{"id":44972,"date":"2015-09-04T20:19:43","date_gmt":"2015-09-04T23:19:43","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=44972"},"modified":"2023-03-29T03:16:42","modified_gmt":"2023-03-29T06:16:42","slug":"problema-problema-ordenado","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-problema-ordenado\/","title":{"rendered":".Problema:  Problema ordenado"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 7\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nCompare as fra\u00e7\u00f5es [tex]x=\\dfrac{111110}{111111}[\/tex], [tex]y=\\dfrac{222221}{222223}[\/tex] e [tex]z=\\dfrac{333331}{333334}[\/tex] e as escreva em ordem crescente.<\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\" style=\"line-height:30px;\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nSe <\/p>\n<ul>\n<li>[tex]x=\\dfrac{111110}{111111}[\/tex],<\/li>\n<li>[tex]y=\\dfrac{222221}{222223}[\/tex],<\/li>\n<li>[tex]z=\\dfrac{333331}{333334}[\/tex],<\/li>\n<\/ul>\n<p>ent\u00e3o <\/p>\n<ul>\n<li>[tex]1-x=\\dfrac{1}{111111}[\/tex],<\/li>\n<li>[tex]1-y=\\dfrac{2}{222223}[\/tex],<\/li>\n<li>[tex]1-z=\\dfrac{3}{333334}[\/tex],<\/li>\n<\/ul>\n<p>donde<\/p>\n<ul>\n<li>[tex]\\dfrac{1}{1-x}=111111[\/tex],<\/li>\n<li>[tex]\\dfrac{1}{1-y}=111111\\dfrac{1}{2}[\/tex],<\/li>\n<li>[tex]\\dfrac{1}{1-z}=111111\\dfrac{1}{3}[\/tex].<\/li>\n<\/ul>\n<p>Como<br \/>\n[tex]\\qquad \\dfrac{1}{1-x} \\lt \\dfrac{1}{1-z} \\lt \\dfrac{1}{1-y}[\/tex],<br \/>\ne todos os tr\u00eas n\u00fameros s\u00e3o positivos, temos<br \/>\n[tex]\\qquad 1-x \\gt 1-z \\gt 1-y[\/tex].<br \/>\nPortanto, [tex]x\\lt z\\lt y[\/tex].<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g3\">\nParticipou da discuss\u00e3o o Clube <span style=\" color: #686461;\"><strong> MIRIM APRENDIZ<\/strong><\/span>.\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 7\u00ba ano do E. F.) Compare as fra\u00e7\u00f5es [tex]x=\\dfrac{111110}{111111}[\/tex], [tex]y=\\dfrac{222221}{222223}[\/tex] e [tex]z=\\dfrac{333331}{333334}[\/tex] e as escreva em ordem crescente. Solu\u00e7\u00e3o Se [tex]x=\\dfrac{111110}{111111}[\/tex], [tex]y=\\dfrac{222221}{222223}[\/tex], [tex]z=\\dfrac{333331}{333334}[\/tex], ent\u00e3o [tex]1-x=\\dfrac{1}{111111}[\/tex], [tex]1-y=\\dfrac{2}{222223}[\/tex], [tex]1-z=\\dfrac{3}{333334}[\/tex], donde [tex]\\dfrac{1}{1-x}=111111[\/tex], [tex]\\dfrac{1}{1-y}=111111\\dfrac{1}{2}[\/tex], [tex]\\dfrac{1}{1-z}=111111\\dfrac{1}{3}[\/tex]. Como [tex]\\qquad \\dfrac{1}{1-x} \\lt \\dfrac{1}{1-z} \\lt \\dfrac{1}{1-y}[\/tex], e todos os tr\u00eas n\u00fameros s\u00e3o positivos, temos [tex]\\qquad 1-x \\gt 1-z &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-problema-ordenado\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":166,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-44972","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/44972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/166"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=44972"}],"version-history":[{"count":25,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/44972\/revisions"}],"predecessor-version":[{"id":185706,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/44972\/revisions\/185706"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=44972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}