{"id":15784,"date":"2023-02-09T08:41:07","date_gmt":"2023-02-09T07:41:07","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=15784"},"modified":"2025-12-22T08:38:40","modified_gmt":"2025-12-22T07:38:40","slug":"chapitre-9-multiplication-et-division-de-nombres-rationnels","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-9-multiplication-et-division-de-nombres-rationnels\/","title":{"rendered":"Chapitre 9 : Multiplication de nombres rationnels"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"15784\" class=\"elementor elementor-15784\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-67d34613 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"67d34613\" data-element_type=\"section\" 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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-92882a6\" data-id=\"92882a6\" 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-40d7e9bf elementor-widget elementor-widget-heading\" data-id=\"40d7e9bf\" 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 9<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1fcb20f3 elementor-widget elementor-widget-heading\" data-id=\"1fcb20f3\" 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\">Multiplication de nombres rationnels<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bbe5f65 elementor-widget elementor-widget-text-editor\" data-id=\"bbe5f65\" 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-41579aa4\" data-id=\"41579aa4\" 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-3257d4fc elementor-widget elementor-widget-image\" data-id=\"3257d4fc\" 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-812f076 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"812f076\" 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-81af3c8\" data-id=\"81af3c8\" 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-ae4fdcd elementor-widget elementor-widget-spacer\" data-id=\"ae4fdcd\" 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-a22b029 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a22b029\" 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-5d2c86a\" data-id=\"5d2c86a\" 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-cae9fb4 elementor-widget elementor-widget-heading\" data-id=\"cae9fb4\" 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 9 : Multiplication de nombres rationnels<\/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-4b8d2c5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4b8d2c5\" 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-0cf753d\" data-id=\"0cf753d\" 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-3607782 elementor-widget elementor-widget-spacer\" data-id=\"3607782\" 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-8c33ba5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8c33ba5\" 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-d2cb9a0\" data-id=\"d2cb9a0\" 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-914b88c elementor-widget elementor-widget-heading\" data-id=\"914b88c\" 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) Multiplier deux nombres rationnels<\/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-653dcbb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"653dcbb\" 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-8515376\" data-id=\"8515376\" 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-de29a4e elementor-widget elementor-widget-text-editor\" data-id=\"de29a4e\" 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>R\u00e8gle :<\/strong> Pour multiplier deux nombres en \u00e9criture fractionnaire :<\/p><ul><li>\u00a0on multiplie les num\u00e9rateurs entre eux ;<\/li><li>on multiplie les d\u00e9nominateurs entre eux.<br \/>$a$, $b$, $c$ et $d$ repr\u00e9sentent quatre nombres d\u00e9cimaux, avec $c\\neq 0$ et $d\\neq 0$ :<br \/>\\[\\dfrac{\\textcolor{blue}{a}}{\\textcolor{red}{c}}\\times \\dfrac{\\textcolor{blue}{b}}{\\textcolor{red}{d}}=\\dfrac{\\textcolor{blue}{a\\times b}}{\\textcolor{red}{c\\times d}}\\]<\/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-f40d6ce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f40d6ce\" 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-ebc47e9\" data-id=\"ebc47e9\" 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-405f2d8 elementor-widget elementor-widget-text-editor\" data-id=\"405f2d8\" 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 \u00e0 partir d&rsquo;un exemple :<\/strong><br \/>Par d\u00e9finition du quotient de deux nombres :<br \/>\\[5\\times \\dfrac{4}{5}=4~~\\text{et}~~3\\times \\dfrac{2}{3}=2\\]$\\dfrac{4\\times 2}{5\\times 3}$ est le nombre qui multipli\u00e9 par $5\\times 3$ donne $4\\times 2$ :<br \/>$(5\\times 3)\\times \\dfrac{4\\times 2}{5\\times 3}=4\\times 2$<br \/>Or $(5\\times 3)\\times (\\dfrac{4}{5}\\times \\dfrac{2}{3})=(5\\times \\dfrac{4}{5})\\times (3\\times \\dfrac{2}{3})=4\\times 2$.<br \/>Ainsi :<br \/>$\\dfrac{4}{5}\\times \\dfrac{2}{3}=\\dfrac{4\\times 2}{5\\times 3}$<\/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-ea55681 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ea55681\" 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-33 elementor-top-column elementor-element elementor-element-b9adf04\" data-id=\"b9adf04\" 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-3502808 elementor-widget elementor-widget-text-editor\" data-id=\"3502808\" 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><\/p><ul><li>\\[\\dfrac{2}{3}\\times \\dfrac{4}{5}=\\dfrac{2\\times 4}{3\\times 5}=\\dfrac{8}{15}\\]<\/li><\/ul><p>\u00a0<\/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<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-27dc24e\" data-id=\"27dc24e\" 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-1c91154 elementor-widget elementor-widget-text-editor\" data-id=\"1c91154\" 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>\u00a0<\/p><ul><li>\\[\\dfrac{4,2}{7}\\times \\dfrac{3}{1,2}=\\dfrac{4,2\\times 3}{7\\times 1,2}=\\dfrac{12,6}{8,4}\\]<\/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<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-43968a9\" data-id=\"43968a9\" 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-92b6d91 elementor-widget elementor-widget-text-editor\" data-id=\"92b6d91\" 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>\u00a0<\/p><ul><li>\\[2\\times \\dfrac{4}{3}=\\dfrac{2}{\\textcolor{red}{1}}\\times \\dfrac{4}{3}=\\dfrac{2\\times 4}{1\\times 3}=\\dfrac{8}{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-8e96143 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8e96143\" 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-72cc03f\" data-id=\"72cc03f\" 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-4c249b7 elementor-widget elementor-widget-text-editor\" data-id=\"4c249b7\" 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> Il est parfois utile de simplifier les fractions avant de se lancer dans les calculs.<br \/>\\[\\dfrac{25}{40}\\times \\dfrac{16}{20}=\\dfrac{25\\times 16}{40\\times 20}=\\dfrac{5\\times 5\\times 8\\times 2}{8\\times 5\\times 5\\times 4}=\\dfrac{2}{4}=\\dfrac{1}{2}\\]<br \/><\/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-9b9e2be elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9b9e2be\" 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-a536764\" data-id=\"a536764\" 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-2c15b13 elementor-widget elementor-widget-video\" data-id=\"2c15b13\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/RfNRleqXUZs?si=Zr9GyA-YG3wk4SiE&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-dbc52d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dbc52d0\" 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-362c1a0\" data-id=\"362c1a0\" 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-007e48d elementor-widget elementor-widget-spacer\" data-id=\"007e48d\" 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-c3fd220 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c3fd220\" 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-acf6d8d\" data-id=\"acf6d8d\" 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-ea66d39 elementor-widget elementor-widget-heading\" data-id=\"ea66d39\" 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) Prendre une fraction d\u2019une quantit\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-beb8fa7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"beb8fa7\" 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-47bf792\" data-id=\"47bf792\" 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-25c0bd5 elementor-widget elementor-widget-text-editor\" data-id=\"25c0bd5\" 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>R\u00e8gle :<\/strong> Pour prendre une fraction d&rsquo;une quantit\u00e9, on multiplie cette fraction par cette quantit\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-16b98cf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"16b98cf\" 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-bb0565c\" data-id=\"bb0565c\" 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-bc0bb85 elementor-widget elementor-widget-text-editor\" data-id=\"bc0bb85\" 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> Un triathlon se pr\u00e9sente sous la forme d&rsquo;un parcours\u00a0<span style=\"font-size: 18px; font-style: normal; font-weight: 400;\">de $20~\\text{km}$\u00a0<\/span><span style=\"font-size: 18px;\">partag\u00e9 en trois parties :<\/span><\/p><ul><li>natation pendant $\\dfrac{1}{20}$ du parcours ;<\/li><li>v\u00e9lo pendant $\\dfrac{3}{4}$ du parcours ;<\/li><li>course \u00e0 pied pendant le reste du parcours.<\/li><\/ul><ol><li>Calculer la distance parcourue \u00e0 la nage.<\/li><\/ol><p>On calcule $\\dfrac{1}{20}$ de $20~\\text{km}$<span style=\"font-size: 18px;\">\u00a0:<\/span><\/p><p>$\\dfrac{1}{20}\\times 20~\\text{km}=\\dfrac{1\\times 20~\\text{km}}{20}=\\dfrac{20~\\text{km}}{20}=1~\\text{km}~~(\\text{ou}~~\\dfrac{1}{20}\\times 20~\\text{km}=0,05\\times 20~\\text{km}=1~\\text{km})$<\/p><p>On nage donc pendant $1~\\text{km}$<span style=\"font-size: 18px;\">.<\/span><\/p><p>\u00a0 \u00a0 2. Calculer la distance parcourue \u00e0 v\u00e9lo.<\/p><p>On calcule $\\dfrac{3}{4}$ de $20~\\text{km}$<span style=\"font-size: 18px;\">\u00a0:<\/span><\/p><p>$\\dfrac{3}{4}\\times 20~\\text{km}=\\dfrac{3\\times 20~\\text{km}}{4}=\\dfrac{60~\\text{km}}{4}=15~\\text{km}$<\/p><p>On p\u00e9dale donc pendant $15~\\text{km}$<span style=\"font-size: 18px;\">.<\/span><\/p><p>\u00a0 \u00a0 3. En d\u00e9duire la distance parcourue en courant.<\/p><p>$20~\\text{km}-1~\\text{km}-15~\\text{km}=4~\\text{km}$<br \/>On court donc pendant $4~\\text{km}$<span style=\"font-size: 18px;\">.<\/span><\/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-9bfa669 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9bfa669\" 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-2bad0a6\" data-id=\"2bad0a6\" 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-fe1af56 elementor-widget elementor-widget-video\" data-id=\"fe1af56\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/OUDicIla23I&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-e1d12ae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e1d12ae\" 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-95b08d9\" data-id=\"95b08d9\" 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-65d1a79 elementor-widget elementor-widget-spacer\" data-id=\"65d1a79\" 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-0b97d86 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0b97d86\" 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-9c410be\" data-id=\"9c410be\" 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-dcc997d elementor-widget elementor-widget-heading\" data-id=\"dcc997d\" 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) Encha\u00eenement d\u2019op\u00e9rations<\/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-5bdeb28 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5bdeb28\" 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-3b27bf4\" data-id=\"3b27bf4\" 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-39d3b8c elementor-widget elementor-widget-text-editor\" data-id=\"39d3b8c\" 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>Il faut \u00e9videmment respecter les priorit\u00e9s op\u00e9ratoires pour calculer des expressions avec des nombres en \u00e9criture fractionnaire.<\/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-b7ce8dd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7ce8dd\" 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-50 elementor-top-column elementor-element elementor-element-e073ded\" data-id=\"e073ded\" 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-85e1216 elementor-widget elementor-widget-text-editor\" data-id=\"85e1216\" 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> Calculer les expressions suivantes :<br \/>\\begin{eqnarray*}<br \/>A&amp;=&amp;\\dfrac{7}{4}-\\textcolor{red}{\\dfrac{3}{4}\\times \\dfrac{3}{2}}\\\\<br \/>A&amp;=&amp;\\dfrac{7}{4}-\\dfrac{9}{8}\\\\<br \/>A&amp;=&amp;\\dfrac{7\\textcolor{red}{\\times 2}}{4\\textcolor{red}{\\times 2}}-\\dfrac{9}{8}\\\\<br \/>A&amp;=&amp;\\dfrac{14}{8}-\\dfrac{9}{8}\\\\<br \/>A&amp;=&amp;\\dfrac{5}{8}<br \/>\\end{eqnarray*}<\/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<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-02dd20d\" data-id=\"02dd20d\" 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-95244d0 elementor-widget elementor-widget-text-editor\" data-id=\"95244d0\" 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&nbsp;\n\n\\begin{eqnarray*}\nB&amp;=&amp;\\left(\\textcolor{red}{\\dfrac{5}{6}+\\dfrac{7}{4}}\\right) \\times \\dfrac{3}{5}\\\\\nB&amp;=&amp;\\left(\\dfrac{5\\textcolor{red}{\\times 2}}{6\\textcolor{red}{\\times 2}}+\\dfrac{7\\textcolor{red}{\\times 3}}{4\\textcolor{red}{\\times 3}}\\right)\\times \\dfrac{3}{5}\\\\\nB&amp;=&amp;\\left(\\dfrac{10}{12}+\\dfrac{21}{12}\\right)\\times \\dfrac{3}{5}\\\\\nB&amp;=&amp;\\dfrac{31}{12}\\times \\dfrac{3}{5}\\\\\nB&amp;=&amp;\\dfrac{93}{60}\\\\\nB&amp;=&amp;\\dfrac{93\\div 3}{60\\div 3}\\\\\nB&amp;=&amp;\\dfrac{31}{20}\n\\end{eqnarray*}\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-7119ea0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7119ea0\" 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-195c9f7\" data-id=\"195c9f7\" 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-d4d4cec elementor-widget elementor-widget-spacer\" data-id=\"d4d4cec\" 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-259e360 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"259e360\" 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-fa5db64\" data-id=\"fa5db64\" 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-4c71258 elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"4c71258\" 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\/4oLMecT5sgQWyGD\" 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-1dbd7d8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1dbd7d8\" 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-903a864\" data-id=\"903a864\" 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-fd71a96 elementor-widget elementor-widget-spacer\" data-id=\"fd71a96\" 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 9 Multiplication de nombres rationnels Chapitre 9 : Multiplication de nombres rationnels A) Multiplier deux nombres rationnels R\u00e8gle : Pour multiplier deux nombres en \u00e9criture fractionnaire : \u00a0on multiplie les num\u00e9rateurs entre eux ; on multiplie les d\u00e9nominateurs entre eux.$a$, $b$, $c$ et $d$ repr\u00e9sentent quatre nombres d\u00e9cimaux, avec $cneq 0$ et $dneq 0$ [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":15785,"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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