{"id":10578,"date":"2012-10-16T15:54:24","date_gmt":"2012-10-16T14:54:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10578"},"modified":"2022-01-20T00:50:45","modified_gmt":"2022-01-20T00:50:45","slug":"ponto-de-partida","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10578","title":{"rendered":"Ponto de partida"},"content":{"rendered":"<p><ul id='GTTabs_ul_10578' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10578' class='GTTabs_curr'><a  id=\"10578_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10578' ><a  id=\"10578_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_10578'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Copia e completa de modo a obteres o &#8220;ponto de partida&#8221;:<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10579\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10579\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\" data-orig-size=\"783,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\" class=\"aligncenter wp-image-10579\" title=\"Tabela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\" alt=\"\" width=\"700\" height=\"120\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg 783w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida-300x51.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida-150x25.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida-400x68.jpg 400w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10578' onClick='GTTabs_show(1,10578)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10578'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10579\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10579\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\" data-orig-size=\"783,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\" class=\"aligncenter wp-image-10579\" title=\"Tabela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg\" alt=\"\" width=\"700\" height=\"120\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida.jpg 783w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida-300x51.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida-150x25.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pontopartida-400x68.jpg 400w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/a><\/p>\n<\/p>\n<p>Para obtermos o &#8220;ponto de partida&#8221;, vamos percorrer o percurso inverso (da \u00abchegada\u00bb at\u00e9 \u00e0 \u00abpartida), mas aplicando as correspondentes opera\u00e7\u00f5es inversas:<\/p>\n<p>$$\\begin{array}{*{20}{c}}<br \/>\n{\\left[ {\\left( { &#8211; 2 + \\left( { &#8211; 4} \\right)} \\right) \\div 3} \\right] \\times 5 + 7}&amp; = &amp;A \\\\<br \/>\n{}&amp;{}&amp;{} \\\\<br \/>\n{\\left[ {\\left( { &#8211; 3 \\div 3} \\right) \\times \\left( { &#8211; 3} \\right) + 7} \\right] \\div \\left( { &#8211; 5} \\right)}&amp; = &amp;B \\\\<br \/>\n{}&amp;{}&amp;{} \\\\<br \/>\n{\\left( { &#8211; 30 \\div 3 + 4} \\right) \\times 2 &#8211; \\left( { &#8211; 11} \\right)}&amp; = &amp;C<br \/>\n\\end{array}$$<\/p>\n<p>Calculemos agora os tr\u00eas pontos de partida:<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\nA&amp; = &amp;{\\left[ {\\left( { &#8211; 2 + \\left( { &#8211; 4} \\right)} \\right) \\div 3} \\right] \\times 5 + 7} \\\\<br \/>\n{}&amp; = &amp;{\\left( { &#8211; 6 \\div 3} \\right) \\times 5 + 7} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 2 \\times 5 + 7} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 10 + 7} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 3}<br \/>\n\\end{array}$$<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\nB&amp; = &amp;{\\left[ {\\left( { &#8211; 3 \\div 3} \\right) \\times \\left( { &#8211; 3} \\right) + 7} \\right] \\div \\left( { &#8211; 5} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\left[ {\\left( { &#8211; 1} \\right) \\times \\left( { &#8211; 3} \\right) + 7} \\right] \\div \\left( { &#8211; 5} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\left( {3 + 7} \\right) \\div \\left( { &#8211; 5} \\right)} \\\\<br \/>\n{}&amp; = &amp;{10 \\div \\left( { &#8211; 5} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 2}<br \/>\n\\end{array}$$<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\nC&amp; = &amp;{\\left( { &#8211; 30 \\div 3 + 4} \\right) \\times 2 &#8211; \\left( { &#8211; 11} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\left( { &#8211; 10 + 4} \\right) \\times 2 &#8211; \\left( { &#8211; 11} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 6 \\times 2 &#8211; \\left( { &#8211; 11} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 12 + 11} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 1}<br \/>\n\\end{array}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10578' onClick='GTTabs_show(0,10578)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Copia e completa de modo a obteres o &#8220;ponto de partida&#8221;: Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20716,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[428,330,320,319],"series":[],"class_list":["post-10578","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7-o-ano","category-aplicando","category-numeros-inteiros","tag-7-o-ano","tag-divisao","tag-multiplicacao","tag-numeros-inteiros-2"],"views":2523,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/7V1Pag022-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10578","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=10578"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10578\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20716"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10578"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}