tag:blogger.com,1999:blog-31025730441876483812024-02-08T05:57:28.112-08:00INTERAÇÃO SABER FAZ A DIFERENÇAÉ UM CURSO PRÉ- PARATORIO PARA ALUNOS DE 8ª SERIE DO ENSINO FUNDAMENTAL QUE PRETENDEM EMGREÇAR EM CURSOS TÉCNICO DO IFPA (ANTIGO CEFET).E PREPARA ALUNOS DO ENSINO MÉDIO PARA O PRISE PARA ENGREÇAR NA UNIVERSIDADE DO ESTADO DO PARÁ UEPADYNAMIC DE OLHO NO FUTUROhttp://www.blogger.com/profile/16540242156530658110noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-3102573044187648381.post-58122538253385476442010-11-24T09:47:00.001-08:002010-11-24T09:47:50.910-08:00razão e proporção<div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b style="mso-bidi-font-weight: normal;"><u><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">RAZÕES E PROPORÇÕES</span></u></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">:</span></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b style="mso-bidi-font-weight: normal;"><u><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">RAZÃO:</span></u></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm; text-indent: 35.4pt;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Razão do número </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> para o número </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><stroke joinstyle="miter"></stroke><formulas><f eqn="if lineDrawn pixelLineWidth 0"></f><f eqn="sum @0 1 0"></f><f eqn="sum 0 0 @1"></f><f eqn="prod @2 1 2"></f><f eqn="prod @3 21600 pixelWidth"></f><f eqn="prod @3 21600 pixelHeight"></f><f eqn="sum @0 0 1"></f><f eqn="prod @6 1 2"></f><f eqn="prod @7 21600 pixelWidth"></f><f eqn="sum @8 21600 0"></f><f eqn="prod @7 21600 pixelHeight"></f><f eqn="sum @10 21600 0"></f></formulas><path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"></path><lock aspectratio="t" v:ext="edit"></lock></shapetype><shape id="_x0000_i1025" o:ole="" style="height: 15.75pt; width: 36.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image001.wmz"></imagedata></shape></span>, </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">é o quociente de </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> por </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">. Onde <b>a</b> é o <b>antecedente</b> e <b>b</b> o <b>conseqüente. </b>A palavra razão vem do latim e significa a divisão ou o quociente entre dois números A e B, denotada por:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1026" o:ole="" style="height: 30.75pt; width: 69pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.wmz"></imagedata></shape></span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Lê-se: </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> está para </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b.</span></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Exemplos: </span></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a razão de 2 para 5 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1027" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image005.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>2 / 5.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a razão de 3 para 4 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1035" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>3 / 4.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Razões Inversas: </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span>duas razões são inversas uma da outra quando seu produto é igual a 1.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Exemplo:<span style="mso-spacerun: yes;"> </span>2 / 5 e 5 / 2 são inversas, pois:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1036" o:ole="" style="height: 30.75pt; width: 1in;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image008.wmz"></imagedata></shape></span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Razões Iguais: </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">duas razões são iguais quando as duas frações que representam são equivalentes.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Exemplo: <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1037" o:ole="" style="height: 30.75pt; width: 32.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image010.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>, onde: <span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1038" o:ole="" style="height: 9.75pt; width: 9.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image012.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>= equivalentes</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Podemos dizer que<span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1039" o:ole="" style="height: 30.75pt; width: 32.25pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image014.wmz"></imagedata></shape></span>, note que 3 x 4 = 2 x 6.</span></div><br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom: medium none; border-collapse: collapse; border-left: medium none; border-right: medium none; border-top: medium none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 480;"><tbody>
<tr style="height: 62.4pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; height: 62.4pt; mso-border-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 231.65pt;" valign="top" width="309"><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Existem algumas razões especiais que são muito utilizadas no nosso dia-a-dia e das quais você já deve ter ouvido falar: <b>escala</b>, <b>velocidade média</b>, e <b>densidade</b> <b>demográfica.</b> </span></div></td></tr>
</tbody></table><br />
<div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><u><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">VELOCIDADE MÉDIA:</span></u></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Situação: </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Suponhamos que um trem percorreu 453km em 6h. qual foi a velocidade média do trem nesse percurso?.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><shape id="_x0000_s1026" style="height: 72.15pt; left: 0px; margin-left: -18pt; margin-top: 39.6pt; position: absolute; text-align: left; width: 261pt; z-index: -6;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image016.png"></imagedata></shape><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Outra aplicação de razão entre duas grandezas é no cálculo da velocidade média de um veiculo. Assim, a velocidade média é a razão entre a distância total percorrida pelo veiculo e o tempo por ele gasto para percorrer-la, ou seja:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><u><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">PROPORÇÃO:</span></u></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm; text-indent: 35.4pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">É a igualdade entre duas razões.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Exemplo: <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1040" o:ole="" style="height: 30.75pt; width: 32.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image018.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>é uma proporção pois <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1041" o:ole="" style="height: 30.75pt; width: 32.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image020.wmz"></imagedata></shape></span>.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Leitura: <b>1 está para 2 assim como 3 esta para 6.</b></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><br />
<div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><line from="8.65pt,22.15pt" id="_x0000_s1027" strokecolor="blue" style="left: 0px; position: absolute; text-align: left; z-index: 2;" to="71.65pt,58.15pt"><stroke dashstyle="dash" endarrow="block"></stroke></line><line from="4.15pt,26.65pt" id="_x0000_s1028" strokecolor="red" style="left: 0px; position: absolute; rotation: -3707775fd; text-align: left; z-index: 3;" to="67.15pt,62.65pt"><stroke dashstyle="dash" endarrow="block"></stroke></line><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">1- </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Propriedade fundamental</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">: Em toda proporção o produto dos extremos é igual ao produto dos meios.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 18pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1042" o:ole="" style="height: 30.75pt; width: 45pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image025.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>, então a<span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1043" o:ole="" style="height: 9.75pt; width: 9.75pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image027.wmz"></imagedata></shape></span>b = c<span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1044" o:ole="" style="height: 9.75pt; width: 9.75pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image029.wmz"></imagedata></shape></span>d, temos a . d = c . b</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 18pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">onde <b>a</b> e <b>d</b> são <b>extremos</b> e <b>b</b> e <b>c</b> são <b>meios, </b>e : </span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a<span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1045" o:ole="" style="height: 11.25pt; width: 15pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image030.wmz"></imagedata></shape></span></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">1</span><span style="font-family: Symbol; font-size: 10pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> termo ou antecedente da 1ª razão.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b<span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1046" o:ole="" style="height: 11.25pt; width: 15pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image032.wmz"></imagedata></shape></span></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">2</span><span style="font-family: Symbol; font-size: 10pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> termo ou conseqüente da 1ª razão.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c<span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1047" o:ole="" style="height: 11.25pt; width: 15pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image033.wmz"></imagedata></shape></span></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">3</span><span style="font-family: Symbol; font-size: 10pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> termo ou antecedente da 2ª razão.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d<span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1048" o:ole="" style="height: 11.25pt; width: 15pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image034.wmz"></imagedata></shape></span></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">4</span><span style="font-family: Symbol; font-size: 10pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> termo ou conseqüente da 2ªrazão.<span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1049" o:ole="" style="height: 17.25pt; width: 9pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image035.wmz"></imagedata></shape></span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Exemplo: </span></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1050" o:ole="" style="height: 30.75pt; width: 36.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image037.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1051" o:ole="" style="height: 12pt; width: 17.25pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image039.wmz"></imagedata></shape></span>2 x 10 = 5 x 4 é uma proporção pois: 20 = 20.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1052" o:ole="" style="height: 30.75pt; width: 32.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image041.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1053" o:ole="" style="height: 12pt; width: 17.25pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image043.wmz"></imagedata></shape></span></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">3 x 8 = 9 x 4 não é uma proporção pois: <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1054" o:ole="" style="height: 14.25pt; width: 39.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image044.wmz"></imagedata></shape></span>.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">2 – </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Propriedade da soma</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">: A </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">soma</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> dos </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">dois primeiros termos</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">, está para o </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">primeiro </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">ou</span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">para</span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">o</span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> segundo</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> termo, assim como a </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">soma</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> dos </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">dois últimos</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> termos, está para o </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">terceiro</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> ou para o </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">quarto termo</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">.</span></div><div align="center" class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt; text-align: center;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1055" o:ole="" style="height: 30.75pt; width: 45pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image025.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1056" o:ole="" style="height: 30.75pt; width: 249.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image046.wmz"></imagedata></shape></span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">3 – <b>Propriedade</b>: A <b>soma (ou diferença</b>) dos <b>antecedentes</b> está para a <b>soma (ou diferença) dos conseqüentes</b>, assim como <b>cada antecedente está</b> para o <b>seu conseqüente</b></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div align="center" class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm; text-align: center;"><span style="font-size: 10pt;"><span style="mso-text-raise: -15.0pt; position: relative; top: 15pt;"><shape id="_x0000_i1057" o:ole="" style="height: 33.75pt; width: 29.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image048.wmz"></imagedata></shape></span><span style="font-family: Arial;"><span style="mso-spacerun: yes;"> </span>= </span><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1058" o:ole="" style="height: 30.75pt; width: 45pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image025.wmz"><span style="font-family: Arial;"></span></imagedata></shape></span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">4 – <b>Propriedade</b>: O <b>produto dos antecedentes</b> está para o <b>produto dos conseqüentes</b>, assim como o <b>quadrado</b> de qualquer <b>antecedente</b> está para o <b>quadrado</b> do respectivo <b>conseqüente</b>.</span></div><div align="center" class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt; text-align: center;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1059" o:ole="" style="height: 30.75pt; width: 45pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image025.wmz"></imagedata></shape></span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1060" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image050.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -15.0pt; position: relative; top: 15pt;"><shape id="_x0000_i1061" o:ole="" style="height: 36pt; width: 78.75pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image051.wmz"></imagedata></shape></span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt 9pt; text-align: justify;"><span style="font-size: x-small;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong>Grandezas Diretamente Proporcionais: </strong></span><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;">quando duas grandezas variam sempre na mesma razão, dizemos que essas grandezas são diretamente proporcionais, ou seja, quando uma grandeza aumenta a outra também aumenta e vice-versa.</span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt 9pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">Exemplo:<span style="mso-spacerun: yes;"> </span></span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt 9pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1028" o:ole="" style="height: 30.75pt; width: 48.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image053.wmz"><strong><span style="font-size: x-small;"></span></strong></imagedata></shape></span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-size: x-small;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong>Grandezas Inversamente Proporcionais: </strong></span><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;">quando duas grandezas são inversamente proporcionais, os números que expressam essas grandezas variam um na razão inversa do outro, ou seja quando uma aumenta a outra diminui.</span><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"></span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">Exemplo:<span style="mso-spacerun: yes;"> </span></span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1062" o:ole="" style="height: 30.75pt; width: 38.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image055.wmz"><strong><span style="font-size: x-small;"></span></strong></imagedata></shape></span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><br />
</div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-size: x-small;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong>Números Diretamente Proporcionais: </strong></span><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;">o</span></span><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="font-size: x-small;">s números racionais </span><span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1063" o:ole="" style="height: 12.75pt; width: 42pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image057.wmz"><span style="font-size: x-small;"></span></imagedata></shape></span><span style="font-size: x-small;">são diretamente proporcionais aos números racionais, </span><span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1064" o:ole="" style="height: 15.75pt; width: 41.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image059.wmz"><span style="font-size: x-small;"></span></imagedata></shape></span><span style="font-size: x-small;">quando se tem </span><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1065" o:ole="" style="height: 30.75pt; width: 54pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image061.wmz"><span style="font-size: x-small;"></span></imagedata></shape></span><span style="font-size: x-small;">.</span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">Exemplo: </span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1066" o:ole="" style="height: 30.75pt; width: 141.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image063.wmz"><strong><span style="font-size: x-small;"></span></strong></imagedata></shape></span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><br />
</div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt;"><span style="font-size: x-small;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong>Números Inversamente Proporcionais: </strong></span><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;">o</span></span><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="font-size: x-small;">s números racionais </span><span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1067" o:ole="" style="height: 12.75pt; width: 42pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image057.wmz"><span style="font-size: x-small;"></span></imagedata></shape></span><span style="font-size: x-small;">são inversamente proporcionais aos números racionais </span><span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1068" o:ole="" style="height: 15.75pt; width: 41.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image059.wmz"><span style="font-size: x-small;"></span></imagedata></shape></span><span style="font-size: x-small;">quando se tem </span><span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1069" o:ole="" style="height: 15.75pt; width: 84.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image065.wmz"><span style="font-size: x-small;"></span></imagedata></shape></span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">Exemplo: </span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1070" o:ole="" style="height: 14.25pt; width: 197.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image067.wmz"><strong><span style="font-size: x-small;"></span></strong></imagedata></shape></span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><br />
</div><div align="center" class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: center;"><u><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">DIVISÃO PROPORCIONAL</span></strong></span></u></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-size: x-small;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-style: italic;"><strong>a) Diretamente:</strong></span><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt; mso-bidi-font-style: italic; mso-bidi-font-weight: bold;"> </span><u><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"></span></u></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">Exemplos: </span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="font-size: x-small;">1 – Dividir o número 180 em partes diretamente proporcionais a 5, 6 e 7.</span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-style: italic;"><strong><span style="font-size: x-small;">b) Inversamente:</span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">Exemplos: </span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt;"><span style="font-size: x-small;">1 –<span style="mso-spacerun: yes;"> </span>Três amigos possuem R$ 210,00 e querem divider em partes inversamente proporcionais a 3, 5 e 6. Quanto caberá a cada um?</span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: normal;"><strong><span style="font-size: x-small;">c) Diretamente-Diretamente:</span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong><span style="font-size: x-small;">Exemplos: </span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;"><span style="font-size: x-small;">1 – Dividir o número 310 em partes que sejam<span style="mso-spacerun: yes;"> </span>diretamente proporcionais aos números<span style="mso-spacerun: yes;"> </span>2, 3 e 5 e simultaneamente diretamente proporcional a 6, 3 e 2.</span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong><span style="font-size: x-small;">d) Inversamente-Inversamente:</span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong><span style="font-size: x-small;">Exemplo:</span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;"><span style="font-size: x-small;">1 – Dividir o número 2920 em partes tais que sejam, ao mesmo tempo, inversamente proporcionais a 3, 5, 6 e 4, 6, 9.</span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong><span style="font-size: x-small;">e) Diretamente-Inversamente:<span style="mso-spacerun: yes;"> </span></span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong><span style="font-size: x-small;">Exemplo: </span></strong></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: "Times New Roman", "serif"; font-weight: normal; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;"><span style="font-size: x-small;">1 – Dividir o número em 3.560 em partes, tais<span style="mso-spacerun: yes;"> </span>que sejam, ao mesmo tempo, diretamente proporcionais a 3, 5, 8 e inversamente proporcionais a 4, 6, 9.</span></span></div><div class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: justify;"><br />
</div><div align="center" class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: center;"><u><span style="font-family: "Times New Roman", "serif"; mso-bidi-font-size: 10.0pt;"><strong><span style="font-size: x-small;">EXERCICIOS.</span></strong></span></u></div><div align="center" class="MsoBodyText" style="margin: 0cm 0cm 0pt; text-align: center;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span><strong>1)</strong> Em uma classe mista a razão entre o número de meninos e o número de meninas é 3<span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1071" o:ole="" style="height: 9.75pt; width: 9.75pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image069.wmz"></imagedata></shape></span>2.<span style="mso-spacerun: yes;"> </span>Sabendo-se que o número de meninos é 18, o número de meninas é?</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 3<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>b) 12<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>c) 18<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>d) 36<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>e) 20</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><line from="-9.35pt,-18pt" id="_x0000_s1030" style="left: 0px; position: absolute; text-align: left; z-index: 5;" to="-9.35pt,711pt"></line><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">2)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> A razão entre a quantia que gasto e a quantia que recebo como salário por mês é de 8/9.<span style="mso-spacerun: yes;"> </span>O que resta aplico em caderneta de poupança.<span style="mso-spacerun: yes;"> </span>Se neste mês meu salário foi<span style="mso-spacerun: yes;"> </span>de R$ 2.700,00, então a quantia que devo aplicar na caderneta de poupança é:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 270,00<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>b) 250,00<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>c) 320,00<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>d) 360,00<span style="mso-spacerun: yes;"> </span>e) 300,00</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span>3)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> A idade de um pai está para a de seu filho como 7 está para 5/3.<span style="mso-spacerun: yes;"> </span>Se a soma das idades é 52, qual a idade de cada um?</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 42 anos e 10 anos<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) 38 anos e 14 anos</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 45 anos e 7 anos<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 40 anos e 12 anos</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 44 anos e 8 anos</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">4)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> A razão entre dois números e <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1072" o:ole="" style="height: 30.75pt; width: 12pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image071.wmz"></imagedata></shape></span>, e a soma desses números e igual a 35. Encontre estes dois números?.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 15 e 21</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) 21 e 14</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> 14 e 21</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 15 e 21</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 10 e 20</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">5)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> A diferença entre os comprimentos de duas peças de fazenda é de 15m e estes estão entre sí assim como 7 está para 4. calcule a metragem de cada peça.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 10 e 15</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) 21 e 36</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 35 e 20</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 20 e 35</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 30 e 35</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">6)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> As idades de 2 meninas são tais que: a razão entre elas é <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1073" o:ole="" style="height: 30.75pt; width: 12pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image073.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>e a diferença 2 anos. Determine essas idades.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 8 e 6</span></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) 5 e 4</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 3 e 9</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 7 e 5</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 10 e 6</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">7)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> <b>(TRT-17º REGIÃO) </b>Em uma empresa, o atendimento ao publico é feito por 45 funcionários que se revezam, mantendo a relação de 3 homens para 2 mulheres. E correto a firmar que, nessa empresa dão atendimento a:<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a)16 mulheres<span style="mso-spacerun: yes;"> </span><b>b)</b>18 mulheres<span style="mso-spacerun: yes;"> </span>c)18 homens<span style="mso-spacerun: yes;"> </span>d)25 hoens<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>e) 32 homens</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">8)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> Num exame de vestibular, a razão entre o número de vagas e o número de candidatos é de 3 para 8. sabendo que há 15600 candidatos inscritos, o número de vagas é:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 1950<span style="mso-spacerun: yes;"> </span>b) 1975<span style="mso-spacerun: yes;"> </span><b>c)</b> 5850<span style="mso-spacerun: yes;"> </span>d) 1900<span style="mso-spacerun: yes;"> </span>e) 5700</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">9) (UFRS) </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Uma estrada de <metricconverter productid="315 km" w:st="on">315 km</metricconverter> de extensão foi asfaltada por três equipes, A, B e C, cada uma delas atuando em um trecho diretamente proporcional aos números 2, 3 e 4, respectivamente. O trecho da estrada asfaltada, <b>em km</b>,<span style="mso-spacerun: yes;"> </span>pela turma C foi de:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 70<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>b) 96<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>c) 105<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>d) 126<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><b>e)</b> 140</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">10)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> Um comerciante precisa pagar três dívidas: uma de</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">30 mil reais, outra de 40 mil reais e uma terceira de 50 mil reais. Como ele só tem 90 mil reais, resolve pagar quantias diretamente proporcionais a cada débito. Nessas condições, o maior credor receberá uma quantia de:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 30 mil reais<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> 37,5 mil reais</span><span style="color: red; font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span></span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 36 mil reais<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 22,5 mil reais<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 32 mil reais</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">11)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> Os três donos de uma indústria não possuem partes iguais dessa indústria. As partes que eles possuem são diretamente proporcionais aos números 6, 3 e 2. Sabendo que o lucro atingiu 22 milhões de reais líquidos e que esse lucro será dividido em partes diretamente proporcionais ao que eles possuem na indústria, então a parte do lucro, <b>em milhões</b>, que coube ao sócio que tem maior participação é de:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 4<span style="mso-spacerun: yes;"> </span>b) 6<span style="mso-spacerun: yes;"> </span>c) 8<span style="mso-spacerun: yes;"> </span><b>d)</b> 12<span style="mso-spacerun: yes;"> </span>e)15</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">12)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> Se dividirmos o número 292 em três partes que sejam, ao mesmo tempo, inversamente proporcionais a 3, 5 e 6<span style="mso-spacerun: yes;"> </span>e a<span style="mso-spacerun: yes;"> </span>4,<span style="mso-spacerun: yes;"> </span>6 e<span style="mso-spacerun: yes;"> </span>9, qual a maior parte ?</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> 180</span><span style="color: navy; font-family: "Times New Roman", "serif"; font-size: 10pt;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span>b) 72<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 27</span><span style="color: red; font-family: "Times New Roman", "serif"; font-size: 10pt;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 40<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) N.R.A</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">13)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> <b>(Pref. Ananindeua)</b> Um treinamento de voleibol teve 240 minutos de duração e foi dividido em três partes: a primeira foi dedicada a preparação física.<span style="mso-spacerun: yes;"> </span>A segunda, ao treinamento de jogadas ensaiadas e bloqueios e a terceira, a um “racha”<span style="mso-spacerun: yes;"> </span>entre os jogadores.<span style="mso-spacerun: yes;"> </span>Sabendo-se que os tempos de duração de cada parte são diretamente proporcionais aos números 3, 4 e 1.<span style="mso-spacerun: yes;"> </span>Quanto tempo durou cada parte do treinamento?</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> 90 minutos, 120 minutos e 30 minutos.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) 100 minutos, 110 minutos e 30 minutos.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 80 minutos, 120 minutos e 40 minutos.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 70minutos, 130 minutos e 40 minutos.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 90minutos, 100 minutos e 50 minutos.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">14)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> <b>(UnB/Cespe)</b> Nas docas de um porto, um navio descarrega 3 tipos diferentes de caixas, cujos volumes são grandezas diretamente proporcionais a 1, 3 e 16. Se a soma dos volumes de 3 dessas caixas, sendo cada uma de um tipo, é igual a <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1029" o:ole="" style="height: 18pt; width: 51.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image075.wmz"></imagedata></shape></span>, então a soma dos volumes das 2 caixas maiores é:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1030" o:ole="" style="height: 18pt; width: 51.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image077.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>b) <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1031" o:ole="" style="height: 18pt; width: 51.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image079.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span>c) <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1032" o:ole="" style="height: 18pt; width: 51.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image081.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>d) <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1033" o:ole="" style="height: 18pt; width: 51.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image083.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><b>e) <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1034" o:ole="" style="height: 18pt; width: 51.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image085.wmz"></imagedata></shape></span></b></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><line from="-.35pt,-9pt" id="_x0000_s1031" style="left: 0px; position: absolute; text-align: left; z-index: 6;" to="-.35pt,10in"></line><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">15)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> <b>(UNB/Cespe) </b>Alexandre, Jaime e Vitor são empregados de uma empresa e recebem, respectivamente, salários que são diretamente proporcional aos números 5, 7 e <metricconverter productid="9. A" w:st="on">9. A</metricconverter> soma dos salários desses empregados corresponde a R$ 4.200,00. Nessa situação, após efetuar o cálculos, conclui-se que:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> A soma do salário de Alexandre com o de Vitor é igual ao dobro do salário de Jaime.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) Alexandre recebeu salário superior a R$ 1.200,00</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) O salário de Jaime é maior que R$ 1.600,00.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) O salário de Vitor é 90% maior do que o de Alexandre.</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">16)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> <b>(Unb/Cespe-PGE/PA-2007) </b>Um órgão publico contratou por meio de concurso, 60 servidores de nível superior, com salário mensal de <b>x </b>reais, e <b>y </b>servidores de nível médio, com salário mensal de R$ 600,00. Sabe-se que a folha de salário do órgão será acrescida de R$ 141.000,00 mensais com essas contratações, e que os valores totais dos salários desses novos servidores, por níveis de escolaridade, são diretamente proporcionais a 34 e 13, respectivamente. Nessa situação, é correto afirmar que a soma <span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1074" o:ole="" style="height: 14.25pt; width: 27.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\DOCUME~1\usuario\CONFIG~1\Temp\msohtmlclip1\01\clip_image087.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>é igual a:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 1.765<span style="mso-spacerun: yes;"> </span></span></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) 1.775<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 1.785<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 1.795<span style="mso-spacerun: yes;"> </span></span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 1.876</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">17)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> <b>(Unb/Cespe- Detran-Pa/2006) </b>Uma empresa de transporte coletivo serve 3 localidades de uma cidade. Para atender as 3 localidades, os veículos da empresa são divididos em 3 grupos, em quantidades que são diretamente proporcionais aos números <span style="mso-spacerun: yes;"> </span>5, 7 e 11. O produto das quantidades de veículos dos dois grupos menores é igual a 140. Nessa situação, a frota dessa empresa é composta de:</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 44 veículos</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> 46 veículos</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 48 veículos</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 50 veículos</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">18) (UFPA – 2010 Prova cancelada)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> A orquestra sinfônica do theatro da paz (OSTP) é composta por músico de quatro naipes de instrumentos distintos: Ela conta com 27 músicos de cordas, 11 de metais, 8 de madeiras e 4 de percussão. No caso de se desejar ampliar a orquestra, de modo que ela passe a ter 150 músicos e tal que os naipes de instrumentos mantenham <b>a mesma proporção </b>entre eles, o número de músicos de cordas e o numero de músicos de metais passariam a ser, respectivamente,</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">a) 54 e 22</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">b) 60 e 30</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">c) 50 e 20</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">d) 82 e 40</span></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 9pt;"><b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">e) 81 e 33</span></b></div><div class="MsoNormal" style="margin: 0cm -4.25pt 0pt 0cm;"><br />
</div>DYNAMIC DE OLHO NO FUTUROhttp://www.blogger.com/profile/16540242156530658110noreply@blogger.com0