{"id":6578,"date":"2011-03-02T02:28:47","date_gmt":"2011-03-02T02:28:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6578"},"modified":"2022-01-03T00:34:22","modified_gmt":"2022-01-03T00:34:22","slug":"utilizando-a-nocao-de-m-d-c","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6578","title":{"rendered":"Utilizando a no\u00e7\u00e3o de m.d.c."},"content":{"rendered":"<p><ul id='GTTabs_ul_6578' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6578' class='GTTabs_curr'><a  id=\"6578_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6578' ><a  id=\"6578_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_6578'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Utilizando a no\u00e7\u00e3o de m.d.c., torna irredut\u00edveis as seguintes fra\u00e7\u00f5es:<\/p>\n<ol>\n<li>$\\frac{90}{75}$<\/li>\n<li>$\\frac{297}{77}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6578' onClick='GTTabs_show(1,6578)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6578'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$\\begin{matrix} \u00a0\u00a0 90 &amp; 2 &amp; {} &amp; {} &amp; 75 &amp; 3\u00a0 \\\\ \u00a0\u00a0 45 &amp; 3 &amp; {} &amp; {} &amp; 25 &amp; 5\u00a0 \\\\ \u00a0\u00a0 15 &amp; 3 &amp; {} &amp; {} &amp; 5 &amp; 5\u00a0 \\\\ \u00a0\u00a0 5 &amp; 5 &amp; {} &amp; {} &amp; 1 &amp; {}\u00a0 \\\\ \u00a0\u00a0 1 &amp; {} &amp; {} &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \\end{matrix}$<\/p>\n<p>Logo, $90=2\\times {{3}^{2}}\\times 5$ e $75=3\\times {{5}^{2}}$.<br \/>\nPortanto, $m.d.c.(75,90)=3\\times 5=15$.<\/p>\n<p>Assim, dividindo os termos da fra\u00e7\u00e3o por 15, obt\u00e9m-se: \\[\\frac{90}{75}=\\frac{6}{5}\\]<br \/>\n\u00ad<\/p>\n<\/li>\n<li>Ora,<br \/>\n$\\begin{matrix} \u00a0\u00a0 297 &amp; 3 &amp; {} &amp; {} &amp; 77 &amp; 7\u00a0 \\\\ \u00a0\u00a0 99 &amp; 3 &amp; {} &amp; {} &amp; 11 &amp; 11\u00a0 \\\\ \u00a0\u00a0 33 &amp; 3 &amp; {} &amp; {} &amp; 1 &amp; {}\u00a0 \\\\ \u00a0\u00a0 11 &amp; 11 &amp; {} &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 1 &amp; {} &amp; {} &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \\end{matrix}$<\/p>\n<p>Logo, $297={{3}^{3}}\\times 11$ e $77=7\\times 11$.<br \/>\nPortanto, $m.d.c.(77,297)=11$.<\/p>\n<p>Assim, dividindo os termos da fra\u00e7\u00e3o por 11, obt\u00e9m-se: \\[\\frac{297}{77}=\\frac{27}{7}\\]<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6578' onClick='GTTabs_show(0,6578)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Utilizando a no\u00e7\u00e3o de m.d.c., torna irredut\u00edveis as seguintes fra\u00e7\u00f5es: $\\frac{90}{75}$ $\\frac{297}{77}$ 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":[100,137,97],"tags":[139],"series":[],"class_list":["post-6578","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-ainda-os-numeros","category-aplicando","tag-m-d-c"],"views":2982,"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\/6578","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=6578"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6578\/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=6578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6578"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}