfwzh#

]hykhgk÷c jfl avfno

Ghjh fwzvjkhczf whgh, poy zvyco, vch zhyafzh { jfgkjf xvë lvnhy }h h ogvphy fc flcñbfyo xvf moybhyè5 lvfno, ghjh vco whgh lh wfnvcjh zhyafzh { jfgkjf fc xvë

lvnhy lh vikgh5 gobplfzh goc lh zfygfyh zhyafzh#

Fwgykif zyfw cñbfyow, fc ghjh ghwo, xvf wfhc bfcoyfw xvf low wknvkfczfw1

:00#000 7:#000 86: 8:7#000 ;;#000

776#000 76#000 6#000 900

;#000 8;#000 9>#000 ;;#000 8:6#000



8

GLHW F 7=


Yfwvfl}hc low wknvkfczfw jfwhmâow# Fwgykif vc cñbfyo xvf1

9

■ Wfh bh{oy xvf ;0#000, bfcoy xvf 880#000 { xvf zfcnhgkcgo gfyow#

■ Wfh bfcoy xvf 40#000 { xvf zfcnh zyfw gfyow#

■ Wfh bh{oy xvf 900#000 { zfcnh zyfw gfyow#

■ Zfybkcf fc zyfw gfyow, xvf zfcnh wfkw gkmyhw, bh{oy xvf

800#000, bfcoy xvf 900#000 { xvf zfcnh vc = { vc >#

:00#000 :08#000 :09#000 :07#000 :0:#000 :06#000 :0=#000 :0>#000 :04#000 :0;#000

:80#000

:90#000

:60#000 :66#000

:;0#000 :;8#000

Fc fl gvhjyo jf low gkfc cñbfyow fczyf :00#000 { :;;#000, oyjfchjow jf bkl fc bkl1

■ Gobplfzh lh golvbch { lh mklh xvf fwzèc owgvyfgkjhw#

■ Bhygh fl bh{oy cñbfyo xvf zkfcf vc 7#

■ Bhygh fl bfcoy cñbfyo xvf zkfcf vc ;#



9




7

Phyh fwgykiky goc wâbiolow lh myhwf “zyfkczh { gvhzyo fw bfcoy xvf gvhyfczh { zyfw‒wf hcozh1

Fwzo fw lo bkwbo xvf jfgky xvf “gvhyfczh { zyfw fw bh{oy xvf zyfkczh { gvhzyo‒5 gocwâbiolow wf hcozh1

■ Oiwfy}h xvf fw fl bkwbo wknco pvfwzo fc vco { fc ozyo wfczkjo# Hbihw yh{kzhwfwzèc avczhw hl lhjo jfl cñbfyo bfcoy { fwzèc wfphyhjhw hl lhjo jfl cñbfyobèw nyhcjf#

■ Vzklkqh fwf wknco phyh kcjkghy gvèl jf low cñbfyow fw bh{oy { gvèl bfcoy, fclow wknvkfczfw phyfw jf cñbfyow#

■ Bhygh low cñbfyow xvf zkfcfc jow jânkzow knvhlfw { jkwzkczow jf gfyo# ¿Gvèl fwfl bh{oy? ############ ¿Gvèl fw fl bfcoy? ############

■ Bhygh fl cñbfyo xvf zkfcf zyfw gkmyhw knvhlfw { jkmfyfczfw jf 0# Pkczh zojowlow cñbfyow jf fwzf gvhjyo xvf woc bfcoyfw xvf fwf cñbfyo# Ftplkgh j÷cjffwzèc vikghjow#

:6 6:

6:#000 :6#000

7;#000 7>#000

94=#000 =49#000

■ Jkivah, fc zv gvhjfyco jf bhzfbèzkgh, vch yfgzh cvbëykgh phyh ghjh ghwo {bhygh hbiow cñbfyow fc fllh#

7: < :7

:7 3 7:



8

GLHW F 7>


9

Yfwvfl}f low wknvkfczfw pyoilfbhw1


Ykghyjo

■ Dh{ 9 ihcjfahw goc : phwzflfwghjh vch#

■ Fc ghjh mvyn÷c jf zyhcwpoyzffwgolhy ghifc 80 pfywochw#

Gfgklkh

¿Gvèczow phwzflfw dh{

fc lhw jow ihcjfahw?

Philo

¿Gvèczhw pfywochw pvfjfc

}khahy fc jow mvynocfw?

■ Phyh fl èlivb jfl gocgvywogkfczâmkgo, }fcjfc woiyfw goclèbkchw# Ghjh woiyf zkfcf9 lèbkchw#

■ Dh{ = nhyqhw hl lhjo jfl lhno#

¿Gvèczhw lèbkchw dh{

fc 6 woiyfw?

¿Gvèczhw phzhw jf

nhyqh dh{?

]hlfczkch



:




7

:

Fwgykif low cñbfyow xvf goyyfwpocjfc fc lhw ghwkllhw wobiyfhjhw# Yfgvfyjh xvfwf lff h phyzky jf lh pykbfyh golvbch " —jow }fgfw jow‛ o —wkfzf }fgfw jow‛ fzg#


■ Fc fl gvbplfhøow woiyhyoc = nloiow { wf lowyfphyzkfyoc fczyf jow hbknhw, jf bojo xvflhw jow yfgkikfyoc lh bkwbh ghczkjhj#

■ Wk zv}kfyhw xvf yfphyzky80 lèbkchw fczyf zñ { vcgobphøfyo jf gvywo#

Yogâo

¿Gvèczow nloiow lf zog÷

h ghjh vch?

Jkfno

¿Gvèczhw yfgkif ghjh

vco wk low jow yfgkifc lh

bkwbh ghczkjhj?

■ Gocwkjfyh hdoyh xvf mvfyoc> nloiow low xvf woiyhyoc#¿Gvèczow dh{ phyh ghjh vchjf lhw ckøhw?

■ [, wk low nloiow woiyhczfw mvfyhc 80, ¿gvèczownloiow woc phyh ghjh vch?

9 • = 2 > • 9 2 9 • ; 2

89 1 9 2 8: 1 9 2 84 1 9 2

Gobplfzh lhw wknvkfczfw knvhljhjfw phyh xvf wfhc }fyjhjfyhw1

8 9 7 : 6 = > 4 ; 80

8 •

9 •

7 •

: •

6 •

= •

> •

4 •

; •

80 •



GLHW F 74


8

9



■ Fc lh whlh dh{ 6 fxvkpow jf zyhihao#Fc ghjh vco phyzkgkphc : pfywochw# ■ Fl phxvfzf zkfcf 4 nhllfzhw#

Gfgklkh

¿Gvèczhw pfywochw

fwzèc fc lh whlh?

Philo

¿Gvèczhw dh{ fc 6

phxvfzfw?

■ Fc vc woiyf dh{ 6 lèbkchw jflèlivb jfjkghjo h low èyiolfwchzk}ow#

■ Lklkhch hwkwzk÷ h vc gocgkfyzo jfpkhco h gvhzyo bhcow#

Ykghyjo

¿Gvèczhw lèbkchw dh{

fc : woiyfw?

¿Gvèczow jfjow fwzhihc

yfgoyykfcjo lhw zfglhw jf fwf

pkhco?

]hlfczkch

■ ¿[ fc > woiyfw?

■ ¿[ fc 80 woiyfw?



=




7

:

Hcozh fc fl wknvkfczf gvhjyo, low cñbfyow xvf goyyfwpocjfc fc lhw ghwkllhwwobiyfhjhw1


■ Lh Wyh# Kcëw dkqo 70 phcfw phyh }fcjfy#Xvkfyf pocfylow fc 6 iolwhw#

■ Lh bhbè jf Yhb÷c lf yfnhl÷vch iolwh xvf zyhf :0 ghlvnhw#Ël jfgkjk÷ yfphyzkylhw fc phyzfw

knvhlfw h wvw : hbknow#

Yogâo

¿Gvèczow phcfw jfif pocfy fcghjh iolwh phyh xvf xvfjfc zojhw

goc fl bkwbo cñbfyo jf phcfw?

Jkfno

¿Gvèczhw ghlvnhw

lf goyyfwpocjkfyoc

h ghjh hbkno?

■ Ozyo jâh, dkqo 79 phcfw{ zhbikëc low pvwo fc 6 iolwhw# ¿Gvèczow phcfwpvwo fc ghjh iolwh?

6 • : 2 = • 6 2 6 • 9 2

90 1 6 2 70 1 6 2 80 1 6 2

9 • ; 2 84 1 9 2 > • 6 2


8 9 7 : 6 = > 4 ; 80

8 •

9 •

7 •

: •

6 •

= •

> •

4 •

; •

80 •



8

GLHW F 7;


9

Lh yhch Zhch { wv dkakzh Zhckzh whlkfyoc h phwfhy# Poy ghjh whlzo jf Zhch, lh pfxvføhZhckzh zkfcf xvf jhy 80 whlzkzow#

■ Zhch jko 6 whlzow phyh llfnhy h lh pvfyzh jf ghllf# ¿Gvèczow whlzow dkqo Zhckzhphyh llfnhy h lh pvfyzh? #########

■ Wk Zhckzh jko ;0 whlzow phyh llfnhy h lh fwxvkch, ¿gvèczow whlzow lf ihwzhyoc hZhch phyh llfnhy h lh fwxvkch? #########

■ Wk lh yhckzh jko 40 whlzow phyh llfnhy hl gdhygo, ¿gvèczow whlzow cfgfwkz÷ jhy wvbhbè phyh llfnhy hl gdhygo? #########

Fwgykif xvë wf gvbplf wkfbpyf xvf bvlzkplkghw poy 80#

Fwgykif xvë wf gvbplf wkfbpyf hl jk}kjky poy 80#

4 • 80 2 86 • 80 2 970 1 80 2

40 1 80 2 860 1 80 2 8#000 1 80 2


> • 80 2 ; • 80 2 80 • 7 2 89 • 80 2

80 • 86 2 97 • 80 2 80 • 897 2 8#0:0 • 80 2



■ Dh{ 80 }flkzhw hyobèzkghw woiyfghjh ghyz÷c#

■ Fl èlivb jf Mfychcjo zkfcf 80 doahw{ ghjh doah zkfcf 4 fwzhbpkllhw#

Gfgklkh

¿Gvèczhw }flkzhw

dh{ fc 9 jf fwzow

ghyzocfw? ¿[ fc : jf

fwzow ghyzocfw?

¿Gvèczhw fwzhbpkllhw

zkfcf Mfychcjo?

Philo



4




7

Gobplfzh low ghwkllfyow }fyjfw goc low cñbfyow xvf goyyfwpocjh1

:

6

:#600 2 ########## • ########## 9#000 2 ########## • ########## 894#000 2 ########## • ##########

79#000 2 ########## • ########## 700 2 ########## • ########## =0 2 ########## • ##########

94 • 800 2 :70 • 800 2 7: • 8#000 2

8#000 • 7:6 2 970 • 8#000 2 6 • 80#000 2

Gobplfzh lhw wknvkfczfw knvhljhjfw phyh xvf wfhc }fyjhjfyhw# Flkaf •80, •800 ÷ •8#000#


Fc nyvpow jf zyhihao, cfgfwkzhc cvf}f zhyafzhw fc lhw xvf fwzèc fwgykzow low jânkzowjfl 8 hl ;, jkwpvfwzhw iogh hihao woiyf lh bfwh#

■ Vc fwzvjkhczf jh }vflzh vch zhyafzh5 ghjh vco bvlzkplkgh fwf cñbfyo poy 6 {fwgykif fwzh opfyhgk÷c fc wv gvhjfyco jf bhzfbèzkgh#

■ H goczkcvhgk÷c bvlzkplkghc fwf yfwvlzhjo poy 95 lo fwgykifc fc moybh wfphyhjhfc wv gvhjfyco# Gobphyhc fl yfwvlzhjo oizfckjo goc fl cñbfyo jf lh zhyafzh#

■ Yfpkzfc jow o zyfw }fgfw bèw fwzh wfgvfcgkh#

■ Pyopocfc gocglvwkocfw { lhwgoc}fywhc fc fl gvywo#

■ Gobplfzhc fl wknvkfczf fwxvfbh1

> • 6 2

• 9 2 >0

8 9 7 : 6 = > 4 ; 80

8 • 9 6

9 • 9 : = 4 80 89 8: 8= 84 90

7 • = 86

: • 4 90

6 • 80 96

= • 89 70

> • 8: 76

4 • 8= :0

; • 84 :6

80 • 90 60



0




9

7

Gobplfzh fl wknvkfczf gvhjyo goc pyojvgzow1

:

Gobplfzh low wknvkfczfw pyojvgzow1

Yfwvfl}f low wknvkfczfw pyoilfbhw# Flknf lh fwzyhzfnkh xvf bèw zf hgobojf#

■ Phyh lh mkfwzh jfl golfnko, wf cfgfwkzh gobpyhy 8#000 ihcjfykzhw jf yfgvfyjo#Ghjh vch }hlf * :9# ¿Gvèczo jkcfyo wf cfgfwkzh?

■ ¿Gvèczhw iolwhw jf hyyoq dh{ fc 800 ghahw? Wf whif xvf ghjh ghah goczkfcf 790

iolwhw#

■ Fc lh zkfcjh “Whghy h bkl‒ }fcjkfyoc =: oiafzow fc vc jâh# ¿Gvèczo jkcfyoyfgkikfyoc poy fwhw }fczhw?

Gobphyzf goc zv gvywo lhw yfwpvfwzhw h low pyoilfbhw { lhw fwzyhzfnkhw vzklkqhjhw#

• 8 9 7 : 6 = > 4 ;

80 80 90 70

800 800 900 700

8#000 8#000

80#000 80#000

800#000 800#000

800 • := 2 := • 800 2 ; • 80 2

8#000 • ;= 2 ;= • 8#000 2 6 • 800 2

8#000 • >> 2 >> • 8#000 2 : • 8#000 2

Vc gobphøfyo jfl gvywo fwzv}o fcmfybo { co dh }fckjo h glhwfw#

■ ¿Lf pvfjfw h{vjhy phyh xvf ël hpyfcjh h bvlzkplkghy poy 80, 800, 8#000?

■ ¿G÷bo lf ftplkghyâhw?



9

Fc low fafygkgkow xvf wknvfc fmfgzñh vch jfwgobpowkgk÷c hjkzk}h jf low cñbfyowxvf wf kcjkghc#

> • 8 2

> • 80 2

> • 800 2

> • 8#000 2

> • 80#000 2

> • 800#000 2

74 2 #################### % #################### % ####################

6>0 2 #################### % #################### % ####################

;=#000 2 #################### % #################### % ####################

>;#000 2 #################### % #################### % ####################

:67#000 2 #################### % #################### % ####################

GLHW F :8


8

Gobplfzh lhw wknvkfczfw knvhljhjfw1

Gobphyzf goc zvw gobphøfyow { gobphøfyhw g÷bo lo yfwol}kwzf#



9




7

:0> 2

8#070 2

=0:#000 2

>0>#000 2

=4> 2

999 2

70; 2

:6#000 2

907#000 2

808#000 2

Fwgykif hdoyh lh jfwgobpowkgk÷c jf low wknvkfczfw cñbfyow# Oiwfy}h lh vikghgk÷cjfl gfyo fc low fafygkgkow hczfykoyfw { fc low xvf yfhlkqhyèw h goczkcvhgk÷c#

Fc low fafygkgkow hczfykoyfw dhw dfgdo vch jfwgobpowkgk÷c hjkzk}h jf low cñbfyow#Hjfbèw, {h whifw bvlzkplkghy poy 80, 800, 8#000#

■ Fcgvfczyh hdoyh vch moybh jf ftpyfwhy gvhlxvkfy cñbfyo vzklkqhcjo lhjfwgobpowkgk÷c xvf {h whifw, kcglv{fcjo lh bvlzkplkghgk÷c poy 80, 800 ÷8#000#

■ Gobplfzh :96 2 ##################################################

■ Gobphyzf lh yfwpvfwzh goc zv gvywo#

Gobplfzh hdoyh lhw wknvkfczfw jfwgobpowkgkocfw1

Yfgvfyjh xvf :00 2 : • 800



9

GLHW F :9


8

Jkivah fc zv gvhjfyco vc gvhjyo goc zyfw golvbchw { gvhzyo mklhw gobo hghihjf dhgfylo zv pyomfwoy o pyomfwoyh fc lh pkqhyyh# H goczkcvhgk÷c, fwgykif gvhzyocñbfyow fc ghjh golvbch# Fc lh pykbfyh golvbch fwgykif cñbfyow moybhjow poyvc jânkzo wfnvkjo jf gkcgo gfyow# Fc lh jfl bfjko, vc jânkzo wfnvkjo poy gvhzyogfyow5 fc lh ñlzkbh, vc jânkzo wfnvkjo jf zyfw gfyow#

■ Wflfggkoch vc cñbfyo jf ghjh golvbch, ghlgvlh bfczhlbfczf lh wvbh jf fllow{ fwgykif fwf yfwvlzhjo#

■ Kczfyghbikh zv gvhjfyco goc fl jf zv gobphøfyo o gobphøfyh phyh xvf ghjhvco yfgocoqgh xvë cñbfyow jf lhw golvbchw flknk÷ fl ozyo# Gobphyfc lhwzhyfhw yfhlkqhjhw#

Jkivah fc zv gvhjfyco ozyo gvhjyo goc zyfw golvbchw { fwgykif cñbfyow moybhjowpoy vc jânkzo wfnvkjo jf gkcgo, gvhzyo { zyfw gfyow# Fc fwzh opoyzvckjhj, fchlnvchw ghwkllhw, fwgykif fl cñbfyo 0#

■ Fc moybh wkbklhy h lh hczfykoy, ghlgvlh zyfw wvbhw { fwgyâiflhw# Kczfyghbikh flgvhjfyco goc zv gobphøfyo phyh yfgocogfy xvë cñbfyow jf lhw golvbchwvzklkq÷ ghjh vco#

700 % 8 2

8#000 % 70#000 2

:00#000 % 8#000 2

60#000 % 600#000 % 6#000 2

■ ¿Zkfcfw hlnñc gobfczhyko fc yflhgk÷c goc low pyogfjkbkfczow xvf fbplfhwzf?

Ghlgvlh lhw wknvkfczfw wvbhw1



:




7

:


Zyhihah goc ozyow gobphøfyow { gobphøfyhw fc zyâow o phyfahw# Pocnhc woiyf lhbfwh lhw zhyafzhw goc low jânkzow jf bojo xvf fwzow co wf }fhc#

■ Ghjh vco zkfcf fc wv bhco zyfw zhyafzhw gobo lhw wknvkfczfw1

■ Poy zvyco, ghjh vco whgh zyfw zhyafzhw goc jânkzow# Gobikchc fwhw zhyafzhw goclhw xvf zkfcfc fc lh bhco5 hybhc vc cñbfyo { lo fwgykifc fc wv gvhjfyco#Ghjh vco gobfczh wv zyhihao hl nyvpo#

■ Fc moybh wkbklhy h lo hczfykoy, hdoyh ghjh vco ivwgh moybhy fl cñbfyo bh{oy#

■ Hdoyh, ghjh vco ivwgh moybhy fl cñbfyo bfcoy#

• 800#000 • 80#000 • 8#000

7 • 800#000 % 6 • 80#000 % ; • 8#000 2

= • 80#000 % 4 • 800#000 2

> • 800#000 % 9 • 8#000 2

6 • 8#000 % 6 • 800#000 2



GLHW F :7

8

Fwgykif low cñbfyow xvf mhlzhc fc lhw ghwkllhw phyh xvf ghjh lhjo jfl zykècnvlowvbf 76#

9

Fwgykif fc low ghwkllfyow low cñbfyow 8, 9, 7, :, 6 { = phyh xvf lh wvbh jf low lhjowwfh knvhl h 89#

80

86

86

Hgzk}kjhjfw phyh jfwpvëw jf lh f}hlvhgk÷c



=




7

Gobplfzh fwzf gvhjyhjo goc cñbfyow, jf bojo xvf lh wvbh jf low cñbfyow jflhw golvbchw, jf lhw mklhw { jf lhw jkhnochlfw wfh lh bkwbh1

8>

8: 86

87



GLHW F ::

6

Hckzh yfphyzf fc ghczkjhjfw knvhlfw, 60 nhllfzhw fczyf wvw 6 ckfzow#¿Gvèczhw yfgkif ghjh vco? Pvfjfw hpo{hyzf fc vc jkivao#

4

Fwgykif lh jfwgobpowkgk÷c ghc÷ckgh jfl cñbfyo 906#000

80

Yf}kwh lhw wknvkfczfw gvhzyo yfgzhw cvbëykghw# ¿Fwzèc zojhw ikfc gocwzyvkjhw?Yf}kwh ghjh vch jfwgykikfcjo fl fyyoy wk lo dh{#

Yf}kwk÷c jf lh f}hlvhgk÷c

0 600 >00 8#000

800 900 700 :00

600 >00 ;00

0 80 >0 800



4




88

¿Xvë gkvjhj fwzè bèw lfaow jf Whczkhno? ¿[ bèw gfygh?

Jfwjf Whczkhno h1 Jkwzhcgkh1

Gvykg÷ 900 ebHykgh 9#000 eb

]kgzoykh =00 eb

Pvfyzo Boczz 8#000 eb

8:

Oyjfch low wknvkfczfw cñbfyow jf bfcoy h bh{oy1

760#000 964#000 968#000 948#000

87

Oiwfy}h lh wknvkfczf wfgvfcgkh { gocwkjfyhcjo fl bkwbo phzy÷c, jfzfybkch flcñbfyo xvf wknvf1

Hnyfnh low gvhzyo cñbfyow xvf wknvfc1

680#000 604#000 60=#000



GLHW F :6

8

■ Lff low fcghifqhbkfczow jf lhw golvbchw#

■ Gobplfzh jf hgvfyjo h lhw gocjkgkocfw fc fl kckgko jf ghjh mklh#

■ Gobphyh zv yfwpvfwzh goc lh jf zvw gobphøfyow { gobphøfyhw#

■ Goczkcñh gobplfzhcjo fl gvhjyo#

Fwgykif vc cñbfyoBvlzkplâghlo

poy 8#000Fwgyâiflo fc phlhiyhw

3 = { < ;

< 4; { 3 47

phy

3 900 { < 960

kbphy

< ;00 { 3 ;=0

3 6=0 { < :>0

< 4=0 { 3 >00


■ Vch }fq zfybkchjh fwzh hgzk}kjhj, phyzkgkph fc fl zyhihao golfgzk}o phyh lhyf}kwk÷c jf zvw yfwpvfwzhw#



0




9

Zyhqh vch lâcfh phyh vcky low cñbfyow xvf woc knvhlfw#

7

Gobplfzh fl gvhjyo xvf wknvf1

8 9 7 : 6 = > 4 ; 80

• 9 9 : =

• 90

• 900

900 • 70 2 600 • 900 2 700 • 80 2

6#000 • 90 2 :0 • 800 2 600 • 90 2


700#000 % :#000

=00#000 % 70#000 % :#000

6 • 800#000 % 9 • 80#000 % 6 • 8#000

= GB % 4 VB

4 VB % 7 JB % 9 GB

6 • 8#000 % : • 800#000 % 7 • 80#000

696#000

6:=#000

70:#000

64:#000

974#000

=04#000

=7:#000

:76#000

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