{"id":10295,"date":"2012-10-13T14:11:45","date_gmt":"2012-10-13T13:11:45","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10295"},"modified":"2021-12-31T23:21:53","modified_gmt":"2021-12-31T23:21:53","slug":"indica-se-as-igualdades-sao-verdadeiras-ou-falsas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10295","title":{"rendered":"Indica se as igualdades s\u00e3o verdadeiras ou falsas"},"content":{"rendered":"<p><ul id='GTTabs_ul_10295' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10295' class='GTTabs_curr'><a  id=\"10295_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10295' ><a  id=\"10295_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_10295'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Indica se as igualdades abaixo s\u00e3o verdadeiras ou falsas. Nas verdadeiras indica a propriedade da multiplica\u00e7\u00e3o usada. Corrige as falsas.<\/p>\n<ol>\n<li>$\\left( { + 5} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { + 2} \\right) = \\left( { &#8211; 3} \\right) \\times \\left( { + 5} \\right) \\times \\left( { + 2} \\right)$<\/li>\n<li>$\\left( { &#8211; 7} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 3} \\right) = \\left( { &#8211; 7} \\right) \\times \\left( { &#8211; 6} \\right)$<\/li>\n<li>$ &#8211; 4 \\times \\left( {8 &#8211; 5} \\right) =\u00a0 &#8211; 32 &#8211; 20$<\/li>\n<li>$3 \\times 1 = 1$<\/li>\n<li>$2 \\times 0 = 0$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10295' onClick='GTTabs_show(1,10295)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10295'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>$$\\left( { + 5} \\right) \\times \\left( { &#8211; 3} \\right) \\times \\left( { + 2} \\right) = \\left( { &#8211; 3} \\right) \\times \\left( { + 5} \\right) \\times \\left( { + 2} \\right)$$<br \/>\nA igualdade \u00e9 verdadeira. Foi usada a <span style=\"text-decoration: underline;\">propriedade comutativa<\/span> da multiplica\u00e7\u00e3o: <span style=\"color: #0000ff;\">$a \\times b = b \\times a$<\/span>.<br \/>\n\u00ad<\/li>\n<li><span style=\"color: #ff0000;\">$$\\left( { &#8211; 7} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 3} \\right) = \\left( { &#8211; 7} \\right) \\times \\underbrace {\\left( { &#8211; 6} \\right)}_{Erro!}$$<\/span><br \/>\nA igualdade \u00e9 falsa. Pretendia-se utilizar a <span style=\"text-decoration: underline;\">propriedade associativa<\/span> da multiplica\u00e7\u00e3o: <span style=\"color: #0000ff;\">$\\left( {a \\times b} \\right) \\times c = a \\times \\left( {b \\times c} \\right)$<\/span>.<br \/>\nA igualdade corrigida \u00e9:<br \/>\n<span style=\"color: #008000;\">$$\\left( { &#8211; 7} \\right) \\times \\left( { &#8211; 2} \\right) \\times \\left( { &#8211; 3} \\right) = \\left( { &#8211; 7} \\right) \\times \\underbrace {\\left( { + 6} \\right)}_{Certo!}$$<br \/>\n\u00ad<br \/>\n<\/span><\/li>\n<li><span style=\"color: #ff0000;\">$$ &#8211; 4 \\times \\left( {8 &#8211; 5} \\right) =\u00a0 &#8211; 32\\underbrace { &#8211; 20}_{Erro!}$$<\/span><br \/>\nA igualdade \u00e9 falsa. Pretendia-se utilizar a <span style=\"text-decoration: underline;\">propriedade distributiva<\/span> da multiplica\u00e7\u00e3o em rela\u00e7\u00e3o \u00e0 adi\u00e7\u00e3o: <span style=\"color: #0000ff;\">$a \\times \\left( {b + c} \\right) = a \\times b + a \\times c$<\/span>.<br \/>\nA igualdade corrigida \u00e9:<br \/>\n<span style=\"color: #008000;\">$$ &#8211; 4 \\times \\left( {8 &#8211; 5} \\right) =\u00a0 &#8211; 32\\underbrace { + 20}_{Certo!}$$<\/span><br \/>\nCom efeito, tem-se:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 { &#8211; 4 \\times \\left( {8 &#8211; 5} \\right)}&amp; = &amp;{ &#8211; 4 \\times 8 &#8211; 4 \\times \\left( { &#8211; 5} \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 32 + 20} \\end{array}$$<br \/>\n\u00ad<\/li>\n<li><span style=\"color: #ff0000;\">$$3 \\times 1 = \\underbrace 1_{Erro!}$$<\/span><br \/>\nA igualdade \u00e9 falsa. Pretendia-se utilizar a propriedade da exist\u00eancia de <span style=\"text-decoration: underline;\">elemento neutro<\/span> da multiplica\u00e7\u00e3o (o n\u00famero $1$): <span style=\"color: #0000ff;\">$a \\times 1 = 1 \\times a = a$<\/span>.<br \/>\nA igualdade corrigida \u00e9:<br \/>\n<span style=\"color: #008000;\">$$3 \\times 1 = \\underbrace 3_{Certo!}$$<br \/>\n\u00ad<br \/>\n<\/span><\/li>\n<li>$$2 \\times 0 = 0$$<br \/>\nA igualdade \u00e9 verdadeira. Foi usada a propriedade da exist\u00eancia de <span style=\"text-decoration: underline;\">elemento absorvente<\/span> da multiplica\u00e7\u00e3o (o n\u00famero $0$): <span style=\"color: #0000ff;\">$a \\times 0 = 0 \\times a = 0$<\/span>.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10295' onClick='GTTabs_show(0,10295)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Indica se as igualdades abaixo s\u00e3o verdadeiras ou falsas. Nas verdadeiras indica a propriedade da multiplica\u00e7\u00e3o usada. Corrige as falsas. $\\left( { + 5} \\right) \\times \\left( { &#8211; 3} \\right)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19266,"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-10295","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":3804,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat87.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10295","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=10295"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10295\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10295"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}