{"id":119505,"date":"2019-01-09T00:39:08","date_gmt":"2019-01-09T02:39:08","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=119505"},"modified":"2024-06-04T00:12:07","modified_gmt":"2024-06-04T03:12:07","slug":"sala-de-estudo-operacoes-com-algarismos-romanos-adicao","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudo-operacoes-com-algarismos-romanos-adicao\/","title":{"rendered":".Sala de Estudo:  Opera\u00e7\u00f5es com algarismos romanos &#8211; ADI\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=\"margin:10px;line-height:40px;\">Algoritmo da adi\u00e7\u00e3o<\/p>\n<hr style=\"height:2px; background-color:#8B5A2B; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p style=\"margin:40px 60px 10px 60px;\">\nEste algoritmo da adi\u00e7\u00e3o entre n\u00fameros representados a partir do sistema de numera\u00e7\u00e3o romano tem como finalidade obter somas do tipo <\/p>\n<p>[tex]\\qquad \\qquad \\quad \\quad \\boxed{a_1+a_2+ \\cdots +a_n} \\, [\/tex], sendo [tex]a_1,a_2,\\cdots,a_n[\/tex] n\u00fameros naturais n\u00e3o nulos. <\/p>\n<p style=\"margin:10px 60px 50px 60px;\">\nA vers\u00e3o apresentada tem cinco etapas e descreve o processo para somas com duas parcelas, mas pode ser facilmente generalizada para soma com mais parcelas.<\/p>\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 uma das parcelas a serem somadas.<\/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> Agrupar todos os s\u00edmbolos de mesmo valor, independente da parcela em que estejam.<\/p>\n<ul>\n<li>Por exemplo:  [tex](CCCCC)[\/tex];  [tex](XXX)[\/tex];  [tex](IIII)[\/tex]; [tex](VVVVV)[\/tex]; [tex](LL)[\/tex]; etc.<\/li>\n<\/ul>\n<p><span style=\"color:#8B5A2B;\"><strong> Etapa 3:<\/strong> <\/span> Se necess\u00e1rio, organizar todos os s\u00edmbolos em ordem, da esquerda para a direita, com os s\u00edmbolos de maior valor \u00e0 esquerda.<\/p>\n<ul>\n<li>  [tex](M\\cdots M)[\/tex];  [tex](D \\cdots D)[\/tex];  [tex](C \\cdots C)[\/tex]; [tex](L \\cdots L)[\/tex]; [tex](X \\cdots X)[\/tex]; [tex](V \\cdots V)[\/tex];  [tex](I \\cdots I)[\/tex].<\/li>\n<\/ul>\n<p><span style=\"color:#8B5A2B;\"><strong> Etapa 4:<\/strong> <\/span> Come\u00e7ando pelo lado direito, agrupar s\u00edmbolos iguais que possam ser substitu\u00eddos 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. (Mantenha sempre a ordem estabelecida pela Etapa 3.)<\/p>\n<ul>\n<li>Por exemplo: transformar [tex]IIIII[\/tex] em [tex]V[\/tex]; transformar [tex]XXXXX[\/tex] em [tex]L[\/tex]; transformar [tex]CCCCC[\/tex] em [tex]D[\/tex]; etc.<\/li>\n<\/ul>\n<p><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: 40px;border: 0 none\"\/>\n<p class=\"tis1 cm\">Alguns exemplos<\/p>\n<p><strong>Exemplo 1:<\/strong> [tex]CCXIX + XLVII[\/tex]<\/p>\n<p style=\"padding-left:30px;\"><span style=\"color:#8B5A2B;\"><strong> Etapa 1:<\/strong><\/span> [tex]CCX\\textcolor{#00FF00}{IX} + \\textcolor{#00FF00}{XL}VII \\mapsto CCXVIIII + XXXXVII[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 2:<\/strong><\/span> [tex](CC) \\, (XXXXX) \\, (VV) \\, (IIIIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 3:<\/strong><\/span> [tex](CC) \\, (XXXXX) \\, (VV) \\, (IIIIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 4:<\/strong><\/span> [tex](CC) \\, (XXXXX) \\, (VV) \\, (\\textcolor{red}{IIIII}I) \\mapsto  \\,  (CC) \\, (XXXXX)(VV\\textcolor{red}{V})I[\/tex]<br \/>\n[tex]\\qquad\\qquad  (CC) \\, (XXXXX) \\, (\\textcolor{blue}{VV}V)I \\mapsto (CC) \\, (XXXXX\\textcolor{blue}{X})VI[\/tex]<br \/>\n[tex]\\qquad\\qquad  (CC)(\\textcolor{#FF00FF}{XXXXX}X)VI \\mapsto (CC)(\\textcolor{#FF00FF}{L})XVI[\/tex]<br \/>\n[tex]\\qquad\\qquad  (CC)LXVI[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 5:<\/strong><\/span> [tex]CCLXVI[\/tex]<\/p>\n<p>Assim, [tex]\\boxed{CCXIX + XLVII=CCLXVI}[\/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 + XCVI[\/tex]<\/p>\n<p style=\"padding-left:30px;\"><span style=\"color:#8B5A2B;\"><strong> Etapa 1:<\/strong><\/span> [tex]DLXIII + \\textcolor{#00FF00}{XC}VI \\mapsto DLXIII + LXXXXVI[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 2:<\/strong><\/span> [tex](D) \\, (LL) \\, (XXXXX) \\, (V) \\, (IIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 3:<\/strong><\/span> [tex](D) \\, (LL) \\, (XXXXX) \\, (V) \\, (IIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 4:<\/strong><\/span> [tex](D) \\, (LL) \\, (\\textcolor{red}{XXXXX}) \\, (V) \\, (IIII) \\, \\mapsto  \\,  (D) \\, (LL\\textcolor{red}{L}) \\, (V) \\, (IIII)[\/tex]<br \/>\n[tex]\\qquad\\qquad  (D) \\, (\\textcolor{blue}{LL}L) \\, (V) \\, (IIII) \\mapsto (D) \\, (\\textcolor{blue}{C}) \\, LV \\, (IIII)[\/tex]<br \/>\n[tex]\\qquad\\qquad  (D) \\, CLV \\, (IIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 5:<\/strong><\/span> [tex] DCL\\textcolor{#00FF00}{VIIII} \\mapsto  DCLIX[\/tex]<\/p>\n<p>Logo, [tex]\\boxed{DLXIII + XCVI=DCLIX}[\/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 3:<\/strong> [tex]CCXV+ CCCXXXIII+LXXIX[\/tex]<\/p>\n<p style=\"padding-left:10px;\"><span style=\"color:#8B5A2B;\"><strong> Etapa 1:<\/strong><\/span><br \/>\n[tex]CCXV+ CCCXXXIII+LXX\\textcolor{#00FF00}{IX} \\, \\mapsto  \\,  CCXV+ CCCXXXIII+LXXVIIII[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 2:<\/strong><\/span><br \/>\n[tex](CCCCC) \\, (L) \\, (XXXXXX) \\, (VV) \\, (IIIIIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 3:<\/strong><\/span><br \/>\n[tex](CCCCC) \\, (L) \\, (XXXXXX) \\, (VV) \\, (IIIIIII)[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 4:<\/strong><\/span><br \/>\n[tex](CCCCC) \\, (L) \\, (XXXXXX) \\, (VV) \\, (\\textcolor{red}{IIIII}II)  \\mapsto  (CCCCC) \\, (L) \\, (XXXXXX) \\, (VV) \\, \\textcolor{red}{V}II[\/tex]<br \/>\n[tex](CCCCC) \\, (L) \\, (XXXXXX) \\, (\\textcolor{blue}{VV}V)II  \\mapsto  (CCCCC) \\, (L) \\, (XXXXXX) \\, \\textcolor{blue}{X}VII[\/tex]<br \/>\n[tex](CCCCC) \\, (L) \\, (\\textcolor{#FF00FF}{XXXXX}XX)VII  \\mapsto  (CCCCC) \\, (L) \\, \\textcolor{#FF00FF}{L}XXVII[\/tex]<br \/>\n[tex](CCCCC) \\, (\\textcolor{#00BFFF}{LL}) \\, XXVII  \\mapsto  (CCCCC) \\, (\\textcolor{#00BFFF}{C}) \\, XXVII[\/tex]<br \/>\n[tex](\\textcolor{#912CEE}{CCCCC}C)XXVII  \\mapsto  \\textcolor{#912CEE}{D}CXXVII[\/tex]<br \/>\n[tex]DCXXVII[\/tex]<br \/>\n<span style=\"color:#8B5A2B;\"><strong> Etapa 5:<\/strong><\/span> [tex] DCXXVII[\/tex]<\/p>\n<p>Logo, [tex]\\boxed{CCXV+ CCCXXXIII+LXXIX=DCXXVII}[\/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{CCXIX + XLVII=CCLXVI}\\mapsto \\boxed{219+47=266}[\/tex] &#10003;<\/li>\n<li>[tex]\\boxed{DLXIII + XCVI=DCLIX}\\mapsto \\boxed{563+96=659}[\/tex] &#10003;<\/li>\n<li>[tex]\\boxed{CCXV+ CCCXXXIII+LXXIX=DCXXVII}\\mapsto \\boxed{215+333+79=627}[\/tex] &#10003;<\/li>\n<\/ul>\n<\/div>\n<p class=\"fim\">\n<a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=120097\" 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 adi\u00e7\u00e3o Este algoritmo da adi\u00e7\u00e3o entre n\u00fameros representados a partir do sistema de numera\u00e7\u00e3o romano tem como finalidade obter somas do tipo [tex]\\qquad \\qquad \\quad \\quad \\boxed{a_1+a_2+ \\cdots +a_n} \\, [\/tex], sendo [tex]a_1,a_2,\\cdots,a_n[\/tex] n\u00fameros naturais n\u00e3o nulos. A vers\u00e3o apresentada tem cinco etapas e descreve o processo para somas com duas parcelas, mas &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudo-operacoes-com-algarismos-romanos-adicao\/\">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-119505","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/119505","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=119505"}],"version-history":[{"count":14,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/119505\/revisions"}],"predecessor-version":[{"id":219753,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/119505\/revisions\/219753"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=119505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}