{"id":149,"date":"2008-04-28T15:46:33","date_gmt":"2008-04-28T13:46:33","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/larithmetique-au-college-avec-xcas\/"},"modified":"2023-10-14T20:13:45","modified_gmt":"2023-10-14T18:13:45","slug":"larithmetique-au-college-avec-xcas","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/arithmetique-avec-xcas\/larithmetique-au-college-avec-xcas\/","title":{"rendered":"L&rsquo;arithm\u00e9tique au coll\u00e8ge avec Xcas"},"content":{"rendered":"<p>Voici comment on peut r\u00e9soudre un exercice classique de brevet sur l&rsquo;arithm\u00e9tique.<\/p>\n<h2>Enonc\u00e9<\/h2>\n<hr>\n<p>1) Calculer le PGCD de <span class=\"katex-eq\" data-katex-display=\"false\">114\\,400<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">60\\,775<\/span>.<\/p>\n<p>2) Simplifier la fraction <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{60\\,775}{114\\,400}<\/span>.<\/p>\n<h2>R\u00e9solution \u00e0 l&rsquo;aide de Xcas<\/h2>\n<hr>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\nA:=114400<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">114400<\/span>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\nB:=60775<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">60775<\/span>\n<p>1) Calculer le PGCD de <span class=\"katex-eq\" data-katex-display=\"false\">114\\,400<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">60\\,775<\/span>.<\/p>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\ngcd(A,B)<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">3575<\/span>\n<p>Si on veut les d\u00e9tails ;<\/p>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\niquorem(114400,60775)<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">[1,53625]<\/span>\n<p><em>Interpr\u00e9tation :<\/em> <span class=\"katex-eq\" data-katex-display=\"false\">114\\,400=60\\,775 \\times 1 +53\\,625<\/span>.<\/p>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\niquorem(60775,53625)<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">[1,7150]<\/span><br \/>\n<em><br \/>\nInterpr\u00e9tation :<\/em> <span class=\"katex-eq\" data-katex-display=\"false\">60\\,775=53\\,625 \\times 1 +7\\,150<\/span>.<\/p>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\niquorem(53625,7150)<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">[7,3575]<\/span><br \/>\n<em><br \/>\nInterpr\u00e9tation :<\/em> <span class=\"katex-eq\" data-katex-display=\"false\">53\\,625=7\\,150 \\times 7 +3\\,575<\/span>.<\/p>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\niquorem(7150,3575)<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">[2,0]<\/span><br \/>\n<em><br \/>\nInterpr\u00e9tation<\/em> : <span class=\"katex-eq\" data-katex-display=\"false\">7\\,150=3\\,575 \\times 2 +0<\/span>.<\/p>\n<p>2) Simplifier la fraction <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{60\\,775}{114\\,400}<\/span>.<\/p>\n<p><span style=\"color: red;\"><br \/>\n<code><br \/>\nA\/B<br \/>\n<\/code><br \/>\n<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\frac{32}{17}<\/span>\n","protected":false},"excerpt":{"rendered":"<p>Voici comment on peut r\u00e9soudre un exercice classique de brevet sur l&rsquo;arithm\u00e9tique. Enonc\u00e9 1) Calculer le PGCD de et . 2) Simplifier la fraction . R\u00e9solution \u00e0 l&rsquo;aide de Xcas&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2222,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-149","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>L&#039;arithm\u00e9tique au coll\u00e8ge avec Xcas - Maths &amp; Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/arithmetique-avec-xcas\/larithmetique-au-college-avec-xcas\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"L&#039;arithm\u00e9tique au coll\u00e8ge avec Xcas - Maths &amp; Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Voici comment on peut r\u00e9soudre un exercice classique de brevet sur l&rsquo;arithm\u00e9tique. 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