{"id":120325,"date":"2019-01-10T21:59:36","date_gmt":"2019-01-10T23:59:36","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=120325"},"modified":"2024-06-04T00:24:31","modified_gmt":"2024-06-04T03:24:31","slug":"sala-de-estudos-sistema-de-numeracao-romanos-subtracao","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudos-sistema-de-numeracao-romanos-subtracao\/","title":{"rendered":".Sala de Estudo: Sistema de Numera\u00e7\u00e3o Romano &#8211; SUBTRA\u00c7\u00c3O"},"content":{"rendered":"<p style=\"margin:20px;\">\n<div class=\"gres cbm2\" style=\"font-size:20px; margin-left:auto; margin-right:auto;line-height:30px\">\n<p class=\"tiss cm\"  style=\"line-height:25px;margin:10px\">Algoritmo da subtra\u00e7\u00e3o<\/p>\n<hr style=\"height:2px; background-color:#8B5A2B; margin-top: 30px; margin-bottom: 20px;border: 0 none\"\/>\n<p style=\"margin:40px 60px 10px 60px;\">\nO algoritmo da subtra\u00e7\u00e3o que apresentaremos tem como finalidade obter diferen\u00e7as do tipo [tex]a-b[\/tex], sendo [tex]a,b[\/tex] n\u00fameros naturais, com [tex]a \\gt b[\/tex], e para isso o objetivo ser\u00e1 <strong>eliminar <\/strong> todos os s\u00edmbolos romanos que aparecem em [tex]b[\/tex]. Lembrem-se sempre disso: <\/p>\n<p class=\"tis1 \"> eliminar todos os s\u00edmbolos do segundo n\u00famero (subtraendo).<\/p>\n<p style=\"margin:50px;\">\n<div class=\"gres cbm5\" style=\"margin-left:auto; margin-right:auto; width:90%;\">\n<p class=\"tis1 cm\">O algoritmo<\/p>\n<p><span style=\"color:#8B5A2B;\"><strong> Etapa 1:<\/strong> <\/span>Descompactar todas as nota\u00e7\u00f5es subtrativas de cada um dos dois termos da subtra\u00e7\u00e3o: minuendo e subtraendo.<\/p>\n<ul>\n<li>Por exemplo: transformar [tex]IV[\/tex] em [tex]IIII[\/tex]; transformar [tex]IX[\/tex] em [tex]VIIII[\/tex]; transformar [tex]XL[\/tex] em [tex]XXXX[\/tex]; etc.<\/li>\n<\/ul>\n<p><span style=\"color:#8B5A2B;\"><strong> Etapa 2:<\/strong> <\/span> Qualquer s\u00edmbolo que ocorra no segundo valor deve ser &#8220;riscado&#8221; no primeiro.<\/p>\n<ul>\n<li>Se um s\u00edmbolo aparecer explicitamente no primeiro n\u00famero, simplesmente risque-o.<\/li>\n<ul>\n<li>Por exemplo, na subtra\u00e7\u00e3o [tex]XXVII-XVI[\/tex], basta eliminarmos os s\u00edmbolos comuns dos dois n\u00fameros (minuendo e subtraendo):[tex]X\\bcancel{\\textcolor{#FF00FF}{X}}\\bcancel{\\textcolor{blue}{V}}I\\bcancel{\\textcolor{red}{I}}-\\bcancel{\\textcolor{#FF00FF}{X}} \\bcancel{\\textcolor{blue}{V}}\\bcancel{\\textcolor{red}{I}}[\/tex]. <\/li>\n<\/ul>\n<li>Se um s\u00edmbolo do segundo n\u00famero n\u00e3o aparecer explicitamente no primeiro, converta um s\u00edmbolo &#8220;maior&#8221; do primeiro n\u00famero em m\u00faltiplos apropriados do s\u00edmbolo a ser eliminado e, em seguida, risque-o.<\/li>\n<ul>\n<li>Na subtra\u00e7\u00e3o [tex]LV-XXII[\/tex], observe que no primeiro n\u00famero n\u00e3o temos os s\u00edmbolos [tex]I[\/tex] e [tex]X[\/tex] a serem eliminados do segundo n\u00famero. Mas podemos converter [tex]V[\/tex] em [tex]IIIII[\/tex] e [tex]L[\/tex] em [tex]XXXXX[\/tex]:<br \/>\n[tex]\\qquad \\qquad LV-XXII \\, \\mapsto \\, (XXXXX)(IIIII)-XXII[\/tex].<br \/>\n[tex]\\qquad \\qquad(XXX\\cancel{\\textcolor{blue}{XX}})(III\\cancel{\\textcolor{red}{II}})-\\cancel{\\textcolor{blue}{XX}}\\cancel{\\textcolor{red}{II}}.[\/tex]<\/li>\n<\/ul>\n<\/ul>\n<p><span style=\"color:#8B5A2B;\"><strong> Etapa 3:<\/strong> <\/span> Reescrever o primeiro n\u00famero, minuendo,  sem os s\u00edmbolos riscados.<\/li>\n<\/ul>\n<ul>\n<li> Voltando \u00e0 subtra\u00e7\u00e3o [tex]XXVII-XVI[\/tex]:<br \/>\n[tex]\\qquad \\qquad X\\bcancel{\\textcolor{#FF00FF}{X}}\\bcancel{\\textcolor{blue}{V}}I\\bcancel{\\textcolor{red}{I}}-\\bcancel{\\textcolor{#FF00FF}{X}} \\bcancel{\\textcolor{blue}{V}}\\bcancel{\\textcolor{red}{I}} \\, \\mapsto \\, XI[\/tex]. <\/li>\n<\/ul>\n<ul>\n<li>Na subtra\u00e7\u00e3o [tex]LV-XXII[\/tex]:<br \/>\n[tex]\\qquad \\qquad(XXX\\cancel{\\textcolor{blue}{XX}})(III\\cancel{\\textcolor{red}{II}})-\\cancel{\\textcolor{blue}{XX}}\\cancel{\\textcolor{red}{II}} \\, \\mapsto \\,  XXXIII[\/tex].<\/li>\n<\/ul>\n<p><span style=\"color:#8B5A2B;\"><strong> Etapa 4:<\/strong> <\/span> Verificar se existe algum agrupamento do mesmo s\u00edmbolo que possa ser substitu\u00eddo por um  \u00fanico s\u00edmbolo, de maneira que seja mantida a soma dos valores dos s\u00edmbolos que ser\u00e3o substitu\u00eddos, e fazer as respectivas substitui\u00e7\u00f5es. Se a Etapa 2  for feita com o devido cuidado, ent\u00e3o n\u00e3o haver\u00e1 nada para se fazer na  Etapa 4.<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 5:<\/strong> <\/span> Sempre que necess\u00e1rio, compactar os s\u00edmbolos finais obtidos pelas sucessivas aplica\u00e7\u00f5es da Etapa 4, utilizando as regras subtrativas.\n<\/div>\n<hr style=\"height:1px; width:100%;background-color:#8B5A2B; margin-top: 40px; margin-bottom: 5px;border: 0 none\"\/>\n<hr style=\"height:4px; width:100%;background-color:#8B5A2B;margin-top: 5px; margin-bottom: 5px; border: 0 none\"\/>\n<hr style=\"height:1px; width:100%;background-color:#8B5A2B; margin-top: 5px; margin-bottom: 30px;border: 0 none\"\/>\n<p class=\"tis1 cm\">Alguns exemplos<\/p>\n<p><strong>Exemplo 1:<\/strong> [tex]DXXVI &#8211; CXIV[\/tex]<\/p>\n<p style=\"padding-left:30px;\"><span style=\"color:#8B5A2B;\"><strong> Etapa 1:<\/strong><\/span> [tex] DXXVI &#8211;  CX\\textcolor{#00FF00}{IV} \\mapsto DXXVI  &#8211; CX(IIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 2:<\/strong><\/span>[tex]DX\\cancel{\\textcolor{blue}{X}}V\\cancel{\\textcolor{red}{I}}  &#8211; C\\cancel{\\textcolor{blue}{X}}(III\\cancel{\\textcolor{red}{I}})\\mapsto DXV-C(III)[\/tex]<br \/>\n[tex]\\qquad \\qquad \\textcolor{#00FF00}{D}X\\textcolor{#00FF00}{V}-C(III) \\, \\mapsto \\, (CCCCC)X(IIIII)-C(III)[\/tex]<br \/>\n[tex]\\qquad \\qquad (\\cancel{\\textcolor{blue}{C}}CCCC)X(\\cancel{\\textcolor{red}{III}}II)-\\cancel{\\textcolor{blue}{C}}(\\cancel{\\textcolor{red}{III}})[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 3:<\/strong><\/span> [tex] (CCCC)XII[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 4:<\/strong><\/span> [tex] (CCCC)XII[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 5:<\/strong><\/span> [tex] (\\textcolor{red}{CCCC})XII \\, \\mapsto \\, (\\textcolor{red}{CD})XII[\/tex]<\/p>\n<p>Assim, [tex]\\boxed{DXXVI &#8211; CXIV=CDXII}[\/tex]<\/p>\n<hr style=\"width:70%;border-top:4px solid #630;margin-top: 40px; margin-bottom: 40px; border-bottom:4px solid #c7b5a2; height:0px;\" \/>\n<p><strong>Exemplo 2:<\/strong> [tex]DLXIII &#8211; XCVI[\/tex]<\/p>\n<p style=\"padding-left:30px;\"><span style=\"color:#8B5A2B;\"><strong> Etapa 1:<\/strong><\/span> [tex]DLXIII &#8211; \\textcolor{#00FF00}{XC}VI  \\, \\mapsto \\,  DLXIII &#8211; LXXXXVI[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 2:<\/strong><\/span> [tex]D\\cancel{\\textcolor{#FF00FF}{L}}\\cancel{\\textcolor{blue}{X}}II\\cancel{\\textcolor{red}{I}} &#8211; \\cancel{\\textcolor{#FF00FF}{L}}XXX\\cancel{\\textcolor{blue}{X}}V\\cancel{\\textcolor{red}{I}} \\, \\mapsto \\, DII &#8211; XXXV[\/tex]<br \/>\n[tex]\\qquad \\qquad \\textcolor{#00FF00}{D}II &#8211; XXXV \\, \\mapsto \\, (CCCCC)II &#8211; XXXV[\/tex]<br \/>\n[tex]\\qquad \\qquad (CCCC\\textcolor{#00FF00}{C})II &#8211; XXXV \\, \\mapsto \\, (CCCC(LXXXXX))II &#8211; XXXV[\/tex]<br \/>\n[tex]\\qquad \\qquad (CCCC)(LXX\\cancel{\\textcolor{red}{XXX}})II &#8211; \\cancel{\\textcolor{red}{XXX}}V \\, \\mapsto \\, (CCCC)(LXX)II -V[\/tex]<br \/>\n[tex]\\qquad \\qquad (CCCC)(LX\\textcolor{#00FF00}{X})II -V \\, \\mapsto \\, (CCCC)(LX(VV))II -V [\/tex]<br \/>\n[tex]\\qquad \\qquad (CCCC)(LX(V\\cancel{\\textcolor{blue}{V}}))II -\\cancel{\\textcolor{blue}{V}} [\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 3:<\/strong><\/span> [tex](CCCC)LXVII [\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 4:<\/strong><\/span>   [tex](CCCC)LXVII [\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 5:<\/strong><\/span>  [tex] (\\textcolor{red}{CCCC})LXVII \\, \\mapsto \\, (\\textcolor{red}{CD})LXVII[\/tex]\n<\/p>\n<p>Assim, [tex]\\boxed{DLXIII &#8211; XCVI=CDLXVII}[\/tex]<\/p>\n<hr style=\"width:70%;border-top:4px solid #630;margin-top: 40px; margin-bottom: 40px; border-bottom:4px solid #c7b5a2; height:0px;\" \/>\n<p><strong>Conferindo:<\/strong> Voc\u00eas podem verificar se as contas est\u00e3o corretas, convertendo os valores para a nota\u00e7\u00e3o regular: <\/p>\n<ul>\n<li>[tex]\\boxed{DXXVI &#8211; CXIV=CDXII}\\mapsto \\boxed{526-114=412}[\/tex] &#10003;<\/li>\n<li>[tex]\\boxed{DLXIII &#8211; XCVI=CDLXVII}\\mapsto \\boxed{563-96=467}[\/tex] &#10003;<\/li>\n<\/ul>\n<\/div>\n<p class=\"fim\">\n<a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=120338\" title=\"Voltar.\" target=\"_blank\"><span style=\"color: #a56b33;\"><strong>Voltar para a P\u00e1gina Inicial.<\/strong><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Algoritmo da subtra\u00e7\u00e3o O algoritmo da subtra\u00e7\u00e3o que apresentaremos tem como finalidade obter diferen\u00e7as do tipo [tex]a-b[\/tex], sendo [tex]a,b[\/tex] n\u00fameros naturais, com [tex]a \\gt b[\/tex], e para isso o objetivo ser\u00e1 eliminar todos os s\u00edmbolos romanos que aparecem em [tex]b[\/tex]. Lembrem-se sempre disso: eliminar todos os s\u00edmbolos do segundo n\u00famero (subtraendo). O algoritmo Etapa 1: &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudos-sistema-de-numeracao-romanos-subtracao\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-120325","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/120325","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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=120325"}],"version-history":[{"count":11,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/120325\/revisions"}],"predecessor-version":[{"id":219795,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/120325\/revisions\/219795"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=120325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}