{"id":4419,"date":"2025-02-01T14:14:26","date_gmt":"2025-02-01T13:14:26","guid":{"rendered":"https:\/\/www.gastonternes.eu\/?page_id=4419"},"modified":"2025-07-16T12:04:27","modified_gmt":"2025-07-16T10:04:27","slug":"mpr-solutions-ch-5","status":"publish","type":"page","link":"https:\/\/www.gastonternes.eu\/lu\/mpr-solutions-ch-5\/","title":{"rendered":"Maths: Plaisir et r\u00e9ussite &#8211; Solutions &#8211; Chapitre 5"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"4419\" class=\"elementor elementor-4419\" 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 class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2765530\" data-id=\"2765530\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\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-2d62dc8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2d62dc8\" 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-06f31bc\" data-id=\"06f31bc\" 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-d905bbe elementor-widget elementor-widget-html\" data-id=\"d905bbe\" 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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.header nav ul li {\n        margin: 10px 0;\n    }\n}\n\n@media (max-width: 480px) {\n    .header nav ul li a {\n        font-size: 16px;\n        padding: 10px 15px;\n    }\n}\n\n  <\/style>\n<\/head>\n\n<body>\n  \n  <div class=\"header\">\n     \n        <nav>\n            <ul>\n               <li><a href=\"https:\/\/www.gastonternes.eu\/lu\/mpr-accueil\/\" target=\"_blank\">Accueil<\/a><\/li>\n                \n                  <li><a href=\"https:\/\/www.gastonternes.eu\/lu\/mpr-auteurs\/\" target=\"_blank\">Auteurs<\/a><\/li>\n                \n                <li><a href=\"mailto:maths.plaisir.reussite@gmail.com\">Contact<\/a><\/li>\n            <\/ul>\n        <\/nav>\n    <\/div>\n    \n    \n    <\/body>\n<\/html>\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-603245f elementor-section-boxed 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            color: #004e92;\n            border-bottom: 2px solid #ddd;\n            padding-bottom: 5px;\n            margin-top: 40px\n            margin-bottom: 20px;\n        }\n        h1 {\n            font-size: 2em;\n        }\n        h2 {\n            font-size: 1.5em;\n        }\n        h3 {\n            font-size: 1.2em;\n        }\n        p {\n            line-height: 1.6;\n            margin: 20px 0;\n        }\n        ul {\n            list-style-type: disc;\n            margin: 20px 0;\n            padding-left: 40px;\n        }\n        ul li {\n            margin: 10px 0;\n        }\n        .highlight {\n            background-color: #e0f7fa;\n            border-left: 4px solid #004e92;\n            padding: 10px 15px;\n            margin: 20px 0;\n        }\n        .button {\n            display: inline-block;\n            padding: 10px 20px;\n            margin-top: 20px;\n            background-color: #004e92;\n            color: #fff;\n            text-decoration: none;\n            border-radius: 5px;\n        }\n        .button:hover {\n            background-color: #003366;\n        }\n         .fraction {\n            display: inline-block;\n            text-align: center;\n            vertical-align: middle;\n        }\n        .fraction .numerator,\n        .fraction .denominator {\n            display: block;\n        }\n        .fraction .numerator {\n            border-bottom: 1px solid #000;\n        }\n        .fraction .denominator {\n            margin-top: -0.2em;\n        }\n   \n@media (max-width: 768px) {\n    .header nav ul {\n        flex-direction: column;\n        align-items: center;\n    }\n\n    .header nav ul li {\n        margin: 10px 0;\n    }\n}\n\n@media (max-width: 480px) {\n    .header nav ul li a {\n        font-size: 16px;\n        padding: 10px 15px;\n    }\n}\n      \n      table, th, td {\n  border: 1px solid;\n  margin-left: p;\n  margin-right: px;\n}\n        \n    <\/style>\n<\/head>\n<body>\n   \n \n    \n    <div class=\"container\">\n        \n       \n        \n          <p id=\"Chapitre5\"><h1>Chapitre 5<\/h1><\/p> \n        <p>Vous trouvez ci-dessous toutes les solutions des activit\u00e9s, \u00e9nigmes ou jeux du chapitre 5.<\/p>\n        \n        <p id=\"p165\"><h2>Page 167: Transformer une fraction en \u00e9criture d\u00e9cimale<\/h2>\n        <p><ol>\n            <li>b<\/li> \n            <li>b<\/li><\/p>\n        <\/ol>\n        \n        \n        <p id=\"p166\"><h2>Page 168: Les morceaux de pizza<\/h2>\n        <p>a et d<\/p>\n        \n        <p id=\"p167\"><h2>Page 169: \u00c0 vos jeux<\/h2>\n        <p><span class=\"fraction\"><span class=\"numerator\">1<\/span><span class=\"denominator\">2<\/span><\/span> ; \n        <span class=\"fraction\"><span class=\"numerator\">2<\/span><span class=\"denominator\">1<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">1<\/span><span class=\"denominator\">3<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">3<\/span><span class=\"denominator\">1<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">1<\/span><span class=\"denominator\">4<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">4<\/span><span class=\"denominator\">1<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">2<\/span><span class=\"denominator\">3<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">3<\/span><span class=\"denominator\">2<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">3<\/span><span class=\"denominator\">4<\/span><\/span> ;\n        <span class=\"fraction\"><span class=\"numerator\">4<\/span><span class=\"denominator\">3<\/span><\/span>\n        <\/p>\n        \n         <p id=\"p172\"><h2>Page 174: Une question de r\u00e9gime et d'effet yoyo<\/h2>\n        <p><ul><li>Claude a grossi de 20 kg. Son poids de r\u00e9f\u00e9rence \u00e9tait de 80 kg. Il a donc grossi de : 100 \u00b7 <span class=\"fraction\"><span class=\"numerator\">20<\/span><span class=\"denominator\">80<\/span><\/span> = 25%<\/li>\n        <li>Pierre a maigri de 20 kg par rapport \u00e0 son poids de r\u00e9f\u00e9rence de 100 kg. Il a donc maigri de : 100 \u00b7 <span class=\"fraction\"><span class=\"numerator\">20<\/span><span class=\"denominator\">100<\/span><\/span> = 20%<\/li>\n        <\/ul><\/p>\n        \n        <p id=\"p174\"><h2>Page 176: Jeu de cartes<\/h2>\n        <p>Cl\u00e9 de l'\u00e9nigme:<br>\nAu d\u00e9but du tour de magie, la carte est en 13<sup>e<\/sup> position. Vous voulez la faire passer au 8<sup>e<\/sup> rang. Le magicien prend du bas du paquet successivement 8 cartes qu'il met sur le paquet. La carte cherch\u00e9e sera donc en position: 8 + 13.\n<br>Le magicien demande de v\u00e9rifier qu'elle n'est plus en 13<sup>e<\/sup> position. Il enl\u00e8ve donc successivement 13 cartes. La carte cherch\u00e9e sera alors \u00e0 la position 8, car:\n8 + 13 = 13 + 8.\n<br>L'addition est commutative!<\/p>\n        \n        <p id=\"p177\"><h2>Page 179: Le calcul de fractions par un logiciel CAS<\/h2>\n        \n       <video width=\"640\" height=\"360\" controls>\n    <source src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/07\/chap-5-GEOGEBRA.mp4\" type=\"video\/mp4\">\n    Your browser does not support the video tag.\n        <\/video>\n       \n        \n       <p id=\"p186\"><h2>Page 188: Pour les bosses math\u00e9matiques<\/h2>\n        <p>Voici deux arguments :<\/p>\n        <ol>\n        <li><span class=\"fraction\"><span class=\"numerator\">1<\/span><span class=\"denominator\">3<\/span><\/span> = 0,33333... ; multiplier les deux c\u00f4t\u00e9s par 3, ce qui donne 1 = 0,99999...<\/li>\n        <li>Posons : <i>a<\/i> = 0,99999...\n        <p>Multiplier par 10 les deux c\u00f4t\u00e9s ce qui donne 10<i>a<\/i> = 9,99999... <\/p>\n        <p>Soustraire <i>a<\/i> des deux c\u00f4t\u00e9s : 9<i>a<\/i> = 9, donc <i>a<\/i> = 1.<\/p><\/li>\n        <\/ol>\n        \n        <div class=\"highlight\">\n            <p><\/p>\n        <\/div>\n        \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 5 Vous trouvez ci-dessous toutes les solutions des activit\u00e9s, \u00e9nigmes ou jeux du chapitre 5. Page 167: Transformer une fraction en \u00e9criture d\u00e9cimale b b Page 168: Les morceaux de pizza a et d Page 169: \u00c0 vos jeux 12 ; 21 ;&#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-4419","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/pages\/4419","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/comments?post=4419"}],"version-history":[{"count":25,"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/pages\/4419\/revisions"}],"predecessor-version":[{"id":5576,"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/pages\/4419\/revisions\/5576"}],"wp:attachment":[{"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/media?parent=4419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}