{"id":2399,"date":"2026-01-16T20:01:24","date_gmt":"2026-01-16T20:01:24","guid":{"rendered":"https:\/\/nachhilfe-madrid.com\/gurke-in-der-sonne-eine-knifflige-prozentrechnung-mit-loesung\/"},"modified":"2026-02-18T00:05:10","modified_gmt":"2026-02-18T00:05:10","slug":"gurke-in-der-sonne-eine-knifflige-prozentrechnung-mit-loesung","status":"publish","type":"post","link":"https:\/\/nachhilfe-madrid.com\/de\/gurke-in-der-sonne-eine-knifflige-prozentrechnung-mit-loesung\/","title":{"rendered":"Gurke in der Sonne: eine knifflige Prozentrechnung (mit L\u00f6sung)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2399\" class=\"elementor elementor-2399 elementor-372\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-18a06de e-flex e-con-boxed sc_layouts_column_icons_position_left e-con e-parent\" data-id=\"18a06de\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0050ffc sc_fly_static elementor-widget elementor-widget-heading\" data-id=\"0050ffc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Einf\u00fchrung<\/h3>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c363623 e-flex e-con-boxed sc_layouts_column_icons_position_left e-con e-parent\" data-id=\"c363623\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b44fe85 sc_fly_static elementor-widget elementor-widget-text-editor\" data-id=\"b44fe85\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span dir=\"auto\">Prozentrechnungen begegnen uns im Alltag h\u00e4ufig, manchmal auf unerwartete Weise. Diese kurze \u00dcbung verdeutlicht, wie leicht Fehler passieren k\u00f6nnen, wenn sich Verh\u00e4ltnisse \u00e4ndern. Sie eignet sich ideal als Einstiegs\u00fcbung im Nachhilfeunterricht oder als Denksportaufgabe f\u00fcr Sch\u00fcler.  <\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8518777 e-flex e-con-boxed sc_layouts_column_icons_position_left e-con e-parent\" data-id=\"8518777\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-05446af sc_fly_static elementor-widget elementor-widget-heading\" data-id=\"05446af\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Aufgabe\n<\/h3>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0685d94 e-flex e-con-boxed sc_layouts_column_icons_position_left e-con e-parent\" data-id=\"0685d94\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-de8dba6 e-con-full e-flex sc_layouts_column_icons_position_left e-con e-child\" data-id=\"de8dba6\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e750167 sc_fly_static elementor-widget elementor-widget-heading\" data-id=\"e750167\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">Problemstellung<\/h5>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1c6f684 sc_fly_static elementor-widget elementor-widget-text-editor\" data-id=\"1c6f684\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><strong><span dir=\"auto\">Aufgabe:<\/span><\/strong><\/p><p>Eine Gurke wiegt <strong><span dir=\"auto\">500 g.<\/span><\/strong> Sie besteht zu <strong><span dir=\"auto\">99 %<\/span><\/strong> aus Wasser, der Rest aus Feststoffen. Nach einiger Zeit in der Sonne enth\u00e4lt die Gurke nur noch <strong><span dir=\"auto\">98 %<\/span><\/strong> Wasser. <em>Wie viel wiegt sie jetzt?<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f50dc41 e-con-full e-flex sc_layouts_column_icons_position_left e-con e-child\" data-id=\"f50dc41\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3e1449a sc_fly_static elementor-widget elementor-widget-image\" data-id=\"3e1449a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"346\" src=\"https:\/\/nachhilfe-madrid.com\/wp-content\/uploads\/2026\/01\/cucumber-575647_1280-1-1110x500-1-768x346-1.webp\" class=\"attachment-full size-full wp-image-2401\" alt=\"\" srcset=\"https:\/\/nachhilfe-madrid.com\/wp-content\/uploads\/2026\/01\/cucumber-575647_1280-1-1110x500-1-768x346-1.webp 768w, https:\/\/nachhilfe-madrid.com\/wp-content\/uploads\/2026\/01\/cucumber-575647_1280-1-1110x500-1-768x346-1-300x135.webp 300w, https:\/\/nachhilfe-madrid.com\/wp-content\/uploads\/2026\/01\/cucumber-575647_1280-1-1110x500-1-768x346-1-370x167.webp 370w, https:\/\/nachhilfe-madrid.com\/wp-content\/uploads\/2026\/01\/cucumber-575647_1280-1-1110x500-1-768x346-1-410x185.webp 410w, https:\/\/nachhilfe-madrid.com\/wp-content\/uploads\/2026\/01\/cucumber-575647_1280-1-1110x500-1-768x346-1-600x270.webp 600w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\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\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a6bdc8b e-flex e-con-boxed sc_layouts_column_icons_position_left e-con e-parent\" data-id=\"a6bdc8b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-57a90a7 sc_fly_static elementor-widget elementor-widget-heading\" data-id=\"57a90a7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Schritt-f\u00fcr-Schritt-L\u00f6sung<\/h3>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-901d57e e-flex e-con-boxed sc_layouts_column_icons_position_left e-con e-parent\" data-id=\"901d57e\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0afd16e sc_fly_static elementor-widget elementor-widget-n-accordion\" data-id=\"0afd16e\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;default_state&quot;:&quot;expanded&quot;,&quot;max_items_expended&quot;:&quot;one&quot;,&quot;n_accordion_animation_duration&quot;:{&quot;unit&quot;:&quot;ms&quot;,&quot;size&quot;:400,&quot;sizes&quot;:[]}}\" data-widget_type=\"nested-accordion.default\">\n\t\t\t\t\t\t\t<div class=\"e-n-accordion\" aria-label=\"Accordion. Open links with Enter or Space, close with Escape, and navigate with Arrow Keys\">\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1150\" class=\"e-n-accordion-item\" open>\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"1\" tabindex=\"0\" aria-expanded=\"true\" aria-controls=\"e-n-accordion-item-1150\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> L\u00f6sung anzeigen <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-up\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M240.971 130.524l194.343 194.343c9.373 9.373 9.373 24.569 0 33.941l-22.667 22.667c-9.357 9.357-24.522 9.375-33.901.04L224 227.495 69.255 381.516c-9.379 9.335-24.544 9.317-33.901-.04l-22.667-22.667c-9.373-9.373-9.373-24.569 0-33.941L207.03 130.525c9.372-9.373 24.568-9.373 33.941-.001z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-down\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div role=\"region\" aria-labelledby=\"e-n-accordion-item-1150\" class=\"elementor-element elementor-element-2027cf7 e-con-full e-flex sc_layouts_column_icons_position_left e-con e-child\" data-id=\"2027cf7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2ce3c40 sc_fly_static elementor-widget elementor-widget-text-editor\" data-id=\"2ce3c40\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Viele gehen intuitiv davon aus, dass sich das Gewicht der Gurke kaum ver\u00e4ndert hat; die h\u00e4ufigsten falschen Antworten sind 495 g oder 490 g. Die Aufgabe zeigt jedoch, dass die Prozents\u00e4tze vom Gesamtgewicht abh\u00e4ngen und die verbleibenden Feststoffe den Schl\u00fcssel liefern. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-242eba5 sc_fly_static elementor-widget elementor-widget-heading\" data-id=\"242eba5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h6 class=\"elementor-heading-title elementor-size-default\">Funktioniert das wirklich immer? Hier die Erkl\u00e4rung: <\/h6>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2d865e4 sc_fly_static elementor-widget elementor-widget-text-editor\" data-id=\"2d865e4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ol><li>Ausgangszustand (500 g):<br>Wassergehalt = 99 % von 500 g = 0,99 \u00d7 500 = 495 g.<br>Feststoffgehalt = Rest = 500 \u2212 495 = 5 g.<\/li><li><span dir=\"auto\"><strong>W\u00e4hrend des Trocknungsprozesses:<\/strong><\/span><br>Die Menge des Feststoffs \u00e4ndert sich nicht, sie bleibt bei 5 g.<\/li><li><span dir=\"auto\"><strong>Nach dem Trocknen:<\/strong><\/span><br>98 % Wasser, daher 2 % Feststoffe. Die 5 g Feststoffe entsprechen somit 2 % des neuen Gesamtgewichts G.<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7e8a537 sc_fly_static elementor-widget elementor-widget-html\" data-id=\"7e8a537\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mn>0<\/mn>\n  <mrow data-mjx-texclass=\"ORD\">\n    <mo>,<\/mo>\n  <\/mrow>\n  <mn>02<\/mn>\n  <mo>\u22c5<\/mo>\n  <mi>G<\/mi>\n  <mo>=<\/mo>\n  <mn>5<\/mn>\n  <mo stretchy=\"false\">\u21d2<\/mo>\n  <mi>G<\/mi>\n  <mo>=<\/mo>\n  <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n    <mfrac>\n      <mn>5<\/mn>\n      <mrow>\n        <mn>0<\/mn>\n <mrow data-mjx-texclass=\"ORD\">\n <mo>,<\/mo>\n <\/mrow>\n <mn>02<\/mn>\n      <\/mrow>\n    <\/mfrac>\n  <\/mstyle>\n  <mo>=<\/mo>\n<mn>250 Gramos<\/mn>\n<\/math>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c0d5fc1 sc_fly_static elementor-widget elementor-widget-text-editor\" data-id=\"c0d5fc1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>4. Ergebnis: Die Gurke wiegt nach dem Trocknen 250 g. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cdc6a88 elementor-icon-list--layout-traditional elementor-list-item-link-full_width sc_fly_static elementor-widget elementor-widget-icon-list\" data-id=\"cdc6a88\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"icon-list.default\">\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-check-circle\" viewBox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M504 256c0 136.967-111.033 248-248 248S8 392.967 8 256 119.033 8 256 8s248 111.033 248 248zM227.314 387.314l184-184c6.248-6.248 6.248-16.379 0-22.627l-22.627-22.627c-6.248-6.249-16.379-6.249-22.628 0L216 308.118l-70.059-70.059c-6.248-6.248-16.379-6.248-22.628 0l-22.627 22.627c-6.248 6.248-6.248 16.379 0 22.627l104 104c6.249 6.249 16.379 6.249 22.628.001z\"><\/path><\/svg>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\"> Antwort: Die Gurke wiegt nach dem Trocknen 250 g.<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t<div role=\"region\" aria-labelledby=\"e-n-accordion-item-1150\" class=\"elementor-element elementor-element-d182138 e-flex e-con-boxed sc_layouts_column_icons_position_left e-con e-child\" data-id=\"d182138\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-67e5cce sc_fly_static elementor-widget elementor-widget-text-editor\" data-id=\"67e5cce\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h6 style=\"color: #fff;\">Warum ist das Problem kompliziert?<\/h6><p>Der Prozentsatz bezieht sich auf das Gesamtgewicht, nicht nur auf den Wassergehalt. Da der Feststoffgehalt (in Gramm) konstant bleibt, \u00e4ndert sich das relative Verh\u00e4ltnis drastisch; daher sinkt das Gesamtgewicht viel st\u00e4rker, als viele erwarten w\u00fcrden. Aufgaben wie diese helfen Sch\u00fclern, verbale Beschreibungen pr\u00e4zise in mathematische Operationen umzusetzen.  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Prozentrechnung: Eine Gurke (500 g, 99 % Wasser) wird in der Sonne getrocknet, bis sie nur noch 98 % Wasser enth\u00e4lt. Wie viel wiegt sie dann? Schritt f\u00fcr Schritt erkl\u00e4rt.  <\/p>\n","protected":false},"author":1,"featured_media":2400,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","_joinchat":[],"footnotes":""},"categories":[41,51,50],"tags":[],"class_list":["post-2399","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ausbildung","category-mathe-2","category-physik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Gurke in der Sonne: eine knifflige Prozentrechnung (mit L\u00f6sung) - Nachhilfe-Madrid<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nachhilfe-madrid.com\/de\/gurke-in-der-sonne-eine-knifflige-prozentrechnung-mit-loesung\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Gurke in der Sonne: eine knifflige Prozentrechnung (mit L\u00f6sung) - Nachhilfe-Madrid\" \/>\n<meta property=\"og:description\" content=\"Prozentrechnung: Eine Gurke (500 g, 99 % Wasser) wird in der Sonne getrocknet, bis sie nur noch 98 % Wasser enth\u00e4lt. 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