{"id":4416,"date":"2025-02-01T14:13:40","date_gmt":"2025-02-01T13:13:40","guid":{"rendered":"https:\/\/www.gastonternes.eu\/?page_id=4416"},"modified":"2025-07-16T12:02:05","modified_gmt":"2025-07-16T10:02:05","slug":"mpr-solutions-ch-2","status":"publish","type":"page","link":"https:\/\/www.gastonternes.eu\/lu\/mpr-solutions-ch-2\/","title":{"rendered":"Maths: Plaisir et r\u00e9ussite &#8211; Solutions &#8211; Chapitre 2"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"4416\" class=\"elementor elementor-4416\" 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-69ffa98 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"69ffa98\" 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-2315f10\" data-id=\"2315f10\" 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-f009837 elementor-widget elementor-widget-html\" data-id=\"f009837\" 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: column;\n                width: 100%;\n                position: absolute;\n                top: 60px;\n                left: 0;\n                background-color: #333;\n                text-align: center;\n            }\n\n            .nav-links.active {\n                display: flex;\n            }\n\n            .nav-links li {\n                margin: 10px 0;\n            }\n\n            \n        }\n\n.header nav ul {\n    list-style-type: none;\n    padding: 0;\n    margin: 0;\n    display: flex;\n    justify-content: center;\n}\n\n.header nav ul li {\n    margin: 0 20px;\n}\n\n.header nav ul li a {\n    color: #fff;\n    text-decoration: none;\n    font-size: 18px;\n    padding: 15px 20px;\n    display: block;\n    transition: background-color 0.3s ease;\n}\n\n.header nav ul li a:hover {\n    background-color: #003366;\n    border-radius: 5px;\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  <\/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      \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        \n        <p id=\"Chapitre2\"><h1>Chapitre 2<\/h1>\n        <p>Vous trouvez ci-dessous toutes les solutions des activit\u00e9s, \u00e9nigmes ou jeux du chapitre 2.<\/p>\n        \n       <p id=\"p41\"><h2>Page 43: Jeu d'entr\u00e9e : une \u00e9nigme arithm\u00e9tique<\/h2>\n        <p>Voici des exemples de solutions : (Il en existe d'autres)<\/p>\n         <ul>\n            <li>Exemple 1 : 36 = 4 &middot; 12 - 2 &middot; 6 <\/li>\n            <li>Exemple 2 : 60 = 2 &middot; 15 + 3 &middot; 10 <\/li>\n            <li>Exemple 3 : 16 = 12 + 2 + 6:3 <\/li>\n            <li>Exemple 4 : 11 = 2 &middot; 4 + 1 &middot; 3 <\/li>\n            <li>Exemple 5 : 0 = (12 - 9 - 3) &middot; 6 <\/li>\n            <li>Exemple 6 : 7 = 18:2 - 16:8 <\/li>\n        <\/ul>\n       \n       \n       <p id=\"p47\"><h2>Page 49: 0 et 1, un duo malin<\/h2>\n        <p><\/p>\n         <video width=\"640\" height=\"360\" controls>\n    <source src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/07\/chap2-DUO-MALIN.mp4\" type=\"video\/mp4\">\n    Your browser does not support the video tag.\n        <\/video>\n       \n       \n       <p id=\"p51\"><h2>Page 53: Un casse-t\u00eate<\/h2>\n        <p>4 + 5 = 9<\/p>\n        <p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/ALLUMETTESp51-corrige1.png\" alt=\"Description of Image\" width=\"250\" height=\"100\"><\/p>\n         <p>Autre solution : 4 + 0 = 4<\/p>\n         <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/ALLUMETTESp51-corrige.png\" alt=\"Description of Image\" width=\"250\" height=\"100\">\n       \n       <p id=\"p52\"><h2>Page 54: Un ph\u00e9nom\u00e8ne : l'orage <\/h2>\n        <p><ul>\n            \n            <li>1<sup>\u00e8re<\/sup> m\u00e9thode: Le son circule en 3 secondes de 3 &middot; 0,337 m = 1 011 m &asymp; 1km. En divisant par 3, on peut donc estimer que pour 1 seconde, le son circule d'un tiers de km. <\/li>\n            <li>2<sup>e<\/sup> m\u00e9thode: Au lieu de calculer 337 &middot; 9 on se contente de l'approximation 300 &middot; 9 = 2 700 m.<\/li>\n            <p>La premi\u00e8re m\u00e9thode donne une meilleure approximation.<\/p><\/ul><\/p>\n       \n       \n       <p id=\"p53\"><h2>Page 55: Le pliage d'une feuille<\/h2>\n        <p>Faites le pliage ! <br>Apr\u00e8s un pliage, vous aurez deux \u00e9paisseurs, apr\u00e8s 2 pliages 4, apr\u00e8s 3 pliages 8, apr\u00e8s 4 pliages 16 et apr\u00e8s 5 pliages 32...<\/p>\n        <p>Nous avons donc doubl\u00e9 l'\u00e9paisseur par chaque pliage !<\/p>\n        <p>D'o\u00f9 la r\u00e8gle suivante : l'\u00e9paisseur sera \u00e9gal \u00e0 2<sup><i>n<\/i><\/sup> avec <i>n<\/i> = nombre de pliages.<\/p>\n        <p>Pour <i>n<\/i> = 10, on aura donc 2<sup>10<\/sup> \u00e9paisseurs de la feuille, donc 1 024.<\/p>\n       \n       \n       \n        <p id=\"p55\"><h2>Page 57: Une petite recherche<\/h2>\n        <p>\n        NON, car par exemple pour <i>n<\/i> = 41 on a 41<sup>2<\/sup> - 41 + 41 = 1681.<\/p>\n        <p>1 681 est donc divisible par 1, 41 et 1681.<\/p>\n        \n         <p id=\"p57\"><h2>Page 59: Un jeu : La course \u00e0 20 !<\/h2>\n        <p>La recherche d\u2018une strat\u00e9gie gagnante montre que le gagnant est celui qui dira 17, et avant 14, et avant 11, \u2026, c\u2018est-\u00e0-dire que celui qui commence est s\u00fbr de gagner s\u2018il dit 2 (et s\u2018il sait jouer!). <br>\n        On gagne si l'on choisit les nombres qui ont un reste 2 dans la division par 3.\n        <br>En rempla\u00e7ant 20 par 21 ou 22, on fait appara\u00eetre les diff\u00e9rents restes dans la division par 3.<\/p>\n        \n        \n        <p id=\"p61\"><h2>Page 63: Les maths en pratique : La cl\u00e9 USB<\/h2>\n        <p>75 &middot; 3 + 5 &middot; 13 + 13 &middot; 35 + 252 = 998. Il reste : 26 MB.<\/p>\n        \n        \n        <p id=\"p62\"><h2>Page 64: \u00c0 la d\u00e9couverte d'un tableur<\/h2>\n        <p><ul>\n            <li>1b: Voici les formules pour les diff\u00e9rentes cases : D2: \"=B2*C2\" ; D3: \"=B3*C3\" ; D4: \"=B4*C4\" ; D6: \"=SOMME(D2:D4)\" ou bien \"=D2+D3+D4\"\n<\/li>\n            <li>2a: On doit modifier les quantit\u00e9s, donc les cellules C2, C3 et C4.\n<\/li>\n<li>2b: 45 078 \u20ac\n<\/li>\n        <\/ul><\/p>\n        \n        \n         <p id=\"p63\"><h2>Page 65: Si vous \u00e9tiez restaurateur<\/h2>\n        <p>Il suffit d'\u00e9crire les cat\u00e9gories de plats dans une 1<sup>\u00e8re<\/sup> colonne et les prix dans une 2<sup>e<\/sup> colonne. En dessous des prix, ajouter le calcul de la somme totale, p.ex. : \"=SOMME(B2:B6)\" pour la case B7.<\/p>\n        <p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/tableur-p63.png\" alt=\"Description of Image\" width=\"250\" height=\"100\"><\/p>\n        \n        <p id=\"p63-2\"><h2>Page 65: Tableur et division euclidienne<\/h2>\n        <p>Case D2: \"=A2-B2*C2\"<\/p>\n        <p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/tableur-p63-2.png\" alt=\"Description of Image\" width=\"350\" height=\"100\"><\/p>\n        <p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2025\/02\/tableur-p63-3.png\" alt=\"Description of Image\" width=\"350\" height=\"100\"><\/p>\n        \n        \n         <p id=\"p69\"><h2>Page 71: \u00c9nigme : Vrai ou faux ?<\/h2>\n        <p>Vrai car, 2 \u00b7 19 - 29 = 38 - 29 = 9 \u20ac.<\/p>\n        \n        <p id=\"p81\"><h2>Page 83: Les agendas de 2025 & 2031<\/h2>\n        <p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2024\/11\/IMG_6A238683972A-1.jpeg\" alt=\"Description of Image\" width=\"250\" height=\"100\"> <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.gastonternes.eu\/wp-content\/uploads\/2024\/11\/IMG_8D054CFACE0B-1.jpeg\" alt=\"Description of Image\" width=\"250\" height=\"100\"><\/p>\n        \n        \n         <p id=\"binaire\"><h2>Le syst\u00e8me binaire<\/h2>\n        <p>2<sup>10<\/sup> = 1 024.<\/p>\n        \n        <div class=\"highlight\">\n            <p><\/p>\n        <\/div>\n        \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 2 Vous trouvez ci-dessous toutes les solutions des activit\u00e9s, \u00e9nigmes ou jeux du chapitre 2. Page 43: Jeu d&rsquo;entr\u00e9e : une \u00e9nigme arithm\u00e9tique Voici des exemples de solutions : (Il en existe d&rsquo;autres) Exemple 1 : 36 = 4 &middot; 12 &#8211; 2&#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-4416","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/pages\/4416","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=4416"}],"version-history":[{"count":31,"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/pages\/4416\/revisions"}],"predecessor-version":[{"id":5573,"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/pages\/4416\/revisions\/5573"}],"wp:attachment":[{"href":"https:\/\/www.gastonternes.eu\/lu\/wp-json\/wp\/v2\/media?parent=4416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}