{"id":51228,"date":"2020-05-29T10:09:58","date_gmt":"2020-05-29T09:09:58","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=51228"},"modified":"2026-10-20T15:06:43","modified_gmt":"2026-10-20T14:06:43","slug":"cours-en-ligne-fractions","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/","title":{"rendered":"Cours sur les fractions"},"content":{"rendered":"<div class=\"Latex_page\"><\/div>\n<div><\/div>\n<div class=\"Latex_page\">\n<section class=\"has_ae_slider elementor-element elementor-section-full_width elementor-reverse-mobile elementor-section-stretched elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default elementor-section elementor-top-section\">\n<div class=\"elementor-container elementor-column-gap-no\">\n<div class=\"elementor-row\">\n<div class=\"elementor-column-wrap elementor-element-populated colone_elementor\">\n<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"page\" data-elementor-id=\"86176\" class=\"elementor elementor-86176\">\n\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-6f9fb2b3 elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"6f9fb2b3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5032621c sticky_badeau_colone strick_col ae-bg-gallery-type-default\" data-id=\"5032621c\" data-element_type=\"column\" data-e-type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-611bd75f elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"611bd75f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-55718945 strick_col ae-bg-gallery-type-default\" data-id=\"55718945\" data-element_type=\"column\" data-e-type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5940f45c elementor-widget elementor-widget-heading\" data-id=\"5940f45c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne Tage Mage <\/a><\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9bc725 elementor-widget elementor-widget-heading\" data-id=\"f9bc725\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Chapitres du sous-test 2 du Tage Mage<\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56c02cf0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"56c02cf0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Fractions<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-390da5ff elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"390da5ff\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pourcentages\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pourcentages<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da8d658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"da8d658\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-algebre\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Alg\u00e8bre<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-490ac2aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"490ac2aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">G\u00e9om\u00e9trie<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3fd40310 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3fd40310\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-vitesse\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Vitesse<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6edf1c7e elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6edf1c7e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Arithm\u00e9tique<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4f2c805 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4f2c805\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-puissances\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Puissances<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-447b658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"447b658\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-regle-de-trois\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Proportionnalit\u00e9<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53863aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"53863aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-denombrement\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9nombrement<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11741389 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"11741389\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Probabilit\u00e9s<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ace8ace elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6ace8ace\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-moyenne-arithmetique-moyenne-ponderee\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Moyenne<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-13f1db2f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"13f1db2f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Th\u00e9or\u00e8me de Pythagore<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-10d04684 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"10d04684\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-thales\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Th\u00e9or\u00e8me de Thal\u00e8s<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-691a3a8a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"691a3a8a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Racines Carr\u00e9es<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2a5f7bd6 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2a5f7bd6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/nous-contacter\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">CONTACTEZ-NOUS<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"elementor-column-wrap elementor-element-populated colone_latex\" style=\"text-align: justify;\">\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<div class=\"elementor-text-editor elementor-clearfix\" style=\"color: #000000; font-family: Lato, sans-serif;\">\n<h1 class=\"Latex_page_title\" style=\"text-align: center;\">Op\u00e9rations sur les fractions : addition, soustraction, multiplication et division<\/h1>\n<p><em>Par Seda Biber, le 20\/10\/2026<\/em><\/p>\n<\/div>\n<p dir=\"ltr\" style=\"text-align: justify;\">Pour <strong>additionner ou soustraire des fractions<\/strong>, on les met d&rsquo;abord au m\u00eame d\u00e9nominateur, puis on additionne ou on soustrait les num\u00e9rateurs. Pour <strong>multiplier des fractions<\/strong>, on multiplie les num\u00e9rateurs entre eux et les d\u00e9nominateurs entre eux. Pour <strong>diviser par une fraction<\/strong>, on multiplie par son inverse. On termine en simplifiant le r\u00e9sultat jusqu&rsquo;\u00e0 obtenir une <strong>fraction irr\u00e9ductible<\/strong>. Ces r\u00e8gles servent du CM1 jusqu&rsquo;aux \u00e9preuves de calcul du <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Tage Mage<\/a>. Si les fractions vous posent probl\u00e8me, des <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\">cours particuliers de maths<\/a> ou un <a href=\"https:\/\/groupe-reussite.fr\/stages\/toutes-matieres\/tous-niveaux\/france\/toutes-periodes\/\">stage intensif<\/a> permettent de reprendre les bases.<\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\">Ce cours fait partie des fiches en ligne de Groupe R\u00e9ussite. Ces fiches sont r\u00e9dig\u00e9es par l&rsquo;\u00e9quipe qui organise nos <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/toutes-matieres\/tous-niveaux\/france\/\">cours particuliers<\/a> \u00e0 domicile et nos <a href=\"https:\/\/groupe-reussite.fr\/cours-en-ligne\/toutes-matieres\/tous-niveaux\/france\/\">cours particuliers en ligne<\/a>. Vous \u00eates \u00e9tudiant ou enseignant et vous ma\u00eetrisez ces notions ? Vous pouvez <a href=\"https:\/\/groupe-reussite.fr\/donner-cours-particuliers\/\">donner des cours particuliers<\/a> avec nous.<\/p>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-fractions\/\">Exercices et corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne du Tage Mage<\/a><\/p>\n<h2 dir=\"ltr\">R\u00e9sum\u00e9 : les r\u00e8gles de calcul sur les fractions<\/h2>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Op\u00e9ration<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>R\u00e8gle<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Exemple<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>Addition<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">M\u00eame d\u00e9nominateur, puis on additionne les num\u00e9rateurs<\/td>\n<td style=\"border: 1px solid #0F2742;\"><img decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c309c4843af64afc03836f5f025cf271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"177\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>Soustraction<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">M\u00eame d\u00e9nominateur, puis on soustrait les num\u00e9rateurs<\/td>\n<td style=\"border: 1px solid #0F2742;\"><img decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5831007cc7cd3179f8dc9fdcac839c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#49;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"177\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>Multiplication<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">Num\u00e9rateur \u00d7 num\u00e9rateur, d\u00e9nominateur \u00d7 d\u00e9nominateur<\/td>\n<td style=\"border: 1px solid #0F2742;\"><img decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f3c3f33177f7e6fc8a94aac3ca1ea4ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"89\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>Division<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">On multiplie par l&rsquo;inverse du diviseur<\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7e7374e4586905736c0fbb7617556b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#100;&#105;&#118;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#49;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#57;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#125;&#123;&#54;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"177\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>Simplification<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">On divise le num\u00e9rateur et le d\u00e9nominateur par un m\u00eame nombre<\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-9d12c5ed9cbb8672eb5152a438b03234_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#53;&#125;&#123;&#51;&#50;&#48;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#125;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"72\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<p dir=\"ltr\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"186409\" class=\"elementor elementor-186409\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-208557d4 elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"208557d4\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-5c1307a9 ae-bg-gallery-type-default\" data-id=\"5c1307a9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a42a1b elementor-widget elementor-widget-heading\" data-id=\"a42a1b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">AVOIR LES MEILLEURS PROFS DE MATHS<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53b6892b elementor-widget elementor-widget-heading\" data-id=\"53b6892b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">C'est gagner en autonomie<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-339aefc1 elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"339aefc1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-md\" href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours de maths particulier<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-461d5d63 ae-bg-gallery-type-default\" data-id=\"461d5d63\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<h2 dir=\"ltr\">Qu&rsquo;est-ce qu&rsquo;une fraction ?<\/h2>\n<p dir=\"ltr\">Une fraction s&rsquo;\u00e9crit <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0bfd55df50a9a215ae8bf09c792fca21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"10\" style=\"vertical-align: -12px;\"\/>, avec b diff\u00e9rent de 0.<\/p>\n<ul>\n<li><strong>Le num\u00e9rateur<\/strong> (a, en haut) indique combien de parts on prend.<\/li>\n<li><strong>Le d\u00e9nominateur<\/strong> (b, en bas) indique en combien de parts \u00e9gales on a partag\u00e9 l&rsquo;unit\u00e9.<\/li>\n<\/ul>\n<p dir=\"ltr\">Dans <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c5ebd9d3766fcdac5860e5f2039b3782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/>, l&rsquo;unit\u00e9 est partag\u00e9e en 4 parts \u00e9gales et on en prend 3. On peut le repr\u00e9senter en coloriant 3 quarts d&rsquo;un carr\u00e9 ou d&rsquo;un disque, comme dans le cours sur les <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\">figures g\u00e9om\u00e9triques<\/a>. Une fraction est aussi un quotient : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c5ebd9d3766fcdac5860e5f2039b3782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> est le nombre qui, multipli\u00e9 par 4, donne 3, c&rsquo;est-\u00e0-dire 0,75. Deux fractions \u00e9gales, comme <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c5ebd9d3766fcdac5860e5f2039b3782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> et <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a09adbeb40818e05983c1e83905e7957_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/>, traduisent une situation de <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-regle-de-trois\/\">proportionnalit\u00e9<\/a>.<\/p>\n<p dir=\"ltr\">Un nombre entier peut s&rsquo;\u00e9crire comme une fraction de d\u00e9nominateur 1 : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7edc94de0250747a12bb02ac66511245_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"43\" style=\"vertical-align: -12px;\"\/>. Cette \u00e9criture est utile pour multiplier ou diviser une fraction par un entier.<\/p>\n<h2 dir=\"ltr\">Comment additionner ou soustraire des fractions ?<\/h2>\n<p dir=\"ltr\"><strong>Si les d\u00e9nominateurs sont \u00e9gaux<\/strong>, on garde le d\u00e9nominateur et on additionne ou on soustrait les num\u00e9rateurs :<\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ef7551c7d90fdda9c65b1e26b27459e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#55;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"80\" style=\"vertical-align: -12px;\"\/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f1e79826439870d941bdd0012bdb86ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#57;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#57;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"116\" style=\"vertical-align: -12px;\"\/><\/li>\n<\/ul>\n<p dir=\"ltr\"><strong>Si les d\u00e9nominateurs sont diff\u00e9rents<\/strong>, on met d&rsquo;abord les fractions au m\u00eame d\u00e9nominateur. On choisit en g\u00e9n\u00e9ral le plus petit multiple commun aux d\u00e9nominateurs, ce qui donne des nombres plus petits. La m\u00e9thode pour le trouver est expliqu\u00e9e dans le cours d&rsquo;<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\">arithm\u00e9tique<\/a>.<\/p>\n<p dir=\"ltr\">Exemple 1 : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-547079a56ceb2d90bd90a4077a2166ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"43\" style=\"vertical-align: -12px;\"\/><\/p>\n<ul>\n<li>12 est le plus petit multiple commun \u00e0 3 et 4.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-61580794398fd27aa64cfa64c35f144b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"54\" style=\"vertical-align: -12px;\"\/> (on multiplie en haut et en bas par 4) et <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7a37509f86a236767a6527b70ed48328_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"54\" style=\"vertical-align: -12px;\"\/> (on multiplie par 3).<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5e80e41baa776e1dab2c26469ebb4bef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"106\" style=\"vertical-align: -12px;\"\/><\/li>\n<\/ul>\n<p dir=\"ltr\">Exemple 2 : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-68eb2554a3e620e5132ec2649d9eab04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"78\" style=\"vertical-align: -12px;\"\/><\/p>\n<ul>\n<li>Le plus petit multiple commun \u00e0 2, 6 et 9 est 18.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2922836806a9e7fdbfd5cd6edd0e203f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#56;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#56;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#49;&#56;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#49;&#56;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"186\" style=\"vertical-align: -12px;\"\/><\/li>\n<\/ul>\n<p dir=\"ltr\">Exemple 3 (soustraction) : <img decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5831007cc7cd3179f8dc9fdcac839c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#49;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"177\" style=\"vertical-align: -12px;\"\/><\/p>\n<div style=\"background: #FFF8EC; border-left: 6px solid #C77F0C; padding: 15px; margin: 20px 0; color: #0f2742;\"><strong>&#x1f4a1; Astuce :<\/strong> si vous ne trouvez pas tout de suite le plus petit d\u00e9nominateur commun, multipliez les deux d\u00e9nominateurs entre eux (3 \u00d7 4 = 12). Le calcul reste juste : il faudra seulement simplifier \u00e0 la fin.<\/div>\n<p dir=\"ltr\">L&rsquo;addition de fractions sert aussi pour calculer une <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-moyenne-arithmetique-moyenne-ponderee\/\">moyenne pond\u00e9r\u00e9e<\/a>, quand les coefficients sont exprim\u00e9s en fractions du total.<\/p>\n<h2 dir=\"ltr\">Comment multiplier des fractions ?<\/h2>\n<p dir=\"ltr\">Pour multiplier deux fractions, on multiplie les num\u00e9rateurs entre eux et les d\u00e9nominateurs entre eux. Contrairement \u00e0 l&rsquo;addition, <strong>il n&rsquo;est pas n\u00e9cessaire de mettre au m\u00eame d\u00e9nominateur<\/strong>.<\/p>\n<p dir=\"ltr\" style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-bc23464f57e6ae18e64dd71876923d12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#99;&#125;&#123;&#98;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"111\" style=\"vertical-align: -12px;\"\/><\/p>\n<p dir=\"ltr\">Exemple : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b538b1c5b773974edf92882bc852c40e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#49;&#50;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"61\" style=\"vertical-align: -12px;\"\/><\/p>\n<ul>\n<li>Sans simplifier : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-916c0ac9ef007a351ced9c924bc9ec98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#56;&#125;&#123;&#49;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#48;&#125;&#123;&#49;&#56;&#48;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"148\" style=\"vertical-align: -12px;\"\/><\/li>\n<li>En simplifiant avant de calculer : le 15 se trouve en haut et en bas, on l&rsquo;\u00e9limine. Il reste <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-397f4e2218b4dfcb21be31593ce15df9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"54\" style=\"vertical-align: -12px;\"\/>.<\/li>\n<\/ul>\n<div style=\"background: #FFF8EC; border-left: 6px solid #C77F0C; padding: 15px; margin: 20px 0; color: #0f2742;\"><strong>&#x1f4a1; Astuce :<\/strong> simplifiez avant de multiplier. D\u00e9composez num\u00e9rateurs et d\u00e9nominateurs en facteurs et barrez ceux qui apparaissent en haut et en bas : les nombres restent petits et le r\u00e9sultat est souvent d\u00e9j\u00e0 irr\u00e9ductible.<\/div>\n<h3 dir=\"ltr\">Multiplier une fraction par un nombre entier<\/h3>\n<p dir=\"ltr\">On multiplie seulement le num\u00e9rateur par l&rsquo;entier, car l&rsquo;entier s&rsquo;\u00e9crit avec un d\u00e9nominateur 1.<\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3b2ff2bd6f1f9a7c82205c8ab389a25e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#50;&#48;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#125;&#123;&#49;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#48;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"182\" style=\"vertical-align: -12px;\"\/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-70ed5d61d885d499ece8e9f1614752d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"78\" style=\"vertical-align: -12px;\"\/><\/li>\n<\/ul>\n<p dir=\"ltr\">Multiplier une fraction par elle-m\u00eame plusieurs fois revient \u00e0 l&rsquo;\u00e9lever \u00e0 une <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-puissances\/\">puissance<\/a> : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a2e2bacdb648e54ab1043e59661e37d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#50;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"78\" style=\"vertical-align: -17px;\"\/>.<\/p>\n<h3 dir=\"ltr\">Calculer la fraction d&rsquo;une quantit\u00e9<\/h3>\n<p dir=\"ltr\">Dans un \u00e9nonc\u00e9, \u00ab les <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c5ebd9d3766fcdac5860e5f2039b3782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> de \u00bb se traduit par une multiplication.<\/p>\n<ul>\n<li>Les <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c5ebd9d3766fcdac5860e5f2039b3782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> de 60 \u20ac : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1739cbe41415281e7c0b7b8c49c0b84a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#54;&#48;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#48;&#125;&#123;&#52;&#125;&#61;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"145\" style=\"vertical-align: -12px;\"\/> \u20ac<\/li>\n<li>Les <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2f555bfd0c034276aafa1f59270cc183_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> de <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-921e5d2a49b3d7a807918f39d7903e9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8d5096a9cd3bbb3771f9351cbff4eaaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"125\" style=\"vertical-align: -12px;\"\/><\/li>\n<li>Un trajet de 20 minutes dure <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e1435fbb34dc827f8ae4d908bf2364d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> d&rsquo;heure. \u00c0 90 km\/h, on parcourt <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-acb49fa10d5d490da49a47f1d302ee50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#57;&#48;&#61;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"92\" style=\"vertical-align: -12px;\"\/> km (voir le cours sur la <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-vitesse\/\">vitesse<\/a>).<\/li>\n<\/ul>\n<p dir=\"ltr\">La m\u00eame logique sert pour les <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pourcentages\/\">pourcentages<\/a> : prendre 25 %, c&rsquo;est multiplier par <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5bc0babc1a3e8c7d0f6eb5a6b5268987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"27\" style=\"vertical-align: -12px;\"\/>. Vous pouvez vous entra\u00eener avec nos <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-pourcentages\/\">exercices corrig\u00e9s sur les pourcentages<\/a>. En <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites\/\">probabilit\u00e9s<\/a>, on multiplie aussi des fractions pour obtenir la probabilit\u00e9 de deux \u00e9v\u00e9nements successifs : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1b0d12f2eace84aeac61c147cb181a0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"89\" style=\"vertical-align: -12px;\"\/>. Le <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-denombrement\/\">d\u00e9nombrement<\/a> aide \u00e0 trouver ces fractions.<\/p>\n<h2 dir=\"ltr\">Comment diviser des fractions ?<\/h2>\n<p dir=\"ltr\">Diviser par une fraction revient \u00e0 multiplier par son inverse. L&rsquo;inverse de <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3706d2d26cc8e566a06c1bcab9127c1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"10\" style=\"vertical-align: -12px;\"\/> est <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e9a90fd3528abf46a1312d226466e92b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"10\" style=\"vertical-align: -12px;\"\/> : on \u00e9change le num\u00e9rateur et le d\u00e9nominateur.<\/p>\n<p dir=\"ltr\" style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-499bb1a87c242c48cb1d9066e06c5344_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#100;&#105;&#118;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"117\" style=\"vertical-align: -12px;\"\/><\/p>\n<p dir=\"ltr\">Exemple : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7e7374e4586905736c0fbb7617556b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#100;&#105;&#118;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#49;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#57;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#125;&#123;&#54;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"177\" style=\"vertical-align: -12px;\"\/><\/p>\n<p dir=\"ltr\">Seule la fraction par laquelle on divise (la seconde) est invers\u00e9e. La premi\u00e8re reste telle quelle.<\/p>\n<h3 dir=\"ltr\">Diviser par un nombre entier<\/h3>\n<p dir=\"ltr\">L&rsquo;inverse de 3 est <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e1435fbb34dc827f8ae4d908bf2364d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/>.<\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5290cf7f90a9e392d6d6e62ce4a689a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#100;&#105;&#118;&#32;&#51;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"156\" style=\"vertical-align: -12px;\"\/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-93749651326d12f3286b182ddca6472e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#100;&#105;&#118;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#61;&#52;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#50;&#125;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"188\" style=\"vertical-align: -12px;\"\/><\/li>\n<\/ul>\n<h3 dir=\"ltr\">Fraction de fraction : a sur b sur c<\/h3>\n<p dir=\"ltr\">Selon l&#8217;emplacement de la grande barre de fraction, le r\u00e9sultat change :<\/p>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>\u00c9criture<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>R\u00e8gle<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Exemple<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a24eef28386f79814a663312ab398283_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"14\" style=\"vertical-align: -12px;\"\/><\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d60a36a6e47cfcc77a380032795a1bbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"37\" style=\"vertical-align: -12px;\"\/><\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1e81ec47962e6bcfec224f017afd045a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#125;&#123;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"49\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-69daa4d0611936b9fa01179653cd4800_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"12\" style=\"vertical-align: -35px;\"\/><\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2c1f7971f58967c01519ac3228549d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#99;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"39\" style=\"vertical-align: -12px;\"\/><\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d39fce89b7207ba2e047a1919da5ff4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"58\" style=\"vertical-align: -34px;\"\/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 dir=\"ltr\">Comment rendre une fraction irr\u00e9ductible ?<\/h2>\n<p dir=\"ltr\">Une fraction est irr\u00e9ductible quand on ne peut plus la simplifier, c&rsquo;est-\u00e0-dire quand le seul diviseur commun du num\u00e9rateur et du d\u00e9nominateur est 1. Pour y arriver, on divise le num\u00e9rateur et le d\u00e9nominateur par leur plus grand diviseur commun (PGCD), ou par \u00e9tapes successives. Le calcul du PGCD et les crit\u00e8res de divisibilit\u00e9 par 2, 3, 5 et 9 sont d\u00e9taill\u00e9s dans le cours d&rsquo;<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\">arithm\u00e9tique<\/a>.<\/p>\n<p dir=\"ltr\">Exemple 1 : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-52102d88c4cc727fbf64511030c7a1ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#53;&#125;&#123;&#51;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"27\" style=\"vertical-align: -12px;\"\/><\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-eb5fe015caf341b948e01b7b05323453_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;&#53;&#61;&#51;&#94;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#53;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"104\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3a6ab42cbd411183be9936f21009100a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#48;&#61;&#50;&#94;&#54;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"96\" style=\"vertical-align: 0px;\"\/>. Le seul facteur commun est 5.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-48600e0b97fd71ba6cf284ff7808a65d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#53;&#125;&#123;&#51;&#50;&#48;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#53;&#125;&#123;&#54;&#52;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#125;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"148\" style=\"vertical-align: -12px;\"\/>, qui est irr\u00e9ductible.<\/li>\n<\/ul>\n<p dir=\"ltr\">Exemple 2 : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-71dff7a26edcc97ec702bf1f156a1d24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#50;&#125;&#123;&#57;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"36\" style=\"vertical-align: -12px;\"\/><\/p>\n<ul>\n<li>Les deux nombres sont pairs : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c99cb5ba74771cb22939f94136346235_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#50;&#125;&#123;&#57;&#56;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#48;&#49;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#50;&#125;&#123;&#52;&#57;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#50;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#48;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"175\" style=\"vertical-align: -12px;\"\/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-800dbc3c5f979ca3d83555cefe1eaf12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;&#49;&#61;&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#54;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"108\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7a02e5b34a483e04ba10b4869a9fd156_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#57;&#61;&#55;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\"\/>. Il n&rsquo;y a plus de facteur commun : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a7db7a9b882b8a5298e1d26e6b73afab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#48;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"27\" style=\"vertical-align: -12px;\"\/> est irr\u00e9ductible.<\/li>\n<\/ul>\n<p dir=\"ltr\">On simplifie de la m\u00eame fa\u00e7on les fractions qui contiennent des <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\">racines carr\u00e9es<\/a>, par exemple quand on calcule une longueur avec le <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\">th\u00e9or\u00e8me de Pythagore<\/a>.<\/p>\n<h2 dir=\"ltr\">Dans quel ordre calculer avec des fractions ?<\/h2>\n<p dir=\"ltr\">On applique les m\u00eames priorit\u00e9s qu&rsquo;avec les nombres entiers : d&rsquo;abord les parenth\u00e8ses, puis les multiplications et les divisions, puis les additions et les soustractions.<\/p>\n<p dir=\"ltr\">Exemple : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c032d865007ebe25ee53ca6d607256e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"78\" style=\"vertical-align: -12px;\"\/><\/p>\n<ul>\n<li>On commence par la multiplication : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-db6bfd28633657964adacc15b139fb2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#54;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"116\" style=\"vertical-align: -12px;\"\/><\/li>\n<li>Puis l&rsquo;addition : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-707d2828035690d458c1480787a1a760_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#54;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#54;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"151\" style=\"vertical-align: -12px;\"\/><\/li>\n<\/ul>\n<p dir=\"ltr\">Si l&rsquo;on additionne d&rsquo;abord (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e2c08080131fe75694045ac4742e944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"77\" style=\"vertical-align: -12px;\"\/>, puis <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-dc9a353cc23ee99cf377e9b4c24515c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"40\" style=\"vertical-align: -12px;\"\/>), on obtient <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2f555bfd0c034276aafa1f59270cc183_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/>, ce qui est faux. Ces priorit\u00e9s s&rsquo;appliquent aussi quand on r\u00e9sout une \u00e9quation avec des fractions en <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-algebre\/\">alg\u00e8bre<\/a>.<\/p>\n<h2 dir=\"ltr\">Quelles erreurs \u00e9viter avec les fractions ?<\/h2>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Erreur fr\u00e9quente<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Calcul correct<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a75b23990836d27b70055a34310025a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"80\" style=\"vertical-align: -12px;\"\/> (num\u00e9rateurs et d\u00e9nominateurs additionn\u00e9s)<\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-707d2828035690d458c1480787a1a760_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#54;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#54;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"151\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Mettre au m\u00eame d\u00e9nominateur pour multiplier<\/td>\n<td style=\"border: 1px solid #0F2742;\">Inutile : <img decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f3c3f33177f7e6fc8a94aac3ca1ea4ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"89\" style=\"vertical-align: -12px;\"\/> directement<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7b9ae8b47d5f84fa71b7fea737fd54eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\"\/> (entier multipli\u00e9 en haut et en bas)<\/td>\n<td style=\"border: 1px solid #0F2742;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-70ed5d61d885d499ece8e9f1614752d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"78\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Inverser la premi\u00e8re fraction dans une division<\/td>\n<td style=\"border: 1px solid #0F2742;\">On inverse le diviseur : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0b229e13af6eafbd910eaf352b4398b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#100;&#105;&#118;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#49;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"132\" style=\"vertical-align: -12px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Simplifier dans une somme : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f51e0e05644c7b07b52fe0379b55c416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#43;&#51;&#125;&#123;&#50;&#43;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -14px;\"\/><\/td>\n<td style=\"border: 1px solid #0F2742;\">On simplifie seulement des facteurs : <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f9872b836527dc27de068ce8f5478cf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#43;&#51;&#125;&#123;&#50;&#43;&#53;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"76\" style=\"vertical-align: -14px;\"\/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 dir=\"ltr\">En quelle classe apprend-on les fractions ?<\/h2>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Classe<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Ce que l&rsquo;\u00e9l\u00e8ve apprend<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>CM1, CM2, 6e (cycle 3)<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">Fractions simples pour partager une grandeur, puis <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0bfd55df50a9a215ae8bf09c792fca21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"10\" style=\"vertical-align: -12px;\"\/> comme \u00ab le nombre qui, multipli\u00e9 par b, donne a \u00bb<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>5e<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">Comparer des fractions, additionner et soustraire des fractions de d\u00e9nominateurs quelconques<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>4e<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">Simplifier, multiplier, calculer la fraction d&rsquo;une quantit\u00e9, d\u00e9terminer l&rsquo;inverse, diviser des fractions<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\"><strong>3e<\/strong><\/td>\n<td style=\"border: 1px solid #0F2742;\">Mettre une fraction sous forme irr\u00e9ductible, r\u00e9soudre des probl\u00e8mes avec des fractions<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p dir=\"ltr\">Cette r\u00e9partition suit le programme de cycle 4 publi\u00e9 au Bulletin officiel du 5 mars 2026. Il s&rsquo;applique en 5e depuis la rentr\u00e9e 2026, en 4e \u00e0 la rentr\u00e9e 2027 et en 3e \u00e0 la rentr\u00e9e 2028. Au coll\u00e8ge, les fractions servent aussi pour le <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-thales\/\">th\u00e9or\u00e8me de Thal\u00e8s<\/a>, qui repose sur l&rsquo;\u00e9galit\u00e9 de rapports. Au Tage Mage, elles reviennent dans le calcul et dans les <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-series-lettres-nombres\/\">s\u00e9ries de lettres et de nombres<\/a>.<\/p>\n<p>&nbsp;<\/p>\n<p dir=\"ltr\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"205992\" class=\"elementor elementor-205992\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-df11d1e elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"df11d1e\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-54ab74af ae-bg-gallery-type-default\" data-id=\"54ab74af\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2c1ca7d elementor-widget elementor-widget-heading\" data-id=\"2c1ca7d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">STAGE DE MATHS PENDANT LES VACANCES<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3e600302 elementor-widget elementor-widget-heading\" data-id=\"3e600302\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Gagner en s\u00e9r\u00e9nit\u00e9 et progresser en confiance<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-598c6a68 elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"598c6a68\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-md\" href=\"https:\/\/groupe-reussite.fr\/stages\/maths\/tous-niveaux\/france\/toutes-periodes\/\" target=\"_blank\" id=\"CTA_PRD_STAGE\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Stage maths vacances<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-14415dfd ae-bg-gallery-type-default\" data-id=\"14415dfd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<h2 dir=\"ltr\">FAQ : questions fr\u00e9quentes sur les fractions<\/h2>\n        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Comment multiplier une fraction par un nombre entier ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tOn multiplie le num\u00e9rateur par l'entier et on garde le d\u00e9nominateur, car un entier s'\u00e9crit avec un d\u00e9nominateur 1. Exemple : 3 \u00d7 2\/5 = 6\/5.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Faut-il le m\u00eame d\u00e9nominateur pour multiplier des fractions ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tNon. Le m\u00eame d\u00e9nominateur est n\u00e9cessaire seulement pour additionner ou soustraire. Pour multiplier, on multiplie directement les num\u00e9rateurs entre eux et les d\u00e9nominateurs entre eux : 2\/3 \u00d7 4\/5 = 8\/15.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Comment diviser une fraction par une fraction ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tOn multiplie la premi\u00e8re fraction par l'inverse de la seconde. Exemple : 5\/6 \u00f7 10\/9 = 5\/6 \u00d7 9\/10 = 45\/60 = 3\/4.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Comment comparer deux fractions ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tSi les d\u00e9nominateurs sont \u00e9gaux, la plus grande fraction est celle qui a le plus grand num\u00e9rateur. Sinon, on les met au m\u00eame d\u00e9nominateur. Exemple : 3\/4 = 21\/28 et 5\/7 = 20\/28, donc 3\/4 est plus grand que 5\/7.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Qu&#039;est-ce qu&#039;une fraction irr\u00e9ductible ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tC'est une fraction qu'on ne peut plus simplifier : son num\u00e9rateur et son d\u00e9nominateur n'ont pas d'autre diviseur commun que 1. Exemple : 2\/3 est irr\u00e9ductible, 4\/6 ne l'est pas.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Une fraction est-elle toujours un nombre d\u00e9cimal ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tNon. 3\/4 = 0,75 est un nombre d\u00e9cimal, mais 1\/3 = 0,333\u2026 ne l'est pas, car son \u00e9criture d\u00e9cimale ne s'arr\u00eate jamais. Une fraction irr\u00e9ductible donne un nombre d\u00e9cimal seulement si son d\u00e9nominateur ne contient que les facteurs 2 et 5.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t\n<script type=\"application\/ld+json\">\n    {\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Comment multiplier une fraction par un nombre entier ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"On multiplie le num\u00e9rateur par l'entier et on garde le d\u00e9nominateur, car un entier s'\u00e9crit avec un d\u00e9nominateur 1. Exemple : 3 \u00d7 2\/5 = 6\/5.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Faut-il le m\u00eame d\u00e9nominateur pour multiplier des fractions ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Non. Le m\u00eame d\u00e9nominateur est n\u00e9cessaire seulement pour additionner ou soustraire. Pour multiplier, on multiplie directement les num\u00e9rateurs entre eux et les d\u00e9nominateurs entre eux : 2\/3 \u00d7 4\/5 = 8\/15.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Comment diviser une fraction par une fraction ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"On multiplie la premi\u00e8re fraction par l'inverse de la seconde. Exemple : 5\/6 \u00f7 10\/9 = 5\/6 \u00d7 9\/10 = 45\/60 = 3\/4.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Comment comparer deux fractions ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Si les d\u00e9nominateurs sont \u00e9gaux, la plus grande fraction est celle qui a le plus grand num\u00e9rateur. Sinon, on les met au m\u00eame d\u00e9nominateur. Exemple : 3\/4 = 21\/28 et 5\/7 = 20\/28, donc 3\/4 est plus grand que 5\/7.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Qu'est-ce qu'une fraction irr\u00e9ductible ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"C'est une fraction qu'on ne peut plus simplifier : son num\u00e9rateur et son d\u00e9nominateur n'ont pas d'autre diviseur commun que 1. Exemple : 2\/3 est irr\u00e9ductible, 4\/6 ne l'est pas.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Une fraction est-elle toujours un nombre d\u00e9cimal ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Non. 3\/4 = 0,75 est un nombre d\u00e9cimal, mais 1\/3 = 0,333\u2026 ne l'est pas, car son \u00e9criture d\u00e9cimale ne s'arr\u00eate jamais. Une fraction irr\u00e9ductible donne un nombre d\u00e9cimal seulement si son d\u00e9nominateur ne contient que les facteurs 2 et 5.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t    ]\n}\n<\/script>\n\n<h2 dir=\"ltr\">Sources<\/h2>\n<ul>\n<li>Minist\u00e8re de l&rsquo;\u00c9ducation nationale, <a href=\"https:\/\/www.education.gouv.fr\/sites\/default\/files\/document\/Annexe%202%20%E2%80%93%20Programme%20de%20math%C3%A9matiques%20pour%20le%20cycle%204-480716.pdf\" target=\"_blank\" rel=\"noopener\">Programme de math\u00e9matiques du cycle 4<\/a>, annexe 2, BO du 5 mars 2026<\/li>\n<li>Minist\u00e8re de l&rsquo;\u00c9ducation nationale, \u00c9duscol, <a href=\"https:\/\/eduscol.education.fr\/document\/14026\/download\" target=\"_blank\" rel=\"noopener\">Rep\u00e8res annuels de progression, math\u00e9matiques cycle 3<\/a><\/li>\n<li>Acad\u00e9mie de Bordeaux, <a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=12479\" target=\"_blank\" rel=\"noopener\">Publication du nouveau programme de cycle 4<\/a> (calendrier d&rsquo;application)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Op\u00e9rations sur les fractions : addition, soustraction, multiplication et division Par Seda Biber, le 20\/10\/2026 Pour additionner ou soustraire des fractions, on les met d&rsquo;abord au m\u00eame d\u00e9nominateur, puis on additionne ou on soustrait les num\u00e9rateurs. Pour multiplier des fractions, on multiplie les num\u00e9rateurs entre eux et les d\u00e9nominateurs entre eux. Pour diviser par une [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ocean_post_layout":"full-screen","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"ressource","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"on","ocean_disable_heading":"on","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"on","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-51228","page","type-page","status-publish","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - 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