{"id":93422,"date":"2017-01-09T14:58:50","date_gmt":"2017-01-09T16:58:50","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=93422"},"modified":"2026-05-18T16:23:52","modified_gmt":"2026-05-18T18:23:52","slug":"divisao-proporcional","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/divisao-proporcional","title":{"rendered":"Divis\u00e3o Proporcional"},"content":{"rendered":"<p>A\u00a0<b>divis\u00e3o proporcional<\/b>\u00a0divide um valor total em partes com base em \u00edndices ou quotas espec\u00edficas, garantindo que cada benefici\u00e1rio receba uma parte proporcional ao seu valor.<\/p>\n<p>\u00c0s vezes nos deparamos com problemas que solicitam a divis\u00e3o de um n\u00famero em partes diretamente proporcionais a outro grupo de n\u00fameros.<\/p>\n<p>A divis\u00e3o de um n\u00famero em partes diretamente proporcionais a outros n\u00fameros dados, consiste em se determinar as parcelas que s\u00e3o diretamente proporcionais a cada um dos n\u00fameros dados e que somadas, totalizam o n\u00famero original.<\/p>\n<p><b>A divis\u00e3o do n\u00famero N\u00a0em partes\u00a0p<sub>1<\/sub>, p<sub>2<\/sub>, p<sub>3<\/sub>, &#8230;, p<sub>n<\/sub> diretamente proporcionais aos n\u00fameros reais, diferentes de zero a<sub>1<\/sub>, a<sub>2<\/sub>, a<sub>3<\/sub>, &#8230;, a<sub>n<\/sub> respectivamente, baseia-se em encontrar a constante K, real n\u00e3o nula, tal que:<\/b><\/p>\n<p align=\"center\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-177830\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/divisao-proporcional.gif\" alt=\"Divis\u00e3o Proporcional\" width=\"229\" height=\"199\" \/><\/p>\n<p>Depois de calculado o valor da constante\u00a0<b>K<\/b>, basta substitu\u00ed-lo nas igualdades onde foi usado e realizar as contas para descobrir o valor de cada uma das partes.<\/p>\n<p><b>Exemplos<\/b><\/p>\n<p class=\"Pergunta\">Divida o n\u00famero 630 em partes diretamente proporcionais a 6, 7, 8 e 9.<\/p>\n<p><b>Conforme o explicado sabemos que:<\/b><\/p>\n<p><b>p1 = K . 6<br \/>\np2 = K . 7<br \/>\np3 = K . 8<br \/>\np4 = K . 9<br \/>\np1 + p2 + p3 + p4 = 630<\/b><\/p>\n<p><b>Para encontrarmos o valor da constante K devemos substituir o valor de p<sub>1<\/sub>, p<sub>2<\/sub>, p<sub>3<\/sub>\u00a0e p<sub>4<\/sub>\u00a0na \u00faltima igualdade<\/b>:<\/p>\n<p><b>Logo:<\/b><\/p>\n<p><b>p1 = 21 . 6 = 126<br \/>\np2 = 21 . 7 = 147<br \/>\np3 = 21 . 8 = 168<br \/>\np4 = 21 . 9 = 189<\/b><\/p>\n<p align=\"left\"><b>Resposta:\u00a0<\/b>As partes procuradas s\u00e3o respectivamente 126, 147, 168 e 189.<\/p>\n<p class=\"Pergunta\">Divida o n\u00famero 140 em parcelas diretamente proporcionais a 2, 4 e 8.<\/p>\n<p><b>Do enunciado tiramos que:<\/b><\/p>\n<p><b>p1\u00a0=\u00a0K\u00a0.\u00a02<br \/>\np2\u00a0=\u00a0K\u00a0.\u00a04<br \/>\np3\u00a0=\u00a0K\u00a0.\u00a08<br \/>\np1\u00a0+\u00a0p2\u00a0+\u00a0p3\u00a0=\u00a0140<\/b><\/p>\n<p><b>Para encontrarmos o valor da constante K devemos substituir o valor de p<sub>1<\/sub>, p<sub>2<\/sub>\u00a0e p<sub>3<\/sub>\u00a0na \u00faltima express\u00e3o<\/b>:<\/p>\n<p><b>Portanto:<\/b><\/p>\n<p><b>p1 = K . 2<br \/>\np2 = K . 4<br \/>\np3 = K . 8<br \/>\np1 + p2 + p3 = 140<\/b><\/p>\n<p><b>Resposta:<\/b>\u00a0As parcelas procuradas s\u00e3o respectivamente 20, 40 e 80.<\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/www.matematicadidatica.com.br<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A\u00a0divis\u00e3o proporcional\u00a0divide um valor total em partes com base em \u00edndices ou quotas espec\u00edficas, garantindo que cada benefici\u00e1rio receba uma parte proporcional ao seu valor. \u00c0s vezes nos deparamos com problemas que solicitam a divis\u00e3o de um n\u00famero em partes diretamente proporcionais a outro grupo de n\u00fameros. A divis\u00e3o de um n\u00famero em partes diretamente [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-93422","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Divis\u00e3o Proporcional, N\u00famero, Valor Divis\u00e3o Proporcional<\/title>\n<meta name=\"description\" content=\"Divis\u00e3o Proporcional, N\u00famero, Valor, Determinar, Partes, Parcelas, \u00cdndices, Express\u00e3o, Exemplos, Divis\u00e3o Proporcional\" \/>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta 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