{"id":9612,"date":"2012-09-30T16:18:20","date_gmt":"2012-09-30T15:18:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9612"},"modified":"2022-01-19T23:45:18","modified_gmt":"2022-01-19T23:45:18","slug":"completa-as-pilhas-de-cubos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9612","title":{"rendered":"Completa as pilhas de cubos"},"content":{"rendered":"<p><ul id='GTTabs_ul_9612' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9612' class='GTTabs_curr'><a  id=\"9612_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9612' ><a  id=\"9612_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_9612'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Estas pilhas de cubos com n\u00fameros foram montadas seguindo um padr\u00e3o.<\/p>\n<p>Descobre-o. Depois completa cada uma das pilhas de cubos.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9613\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9613\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos.jpg\" data-orig-size=\"578,367\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349018028&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=\"Pilhas de cubos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos.jpg\" class=\"aligncenter  wp-image-9613\" title=\"Pilhas de cubos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos.jpg\" alt=\"\" width=\"347\" height=\"220\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos.jpg 578w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-300x190.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-150x95.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-400x253.jpg 400w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9612' onClick='GTTabs_show(1,9612)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9612'>\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\/09\/pilhascubos-sol.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9614\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9614\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" data-orig-size=\"568,360\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349018100&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=\"Pilhas de cubos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" class=\"aligncenter  wp-image-9614\" title=\"Pilhas de cubos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" alt=\"\" width=\"341\" height=\"216\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg 568w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-300x190.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-150x95.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-400x253.jpg 400w\" sizes=\"auto, (max-width: 341px) 100vw, 341px\" \/><\/a><\/p>\n<p>\u00ad<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Ora, \u00a0$\\left( { + 4} \\right)$ \u00e9 o resultado de uma dada opera\u00e7\u00e3o entre os n\u00fameros $\\left( { + 6} \\right)$ e $\\left( { &#8211; 2} \\right)$.<br \/>\nConclui-se, ent\u00e3o, que essa opera\u00e7\u00e3o \u00e9 a <strong>adi\u00e7\u00e3o<\/strong>: $\\left( { + 6} \\right) + \\left( { &#8211; 2} \\right) = \\left( { + 4} \\right)$.<br \/>\nAssim, temos:<br \/>\n$$\\begin{array}{*{20}{l}} {\\left( { &#8211; 2} \\right) + \\left( { &#8211; 6} \\right) = \\left( { &#8211; 8} \\right)}&amp;{}&amp;{\\left( { + 4} \\right) + \\left( { &#8211; 8} \\right) = \\left( { &#8211; 4} \\right)}&amp;{}&amp;{\\left( { + 5} \\right) + \\left( { &#8211; 4} \\right) = \\left( { + 1} \\right)} \\end{array}$$<br \/>\nPor \u00faltimo, vem:<br \/>\n$$\\begin{array}{*{20}{l}} {\\left( ? \\right) + \\left( { + 4} \\right) = \\left( { + 5} \\right)}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} {\\left( ? \\right)}&amp; = &amp;{\\left( { + 5} \\right) &#8211; \\left( { + 4} \\right)}\\\\ {}&amp; = &amp;{\\left( { + 1} \\right)} \\end{array}}\\\\ {}&amp;{}&amp;{}\\\\ {\\left( ? \\right) + \\left( { + 6} \\right) = \\left( { + 1} \\right)}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} {\\left( ? \\right)}&amp; = &amp;{\\left( { + 1} \\right) &#8211; \\left( { + 6} \\right)}\\\\ {}&amp; = &amp;{\\left( { &#8211; 5} \\right)} \\end{array}} \\end{array}$$<br \/>\n<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9614\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9614\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" data-orig-size=\"568,360\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349018100&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=\"Pilhas de cubos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" class=\"aligncenter  wp-image-9614\" title=\"Pilhas de cubos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" alt=\"\" width=\"341\" height=\"216\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg 568w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-300x190.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-150x95.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-400x253.jpg 400w\" sizes=\"auto, (max-width: 341px) 100vw, 341px\" \/>\u00ad<\/a><\/li>\n<li>Ora, $\\left( { &#8211; 2} \\right)$ \u00e9 o resultado de uma dada opera\u00e7\u00e3o entre os n\u00fameros $\\left( { &#8211; 1} \\right)$ e $\\left( { + 2} \\right)$.<br \/>\nConclui-se, ent\u00e3o, que essa opera\u00e7\u00e3o \u00e9 a <strong>multiplica\u00e7\u00e3o<\/strong>: $\\left( { &#8211; 1} \\right) \\times \\left( { + 2} \\right) = \\left( { &#8211; 2} \\right)$.<br \/>\nAssim, temos:<br \/>\n$$\\begin{array}{*{20}{l}} {\\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 1} \\right) = \\left( { + 3} \\right)}&amp;{}&amp;{\\left( { + 2} \\right) \\times \\left( { &#8211; 2} \\right) = \\left( { &#8211; 4} \\right)}&amp;{}&amp;{\\left( { + 3} \\right) \\times \\left( { &#8211; 2} \\right) = \\left( { &#8211; 6} \\right)}&amp;{}&amp;{\\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 4} \\right) = \\left( { + 8} \\right)} \\end{array}$$<br \/>\nVerificando-se ainda: $\\left( { &#8211; 6} \\right) \\times \\left( { + 8} \\right) = \\left( { &#8211; 48} \\right)$.<br \/>\n<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9614\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9614\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" data-orig-size=\"568,360\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349018100&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=\"Pilhas de cubos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" class=\"aligncenter  wp-image-9614\" title=\"Pilhas de cubos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg\" alt=\"\" width=\"341\" height=\"216\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol.jpg 568w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-300x190.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-150x95.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/pilhascubos-sol-400x253.jpg 400w\" sizes=\"auto, (max-width: 341px) 100vw, 341px\" \/>\u00ad<\/a><\/li>\n<li>Ora, $\\left( { &#8211; 5} \\right)$ \u00e9 o resultado de uma dada opera\u00e7\u00e3o entre os n\u00fameros $\\left( { &#8211; 3} \\right)$ e $\\left( { + 2} \\right)$.\n<p>Conclui-se, ent\u00e3o, que essa opera\u00e7\u00e3o \u00e9 a <strong>subtra\u00e7\u00e3o<\/strong>: $\\left( { &#8211; 3} \\right) &#8211; \\left( { + 2} \\right) = \\left( { &#8211; 3} \\right) + \\left( { &#8211; 2} \\right) = \\left( { &#8211; 5} \\right)$.<br \/>\nAssim, temos:<br \/>\n$$\\begin{array}{*{20}{l}} {\\left( { + 2} \\right) &#8211; \\left( { + 4} \\right) = \\left( { &#8211; 2} \\right)}&amp;{}&amp;{\\left( { + 4} \\right) &#8211; \\left( { &#8211; 1} \\right) = \\left( { + 5} \\right)}&amp;{}&amp;{\\left( { &#8211; 5} \\right) &#8211; \\left( { &#8211; 2} \\right) = \\left( { &#8211; 3} \\right)}&amp;{}&amp;{\\left( { &#8211; 2} \\right) &#8211; \\left( { + 5} \\right) = \\left( { &#8211; 7} \\right)} \\end{array}$$<br \/>\nVerificando-se ainda: $\\left( { &#8211; 3} \\right) &#8211; \\left( { &#8211; 7} \\right) = \\left( { &#8211; 3} \\right) + \\left( { + 7} \\right) = \\left( { + 4} \\right)$.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9612' onClick='GTTabs_show(0,9612)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Estas pilhas de cubos com n\u00fameros foram montadas seguindo um padr\u00e3o. Descobre-o. Depois completa cada uma das pilhas de cubos. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20703,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[428,320,319],"series":[],"class_list":["post-9612","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-multiplicacao","tag-numeros-inteiros-2"],"views":8125,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/09\/7V1Pag014-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9612","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=9612"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9612\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20703"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9612"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}