{"id":88192,"date":"2023-03-02T07:00:00","date_gmt":"2023-03-02T10:00:00","guid":{"rendered":"https:\/\/vestibulares.estrategia.com\/portal\/?p=88192"},"modified":"2023-08-02T14:05:34","modified_gmt":"2023-08-02T17:05:34","slug":"razao-e-proporcao","status":"publish","type":"post","link":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/razao-e-proporcao\/","title":{"rendered":"Raz\u00e3o e propor\u00e7\u00e3o: o que s\u00e3o, aplica\u00e7\u00f5es e como entender&nbsp;"},"content":{"rendered":"<p class=\"wp-block-paragraph\"><span id=\"urn:enhancement-14c11268-a836-4781-ac85-2f43c66fdb32\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">Raz&atilde;o<\/span> e propor&ccedil;&atilde;o est&atilde;o presentes na maior parte das atividades cotidianas. As escalas dos mapas, os GPS, os desenhos de moda, as <span id=\"urn:enhancement-e52b7060-d61b-4e9d-a35b-174a42f4ba92\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/vegetal\">plantas<\/span> de moradias, os gr&aacute;ficos de jogos em computadores e televis&atilde;o e muitas outras utilidades do dia a dia precisam desse conceito matem&aacute;tico para serem constru&iacute;dos.&nbsp;<p class=\"wp-block-paragraph\">&Eacute; por meio da <span id=\"urn:enhancement-4e4bb661-02a1-4baa-92fe-28ad8d55b173\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> e propor&ccedil;&atilde;o que as imagens n&atilde;o ficam distorcidas, seja durante o desenho de um personagem, um croqui, uma representa&ccedil;&atilde;o cartogr&aacute;fica e etc. Al&eacute;m disso, &eacute; poss&iacute;vel utiliz&aacute;-las para desenvolver receitas, seja para fazer mais ou menos por&ccedil;&otilde;es. Assim como o tema pode ser &uacute;til na resolu&ccedil;&atilde;o de problemas qu&iacute;micos e matem&aacute;ticos, em geral.&nbsp;<\/p><p class=\"wp-block-paragraph\">Note que <span id=\"urn:enhancement-7db95229-c109-400e-8843-eb740db103a2\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> e propor&ccedil;&atilde;o s&atilde;o assuntos de extrema import&acirc;ncia e utilidade no cotidiano e, por isso, muitos vestibulares costumam cobr&aacute;-los. Para te ajudar com isso, a Coruja desenvolveu o artigo a seguir, que traz um resumo sobre os dois temas, com a rela&ccedil;&atilde;o entre eles, al&eacute;m de mostrar aplica&ccedil;&otilde;es pr&aacute;ticas deles na resolu&ccedil;&atilde;o de quest&otilde;es de prova. Leia mais!<\/p><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_86 counter-hierarchy ez-toc-counter ez-toc-transparent ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">Navegue pelo conte\u00fado<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/razao-e-proporcao\/#O-que-e-razao-e-proporcao\" >O que &eacute; raz&atilde;o e propor&ccedil;&atilde;o?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/razao-e-proporcao\/#Propriedades-da-proporcao\" >Propriedades da propor&ccedil;&atilde;o<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/razao-e-proporcao\/#Questoes-de-razao-e-proporcao\" >Quest&otilde;es de raz&atilde;o e propor&ccedil;&atilde;o<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/razao-e-proporcao\/#Estude-com-o-Estrategia-Vestibulares\" >Estude com o Estrat&eacute;gia Vestibulares!<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-o-que-e-razao-e-proporcao\"><span class=\"ez-toc-section\" id=\"O-que-e-razao-e-proporcao\"><\/span>O que &eacute; raz&atilde;o e propor&ccedil;&atilde;o?<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-razao\">Raz&atilde;o<\/h3><p class=\"wp-block-paragraph\">Resumidamente, uma <span id=\"urn:enhancement-34eefaeb-ac33-4851-85b3-831cceecc179\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> &eacute; uma divis&atilde;o de valores, uma fra&ccedil;&atilde;o entre duas grandezas matem&aacute;ticas. O resultado obtido &eacute; conhecido como a <span id=\"urn:enhancement-71617b89-c8b0-47b2-9bf7-1e8909e8df09\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> entre elas, como em: a <span id=\"urn:enhancement-ce58bec1-f64c-4057-ab04-0d6a1eae7f76\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> entre 6 e 3 &eacute; 2, j&aacute; que 6\/3 =2.&nbsp;<\/p><p class=\"wp-block-paragraph\">Uma <span id=\"urn:enhancement-a31d68da-0b3f-45e0-bfbc-24a60fa23e27\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> sempre acontece em rela&ccedil;&atilde;o &agrave; mesma unidade, por exemplo, a cada 18 colheres de &aacute;gua, adiciona-se 3 colheres de a&ccedil;&uacute;car. Note que, embora os ingredientes sejam diferentes, ambos est&atilde;o sendo medidos pela unidade &ldquo;colher&rdquo;. Assim, &eacute; poss&iacute;vel estabelecer uma rela&ccedil;&atilde;o <span id=\"urn:enhancement-1a720ef6-cfa2-48f6-bbe5-af289070410b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">racional<\/span> (18\/3 = 6), que pode ser interpretada como: para cada 6 medidas de &aacute;gua, &eacute; necess&aacute;ria 1 medida de a&ccedil;&uacute;car.<\/p><p class=\"wp-block-paragraph\"><span id=\"urn:enhancement-ebdfac17-701b-4220-b600-7a095f1d5d49\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">Raz&atilde;o<\/span> = A\/B&nbsp;<\/p><p class=\"wp-block-paragraph\">A e B s&atilde;o diferentes de zero e est&atilde;o na mesma unidade de medida<\/p><p class=\"wp-block-paragraph\">Essa f&oacute;rmula tamb&eacute;m pode ser descrita como <span id=\"urn:enhancement-2e787ce1-7b8a-47e0-95c9-9edca246c336\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">Raz&atilde;o<\/span> = A:B. E, a leitura extensa desse c&aacute;lculo &eacute; A est&aacute; para B. Ou seja, &eacute; diferente do que vemos em fra&ccedil;&atilde;o. Isso indica que 5\/8 &eacute; uma <span id=\"urn:enhancement-398ed233-4828-4d33-9841-626951eb052e\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> de &ldquo;5 para 8&rdquo;, enquanto seria uma fra&ccedil;&atilde;o de &ldquo;cinco oitavos&rdquo;.&nbsp;<\/p><p class=\"wp-block-paragraph\">Existem algumas propriedades importantes em termos de <span id=\"urn:enhancement-ad2dade3-5719-44ff-959d-497dc5847cee\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span>. Por exemplo, sempre que o valor do denominador (representado por B na f&oacute;rmula acima) for igual a 100, significa que h&aacute; A valores a cada 100 unidades.<\/p><p class=\"wp-block-paragraph\">Basicamente, esse &eacute; o conceito de <a href=\"https:\/\/www.youtube.com\/watch?v=Wi8Axu9abQU\" target=\"_blank\">porcentagem<\/a>. Ou seja, quantas unidades est&atilde;o presentes a cada cento. Por isso, as raz&otilde;es em que &eacute; B=100, s&atilde;o chamadas de porcentagens, <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/porcentagem-o-que-e-como-calcular\/\" target=\"_blank\">percentagens <\/a>ou percentuais.<\/p><h3 class=\"wp-block-heading\" id=\"h-proporcao\">Propor&ccedil;&atilde;o<\/h3><p class=\"wp-block-paragraph\">No caso da propor&ccedil;&atilde;o, trata-se de uma igualdade entre duas raz&otilde;es diferentes. Ou seja, quando duas fra&ccedil;&otilde;es encontram o mesmo resultado, tratam-se de raz&otilde;es proporcionais. Por exemplo, h&aacute; uma propor&ccedil;&atilde;o entre a <span id=\"urn:enhancement-8b374834-e86a-4a5e-b400-f88ad49d7614\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> de 6 e 3 e a <span id=\"urn:enhancement-d504747d-da15-4f96-8be8-87ae58dc7e7c\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> de 8 e 4, uma vez que 6\/3 = 2 = 8\/4.&nbsp;<\/p><p class=\"wp-block-paragraph\">Propor&ccedil;&atilde;o = A\/B = <span id=\"urn:enhancement-0855f1eb-5a23-43f8-99a8-51be441e1c1e\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span>\/D&nbsp;<\/p><p class=\"wp-block-paragraph\">A, B, <span id=\"urn:enhancement-fc3a9aef-a0e3-4715-8918-4abeb3523c76\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span> e D s&atilde;o diferentes de zero<\/p><p class=\"wp-block-paragraph\">Outra <span id=\"urn:enhancement-51bc4220-7f18-49b4-b204-31c4e11b8a6f\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span> de representa&ccedil;&atilde;o &eacute; dada por:<\/p><p class=\"wp-block-paragraph\">Propor&ccedil;&atilde;o = A:B = C:D<\/p><p class=\"wp-block-paragraph\">E a leitura extensa dessa propor&ccedil;&atilde;o &eacute; &ldquo;A est&aacute; para B, assim como <span id=\"urn:enhancement-e6313b31-01dd-4066-804f-300d9c5ff685\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span> est&aacute; para D&rdquo;, o que demonstra a igualdade entre essas raz&otilde;es.&nbsp;<\/p><p class=\"wp-block-paragraph\">+ Veja tamb&eacute;m: <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/regra-de-tres\/\" target=\"_blank\">Regra de tr&ecirc;s simples e composta: veja como calcular<\/a><\/p><h2 class=\"wp-block-heading\" id=\"h-propriedades-da-proporcao\"><span class=\"ez-toc-section\" id=\"Propriedades-da-proporcao\"><\/span>Propriedades da propor&ccedil;&atilde;o<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Considera-se que os termos A e D s&atilde;o os extremos de uma propor&ccedil;&atilde;o, enquanto que B e <span id=\"urn:enhancement-36e123be-f375-471e-ad0d-2e731d77ef28\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span> s&atilde;o os termos de meio. Com essa informa&ccedil;&atilde;o, aprenda sobre as propriedades da propor&ccedil;&atilde;o.<\/p><h3 class=\"wp-block-heading\" id=\"h-produtos-e-proporcoes\">Produtos e propor&ccedil;&otilde;es<\/h3><p class=\"wp-block-paragraph\">O produto de A e D &eacute; igual ao produto de <span id=\"urn:enhancement-5a41bd76-e059-40b1-b1e4-7619da48e448\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span> e B.<br><\/p><p class=\"wp-block-paragraph\">A.D = B.C<\/p><p class=\"wp-block-paragraph\"><br>Para facilitar, voc&ecirc; pode fazer um X em cima do sinal de igualdade, o que indica quais ser&atilde;o os fatores da multiplica&ccedil;&atilde;o, como voc&ecirc; observa na imagem abaixo.&nbsp;&nbsp;<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/empSxQs6fpRQszgbVyIf6U1Xqkcy7DCcBhVAv5nJxLApyJOOejUWz2mMb3yn3kKWOnt7I3gM0-bnd4Se4BOMTyLQ7kF1MAYrMBCsGYiQ2frJaZTSerHJvhC3-sWP7RWh6X1mmFrqBs4NZys34SUfnHs\" alt=\"raz&atilde;o e propor&ccedil;&atilde;o\"><\/figure>\n<\/div><h3 class=\"wp-block-heading\" id=\"h-mudanca-de-posicoes\">Mudan&ccedil;a de posi&ccedil;&otilde;es<\/h3><p class=\"wp-block-paragraph\">Caso voc&ecirc; troque os extremos de posi&ccedil;&atilde;o entre si, a propor&ccedil;&atilde;o mant&eacute;m-se verdadeira.&nbsp;<\/p><p class=\"wp-block-paragraph\">A\/B = <span id=\"urn:enhancement-4cb7f43d-9840-48ad-8ce2-79ceb2a83d8c\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span>\/D<\/p><p class=\"wp-block-paragraph\">D\/B = <span id=\"urn:enhancement-07420c10-ef0a-4a7e-8900-f330e4548404\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span>\/A<\/p><p class=\"wp-block-paragraph\">Aplica&ccedil;&atilde;o pr&aacute;tica:&nbsp; 15\/5 = 9\/3&nbsp;<\/p><p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3\/5 = 9\/15 (perceba que a simplifica&ccedil;&atilde;o de 9\/15 &eacute; 3\/5, ou seja, a propor&ccedil;&atilde;o &eacute; real)<\/p><p class=\"wp-block-paragraph\">Da mesma <span id=\"urn:enhancement-0f75f105-f776-4e4f-ae87-63e2be0699f4\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span>, &eacute; poss&iacute;vel alternar a localiza&ccedil;&atilde;o dos termos de meio (B e <span id=\"urn:enhancement-536d2449-a6e5-45a0-a4e4-29503a0296cc\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span>), sem que a propor&ccedil;&atilde;o deixe de existir. Embora o resultado seja diferente, a rela&ccedil;&atilde;o proporcional se mant&eacute;m.<\/p><p class=\"wp-block-paragraph\">A\/B = <span id=\"urn:enhancement-085fa60c-cc55-47f1-b57a-dc91c553085c\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span>\/D<\/p><p class=\"wp-block-paragraph\">A\/<span id=\"urn:enhancement-84c6aa5b-83a0-4fb5-b651-133dd3d203ee\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span> = B\/D<\/p><p class=\"wp-block-paragraph\">Aplica&ccedil;&atilde;o pr&aacute;tica:&nbsp; 15\/5 = 9\/3&nbsp;<\/p><p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3\/9 = 5\/15<\/p><p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Simplificando 3\/9 = 1\/3 e, ao simplificar 5\/15 = 1\/3. Ou seja, a rela&ccedil;&atilde;o proporcional se manteve ap&oacute;s a troca dos meios.<\/p><h4 class=\"wp-block-heading\" id=\"h-inversao-das-razoes\">Invers&atilde;o das raz&otilde;es<\/h4><p class=\"wp-block-paragraph\">Se, nas duas raz&otilde;es, o denominador for colocado no lugar do numerador e o numerador no lugar do denominador, a propor&ccedil;&atilde;o entre os valores continuar&aacute; v&aacute;lida.<\/p><p class=\"wp-block-paragraph\">A\/B = <span id=\"urn:enhancement-9eaa92a2-34fc-4ffb-8edf-71e751fcf1c6\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span>\/D<\/p><p class=\"wp-block-paragraph\">B\/A = D\/<span id=\"urn:enhancement-e4c36d56-4007-4cf6-9514-b8d02e02b6ce\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span>&nbsp;<\/p><p class=\"wp-block-paragraph\">Aplica&ccedil;&atilde;o pr&aacute;tica: 35\/7 = 45\/9<\/p><p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;7\/35 = 9\/45<\/p><p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A fra&ccedil;&atilde;o reduzida de 7\/35 &eacute; 1\/5, e a redu&ccedil;&atilde;o de 9\/45=1\/5. Prova-se, portanto, que a propor&ccedil;&atilde;o se manteve.<\/p><p class=\"wp-block-paragraph\">+ Veja mais: <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/formulas-matematicas\/\" target=\"_blank\">F&oacute;rmulas matem&aacute;ticas: principais f&oacute;rmulas que aparecem no vestibular<\/a><\/p><h2 class=\"wp-block-heading\" id=\"h-questoes-de-razao-e-proporcao\"><span class=\"ez-toc-section\" id=\"Questoes-de-razao-e-proporcao\"><\/span>Quest&otilde;es de raz&atilde;o e propor&ccedil;&atilde;o<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">(<span id=\"urn:enhancement-d2227221-e041-4ea1-b323-a166611515b6\" class=\"textannotation disambiguated wl-event\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/enem-64632\">Enem<\/span> 2020) Uma empresa de &ocirc;nibus utiliza um sistema de vendas de passagens que fornece a imagem de todos os assentos do &ocirc;nibus, diferenciando os assentos j&aacute; vendidos, por uma cor mais escura, dos assentos ainda dispon&iacute;veis. A empresa monitora, permanentemente, o n&uacute;mero de assentos j&aacute; vendidos e compara-o com o n&uacute;mero total de assentos do &ocirc;nibus para avaliar a necessidade de aloca&ccedil;&atilde;o de ve&iacute;culos extras.<\/p><p class=\"wp-block-paragraph\">Na imagem tem-se a informa&ccedil;&atilde;o dos assentos j&aacute; vendidos e dos assentos ainda dispon&iacute;veis em um determinado instante.<\/p><figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Dcd1n2IMJ5z-t72fyQyoo9aJhJaQoLdSJr89BcCz7OFZwd5nJUHXX7eoiKNcbGqXvpATDVM5Ob_RmJEH161MVgPV4dpNmuD5FOyEUmTTsWmMto6P15XFzDVtLy72Zxo5oBx8ACpNZ8Eiowz9SBu0ti8\" alt=\"Quest&atilde;o do Enem: Raz&atilde;o e propor&ccedil;&atilde;o\"><\/figure><p class=\"wp-block-paragraph\">A <span id=\"urn:enhancement-27e5d43d-5b22-45fd-83a8-1c221b86431d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> entre o n&uacute;mero de assentos j&aacute; vendidos e o total de assentos desse &ocirc;nibus, no instante considerado na imagem, &eacute;<\/p><p class=\"wp-block-paragraph\">a) 16\/42<br>b) 16\/26<br><span id=\"urn:enhancement-f7c4056d-d87c-4c80-b0a2-785a5109de42\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span>) 26\/42<br>d) 42\/26<br>e) 42\/16<\/p><p class=\"wp-block-paragraph\">O exerc&iacute;cio pede a <span id=\"urn:enhancement-14c41e35-0dc5-40d3-86ba-119b8d31aee3\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> entre o n&uacute;mero de assentos vendidos e o n&uacute;mero total de assentos. Ent&atilde;o, &eacute; necess&aacute;rio contar quantas cadeiras j&aacute; est&atilde;o reservadas, que s&atilde;o 16. O n&uacute;mero total &eacute; dado pela numera&ccedil;&atilde;o encontrada, que &eacute; 42.&nbsp;<\/p><p class=\"wp-block-paragraph\">A fra&ccedil;&atilde;o deve ser montada na ordem em que foi apresentada no enunciado, ou seja:<\/p><p class=\"wp-block-paragraph\">Ass. vendidos\/ Ass. totais<\/p><p class=\"wp-block-paragraph\">16\/42 &rarr; <strong>alternativa A<\/strong>.<\/p><p class=\"wp-block-paragraph\">(<span id=\"urn:enhancement-573749b7-a8f6-4853-9952-27787521a6cd\" class=\"textannotation disambiguated wl-event\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/enem-64632\">Enem<\/span> PPL 2020) Ap&oacute;s o t&eacute;rmino das inscri&ccedil;&otilde;es de um concurso, cujo n&uacute;mero de vagas &eacute; fixo, foi divulgado que a <span id=\"urn:enhancement-ce75abd7-e965-423f-a314-a12f478f4c0d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> entre o n&uacute;mero de candidatos e o n&uacute;mero de vagas, nesta ordem, era igual a 300. Entretanto, as inscri&ccedil;&otilde;es foram prorrogadas, inscrevendo-se mais 4.000 candidatos, fazendo com que a <span id=\"urn:enhancement-5c2e197c-f1cd-4fb8-8037-a135c124eb74\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> anteriormente referida passasse a ser igual a 400. Todos os candidatos inscritos fizeram a prova, e o total de candidatos aprovados foi igual &agrave; quantidade de vagas. Os demais candidatos foram reprovados.<\/p><p class=\"wp-block-paragraph\">Nessas condi&ccedil;&otilde;es, quantos foram os candidatos reprovados?<\/p><p class=\"wp-block-paragraph\">a) 11 960<br>b) 11 970<br><span id=\"urn:enhancement-b8345a10-6653-4967-9510-1c21ab98d23a\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span>) 15 960<br>d) 15 970<br>e) 19 960<\/p><p class=\"wp-block-paragraph\">Essa quest&atilde;o traz uma <span id=\"urn:enhancement-a86d32e5-4b9b-4343-9f04-b6f00a5f3495\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> entre duas grandezas, mas com uma resolu&ccedil;&atilde;o mais elaborada, que suscita mais <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/equacoes\/\" target=\"_blank\">equa&ccedil;&otilde;es <\/a>e c&aacute;lculos. O primeiro passo &eacute; entender a primeira fra&ccedil;&atilde;o apresentada:<\/p><p class=\"wp-block-paragraph\">n&uacute;mero de candidatos iniciais \/ n&uacute;mero de vagas = 300<\/p><p class=\"wp-block-paragraph\">Com a prorroga&ccedil;&atilde;o das inscri&ccedil;&otilde;es, 4000 candidatos se somam aos candidatos iniciais, de <span id=\"urn:enhancement-b758dac0-0122-4b72-8e49-a246422b1e92\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span> que a <span id=\"urn:enhancement-f7f9b4f7-9edd-4f11-ace6-ebc151bd467d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/razao\">raz&atilde;o<\/span> ser&aacute;:<\/p><p class=\"wp-block-paragraph\">n&uacute;mero de candidatos finais \/ n&uacute;mero de vagas = 400<br>n&uacute;mero de candidatos finais = n&uacute;mero de candidatos iniciais + 4000<br>n&uacute;mero de candidatos iniciais + 4000 \/ n&uacute;mero de vagas = 400<\/p><p class=\"wp-block-paragraph\">O primeiro passo &eacute; descobrir o n&uacute;mero de vagas:<\/p><p class=\"wp-block-paragraph\">n&uacute;mero de vagas = v<br>candidatos iniciais = <span id=\"urn:enhancement-b7e93c06-88d9-4c86-9499-7faad88f1680\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span><br><span id=\"urn:enhancement-01a56baa-bc84-4d6c-aae2-21a04d54f74c\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span>\/v = 300<br>(<span id=\"urn:enhancement-8e0cfdf6-b843-43dd-9466-f204a49aa218\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/equacao\">equa&ccedil;&atilde;o<\/span> I) <span id=\"urn:enhancement-26210549-e78f-4e5f-8a3b-976edb5fb2e9\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span> = 300v<\/p><p class=\"wp-block-paragraph\"><span id=\"urn:enhancement-9b6b2900-150e-404a-9ca2-40765912c2ed\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span> + 4000 \/ v = 400<br>(<span id=\"urn:enhancement-dedff1ce-82e1-434b-bf18-6d56b4e22af5\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/equacao\">equa&ccedil;&atilde;o<\/span> II) <span id=\"urn:enhancement-f9c1effe-ca29-4754-a2c7-5d00a9cce86b\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span> + 4000 = 400v<\/p><p class=\"wp-block-paragraph\">Vamos substituir a <span id=\"urn:enhancement-9ccb9d1d-312d-4fc1-a196-e40d1ea9d035\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/equacao\">equa&ccedil;&atilde;o<\/span> I na II:<\/p><p class=\"wp-block-paragraph\">&nbsp;300v + 4000 = 400v<br>4000 = 100v<br>v = 40<\/p><p class=\"wp-block-paragraph\">Agora, vamos encontrar o n&uacute;mero de candidatos iniciais:<\/p><p class=\"wp-block-paragraph\"><span id=\"urn:enhancement-95437c44-2ae2-4d05-afef-bcb9b864ee92\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span>\/v = 300<br><span id=\"urn:enhancement-666dbbac-23e2-454a-bc4c-6e36b80c1d8d\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span>\/40 = 300<br><span id=\"urn:enhancement-3c28b207-b0c3-482a-a397-99bedc84bc81\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">c<\/span> = 12000<\/p><p class=\"wp-block-paragraph\">O total de candidatos &eacute; dado por 12000 + 4000 = 16000. Desses, apenas o n&uacute;mero de vagas foi preenchido (40). Ou seja, o n&uacute;mero de reprovados &eacute; tal que 16000 &ndash; 40 = 15960, como a <strong>alternativa <span id=\"urn:enhancement-5b6b0431-b1d7-4802-ba71-f7f129ef04dc\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/celsius\">C<\/span> <\/strong>indica.&nbsp;<\/p><h2 class=\"wp-block-heading\" id=\"h-estude-com-o-estrategia-vestibulares\"><span class=\"ez-toc-section\" id=\"Estude-com-o-Estrategia-Vestibulares\"><\/span>Estude com o Estrat&eacute;gia Vestibulares!<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">A Coruja tem um banco de quest&otilde;es com exerc&iacute;cios de provas de diversas bancas, resolu&ccedil;&atilde;o e gabarito. Os materiais foram selecionados e separados conforme <span id=\"urn:enhancement-9c6b4cea-3c27-4853-b844-752fcc6f74be\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/disciplina\">disciplina<\/span> e tema, o que facilita seu treino ao longo do tempo. Conhe&ccedil;a o<a href=\"https:\/\/vestibulares.estrategia.com\/portal\/eventos\/banco-de-questoes-estrategia-vestibulares\/\" target=\"_blank\"> BQ do Estrat&eacute;gia Vestibulares<\/a>!&nbsp;<\/p><p class=\"wp-block-paragraph\">D&ecirc; tamb&eacute;m um <span id=\"urn:enhancement-ce9abfca-f30d-4a7f-818e-70972ac36c7c\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/gases\">g&aacute;s<\/span> nos seus estudos com o curso Intensivo da Coruja: as disciplinas est&atilde;o resumidas com os t&oacute;picos mais relevantes para o estudo. Depois, voc&ecirc; pode revisar o conte&uacute;do em um material interativo, que salva tudo que voc&ecirc; grifa e comenta, o que personaliza sua jornada rumo &agrave; aprova&ccedil;&atilde;o. Clique no banner e saiba mais!<\/p><p class=\"wp-block-paragraph\"><a id=\"cta\" class=\"cta-imagem\" href=\"https:\/\/vestibulares.estrategia.com\/cursos\/\" target=\"blank\">\n                <img decoding=\"async\" width=\"100%\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2021\/12\/EV1.jpg\" alt=\"CTA - Estrat\u00e9gia Vestibulares 1\" title=\"CTA - Estrat\u00e9gia Vestibulares 1\">\n        <\/a>\n\n\n\n\n<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"Raz&atilde;o e propor&ccedil;&atilde;o est&atilde;o presentes na maior parte das atividades cotidianas. As escalas dos mapas, os GPS, os&hellip;\n","protected":false},"author":23,"featured_media":88194,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-88192","post","type-post","status-publish","format-standard","has-post-thumbnail","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v25.9 (Yoast SEO v28.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Raz\u00e3o e propor\u00e7\u00e3o: o que s\u00e3o, aplica\u00e7\u00f5es e como entender&nbsp;<\/title>\n<meta name=\"description\" content=\"Raz\u00e3o e propor\u00e7\u00e3o s\u00e3o assuntos importantes e \u00fateis no cotidiano e, por isso, muitos vestibulares costumam cobr\u00e1-los. 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