{"id":15591,"date":"2023-02-06T22:37:08","date_gmt":"2023-02-06T21:37:08","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=15591"},"modified":"2025-12-22T08:28:38","modified_gmt":"2025-12-22T07:28:38","slug":"chapitre-6-la-proportionnalite","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-6-la-proportionnalite\/","title":{"rendered":"Chapitre 6 : La proportionnalit\u00e9"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"15591\" class=\"elementor elementor-15591\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3bc3f83b elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"3bc3f83b\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;,&quot;shape_divider_bottom&quot;:&quot;wave-brush&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 283.5 27.8\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M283.5,9.7c0,0-7.3,4.3-14,4.6c-6.8,0.3-12.6,0-20.9-1.5c-11.3-2-33.1-10.1-44.7-5.7\ts-12.1,4.6-18,7.4c-6.6,3.2-20,9.6-36.6,9.3C131.6,23.5,99.5,7.2,86.3,8c-1.4,0.1-6.6,0.8-10.5,2c-3.8,1.2-9.4,3.8-17,4.7\tc-3.2,0.4-8.3,1.1-14.2,0.9c-1.5-0.1-6.3-0.4-12-1.6c-5.7-1.2-11-3.1-15.8-3.7C6.5,9.2,0,10.8,0,10.8V0h283.5V9.7z M260.8,11.3\tc-0.7-1-2-0.4-4.3-0.4c-2.3,0-6.1-1.2-5.8-1.1c0.3,0.1,3.1,1.5,6,1.9C259.7,12.2,261.4,12.3,260.8,11.3z M242.4,8.6\tc0,0-2.4-0.2-5.6-0.9c-3.2-0.8-10.3-2.8-15.1-3.5c-8.2-1.1-15.8,0-15.1,0.1c0.8,0.1,9.6-0.6,17.6,1.1c3.3,0.7,9.3,2.2,12.4,2.7\tC239.9,8.7,242.4,8.6,242.4,8.6z 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M34.5,12.4c-0.2,0,2.1,0.8,3.3,0.9c1.2,0.1,2,0.1,2-0.2c0-0.3-0.1-0.5-1.6-0.4C36.6,12.8,34.7,12.4,34.5,12.4z M152.2,21.1\tc-0.1,0.1-2.4-0.3-7.5-0.3c-5,0-13.6-2.4-17.2-3.5c-3.6-1.1,10,3.9,16.5,4.1C150.5,21.6,152.3,21,152.2,21.1z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M269.6,18c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC267.7,18.8,269.7,18,269.6,18z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M227.4,9.8c-0.2-0.1-4.5-1-9.5-1.2c-5-0.2-12.7,0.6-12.3,0.5c0.3-0.1,5.9-1.8,13.3-1.2\tS227.6,9.9,227.4,9.8z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M204.5,13.4c-0.1-0.1,2-1,3.2-1.1c1.2-0.1,2,0,2,0.3c0,0.3-0.1,0.5-1.6,0.4\tC206.4,12.9,204.6,13.5,204.5,13.4z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M201,10.6c0-0.1-4.4,1.2-6.3,2.2c-1.9,0.9-6.2,3.1-6.1,3.1c0.1,0.1,4.2-1.6,6.3-2.6\tS201,10.7,201,10.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\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-50 elementor-top-column elementor-element elementor-element-612198d9\" data-id=\"612198d9\" 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-6aa26812 elementor-widget elementor-widget-heading\" data-id=\"6aa26812\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 6<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-57fac957 elementor-widget elementor-widget-heading\" data-id=\"57fac957\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">La proportionnalit\u00e9<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7939d66b elementor-widget elementor-widget-text-editor\" data-id=\"7939d66b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\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<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-46cd72cf\" data-id=\"46cd72cf\" 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-5fa94dd7 elementor-widget elementor-widget-image\" data-id=\"5fa94dd7\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"192\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/cours-maths-4eme.png\" class=\"attachment-medium size-medium wp-image-15214\" alt=\"Cours de math\u00e9matiques de 4\u00e8me\" \/>\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-8c8b1e7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8c8b1e7\" 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-c97b82b\" data-id=\"c97b82b\" 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-6e36039 elementor-widget elementor-widget-spacer\" data-id=\"6e36039\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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-c9b59f9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c9b59f9\" 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-a7230e0\" data-id=\"a7230e0\" 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-5937fb0 elementor-widget elementor-widget-heading\" data-id=\"5937fb0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 6 : La proportionnalit\u00e9<\/h2>\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-0ccb0d6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0ccb0d6\" 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-ea2b7d7\" data-id=\"ea2b7d7\" 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-b8f9140 elementor-widget elementor-widget-spacer\" data-id=\"b8f9140\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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-84839a7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"84839a7\" 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-4ff2b2e\" data-id=\"4ff2b2e\" 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-55ce4f3 elementor-widget elementor-widget-heading\" data-id=\"55ce4f3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">A) Calculer une quatri\u00e8me proportionnelle<\/h3>\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-da7a65a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"da7a65a\" 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-84bf71e\" data-id=\"84bf71e\" 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-98cf7cb elementor-widget elementor-widget-text-editor\" data-id=\"98cf7cb\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Vocabulaire :<\/strong> Dans un tableau de proportionnalit\u00e9, lorsqu\u2019on conna\u00eet trois nombres non nuls, on peut calculer le quatri\u00e8me nombre manquant. Ce nombre manquant est appel\u00e9 une <strong>quatri\u00e8me proportionnelle<\/strong>.<\/p>\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-43539f4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"43539f4\" 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-c4a30cf\" data-id=\"c4a30cf\" 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-c8bbb09 elementor-widget elementor-widget-text-editor\" data-id=\"c8bbb09\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<strong>Propri\u00e9t\u00e9 :<\/strong> Le tableau ci-dessous repr\u00e9sente une situation de proportionnalit\u00e9.\n\n<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-15595 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/produit-en-croix-1.png\" alt=\"\" width=\"101\" height=\"75\" \/>\n\nOn peut alors \u00e9crire l&rsquo;\u00e9galit\u00e9 des produits en croix :\n\\[\\textcolor{red}{a}\\times \\textcolor{red}{d}=\\textcolor{blue}{b}\\times \\textcolor{blue}{c}\\]\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-e96fcb9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e96fcb9\" 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-73f7e14\" data-id=\"73f7e14\" 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-3cf55e9 elementor-widget elementor-widget-text-editor\" data-id=\"3cf55e9\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9monstration :<\/strong> Ce tableau est un tableau de proportionnalit\u00e9 donc les quotients $\\dfrac{a}{b}$ et $\\dfrac{c}{d}$ sont \u00e9gaux.<br \/>Ainsi,<br \/>\\[\\dfrac{a}{b}=\\dfrac{c}{d}\\]Donc :<br \/>\\[\\dfrac{a\\times d}{b\\times d}=\\dfrac{c\\times b}{d\\times b}\\]Ces deux fractions ont des d\u00e9nominateurs \u00e9gaux, donc leurs num\u00e9rateurs sont \u00e9galement \u00e9gaux :<br \/>\\[a\\times d=b\\times c\\]\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-361367d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"361367d\" 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-097b224\" data-id=\"097b224\" 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-23684de elementor-widget elementor-widget-text-editor\" data-id=\"23684de\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemples :<\/strong> $4$ kg de cerises co\u00fbtent $11,20$ euros. Combien co\u00fbtent $5$ kg de cerises ?<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15596 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/produit-en-croix-2.png\" alt=\"\" width=\"309\" height=\"90\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/produit-en-croix-2.png 309w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/produit-en-croix-2-300x87.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/p><p>\\begin{eqnarray*}<br \/>4\\times x&amp;=&amp;5\\times 11,20\\\\<br \/>x&amp;=&amp;\\dfrac{5\\times 11,20}{4}\\\\<br \/>x&amp;=&amp;14<br \/>\\end{eqnarray*}<br \/>$5$ kg de cerises co\u00fbtent $14$ euros.<\/p>\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-4547840 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4547840\" 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-6bebfae\" data-id=\"6bebfae\" 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-9081603 elementor-widget elementor-widget-video\" data-id=\"9081603\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/vf6zZty7PLU&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\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-06957f0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"06957f0\" 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-dee7761\" data-id=\"dee7761\" 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-7925f85 elementor-widget elementor-widget-spacer\" data-id=\"7925f85\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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-7bcd920 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7bcd920\" 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-f11f490\" data-id=\"f11f490\" 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-54ed20c elementor-widget elementor-widget-video\" data-id=\"54ed20c\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/2UDYG_hRCU4&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\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-2e4d50c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2e4d50c\" 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-b2e3cfa\" data-id=\"b2e3cfa\" 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-0e87a53 elementor-widget elementor-widget-spacer\" data-id=\"0e87a53\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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-7aa822a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7aa822a\" 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-37a62c8\" data-id=\"37a62c8\" 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-6d8b271 elementor-widget elementor-widget-heading\" data-id=\"6d8b271\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">B) Reconna\u00eetre un graphique repr\u00e9sentant une situation de proportionnalit\u00e9<\/h3>\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-a6c41b1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a6c41b1\" 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-6bcc051\" data-id=\"6bcc051\" 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-15f6ca5 elementor-widget elementor-widget-text-editor\" data-id=\"15f6ca5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9 (admise) :<\/strong> Une situation repr\u00e9sent\u00e9e par des points align\u00e9s avec l\u2019origine du rep\u00e8re est \u00e9quivalente \u00e0 une situation de proportionnalit\u00e9.<\/p>\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-77b775c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"77b775c\" 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-bc23fb3\" data-id=\"bc23fb3\" 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-4c694bf elementor-widget elementor-widget-text-editor\" data-id=\"4c694bf\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemples :<\/strong> Le(s)quel(s) de ces trois graphiques repr\u00e9sentent une situation de proportionnalit\u00e9 ?<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15597 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/representation-graphique-proportionnalite.png\" alt=\"\" width=\"886\" height=\"265\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/representation-graphique-proportionnalite.png 886w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/representation-graphique-proportionnalite-300x90.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/representation-graphique-proportionnalite-768x230.png 768w\" sizes=\"auto, (max-width: 886px) 100vw, 886px\" \/><\/p><ul><li>Cas 1 : Les points sont align\u00e9s avec l\u2019origine du rep\u00e8re donc c\u2019est une situation de proportionnalit\u00e9.<\/li><li>Cas 2 : Les points sont align\u00e9s mais pas avec l\u2019origine du rep\u00e8re donc ce n\u2019est pas une situation de proportionnalit\u00e9.<\/li><li>Cas 3 : Les points ne sont pas align\u00e9s donc ce n\u2019est pas une situation de proportionnalit\u00e9.<\/li><\/ul>\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-8afffdb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8afffdb\" 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-313aefe\" data-id=\"313aefe\" 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-74ad5cd elementor-widget elementor-widget-video\" data-id=\"74ad5cd\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/Ta0fHOtLJKw&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\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-50c467c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"50c467c\" 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-4499e04\" data-id=\"4499e04\" 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-0bf265b elementor-widget elementor-widget-spacer\" data-id=\"0bf265b\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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-e87f0ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e87f0ee\" 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-6f565b1\" data-id=\"6f565b1\" 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-515ba7a elementor-widget elementor-widget-heading\" data-id=\"515ba7a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">C) Appliquer ou calculer un pourcentage<\/h3>\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-ae62be8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ae62be8\" 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-ce9cd1b\" data-id=\"ce9cd1b\" 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-b2039a3 elementor-widget elementor-widget-text-editor\" data-id=\"b2039a3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9 :<\/strong> $p$ d\u00e9signe un nombre. Calculer $p\\%$ d&rsquo;une quantit\u00e9 c&rsquo;est multiplier cette quantit\u00e9 par $\\dfrac{p}{100}$.<\/p>\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-7eaffff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7eaffff\" 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-fe9b165\" data-id=\"fe9b165\" 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-3769d9e elementor-widget elementor-widget-text-editor\" data-id=\"3769d9e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Calculer $30 \\%$ de $50~\\text{L}$.<\/p><p>\\[\\dfrac{30}{100}\\times 50~\\text{L}=0,30\\times 50~\\text{L}=15~\\text{L}\\]<p>$30 \\%$ de $50~\\text{L}$ c&rsquo;est donc $15~\\text{L}$.<\/p>\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-0e6b046 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0e6b046\" 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-01f6a6b\" data-id=\"01f6a6b\" 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-afb3ac7 elementor-widget elementor-widget-video\" data-id=\"afb3ac7\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/gXcwdDYSMeM?si=hdInGTxcNGHVPPlc&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\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-56479ca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"56479ca\" 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-39a7811\" data-id=\"39a7811\" 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-d31e9bd elementor-widget elementor-widget-text-editor\" data-id=\"d31e9bd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>M\u00e9thode :<\/strong> Calculer un pourcentage revient \u00e0 \u00e9crire une proportion de d\u00e9nominateur 100.<\/p>\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-d68bd5d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d68bd5d\" 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-8dcaa16\" data-id=\"8dcaa16\" 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-877ca85 elementor-widget elementor-widget-text-editor\" data-id=\"877ca85\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<strong>Exemple :<\/strong> $7$ \u00e9l\u00e8ves sur $28$ sont gauchers. Quel est le pourcentage de gauchers ?\n\n\\begin{eqnarray*}\n\\dfrac{7}{28}&#038;=&#038;\\dfrac{x}{100}\\\\\nx&#038;=&#038;\\dfrac{7\\times 100}{28}\\\\\nx&#038;=&#038;25\n\\end{eqnarray*}\nDonc $25\\%$ de ces \u00e9l\u00e8ves sont gauchers.\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-8c0af18 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8c0af18\" 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-c26dbeb\" data-id=\"c26dbeb\" 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-e8ae0ae elementor-widget elementor-widget-video\" data-id=\"e8ae0ae\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/PLDhiVCbZ7c?si=F8qmB-vYZKd0QBcR&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\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-fd8b527 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fd8b527\" 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-86c89cf\" data-id=\"86c89cf\" 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-c528c1c elementor-widget elementor-widget-spacer\" data-id=\"c528c1c\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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-66c9f20 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"66c9f20\" 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-7937594\" data-id=\"7937594\" 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-cba18ad elementor-widget elementor-widget-heading\" data-id=\"cba18ad\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">D) Agrandissement-r\u00e9duction<\/h3>\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-a15b206 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a15b206\" 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-3c2cb4e\" data-id=\"3c2cb4e\" 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-bf0c0f5 elementor-widget elementor-widget-text-editor\" data-id=\"bf0c0f5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9finition :<\/strong> Agrandir ou r\u00e9duire une figure, c\u2019est construire une figure de m\u00eame forme en multipliant les longueurs de la figure initiale par un nombre $k$ strictement positif.<\/p>\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-f2b9bad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f2b9bad\" 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-d26f722\" data-id=\"d26f722\" 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-b888744 elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"b888744\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Vocabulaire :<\/strong> On dit que $k$ est le <strong>rapport<\/strong> (ou coefficient) d&rsquo;agrandissement ou de r\u00e9duction.<\/p><ul><li>Si $k&gt;1$, il s&rsquo;agit d&rsquo;un <strong>agrandissement<\/strong>.<\/li><li>Si $0&lt;k&lt;1$, il s&rsquo;agit d&rsquo;une <strong>r\u00e9duction<\/strong>.<br \/><br \/><\/li><\/ul>\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-05767cf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"05767cf\" 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-894e78c\" data-id=\"894e78c\" 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-71a860a elementor-widget elementor-widget-text-editor\" data-id=\"71a860a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9s :<\/strong> Dans un agrandissement ou une r\u00e9duction, de rapport $k$ :<\/p><ul><li>les longueurs sont toutes multipli\u00e9es par $k$ ;<\/li><li>les mesures des angles sont conserv\u00e9es.<\/li><\/ul>\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-20ddb61 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"20ddb61\" 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-23d4133\" data-id=\"23d4133\" 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-b63428e elementor-widget elementor-widget-text-editor\" data-id=\"b63428e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Sur la figure ci-dessous, le triangle $A&rsquo;B&rsquo;C&rsquo;$ est un agrandissement du triangle $ABC$. Les longueurs ont \u00e9t\u00e9 multipli\u00e9es par $1,5$.<\/p><p>En effet :<br \/>\\[3~\\text{cm}\\textcolor{red}{\\times 1,5}=4,5~\\text{cm}~~~~4~\\text{cm}\\textcolor{red}{\\times 1,5}=6~\\text{cm}~~~~5~\\text{cm}\\textcolor{red}{\\times 1,5}=7,5~\\text{cm}\\]<p>La mesure des angles est en revanche conserv\u00e9e.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-17241 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/11\/agrandissement-triangle.png\" alt=\"\" width=\"800\" height=\"334\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/11\/agrandissement-triangle.png 800w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/11\/agrandissement-triangle-300x125.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/11\/agrandissement-triangle-768x321.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\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-a1235d5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a1235d5\" 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-6690e41\" data-id=\"6690e41\" 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-7adc242 elementor-widget elementor-widget-text-editor\" data-id=\"7adc242\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9s :<\/strong> Dans un agrandissement ou une r\u00e9duction de rapport $k$ :<\/p><ul><li>l&rsquo;aire d&rsquo;une surface est multipli\u00e9e par $k^{2}$ ;<\/li><li>le volume d&rsquo;un solide est multipli\u00e9 par $k^{3}$.<\/li><\/ul>\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-47be9f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"47be9f6\" 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-4f85c3d\" data-id=\"4f85c3d\" 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-f1ad9ca elementor-widget elementor-widget-text-editor\" data-id=\"f1ad9ca\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Sur la figure ci-dessous, le 2\u00e8me pav\u00e9 droit est un agrandissement du 1er pav\u00e9 droit de coefficient $2$.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-17245 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/11\/agrandissement-pave.png\" alt=\"\" width=\"568\" height=\"348\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/11\/agrandissement-pave.png 568w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/11\/agrandissement-pave-300x184.png 300w\" sizes=\"auto, (max-width: 568px) 100vw, 568px\" \/><\/p><p>Or :<br \/>\\[V_{\\text{pav\u00e9 droit 1}}=1~\\text{cm}\\times 1~\\text{cm}\\times 2~\\text{cm}=2~\\text{cm}^{3}\\]\\[V_{\\text{pav\u00e9 droit 2}}=2~\\text{cm}\\times 2~\\text{cm}\\times 4~\\text{cm}=16~\\text{cm}^{3}\\]<p>Le volume a \u00e9t\u00e9 multipli\u00e9 par $2^{3}=8$.<\/p>\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-986a4f3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"986a4f3\" 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-8b4318a\" data-id=\"8b4318a\" 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 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elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7539120\" data-id=\"7539120\" 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-6571f8d elementor-widget elementor-widget-video\" data-id=\"6571f8d\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/rKLmwPqB49c?si=zP4OMQZvCCalZYtG&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\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-7893d68 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7893d68\" 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-f05d086\" data-id=\"f05d086\" 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-bfadf28 elementor-widget elementor-widget-spacer\" data-id=\"bfadf28\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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-78c29e5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"78c29e5\" 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-e78d3f8\" data-id=\"e78d3f8\" 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-da4343f elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"da4343f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/nuage02.apps.education.fr\/index.php\/s\/qkCeiKbKMYty7KG\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-arrow-alt-circle-right\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Exercices corrig\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\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-2785cf0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2785cf0\" 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-19b2144\" data-id=\"19b2144\" 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-595a4c9 elementor-widget elementor-widget-spacer\" data-id=\"595a4c9\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Chapitre 6 La proportionnalit\u00e9 Chapitre 6 : La proportionnalit\u00e9 A) Calculer une quatri\u00e8me proportionnelle Vocabulaire : Dans un tableau de proportionnalit\u00e9, lorsqu\u2019on conna\u00eet trois nombres non nuls, on peut calculer le quatri\u00e8me nombre manquant. Ce nombre manquant est appel\u00e9 une quatri\u00e8me proportionnelle. Propri\u00e9t\u00e9 : Le tableau ci-dessous repr\u00e9sente une situation de proportionnalit\u00e9. On peut alors [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":15592,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"page-builder","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[39],"tags":[],"class_list":["post-15591","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cours-et-exercices-4eme"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Chapitre 6 : La proportionnalit\u00e9<\/title>\n<meta name=\"description\" content=\"Cours de math\u00e9matiques de 4\u00e8me sur la proportionnalit\u00e9, l&#039;activit\u00e9 du chapitre, les exercices corrig\u00e9s...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-6-la-proportionnalite\/\" \/>\n<meta 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