{"id":267837,"date":"2024-05-03T16:30:31","date_gmt":"2024-05-03T14:30:31","guid":{"rendered":"https:\/\/sherpas.com\/blog\/parents\/?p=267837"},"modified":"2024-05-03T16:30:35","modified_gmt":"2024-05-03T14:30:35","slug":"proportionnalite-4eme","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/parents\/a\/proportionnalite-4eme\/","title":{"rendered":"Piq\u00fbre de rappel : la proportionnalit\u00e9 \u2696\ufe0f"},"content":{"rendered":"\n<p><strong>Notion essentielle de la fin de primaire et du coll\u00e8ge, surtout en 4\u1d49<\/strong>, la proportionnalit\u00e9 est un des piliers des math\u00e9matiques lors de la scolarit\u00e9 de votre enfant. \ud83d\udcaa<\/p>\n\n\n\n<p>C\u2019est pourquoi, en tant que parent, vous devez en savoir un minimum sur le sujet. En bons samaritains, on a d\u00e9cid\u00e9 de vous faire un cours pour vous rappeler le bon vieux temps et vous replonger dans votre livre de math\u00e9matiques de quand vous aviez \u00e0 peine 15 ans. \ud83d\udcd6<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/v1.Y2lkPTc5MGI3NjExazJ5MDkyMmZ0ejcxbHlxbnc4NThzNW9qM3JsZHVscG92YzEwNXI4ciZlcD12MV9naWZzX3NlYXJjaCZjdD1n\/3oz8xvr7ikehEe4Dmg\/giphy.gif\" alt=\"homme d\u00e9prim\u00e9\" style=\"width:349px;height:auto\"\/><figcaption class=\"wp-element-caption\"><em>Allez, retour au coll\u00e8ge ! <\/em><\/figcaption><\/figure><\/div>\n\n\n<p>Ne prenez pas peur face aux seringues, il s\u2019agit seulement d\u2019<strong>une piq\u00fbre de rappel<\/strong>. Vous \u00eates concentr\u00e9 ? C\u2019est parti ! \ud83d\udc89<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">La notion de proportionnalit\u00e9 \ud83e\udd14<\/h2>\n\n\n\n<p>Commen\u00e7ons par quelques \u00e9l\u00e9ments de d\u00e9finition, histoire de vous rafra\u00eechir doucement la m\u00e9moire.&nbsp;<\/p>\n\n\n<section class=\"relance\">\n        <div >\n                            <a target=\"_blank\" href=\"https:\/\/sherpas.com\/\">\n                    <div class=\"relance__container\"\n                        >\n                        \n                                                        <picture>\n                            <source srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/01\/Mon-enfant-a-t-il-besoin-de-cours-particuliers.jpg\" media=\"(min-width: 999px)\">\n                            <source srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/01\/Mon-enfant-a-t-il-besoin-de-cours-particuliers.jpg\" media=\"(max-width: 999px)\">\n                                <img decoding=\"async\"\n                                    src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/01\/Mon-enfant-a-t-il-besoin-de-cours-particuliers.jpg\"\n                                    alt=\"Mon enfant a-t-il besoin de cours particuliers ?\"\n                                >\n                            <\/picture>\n                                                <div class=\"relance__content\">\n                            \n                                <div class=\"relance__title\"> <p>Votre enfant gal\u00e8re en cours ? Son premier cours particulier est gratuit !<\/p>\n<\/div>\n                                                        <button type=\"button\"\n                                    class=\"relance__button btn btn-white\">\n                                Trouvez le prof id\u00e9al ! \n                            <\/button>\n                        <\/div>\n                    <\/div>\n                <\/a>\n                    <\/div>\n    <\/section>\n\n    \n\n\n<h3 class=\"wp-block-heading\">Explication &amp; d\u00e9finition \u270d\ufe0f<\/h3>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\u2712\ufe0f D\u00e9finition<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><strong>Deux valeurs sont proportionnelles<\/strong> si lorsqu\u2019on en multiplie une par un nombre, l\u2019autre valeur est \u00e9galement multipli\u00e9e par ce m\u00eame nombre.<\/p>\n<p>&nbsp;<\/p>\n<p>En bref, <strong>les deux grandeurs sont dites \u00ab proportionnelles \u00bb<\/strong> si lorsqu\u2019une grandeur augmente, l\u2019autre augmente aussi dans la m\u00eame proportion. Ce qui signifie qu\u2019elles ont, en effet, le m\u00eame multiplicateur.<\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Vous n\u2019avez toujours pas compris ? On va prendre pour exemple les deux valeurs suivantes : 1 et 3,5. La valeur \u00ab 1 \u00bb devient \u00ab 2 \u00bb et la valeur \u00ab 3,5 \u00bb devient \u00ab 7 \u00bb. <strong>Les grandeurs 1 et 3,5 sont-elles proportionnelles ?<\/strong> \ud83e\uddd0<\/p>\n\n\n\n<p>La r\u00e9ponse est oui, car elles ont toutes les deux \u00e9taient multipli\u00e9es par 2.&nbsp;<\/p>\n\n\n\n<p><strong>1 x 2 = 2.<\/strong><\/p>\n\n\n\n<p><strong>3,5 x 2 = 7.<\/strong><\/p>\n\n\n\n<p>Autre exemple :&nbsp;<\/p>\n\n\n\n<p>On a un 2 qui augmente et devient \u00ab 4 \u00bb et \u00e0 c\u00f4t\u00e9, le chiffre d\u00e9cimal 1,2 qui devient 2,5. <strong>Les valeurs \u00ab 2 \u00bb et \u00ab 1,2 \u00bb sont-elles proportionnelles ?<\/strong> Non, car leur multiplicateur n\u2019est pas le m\u00eame. \u274c<\/p>\n\n\n\n<p>En effet, <strong>2 a \u00e9t\u00e9 multipli\u00e9 par 2 pour obtenir 4, mais 1,2 x 2 n\u2019est pas \u00e9gal \u00e0 2,5 mais bien \u00e0 2,4<\/strong>. Les deux grandeurs n\u2019ont donc pas augment\u00e9 dans la m\u00eame proportion.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Les repr\u00e9sentations graphiques \ud83d\udcc8<\/h3>\n\n\n\n<p>Avant de passer au graphique, prenons un tableau pour mieux nous aider \u00e0 comprendre cette notion de proportionnalit\u00e9.<\/p>\n\n\n\n<table id=\"tablepress-1546\" class=\"tablepress tablepress-id-1546\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\">Grandeur 1<\/td><td class=\"column-2\">1<\/td><td class=\"column-3\">2<\/td><td class=\"column-4\">6<\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Grandeur 2<\/td><td class=\"column-2\">1,5<\/td><td class=\"column-3\">3<\/td><td class=\"column-4\">9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-1546 from cache -->\n\n\n\n<p>Notre question est la suivante : <strong>s\u2019agit-il d\u2019un tableau de proportionnalit\u00e9 ?<\/strong> Eh bien oui, car toutes les valeurs du haut sont multipli\u00e9es par \u00ab 1,5 \u00bb pour obtenir les grandeurs du bas.&nbsp;<\/p>\n\n\n\n<p><strong>1 x 1,5 = 1,5.<\/strong><\/p>\n\n\n\n<p><strong>2 x 1,5 = 3.<\/strong><\/p>\n\n\n\n<p><strong>6 x 1,5 =9.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>1,5 est donc appel\u00e9 \u00ab le coefficient de proportionnalit\u00e9 \u00bb.<\/strong> Dans un tableau, vous pouvez reconna\u00eetre une situation de proportionnalit\u00e9 lorsqu\u2019il existe un coefficient de proportionnalit\u00e9. \ud83d\udc4d<\/p>\n\n\n\n<p>Repr\u00e9sentons tous ces nombres sur un graphique (rep\u00e8re), que voici :&nbsp;&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"744\" height=\"707\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png\" alt=\"graphique avec situation de proportionnalit\u00e9\" class=\"wp-image-267840\" style=\"width:618px;height:auto\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=744 744w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=300 300w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=132 132w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=286 286w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=390 390w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/graphique-proportionnalite.png?w=1080 1080w\" sizes=\"(max-width: 744px) 100vw, 744px\" \/><\/figure><\/div>\n\n\n<p>On a plac\u00e9 1; 2 et 6 sur l\u2019axe des abscisses et les valeurs correspondantes (1,5; 3 et 9) sur l\u2019axe des ordonn\u00e9es.&nbsp;<\/p>\n\n\n\n<p>Sur un graphique, on parle de situation de proportionnalit\u00e9 lorsque cette derni\u00e8re est repr\u00e9sent\u00e9e avec <strong>des points qui sont align\u00e9s avec l\u2019origine<\/strong>. \ud83d\udccf<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zaWdudXA9dHJ1ZQ==\" data-banner=\"2\" data-name=\"Cours part&amp;rsquo; global #1 = CPG1\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n              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  xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">18\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Hugo2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Hugo<\/p>                          <p class=\"push__teachers-school\">Insa Lyon<\/p>                                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          class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Sophie2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Sophie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Bordeaux<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n          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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">12\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Simon2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Simon<\/p>                          <p class=\"push__teachers-school\">4e ann\u00e9e de m\u00e9decine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                  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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Clemence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                        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             <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Fanny2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fanny<\/p>                          <p class=\"push__teachers-school\">Ponts ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                          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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Alma2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Alma<\/p>                          <p class=\"push__teachers-school\">ENS Paris-Saclay<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Besoin d&rsquo;un <span style=\"color: #48b378;\">prof particulier<\/span> exceptionnel ? \u2728<\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos Sherpas sont l\u00e0 pour aider votre enfant \u00e0 progresser et \u00e0 prendre confiance en lui.<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: #ffffff; border-color: ; background-color: \"\n\n                                    >\n                                        PRENDRE UN COURS GRATUIT\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">Produit en croix \u274e<\/h2>\n\n\n\n<p>On consid\u00e8re le tableau suivant :&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"295\" height=\"99\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png\" alt=\"tableau de proportionnalit\u00e9, produit en croix\" class=\"wp-image-267841\" style=\"width:319px;height:auto\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=295 295w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=200 200w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix.png?w=1080 1080w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">Explication et exemple \ud83d\udd0e<\/h3>\n\n\n\n<p><strong>Dans un tableau de proportionnalit\u00e9, on a l\u2019\u00e9galit\u00e9 suivante : a x d = b x c<\/strong>. On a donc une \u00e9galit\u00e9 en croix entre les diagonales b\/c et a\/d, d\u2019o\u00f9 le nom de \u00ab produit (le r\u00e9sultat d\u2019une multiplication) en croix \u00bb.<\/p>\n\n\n\n<p>C&rsquo;est bien beau toutes ces lettres, mais prenons un exemple avec des chiffres et des nombres pour mieux comprendre tout cela :&nbsp;<\/p>\n\n\n\n<table id=\"tablepress-1547\" class=\"tablepress tablepress-id-1547\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\">Grandeur 1<\/td><td class=\"column-2\">4<\/td><td class=\"column-3\">5<\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Grandeur 2<\/td><td class=\"column-2\">6,8<\/td><td class=\"column-3\">8,5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-1547 from cache -->\n\n\n\n<p>Les grandeurs 1 et 2 sont-elles proportionnelles ? \ud83d\udc40<\/p>\n\n\n\n<p>Si 6,8 x 5 = 4 x 8,5, alors ce sera le cas.&nbsp;<\/p>\n\n\n\n<p>Et en effet, 6,8 x 5 = 34 et 4 x 8,5 = 34 aussi <strong>! D\u2019apr\u00e8s la propri\u00e9t\u00e9 des produits en croix, on peut en d\u00e9duire que les deux valeurs (grandeurs) sont proportionnelles<\/strong>.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">La quatri\u00e8me proportionnelle \ud83d\udc41\ufe0f<\/h3>\n\n\n\n<p><strong>Le terme de \u00ab quatri\u00e8me proportionnelle \u00bb<\/strong> est utilis\u00e9 pour d\u00e9crire une situation de proportionnalit\u00e9 dans laquelle on ne conna\u00eet que trois nombres sur les quatre et o\u00f9 il faut donc trouver ce quatri\u00e8me nombre encore inconnu.<\/p>\n\n\n\n<p>Pour comprendre, faisons un petit exercice :&nbsp;<\/p>\n\n\n\n<p>3,5 kg de fraises co\u00fbtent 8 \u20ac. Quel est le prix de 2 kg ? \ud83c\udf53<\/p>\n\n\n\n<p>Commen\u00e7ons par remplir notre joli tableau avec les valeurs que l\u2019on a d\u00e9j\u00e0.&nbsp;<\/p>\n\n\n\n<table id=\"tablepress-1548\" class=\"tablepress tablepress-id-1548\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\">Prix (\u20ac)<\/td><td class=\"column-2\">8<\/td><td class=\"column-3\">\ud835\udc65<\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Masse (kg)<\/td><td class=\"column-2\">3,5<\/td><td class=\"column-3\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-1548 from cache -->\n\n\n\n<p><strong>Ce \u00ab \ud835\udc65 \u00bb, c\u2019est justement ce qu\u2019on appelle \u00ab la quatri\u00e8me de proportionnalit\u00e9 \u00bb<\/strong> et on doit trouver ce qui se cache derri\u00e8re.&nbsp;<\/p>\n\n\n\n<p>\ud835\udc65 = 2 x 8 \u00f7 3,5<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;= 16 \u00f7 3,5&nbsp;<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;= 4,57.&nbsp;&nbsp;<\/p>\n\n\n\n<p><strong>Le prix de 2 kg de fraises est donc de 4,57 \u20ac<\/strong>.<\/p>\n\n\n\n<p>Les fruits, c\u2019est bien pour progresser en maths, des <a href=\"https:\/\/sherpas.com\/cours\/maths\">cours de soutien scolaire<\/a> avec l\u2019un de nos Sherpas, c\u2019est mieux ! \ud83d\udd25<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Applications dans la vie quotidienne \ud83c\udf92<\/h2>\n\n\n\n<p>La proportionnalit\u00e9 ce n\u2019est pas seulement une notion th\u00e9orique qui ne servirait qu\u2019en classe de maths et pas ailleurs. On utilise les proportions dans la vie courante, on va vous le prouver !&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">La cuisine \ud83e\uddd1\u200d\ud83c\udf73<\/h3>\n\n\n\n<p><strong>La proportionnalit\u00e9 est pr\u00e9sente partout dans notre quotidien<\/strong> et notamment en cuisine. Allez aux fourneaux ! \ud83c\udf72<\/p>\n\n\n\n<p>Dans votre recette pour faire votre plus beau risotto, vous devez mettre 125 g de champignons pour 2 personnes, mais vous ne savez pas quelle quantit\u00e9 mettre si vous avez 5 couverts et non plus 2. \ud83c\udf44<\/p>\n\n\n\n<p>C\u2019est l\u00e0 que la quatri\u00e8me de proportionnelle intervient :&nbsp;<\/p>\n\n\n\n<table id=\"tablepress-1549\" class=\"tablepress tablepress-id-1549\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\">Nb de personnes (unit\u00e9)<\/td><td class=\"column-2\">2<\/td><td class=\"column-3\">5<\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Masse (g)<\/td><td class=\"column-2\">125<\/td><td class=\"column-3\">\ud835\udc65<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-1549 from cache -->\n\n\n\n<p><strong>\ud835\udc65 <\/strong>= 125 x 5 \u00f7 2&nbsp;<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;= 625 \u00f7 2<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>&nbsp;&nbsp;&nbsp;= 312,5.&nbsp;<\/strong><\/p>\n\n\n\n<p>Pour votre recette pour 5 personnes, prenez donc 312,5 g (c\u2019est tr\u00e8s pr\u00e9cis) de champignons !&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">La vitesse (moyenne) \ud83d\ude98<\/h3>\n\n\n\n<p><strong>Lors d\u2019un trajet uniforme<\/strong> (en voiture, par exemple), la dur\u00e9e du voyage et la distance parcourue sont proportionnelles. <strong>C\u2019est la vitesse qui est le coefficient de proportionnalit\u00e9.<\/strong> \u26a1<\/p>\n\n\n\n<p>Par exemple, si vous allez \u00e0 110 km\/h de moyenne et vous souhaitez calculer des distances en kilom\u00e8tres et\/ ou des dur\u00e9es en heure :&nbsp;<\/p>\n\n\n\n<p>\ud83d\udc63 vous multipliez les dur\u00e9es en heures par 110 pour avoir les distances parcourues en km,&nbsp;<\/p>\n\n\n\n<p>\ud83d\udd70\ufe0f ou vous divisez les distances en km par 110 pour obtenir les dur\u00e9es en heures.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 Comment conna\u00eetre la vitesse moyenne ?<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p>Lors d\u2019un trajet d\u2019une distance \u00ab d \u00bb en un temps \u00ab t \u00bb, la vitesse moyenne, que l\u2019on va appeler \u00ab v\u00a0 \u00bb, est \u00e9gale \u00e0 : v = d \u00f7 t.<\/p>\n<p>&nbsp;<\/p>\n<p>Exemple :<\/p>\n<p>Vous parcourez 3,4 km en 15 min \u00e0 pied (belle foul\u00e9e). Pour conna\u00eetre votre vitesse moyenne en km\/h, divisez la distance par la dur\u00e9e de votre parcours.<\/p>\n<p>Sachant que 15 minutes = 0,25 heure, on obtient :<\/p>\n<p>v = 3,4 \u00f7 0,25 = 13,6 km\/h.<\/p>\n\n        <\/div>\n              <\/section>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/v1.Y2lkPTc5MGI3NjExbGw5NTRxNXhyenI0NWllOXZicDhoOWs2b2ZweHMwaG92djgxaXRwZCZlcD12MV9naWZzX3NlYXJjaCZjdD1n\/3o7ZetIsjtbkgNE1I4\/giphy.gif\" alt=\"Forrest Gump\" style=\"width:322px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">Retour du produit en croix \ud83d\udd19<\/h4>\n\n\n\n<p>C\u2019est le retour du calcul en croix et de la quatri\u00e8me proportionnelle. Sur le sujet de la vitesse, cela va nous servir aussi.&nbsp;<\/p>\n\n\n\n<p>Imaginez que <strong>vous souhaitiez calculer une distance<\/strong> et que vous connaissez d\u00e9j\u00e0 la vitesse et la dur\u00e9e du chemin <strong>ou que vous voulez conna\u00eetre la dur\u00e9e<\/strong> et que vous avez la vitesse et la distance parcourue. Pour cela, on utilise le fameux produit en croix. \ud83e\udde0<\/p>\n\n\n\n<p>Exercice :&nbsp;<\/p>\n\n\n\n<p>Un cycliste se d\u00e9place \u00e0 48 km\/h de moyenne (et fait donc logiquement 48 km en 1 heure), combien lui faudrait-il de temps pour parcourir 123 km ? \ud83d\udeb4<\/p>\n\n\n\n<p><strong>R\u00e9ponse&nbsp;<\/strong><\/p>\n\n\n\n<p>Vous avez donc le tableau suivant, gr\u00e2ce aux informations que vous avez dans l\u2019\u00e9nonc\u00e9 :&nbsp;<\/p>\n\n\n\n<table id=\"tablepress-1550\" class=\"tablepress tablepress-id-1550\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\">Distance parcourue (km)<\/td><td class=\"column-2\">48<\/td><td class=\"column-3\">123<\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Dur\u00e9e (h)<\/td><td class=\"column-2\">1<\/td><td class=\"column-3\">\ud835\udc65<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-1550 from cache -->\n\n\n\n<p><strong>\ud835\udc65<\/strong>&nbsp; = 1 x 123 \u00f7 48<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;<strong>= 2,5625 (soit environ 2h 34 min)<\/strong><\/p>\n\n\n\n<p>La proportionnalit\u00e9 est pr\u00e9sente dans plein de situations du quotidien, <strong>on aurait aussi pu vous parler de pourcentages de r\u00e9duction ou d\u2019\u00e9chelles sur une carte<\/strong> g\u00e9ographique, etc. \ud83d\uddfa\ufe0f<\/p>\n\n\n\n<p>On pense toutefois avoir fait le tour de <strong>cette notion essentielle dans le programme de maths du coll\u00e8ge<\/strong>. \ud83d\udcda<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zaWdudXA9dHJ1ZQ==\" data-banner=\"2\" data-name=\"Cours part&amp;rsquo; global #2 = CPG2\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Clemence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Thibault2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Thibault<\/p>                          <p class=\"push__teachers-school\">ENS Paris Ulm<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Sophie2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Sophie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Bordeaux<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    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                          class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Noemie2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">No\u00e9mie<\/p>                          <p class=\"push__teachers-school\">M2 en droit \u00e0 Assas<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Fanny2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fanny<\/p>                          <p class=\"push__teachers-school\">Ponts ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Simon2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Simon<\/p>                          <p class=\"push__teachers-school\">4e ann\u00e9e de m\u00e9decine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Nicolas2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Nicolas<\/p>                          <p class=\"push__teachers-school\">CentraleSup\u00e9lec<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2023\/09\/Victor2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Victor<\/p>                          <p class=\"push__teachers-school\">ESCP<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">25\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Le premier <span style=\"color: #48b378;\">cours particulier<\/span> est <span style=\"color: #48b378;\">offert !<\/span> \ud83c\udf81<\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Aidez votre enfant en lui offrant des cours avec un \u00e9tudiant pass\u00e9 par une des meilleures \u00e9coles de France.<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        J&rsquo;EN PROFITE MAINTENANT\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">R\u00e9cap \u2705<\/h2>\n\n\n\n<p>1\ufe0f\u20e3 <strong>Deux grandeurs sont dites \u00ab proportionnelles \u00bb<\/strong> si lorsqu\u2019une grandeur augmente, l\u2019autre augmente aussi dans la m\u00eame proportion. Ce qui signifie qu\u2019elles ont, en effet, le m\u00eame multiplicateur.&nbsp;<\/p>\n\n\n\n<p>2\ufe0f\u20e3 Dans un tableau avec deux grandeurs, vous pouvez reconna\u00eetre une situation de proportionnalit\u00e9 lorsqu\u2019il existe <strong>un coefficient de proportionnalit\u00e9<\/strong>.&nbsp;<\/p>\n\n\n\n<p>3\ufe0f\u20e3 <strong>Sur un graphique (un rep\u00e8re)<\/strong>, on parle de situation de proportionnalit\u00e9 lorsque cette derni\u00e8re est repr\u00e9sent\u00e9e avec <strong>des points qui sont ALIGN\u00c9S avec l\u2019origine<\/strong>.&nbsp;<\/p>\n\n\n\n<p>4\ufe0f\u20e3 Dans les tableaux de proportionnalit\u00e9, on a l\u2019\u00e9galit\u00e9 (en croix) suivante : <strong>a x d = b x c<\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"295\" height=\"99\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png\" alt=\"tableau en croix\" class=\"wp-image-267851\" style=\"width:331px;height:auto\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=295 295w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=200 200w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/sites\/3\/2024\/04\/produit-en-croix-1.png?w=1080 1080w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><figcaption class=\"wp-element-caption\"><em>Produit en croix<\/em><\/figcaption><\/figure><\/div>\n\n\n<p>5\ufe0f\u20e3 <strong>La \u00ab quatri\u00e8me proportionnelle \u00bb<\/strong> d\u00e9signe une situation de proportionnalit\u00e9 dans laquelle on ne conna\u00eet que trois nombres sur les quatre et o\u00f9 il faut donc trouver cette quatri\u00e8me (proportionnelle) valeur encore inconnue.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Vous ne serez d\u00e9sormais plus \u00e0 la ramasse sur le programme du coll\u00e8ge en math\u00e9matiques et, plus particuli\u00e8rement, sur <strong>la notion de proportionnalit\u00e9<\/strong>. \ud83d\udca5<\/p>\n\n\n\n<p>Et si votre aide ne suffit pas, votre enfant peut r\u00e9ussir gr\u00e2ce \u00e0 nos <a href=\"https:\/\/sherpas.com\/cours\/maths\/online\">cours de soutien scolaire de maths en ligne<\/a> avec l\u2019un de nos professeurs ! \ud83d\ude42<\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;267837&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;3&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;5&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Vous avez aim\u00e9 cet article ?&quot;,&quot;legend&quot;:&quot;5\\\/5 - (3 votes)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Piq\u00fbre de rappel : la proportionnalit\u00e9 \u2696\ufe0f&quot;,&quot;width&quot;:&quot;142.5&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 142.5px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            5\/5 - (3 votes)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Notion essentielle de la fin de primaire et du coll\u00e8ge, surtout en 4\u1d49, la proportionnalit\u00e9 est un des (&#8230;)<\/p>\n","protected":false},"author":356,"featured_media":267855,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"category":[12,13],"tag":[],"class_list":["post-267837","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mettre-a-niveau","category-fiches-revision-parents"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/posts\/267837","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/users\/356"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/comments?post=267837"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/posts\/267837\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/media\/267855"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/media?parent=267837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/category?post=267837"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/parents\/wp-json\/wp\/v2\/tag?post=267837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}