{"id":10308,"date":"2012-10-13T16:20:48","date_gmt":"2012-10-13T15:20:48","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10308"},"modified":"2022-01-10T23:22:46","modified_gmt":"2022-01-10T23:22:46","slug":"usando-dois-processos-determina","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10308","title":{"rendered":"Usando dois processos, determina"},"content":{"rendered":"<p><ul id='GTTabs_ul_10308' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10308' class='GTTabs_curr'><a  id=\"10308_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10308' ><a  id=\"10308_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_10308'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Usando dois processos, determina:<\/p>\n<ol>\n<li>$\\left( { + 3} \\right) \\times \\left( { &#8211; 7} \\right) \\times \\left( { + 2} \\right)$<\/li>\n<li>$\\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 2} \\right)$<\/li>\n<li>$\\left( { + 3} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 5} \\right) \\times \\left( { + 1} \\right)$<\/li>\n<li>$\\left( { + 2} \\right) \\times \\left( { + 5} \\right) \\times \\left( { &#8211; 2} \\right)$<\/li>\n<li>$\\left( { &#8211; 8} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 1} \\right)$<\/li>\n<li>$\\left( { &#8211; 1} \\right) \\times \\left( { &#8211; 10} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 5} \\right)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10308' onClick='GTTabs_show(1,10308)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10308'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>$$\\left( { + 3} \\right) \\times \\left( { &#8211; 7} \\right) \\times \\left( { + 2} \\right)$$<br \/>\nAplicando a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left[ {\\left( { + 3} \\right) \\times \\left( { &#8211; 7} \\right)} \\right] \\times \\left( { + 2} \\right)}&amp; = &amp;{ &#8211; 21 \\times 2} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 42} \\end{array}$$<br \/>\nAplicando novamente a propriedade associativa da multiplica\u00e7\u00e3o, mas associando agora os dois \u00faltimos fatores:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( { + 3} \\right) \\times \\left[ {\\left( { &#8211; 7} \\right) \\times \\left( { + 2} \\right)} \\right]}&amp; = &amp;{3 \\times \\left( { &#8211; 14} \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 42} \\end{array}$$<br \/>\n\u00ad<\/li>\n<li>$$\\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 2} \\right)$$<br \/>\nAplicando a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left[ {\\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 2} \\right)} \\right] \\times \\left( { &#8211; 2} \\right)}&amp; = &amp;{8 \\times \\left( { &#8211; 2} \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 16} \\end{array}$$<br \/>\nAplicando novamente a propriedade associativa da multiplica\u00e7\u00e3o, mas associando agora os dois \u00faltimos fatores:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( { &#8211; 4} \\right) \\times \\left[ {\\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 2} \\right)} \\right]}&amp; = &amp;{ &#8211; 4 \\times 4} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 16} \\end{array}$$<br \/>\n\u00ad<\/li>\n<li>$$\\left( { + 3} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 5} \\right) \\times \\left( { + 1} \\right)$$<br \/>\nAplicando a propriedade associativa e a propriedade de exist\u00eancia de elemento neutro da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left[ {\\left( { + 3} \\right) \\times \\left( { &#8211; 2} \\right)} \\right] \\times \\left[ {\\left( { &#8211; 5} \\right) \\times \\left( { + 1} \\right)} \\right]}&amp; = &amp;{ &#8211; 6 \\times \\left( { &#8211; 5} \\right)} \\\\ \u00a0 {}&amp; = &amp;{30} \\end{array}$$<br \/>\nAplicando a propriedade de exist\u00eancia de elemento neutro e a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( { + 3} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 5} \\right) \\times \\left( { + 1} \\right)}&amp; = &amp;{\\left[ {\\left( { + 3} \\right) \\times \\left( { &#8211; 2} \\right)} \\right] \\times \\left( { &#8211; 5} \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 6 \\times \\left( { &#8211; 5} \\right)} \\\\ \u00a0 {}&amp; = &amp;{30} \\end{array}$$<br \/>\n\u00ad<\/li>\n<li>$$\\left( { + 2} \\right) \\times \\left( { + 5} \\right) \\times \\left( { &#8211; 2} \\right)$$<br \/>\nAplicando a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left[ {\\left( { + 2} \\right) \\times \\left( { + 5} \\right)} \\right] \\times \\left( { &#8211; 2} \\right)}&amp; = &amp;{10 \\times \\left( { &#8211; 2} \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 20} \\end{array}$$<br \/>\nAplicando a propriedade comutativa e a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( { + 2} \\right) \\times \\left( { + 5} \\right) \\times \\left( { &#8211; 2} \\right)}&amp; = &amp;{\\left[ {\\left( { + 2} \\right) \\times \\left( { &#8211; 2} \\right)} \\right] \\times 5} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 4 \\times 5} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 20} \\end{array}$$<br \/>\n\u00ad<\/li>\n<li>$$\\left( { &#8211; 8} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 1} \\right)$$<br \/>\nAplicando a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left[ {\\left( { &#8211; 8} \\right) \\times \\left( { &#8211; 2} \\right)} \\right] \\times \\left[ {\\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 1} \\right)} \\right]}&amp; = &amp;{16 \\times 3} \\\\ \u00a0 {}&amp; = &amp;{48} \\end{array}$$<br \/>\nAplicando a propriedade comutativa e a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( { &#8211; 8} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 1} \\right)}&amp; = &amp;{\\left[ {\\left( { &#8211; 8} \\right) \\times \\left( { &#8211; 3} \\right)} \\right] \\times \\left[ {\\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 1} \\right)} \\right]} \\\\ \u00a0 {}&amp; = &amp;{24 \\times 2} \\\\ \u00a0 {}&amp; = &amp;{48} \\end{array}$$<br \/>\n\u00ad<\/li>\n<li>$$\\left( { &#8211; 1} \\right) \\times \\left( { &#8211; 10} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 5} \\right)$$<br \/>\nAplicando a propriedade associativa da multiplica\u00e7\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left[ {\\left( { &#8211; 1} \\right) \\times \\left( { &#8211; 10} \\right) \\times \\left( { &#8211; 3} \\right)} \\right] \\times \\left[ {\\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 5} \\right)} \\right]}&amp; = &amp;{ &#8211; 30 \\times 20} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 600} \\end{array}$$<br \/>\nAplicando a propriedade associativa da multiplica\u00e7\u00e3o (mas associando fatores diferentes):<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( { &#8211; 1} \\right) \\times \\left( { &#8211; 10} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 5} \\right)}&amp; = &amp;{\\left[ {\\left( { &#8211; 1} \\right) \\times \\left( { &#8211; 10} \\right)} \\right] \\times \\left[ {\\left( { &#8211; 3} \\right) \\times \\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 5} \\right)} \\right]} \\\\ \u00a0 {}&amp; = &amp;{10 \\times \\left( { &#8211; 60} \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 600} \\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10308' onClick='GTTabs_show(0,10308)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Usando dois processos, determina: $\\left( { + 3} \\right) \\times \\left( { &#8211; 7} \\right) \\times \\left( { + 2} \\right)$ $\\left( { &#8211; 4} \\right) \\times \\left( { &#8211; 2}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19176,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[428,320,327],"series":[],"class_list":["post-10308","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7-o-ano","category-aplicando","category-numeros-inteiros","tag-7-o-ano","tag-multiplicacao","tag-propriedades-da-multiplicacao"],"views":2066,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat67.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10308","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=10308"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10308\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19176"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10308"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10308"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}