{"id":22661,"date":"2022-10-22T18:38:21","date_gmt":"2022-10-22T17:38:21","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22661"},"modified":"2022-10-22T19:03:36","modified_gmt":"2022-10-22T18:03:36","slug":"o-numero-racional-4left-5-right","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22661","title":{"rendered":"O n\u00famero racional \\(4,\\left( 5 \\right)\\)"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22661' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22661' class='GTTabs_curr'><a  id=\"22661_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22661' ><a  id=\"22661_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_22661'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O n\u00famero racional \\(4,\\left( 5 \\right)\\) pode ser representado pela fra\u00e7\u00e3o:<\/p>\n<p><strong>[A]<\/strong> \\(\\frac{{45}}{5}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> \\(\\frac{{41}}{9}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> \\(\\frac{{41}}{4}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> \\(\\frac{{45}}{3}\\)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22661' onClick='GTTabs_show(1,22661)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22661'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Designando a d\u00edzima por \\(x\\), vem: \\(x = 4,\\left( 5 \\right)\\).<br \/>Logo, multiplicando por \\(10\\) os dois membros da igualdade anterior, temos: \\(10x = 45,\\left( 5 \\right)\\).<br \/>Subtraindo, membro a membro, as duas equa\u00e7\u00f5es anteriores, temos:<br \/>\\[\\begin{array}{*{20}{r}}{}&amp;{10x}&amp; = &amp;{45,\\left( 5 \\right)}\\\\ &#8211; &amp;x&amp; = &amp;{4,\\left( 5 \\right)}\\\\\\hline{}&amp;{9x}&amp; = &amp;{41\\quad\\;\\,\\,}\\end{array}\\]<br \/>Donde, \\(x = \\frac{{41}}{9}\\).<br \/>Portanto, \\(4,\\left( 5 \\right) = \\frac{{41}}{9}\\).<\/p>\n<p>Logo, a op\u00e7\u00e3o correta \u00e9 <strong>[B]<\/strong>.<\/p>\n<p>\u00a0<\/p>\n<h6>Escolha da op\u00e7\u00e3o por exclus\u00e3o de tr\u00eas alternativas:<\/h6>\n<p>A op\u00e7\u00e3o <strong>[A]<\/strong> indica um n\u00famero inteiro: \\(\\frac{{45}}{5} = 9\\).<\/p>\n<p>A op\u00e7\u00e3o <strong>[C]<\/strong> indica uma fra\u00e7\u00e3o equivalente a uma fra\u00e7\u00e3o decimal, por isso a d\u00edzima ser\u00e1 finita: \\(\\frac{{41}}{4} = \\frac{{41}}{{2 \\times 2}} = 10,25\\).<\/p>\n<p>A op\u00e7\u00e3o <strong>[D]<\/strong> indica um n\u00famero inteiro: \\(\\frac{{45}}{3} = 15\\)<\/p>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22661' onClick='GTTabs_show(0,22661)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O n\u00famero racional \\(4,\\left( 5 \\right)\\) pode ser representado pela fra\u00e7\u00e3o: [A] \\(\\frac{{45}}{5}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [B] \\(\\frac{{41}}{9}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [C] \\(\\frac{{41}}{4}\\) \u00a0 \u00a0 \u00a0 \u00a0&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19188,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[100,97,664],"tags":[424,666,668],"series":[],"class_list":["post-22661","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-dizima-infinita-periodica","tag-dizimas"],"views":237,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat74.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22661","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=22661"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22661\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22661"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}