{"id":7105,"date":"2011-10-23T20:14:40","date_gmt":"2011-10-23T19:14:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7105"},"modified":"2022-01-11T01:11:23","modified_gmt":"2022-01-11T01:11:23","slug":"os-termos-de-uma-fracao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7105","title":{"rendered":"Os termos de uma fra\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_7105' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7105' class='GTTabs_curr'><a  id=\"7105_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7105' ><a  id=\"7105_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7105'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Se $\\frac{x}{y}$ \u00e9 uma fra\u00e7\u00e3o equivalente a $\\frac{2}{7}$ e a soma dos seus termos \u00e9 igual a 72, ent\u00e3o qual \u00e9 o valor de $x-y$?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7105' onClick='GTTabs_show(1,7105)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7105'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Se $\\frac{x}{y}$ \u00e9 uma fra\u00e7\u00e3o equivalente a $\\frac{2}{7}$ e a soma dos seus termos \u00e9 igual a 72, ent\u00e3o qual \u00e9 o valor de $x-y$?<\/p>\n<\/blockquote>\n<p>Equacionando o problema atrav\u00e9s de um sistema de equa\u00e7\u00f5es e resolvendo-o, temos:<\/p>\n<p>\\[\\begin{array}{*{35}{l}} \u00a0\u00a0 \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 \\frac{x}{y}=\\frac{2}{7}\u00a0 \\\\ \u00a0\u00a0 x+y=72\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 7x=2y\u00a0 \\\\ \u00a0\u00a0 x=72-y\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 x=72-y\u00a0 \\\\ \u00a0\u00a0 504-7y=2y\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 x=72-y\u00a0 \\\\ \u00a0\u00a0 y=\\frac{504}{9}\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 y=56\u00a0 \\\\ \u00a0\u00a0 x=16\u00a0 \\\\ \\end{array} \\right. &amp; {}\u00a0 \\\\ \\end{array}\\]<\/p>\n<p>(Nota que $y\\ne 0$)<\/p>\n<p>Logo, $x-y=16-56=-40$.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7105' onClick='GTTabs_show(0,7105)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Se $\\frac{x}{y}$ \u00e9 uma fra\u00e7\u00e3o equivalente a $\\frac{2}{7}$ e a soma dos seus termos \u00e9 igual a 72, ent\u00e3o qual \u00e9 o valor de $x-y$? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,240],"tags":[426,243],"series":[],"class_list":["post-7105","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-sistemas-de-equacoes","tag-9-o-ano","tag-sistemas-de-equacoes-2"],"views":3169,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7105"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7105\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14114"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7105"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}