{"id":4421,"date":"2025-02-01T14:14:40","date_gmt":"2025-02-01T13:14:40","guid":{"rendered":"https:\/\/www.gastonternes.eu\/?page_id=4421"},"modified":"2025-07-09T15:53:17","modified_gmt":"2025-07-09T13:53:17","slug":"mpr-solutions-ch-7","status":"publish","type":"page","link":"https:\/\/www.gastonternes.eu\/de\/mpr-solutions-ch-7\/","title":{"rendered":"Maths: Plaisir et r\u00e9ussite &#8211; Solutions &#8211; Chapitre 7"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"4421\" class=\"elementor elementor-4421\" data-elementor-settings=\"[]\">\n\t\t\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-760a9ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"760a9ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div 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data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t   <!DOCTYPE html>\n<html lang=\"en\">\n<head>\n    <meta charset=\"UTF-8\">\n    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n    <style>\n   .header {\n    display: flex;\n            justify-content: center;\n            align-items: center;\n            padding: 5px 20px;\n            background-color: #22223b;\n            color: white;\n}\n\n .nav-links {\n            list-style: none;\n            display: flex;\n        }\n\n        .nav-links li {\n            margin: 0 15px;\n        }\n\n        .nav-links a {\n            text-decoration: none;\n            color: white;\n            font-size: 18px;\n        }\n\n       \n\n        \/* Anpassung f\u00fcr kleinere Bildschirme *\/\n        @media screen and (max-width: 768px) {\n            .nav-links {\n                display: none;\n                flex-direction: 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elementor-section-height-default elementor-section-height-default\" data-id=\"603245f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-754fa1f\" data-id=\"754fa1f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c727cde elementor-widget elementor-widget-image\" data-id=\"c727cde\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.5.4 - 23-01-2022 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.gastonternes.eu\/wp-content\/uploads\/2024\/07\/Bildschirmfoto-2024-07-03-um-16.36.00.png\" title=\"Bildschirmfoto 2024-07-03 um 16.36.00\" alt=\"Bildschirmfoto 2024-07-03 um 16.36.00\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-39d3ebf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"39d3ebf\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-da8574c\" data-id=\"da8574c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6fac3fe elementor-widget elementor-widget-html\" data-id=\"6fac3fe\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n    <meta charset=\"UTF-8\">\n    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n    <title>Text Layout Example<\/title>\n    <style>\n        body {\n            font-family: 'Arial', sans-serif;\n            background-color: #f4f4f9;\n            color: #333;\n            margin: 0;\n            padding: 20px;\n        }\n        .container {\n            max-width: 1000px;\n            margin: 0 auto;\n            padding-top: 50px\n            padding: 20px;\n            background-color: #fff;\n            border-radius: 8px;\n            box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);\n        }\n        h1, h2, h3 {\n           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\n    <div class=\"container\">\n        \n      \n        \n          <p id=\"Chapitre7\"><h1>Chapitre 7<\/h1><\/p> \n        <p>Vous trouvez ci-dessous toutes les solutions des activit\u00e9s, \u00e9nigmes ou jeux du chapitre 7.<\/p>\n        \n        <p id=\"p240\"><h2>Page 242: \u00c9nigme : 4 = 5 !<\/h2>\n        <p>Les \u00e9tapes de l'\u00e9quation semblent math\u00e9matiquement correct, MAIS ...<\/p>\n        L'\u00e9quation s'\u00e9crit : <i>b<\/i> = 2<i>a<\/i>. Retranchons <i>b<\/i> dans les deux membres, donc : 2<i>a<\/i> - <i>b<\/i> = 0. \n        <br>La division par (2<i>a<\/i>-<i>b<\/i>) (ligne 4) est impossible car on n'a pas le droit de diviser par 0.\n    <p><\/p>\n        \n        <p id=\"p240-2\"><h2>Page 242: Un concours \u00e0 ne pas rater<\/h2>\n        <p>Soit <i>x<\/i> le nombre de pi\u00e8ces de 5 centimes, <i>y<\/i> le nombre de pi\u00e8ces de 20 centimes et <i>z<\/i> le nombre de pi\u00e8ces de 50 centimes.\n<p>\n    <p>On obtient le syst\u00e8me d\u2019\u00e9quations suivant :\n<p>\n    <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2024\/11\/p240-systeme-equation.png\" alt=\"Description of Image\" width=\"250\" height=\"100\">\n<\/p>\n\nEn retranchant (1) de (2)*, on obtient : <p> 3<i>y<\/i> + 9<i>z<\/i> = 10\n<br>\u21d4 3(<i>y<\/i>+ 3<i>z<\/i>) = 10\n<\/p>\nOr 10 n\u2019est pas divisible par 3 et <i>y<\/i> + 3<i>z<\/i> doit \u00eatre un entier naturel. Les auteurs ne risquent rien !\n<br>* On peut aussi remplacer <i>x<\/i> = 10 - <i>y<\/i> - <i>z<\/i> dans l\u2019\u00e9quation (2).<\/br>\n<\/p>\n        \n       <p id=\"p240-3\"><h2>Page 242: Tu es professeur de math\u00e9matiques<\/h2>\n        <p>Les deux \u00e9l\u00e8ves ont fait des erreurs :<ul>\n            <li>A: L'\u00e9l\u00e8ve A ne prend pas en compte que <i>x<\/i> - 5 peut s'annuler. Il oublie la solution <i>x<\/i> = 5.<\/li>\n            <li>B: L'\u00e9l\u00e8ve B ne prend pas en compte que 2<i>x<\/i> peut s'annuler. Il oublie la solution <i>x<\/i> = 0.<\/li>\n            <\/ul>\n            \n           Correction : (<i>x<\/i> - 5) \u2219 [(3<i>x<\/i>+1) - (<i>x<\/i> + 1)] = 0<br>\n            <=> (<i>x<\/i> - 5) \u2219 2<i>x<\/i> = 0\n            <br>R\u00e9ponse correcte : <i>x<\/i> = 0 ou <i>x<\/i> = 5.<\/p>\n      \n       \n        <p id=\"p243\"><h2>Page 245: Un escalier pratique<\/h2>\n        <p><ul>\n            <li>Si <i>h<\/i> = 17 cm, alors <i>g<\/i> = 29 cm<\/li>\n            <li>Si <i>g<\/i> = 27 cm, alors <i>h<\/i> = 18 cm<\/li>\n            <\/ul><\/p>\n       \n       \n        <p id=\"p254\"><h2>Page 256: Pour les bosses math\u00e9matiques : d\u00e9placer une allumette<\/h2>\n        <p><ul>\n            <li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/p254-ENIGME1-1.png\" alt=\"Description of Image\" width=\"300\" height=\"250\"><\/li>\n            <li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/p254-ENIGME2-2.png\" alt=\"Description of Image\" width=\"300\" height=\"100\"><\/li>\n            <li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/p254-ENIGME3-3.png\" alt=\"Description of Image\" width=\"300\" height=\"100\"><\/li>\n        <\/ul><\/p>\n        \n         <p id=\"p258\"><h2>Page 260: Les unit\u00e9s des temp\u00e9ratures<\/h2>\n        <p><ol><li>12\u00b0C<\/li>\n        <li>40 \u00b0C<\/li>\n        <\/ol><\/p>\n        \n        <div class=\"highlight\">\n            <p><\/p>\n        <\/div>\n        \n         \n       \n    <\/div>\n<\/body>\n<\/html>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Accueil Auteurs Contact Text Layout Example Chapitre 7 Vous trouvez ci-dessous toutes les solutions des activit\u00e9s, \u00e9nigmes ou jeux du chapitre 7. Page 242: \u00c9nigme : 4 = 5 ! Les \u00e9tapes de l&rsquo;\u00e9quation semblent math\u00e9matiquement correct, MAIS &#8230; L&rsquo;\u00e9quation s&rsquo;\u00e9crit : b = 2a. Retranchons b dans les deux&#8230;<\/p>","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_canvas","meta":{"footnotes":""},"class_list":["post-4421","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/pages\/4421","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/comments?post=4421"}],"version-history":[{"count":16,"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/pages\/4421\/revisions"}],"predecessor-version":[{"id":5493,"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/pages\/4421\/revisions\/5493"}],"wp:attachment":[{"href":"https:\/\/www.gastonternes.eu\/de\/wp-json\/wp\/v2\/media?parent=4421"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}