{"id":319,"date":"2017-11-02T20:00:54","date_gmt":"2017-11-02T11:00:54","guid":{"rendered":"http:\/\/tokiensis.com\/cahier\/?p=319"},"modified":"2017-11-02T22:57:35","modified_gmt":"2017-11-02T13:57:35","slug":"french-math-002","status":"publish","type":"post","link":"https:\/\/tokiensis.com\/cahier\/french-math-002\/","title":{"rendered":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff12\uff09Arithm\u00e9tique"},"content":{"rendered":"<p>\u516c\u7d04\u6570\u3001\u7d20\u6570\u3001\u65e2\u7d04\u5206\u6570\u306a\u3069\u306e\u30e1\u30e2<\/p>\n<h3>L&#8217;entier naturel non nul\u00a0<em>m<\/em> est un diviseur de l&#8217;entier naturel\u00a0<em>a<\/em> si la division de\u00a0<em>a<\/em> par\u00a0<em>m<\/em> se fait exactement, c&#8217;est-\u00e0-dire sans rest.<\/h3>\n<p>0\u3067\u306a\u3044\u81ea\u7136\u6570m\u306f\u3001\u3082\u3057\u4ed6\u306e\u81ea\u7136\u6570a\u3092m\u3067\u5272\u3063\u305f\u3068\u304d\u306e\u5546\u304c\u6b63\u78ba\u306b\u51fa\u308b\u3001\u3064\u307e\u308a\u300c\u4f59\u308a\u7121\u3057\u300d\u3067\u3042\u308c\u3070\u3001\u305d\u308c\u306fa\u306e\u9664\u6570\u3067\u3042\u308b\u3002<\/p>\n<ul>\n<li><strong>entier naturel<\/strong> \u81ea\u7136\u6570<\/li>\n<li><strong>diviseur<\/strong> \u9664\u6570<\/li>\n<\/ul>\n<h3>Soient deux entier naturels\u00a0<em>a<\/em> et\u00a0<em>b<\/em>. Si l&#8217;entier naturel non nul\u00a0<em>m<\/em> divise\u00a0<em>a<\/em> et\u00a0<em>b<\/em>, alors il est un diviseur commun \u00e0 ces deux nombres.<\/h3>\n<p>\u81ea\u7136\u6570a\u3068b\u304c\u3042\u308b\u3068\u3059\u308b\u3002\u4eee\u306b0\u3067\u306a\u3044\u81ea\u7136\u6570m\u304ca\u3068b\u3092\u5272\u308b\u306a\u3089\u3070\uff08\uff1d\u5272\u308a\u5207\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306a\u3089\u3070\uff09\u3001\u305d\u308c\u306f\u305d\u306e2\u3064\u306e\u6570\u306b\u5bfe\u3057\u3066\u306e\u516c\u7d04\u6570\u3067\u3042\u308b\u3002<\/p>\n<ul>\n<li><strong>diviseur commun<\/strong> \u516c\u7d04\u6570<\/li>\n<\/ul>\n<h3>Le PGCD de deux entiers naturels est le plus grand commun diviseur de ces deux \u00a0entiers naturels.<\/h3>\n<p>2\u3064\u306e\u81ea\u7136\u6570\u306ePGCD\uff08\u6700\u5927\u516c\u7d04\u6570\uff09\u3068\u306f2\u3064\u306e\u81ea\u7136\u6570\u306e\u4e00\u756a\u5927\u304d\u306a\u516c\u7d04\u6570\u306e\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n<ul>\n<li><strong>PGCD<\/strong>\u00a0\u6700\u5927\u516c\u7d04\u6570\u00a0<strong>P<\/strong>lus <strong>G<\/strong>rand <strong>C<\/strong>ommun <strong>D<\/strong>iviseur<\/li>\n<\/ul>\n<h3>Un nombre premier est un entier naturel divisible seulement par lui-\u00eame et par 1.<\/h3>\n<p>\u7d20\u6570\u3068\u306f\u305d\u306e\u6570\u81ea\u8eab\u30681\u306e\u307f\u3067\u5272\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u81ea\u7136\u6570\u3067\u3042\u308b\u3002<\/p>\n<ul>\n<li><strong>nombre premier<\/strong> \u7d20\u6570<\/li>\n<\/ul>\n<h3>Deux entiers naturels sont premiers entre eux si leur PGCD vaut 1.<\/h3>\n<p>2\u3064\u306e\u81ea\u7136\u6570\u306f\u3001\u305d\u308c\u3089\u306e\u6700\u5927\u516c\u7d04\u6570\u304c1\u3068\u306a\u308b\u5834\u5408\u3001\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b\u3002<\/p>\n<ul>\n<li><strong>premiers entre eux\u00a0<\/strong>\u4e92\u3044\u306b\u7d20<\/li>\n<\/ul>\n<h3>Soit la fraction\u00a0\u200b<span class=\"math inherit-color \">\\( F=\\frac{a}{b} \\)<\/span>\u200b, avec <span class=\"math inherit-color\">\\( a \\)<\/span>\u200bet\u200b<span class=\"math inherit-color\">\\( b \\)<\/span>\u200bdeux entiers naturels et\u00a0\u200b<span class=\"math inherit-color\">\\( b \\neq 0 \\)<\/span>\u200b.<\/h3>\n<p>\u5206\u6570\u200b<span class=\"math inherit-color\">\\( F=\\frac{a}{b} \\)<\/span>\u200b\u304c\u3001\u200b<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b\u3068\u200b<span class=\"math inherit-color\">\\( b \\)<\/span>\u200b\u3068\u3082\u306b\u81ea\u7136\u6570\u3067\u200b<span class=\"math inherit-color\">\\( b \\neq 0 \\)<\/span>\u200b\u306e\u524d\u63d0\u3067\u3042\u308b\u3082\u306e\u3068\u3059\u308b\u3002<\/p>\n<h3>Si\u00a0<span class=\"math inherit-color\">\\( a \\)\u00a0<\/span>\u200bet \u200b<span class=\"math inherit-color\">\\( b \\)\u00a0<\/span>sont premiers entre eux, alors \u200b<span class=\"math inherit-color _focus\">\\( F \\)\u00a0<\/span>\u200best irr\u00e9ductible.<\/h3>\n<p>\u3082\u3057<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b\u3068\u200b<span class=\"math inherit-color\">\\( b \\)<\/span>\u200b\u304c\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b\u306a\u3089\u3070\u3001<span class=\"math inherit-color\">\\( F \\)<\/span> \u306f\u65e2\u7d04\u3067\u3042\u308b\u3002<\/p>\n<ul>\n<li><strong>irr\u00e9ductible\u00a0<\/strong>\u7d04\u5206\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044 = \u65e2\u7d04\u3067\u3042\u308b<\/li>\n<li><strong>fraction irr\u00e9ductible<\/strong> \u65e2\u7d04\u5206\u6570<\/li>\n<\/ul>\n<h3>Sinon, on rend\u00a0<span class=\"math inherit-color\">\\( F \\)<\/span>\u00a0irr\u00e9ductible en divisant\u00a0<span class=\"math inherit-color _focus\">\\( a \\)<\/span>\u200bet\u200b<span class=\"math inherit-color\">\\( b \\)<\/span>\u200b par leur PGCD.<\/h3>\n<p>\u3082\u3057\u305d\u3046\u3067\u306a\u3051\u308c\u3070<span class=\"math inherit-color\">\\( F \\)<\/span>\u00a0\u306f\u00a0<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b\u3068\u200b<span class=\"math inherit-color\">\\( b \\)<\/span>\u200b \u3092\u305d\u308c\u3089\u306e\u6700\u5927\u516c\u7d04\u6570\u3067\u305d\u308c\u305e\u308c\u5272\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u65e2\u7d04\u306b\u3059\u308b\uff08\u3053\u3068\u304c\u3067\u304d\u308b\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u516c\u7d04\u6570\u3001\u7d20\u6570\u3001\u65e2\u7d04\u5206\u6570\u306a\u3069\u306e\u30e1\u30e2 L&#8217;entier naturel non nul\u00a0m est un diviseur de l&#8217;entier naturel\u00a0a si la division d &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/tokiensis.com\/cahier\/french-math-002\/\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff12\uff09Arithm\u00e9tique&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[51],"tags":[57],"jetpack_publicize_connections":[],"aioseo_notices":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9fXRE-59","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":362,"url":"https:\/\/tokiensis.com\/cahier\/french-math-003\/","url_meta":{"origin":319,"position":0},"title":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff13\uff09Racines carr\u00e9es et puissance","date":"2017\u5e7411\u67088\u65e5","format":false,"excerpt":"\u5e73\u65b9\u6839\u3068\u4e57\u6570\u306e\u30ce\u30fc\u30c8 Soit\u00a0\u200b\\( a \\)\u200b un nombre positif. \u6b63\u306e\u6570 \u200b\u2026","rel":"","context":"\u30d5\u30e9\u30f3\u30b9\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":307,"url":"https:\/\/tokiensis.com\/cahier\/french-math-001\/","url_meta":{"origin":319,"position":1},"title":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff11\uff09Calculs sur les fractions","date":"2017\u5e7410\u670831\u65e5","format":false,"excerpt":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u3067\u5206\u6570\u306e\u8a08\u7b97\u3092\u5b66\u7fd2\u3057\u305f\u3068\u304d\u306e\u30ce\u30fc\u30c8 Pour additionner (ou soustr\u2026","rel":"","context":"\u30d5\u30e9\u30f3\u30b9\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":471,"url":"https:\/\/tokiensis.com\/cahier\/french-accords-des-participes-passes\/","url_meta":{"origin":319,"position":2},"title":"\u30d5\u30e9\u30f3\u30b9\u8a9e\uff1a\u904e\u53bb\u5206\u8a5e\u306e\u6027\u6570\u4e00\u81f4","date":"2018\u5e7412\u670822\u65e5","format":false,"excerpt":"\u81ea\u52d5\u8a5e\u3068\u4ed6\u52d5\u8a5e\u3067\u306e\u904e\u53bb\u5206\u8a5e\u306e\u6027\u6570\u4e00\u81f4\u306e\u307e\u3068\u3081\u3002\u6027\u6570\u5909\u5316\u3059\u308b\u5834\u5408\u306f\u8d64\u3001\u3057\u306a\u3044\u5834\u5408\u306f\u9752 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it\u2026","rel":"","context":"\u30a4\u30bf\u30ea\u30a2\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":486,"url":"https:\/\/tokiensis.com\/cahier\/about-yokohama-dialect\/","url_meta":{"origin":319,"position":4},"title":"\u6a2a\u6d5c\u65b9\u8a00\u3042\u308b\u3044\u306f\u6a2a\u6d5c\u30d4\u30b8\u30f3\u65e5\u672c\u8a9e\u306b\u3064\u3044\u3066","date":"2019\u5e743\u670828\u65e5","format":false,"excerpt":"\u6a2a\u6d5c\u30d4\u30b8\u30f3\u65e5\u672c\u8a9e\u306e\u8a95\u751f \u30d4\u30b8\u30f3\u8a00\u8a9e\u3068\u306f\u4e3b\u306b\u4ea4\u6613\u306a\u3069\u3092\u884c\u3046\u7570\u306a\u308b\u8907\u6570\u306e\u8a00\u8a9e\u96c6\u56e3\u304c\u63a5\u89e6\u3059\u308b\u3068\u304d\u306b\u81ea\u7136\u767a\u751f\u2026","rel":"","context":"\u6a2a\u6d5c\u30d4\u30b8\u30f3\u65e5\u672c\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":104,"url":"https:\/\/tokiensis.com\/cahier\/memento-german-01\/","url_meta":{"origin":319,"position":5},"title":"\u30c9\u30a4\u30c4\u8a9e\u6587\u6cd5\u306e\u307e\u3068\u3081\uff08\uff11\uff09","date":"2017\u5e7410\u67083\u65e5","format":false,"excerpt":"\u6027\u6570\u5909\u5316\u306b\u3064\u3044\u3066 \u30c9\u30a4\u30c4\u8a9e\u306b\u306f\u7537\u6027\u3001\u4e2d\u6027\u3001\u5973\u6027\u306e\u5909\u5316\u304c\u3042\u308a\u3001\u8f9e\u66f8\u3067\u306f\u305d\u308c\u305e\u308c\u5b9a\u51a0\u8a5eder, das,\u2026","rel":"","context":"\u30c9\u30a4\u30c4\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts\/319"}],"collection":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/comments?post=319"}],"version-history":[{"count":3,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts\/319\/revisions"}],"predecessor-version":[{"id":361,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts\/319\/revisions\/361"}],"wp:attachment":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/media?parent=319"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/categories?post=319"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/tags?post=319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}