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 ~HH,, ,,..HH>>HH,,,, ////>>HG **** "**//HGHH,,HG 9HG**..+ HG -       21HH,,>> H I JLTPX ^b%d@ gkm nop q s uv 4b$Y!v3k'#kD|*2$4yS |*2$؂SYI82!+2$ ! }e,b$do,=!5?Ng4Q.b$__T`7 9h b2$jobewzpp 0e0e    A AԔ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| "0e@     @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 3fދ3ff33@89:g4kdkd@z[ 0vppp@  g4+d+d@z[ 0rp@ ppʚ;ʚ;<4KdKdl|- 0X80___PPT10 pp?  %O =D;B Uvijeti koriatenja prezentacije:""$ Autorica: Sonja Bani, prof. Ovu prezentaciju dozvoljeno je koristiti za rad s u enicima. U tu svrhu dozvoljeno ju je i izmijeniti prema svojim potrebama. Nije dozvoljeno koristiti i prikazivati ovu prezentaciju na predavanjima, u lancima, knjigama ili objavljivati na CD-u ili internetu. Za te i sli ne namjene potrebno je tra~iti i dobiti pristanak autorice.6sZR  JJRAZMJERNE ( PROPORCIONALNE) VELI INE&&0jUPRAVNO RAZMJERNE VELI INE OBRNUTO RAZMJERNE VELI INE66<=lPrika~imo rezultate iz tablice u koordinatnom sustavu:77 AlPrika~imo rezultate iz tablice u koordinatnom sustavu:77 EVUpravno razmjerne (proporcionalne) veli ine,,H4Primjer 2: Bera i u vonjaku beru jabuke. Jedanom bera u potrebno je 12 dana da zavrai berbu. Koliko je dana potrebno za berbu ako rade 2,3,4,8,12 bera a?& *j Ako se povea broj bera a, smanji se broj dana potrebnih da zavrae berbu.FK %IlPrika~imo rezultate iz tablice u koordinatnom sustavu:77 LlPrika~imo rezultate iz tablice u koordinatnom sustavu:77 N VObrnuto razmjerne (proporcionalne) veli ine,,O#^Usporedimo upravno i obrnuto razmjerne veli ine004Upravno razmjerne veli ine 4Obrnuto razmjerne veli ineS$&Rjeaavanje zadataka P!Zadatak 1: Automobil za 100 km vo~nje potroai 7,8 litara benzina. Koliko e benzina potroaiti za 350 km?&i `T%<Zadatak 2: Ako daktilografkinja radi 6 sati na dan, pretipkat e jedan rukopis za 12 dana. Koliko bi sati na dan trebala raditi da rukopis pretipka za 8 dana?& U&<Zadatak 2: Ako daktilografkinja radi 6 sati na dan, pretipkat e jedan rukopis za 12 dana. Koliko bi sati na dan trebala raditi da rukopis pretipka za 8 dana?& V'jZadatake mo~emo rijeaavati i pomou  pravila trojnog (65$ Q"Zadatak 1: Automobil za 100 km vo~nje potroai 7,8 litara benzina. 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? bv 8 %$D  0  HoZԔ?"0@NNN?N  ,$ 0 XUmno~ak veli ina x " y je stalan6- H  0޽h ? f33f̙f3}'u'___PPT10U'.Z+uQVDi%' = @B D$%' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D~' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*Dz' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*++0+Z ++0+Z ++0+Z ++0+ Z ++0+ Z ++0+Z ++0+Z ++0+Z +      (  r  S [ `     N]Ԕ?"0@NNN?N Va~no je odrediti jesu li veli ine u zadatku upravno ili obrnuto razmjerneLL  TaԔ?"0@NNN?Nek,$ 0 Zadatak 1: Automobil za 100 km vo~nje potroai 7,8 litara benzina. Koliko e benzina potroaiti za 350 km?(i `  NfԔ?"0@NNN?N ,$ 0 rAko automobil vozi viae kilometara, potroai viae benzina.P:    `mԔ?"0@NNN?N1 QQ ,$ 0 ^Ako se jedna veli ina povea i druga se povea.D0    ZtԔ?"0@NNN?N/AO,$ 0 ZVeli ine u ovom zadatku su upravno razmjerne...B   0DԔG ,$D  0B   0DԔpp@ ,$D  0H  0޽h ? f33f̙f3x___PPT10X. yU+-DL' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D~' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* ++0+ ++0+ ++0+ ++0+  +*     } (  x  c $2   ,  004Pp,$  0 fZadatak mo~emo rijeaiti tako da izjedna imo omjere:44R  <Z8c"` V f,$D 0R  <8c"` = ,$D 0V  <9 o ,$  0 rPomno~imo:  vanjski s vanjskim, unutarnji s unutarnjim (: .  0\?K w 7 ,$  0 p100 " x = 7.8 " 350 x = 2730 : 100 x = 27.39 :  <LJ8mX,$   0 hAutomobil e za 350 km potroaiti 27.3 litre benzina.556   0hO [  ,$   0 nZadatak je rijeaen tek kada napiaemo odgovor rije ima!88   00NM) ,$  0 m!100 km : 7.8 lit = 350 km : x lit0"   ZWԔ?"0@NNN?N4,$ 0 nKod upravno razmjernih veli ina njihov omjer je stalan.88H  0޽h ? f33f̙f3NF___PPT10&.4 +o=Dr' = @B D-' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D'  =-o6Bwipe(up)*<3<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*++0+ ++0+ ++0+ ++0+ ++0+  ++0+  ++0+  +l     ( (  r  S t `}     NvԔ?"0@NNN?NT4|Z,$ 0 |Jesu li veli ine u ovom zadatku upravno ili obrnuto razmjerne???  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a b  C   ZԔ?"0@NNN?NJ ,$ 0 M x c&  B  0DԔW W N,$@   0B  0DԔ??1,$D   0B  0DԔ ;,$@  0B @ NDԔ?"0@NNN?N<,$D  0F  ZԔ?"0@NNN?N _f ,$ 0 Px : a = b : c &H  0޽h ? f33f̙f3.4&4___PPT104.i+ Dr1' = @B D-1' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D'  =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D'  =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*Dq' =%(D' =%(D' =A@BBBB0B%(D'  =+4 8?`CB ppt_xBCB1+ppt_w/2B*Y3>B ppt_x<*D '  =+4 8?XCB ppt_yBCB ppt_yB*Y3>B ppt_y<*D' =1:Bhidden*o3>+B#style.visibility<*%( D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(D6' =A@BB BB0B%(D' =-g6B fade*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D)' =4@BB BB%(D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D)' =4@BB BB%(D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*+h+0+0 ++0+0 ++0+0 ++0+0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+0 +8   z   (  x  c $0     0H!0  ,$  0 Vx : 7.8 = 350 : 100 &:  <&0,$   0 hAutomobil e za 350 km potroaiti 27.3 litre benzina.55  <*0O,$  0 Uvjetna re enica: 100 km 7.8 lit Upitna re enica: 350 km x lit4^WB  0D|$ D,$D  0B  0D|$ D,$D  0   0 20z ,$  0 Jer su veli ine upravno razmjerne strjelice vu emo u istom smjeruPB   090 si ,$ 0 HU smjeru strjelica napiaemo razmjer:"%#6   0$0 . ,$  0 nZadatak je rijeaen tek kada napiaemo odgovor rije ima!88R   <Z8c"` ! ,$D 0R   <8c"`  : ,$D  0  NC0Ԕ?"0@NNN?N u T,$  0 p100 " x = 7.8 " 350 x = 2730 : 100 x = 27.39  H  0޽h ? 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WOh+'0X hp   SKUPOVI Olivetti2 Leveltisonjati56jMicrosoft PowerPointP@p Q@L "@@.GDg  I  -- @ !--'f3-- @ !--'3--%2--'f-- @ !--'3-- @ !--'@"Verdana-. 32 NUvijeti%."System-@"Verdana-. 3+2 koritenja prezentacije:  .-@"Verdana-. 3f@"Verdana--.12 fAutorica: Sonja Bani, prof.    .--.@"Verdana-. f3I2 >b,Ovu prezentaciju dozvoljeno je koristiti za        .@"Verdana-. f3hb@"Verdana--.F2 hb*rad s uenicima. U tu svrhu dozvoljeno ju   &   .--.@"Verdana-. f3C2 b(je i izmijeniti prema svojim potrebama.  %   & &&.@"Verdana-. f3I2 b,Nije dozvoljeno koristiti i prikazivati ovu          .@"Verdana-. f3b@"Verdana--.F2 b*prezentaciju na predavanjima, u lancima,   &  & .--.@"Verdana-. f362 Cbknjigama ili objavljivati na CD &    .@"Verdana-. f3 2 C-.@"Verdana-. f32 Cu ili  .@"Verdana-. f32 mb internetu .@"Verdana-. f3m@"Verdana--.:2 m". Za te i sline namjene potrebno    &  .--.@"Verdana-. f3b@"Verdana--.B2 b'je traiti i dobiti pristanak autorice.       .--.՜.+,0    On-screen ShowINA-Naftaplin*A Arial GaramondTimes New RomanVerdana WingdingsLevel Bitmap ImageMicrosoft Equation 3.0" Uvijeti koritenja prezentacije:&RAZMJERNE ( PROPORCIONALNE) VELIINEkPrimjer 1: Cijena jabuka je 10 kuna za kilogram. Koliko treba platiti za 2kg, 3kg, 4 kg, 5kg, 10kg jabuka?7Prikaimo rezultate iz tablice u koordinatnom sustavu:7Prikaimo rezultate iz tablice u koordinatnom sustavu:,Upravno razmjerne (proporcionalne) veliinePrimjer 2: Berai u vonjaku beru jabuke. Jedanom berau potrebno je 12 dana da zavri berbu. Koliko je dana potrebno za berbu ako rade 2,3,4,8,12 beraa?7Prikaimo rezultate iz tablice u koordinatnom sustavu:7Prikaimo rezultate iz tablice u koordinatnom sustavu:,Obrnuto razmjerne (proporcionalne) veliine0Usporedimo upravno i obrnuto razmjerne veliineRjeavanje zadatakaiZadatak 1: Automobil za 100 km vonje potroi 7,8 litara benzina. Koliko e benzina potroiti za 350 km?Zadatak 2: Ako daktilografkinja radi 6 sati na dan, pretipkat e jedan rukopis za 12 dana. Koliko bi sati na dan trebala raditi da rukopis pretipka za 8 dana?Zadatak 2: Ako daktilografkinja radi 6 sati na dan, pretipkat e jedan rukopis za 12 dana. Koliko bi sati na dan trebala raditi da rukopis pretipka za 8 dana?6Zadatake moemo rijeavati i pomou pravila trojnogiZadatak 1: Automobil za 100 km vonje potroi 7,8 litara benzina. Koliko e benzina potroiti za 350 km?Zadatak 2: Ako daktilografkinja radi 6 sati na dan, pretipkat e jedan rukopis za 12 dana. Koliko bi sati na dan trebala raditi da rukopis pretipka za 8 dana?  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