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{"id":10491,"date":"2012-10-14T23:39:12","date_gmt":"2012-10-14T22:39:12","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10491"},"modified":"2022-01-01T00:51:38","modified_gmt":"2022-01-01T00:51:38","slug":"numeros-em-falta","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10491","title":{"rendered":"N\u00fameros em falta"},"content":{"rendered":"<p><ul id='GTTabs_ul_10491' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10491' class='GTTabs_curr'><a  id=\"10491_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10491' ><a  id=\"10491_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_10491'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Que n\u00fameros devemos colocar no lugar de $\\square $ ?<\/p>\n<ol>\n<li>$\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 3} \\right) = 8$<\/li>\n<li>$\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 12} \\right) =\u00a0 &#8211; 10$<\/li>\n<li>$\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 25} \\right) =\u00a0 &#8211; 1$<\/li>\n<li>$\\left( { &#8211; 352} \\right) \\div \\left( \\square\u00a0 \\right) =\u00a0 &#8211; 8$<\/li>\n<li>$\\left( { &#8211; 38} \\right) \\div \\left( \\square\u00a0 \\right) = 19$<\/li>\n<li>$\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 7} \\right) = 0$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10491' onClick='GTTabs_show(1,10491)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10491'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Na divis\u00e3o<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {\\begin{array}{*{20}{c}} \u00a0 1&amp;0&amp;0&amp;0 \\\\ \u00a0 {}&amp;4&amp;0&amp;{} \\\\ \u00a0 {}&amp;{}&amp;4&amp;0 \\\\ \u00a0 {}&amp;{}&amp;{}&amp;4 \\end{array}}&amp;{\\begin{array}{*{20}{c}} \u00a0 6&amp;{}&amp;{}&amp;{} \\\\ \\hline \u00a0 1&amp;6&amp;6&amp;{} \\\\ \u00a0 {}&amp;{}&amp;{}&amp;. \\\\ \u00a0 {}&amp;{}&amp;{}&amp;. \\end{array}} \\end{array}$$<\/p>\n<ul>\n<li>$D$ &#8211; dividendo: $1000$<\/li>\n<li>$d$ &#8211; divisor: $6$<\/li>\n<li>$q$ &#8211; quociente: $166$<\/li>\n<li>$r$ &#8211; resto: $4$<\/li>\n<\/ul>\n<p>Nesta divis\u00e3o verifica-se:<br \/>\n$$1000 = 6 \\times 166 + 4$$<\/p>\n<p>Em qualquer divis\u00e3o, tem-se:<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {D = d \\times q + r}&amp;{{\\text{com}}}&amp;{0 \\leqslant r &lt; d} \\end{array}$$<\/p>\n<p>Se a divis\u00e3o \u00e9 exata, ent\u00e3o $r = 0$ e, por isso, ${D = d \\times q}$, ou seja, $\\frac{D}{d} = q$, com $d \\ne 0$.<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Recordado o que est\u00e1 acima, vem:<\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 3} \\right) = 8}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 \\square &amp; = &amp;{\\left( { &#8211; 3} \\right) \\times 8} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 24} \\end{array}} \\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 12} \\right) =\u00a0 &#8211; 10}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 \\square &amp; = &amp;{\\left( { &#8211; 12} \\right) \\times \\left( { &#8211; 10} \\right)} \\\\ \u00a0 {}&amp; = &amp;{120} \\end{array}} \\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 25} \\right) =\u00a0 &#8211; 1}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 \\square &amp; = &amp;{\\left( { &#8211; 25} \\right) \\times \\left( { &#8211; 1} \\right)} \\\\ \u00a0 {}&amp; = &amp;{25} \\end{array}} \\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {\\left( { &#8211; 352} \\right) \\div \\left( \\square\u00a0 \\right) =\u00a0 &#8211; 8}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 \\square &amp; = &amp;{\\left( { &#8211; 352} \\right) \\div \\left( { &#8211; 8} \\right)} \\\\ \u00a0 {}&amp; = &amp;{44} \\end{array}} \\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {\\left( { &#8211; 38} \\right) \\div \\left( \\square\u00a0 \\right) = 19}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 \\square &amp; = &amp;{\\left( { &#8211; 38} \\right) \\div 19} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 2} \\end{array}} \\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{c}} \u00a0 {\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 7} \\right) = 0}&amp; \\Rightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 \\square &amp; = &amp;{\\left( { &#8211; 7} \\right) \\times 0} \\\\ \u00a0 {}&amp; = &amp;0 \\end{array}} \\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10491' onClick='GTTabs_show(0,10491)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Que n\u00fameros devemos colocar no lugar de $\\square $ ? $\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 3} \\right) = 8$ $\\left( \\square\u00a0 \\right) \\div \\left( { &#8211; 12} \\right) =\u00a0&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19271,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[428,330,319],"series":[],"class_list":["post-10491","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-numeros-inteiros-2"],"views":2178,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat92.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10491","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=10491"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10491\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19271"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10491"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10491"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10491"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}