{"id":59,"date":"2020-04-17T06:59:55","date_gmt":"2020-04-17T04:59:55","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=59"},"modified":"2021-11-20T11:42:08","modified_gmt":"2021-11-20T10:42:08","slug":"rationale-zahlen-die-grundrechenarten","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=59","title":{"rendered":"Rationale Zahlen &#8211; die Grundrechenarten"},"content":{"rendered":"\n<p class=\"has-white-color has-primary-background-color has-text-color has-background has-medium-font-size\">Addition und Subtraktion<\/p>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#ff93d4\"><strong>Jede Additions- und Subtraktionsaufgabe besteht aus 3 Teilen !<\/strong><\/p>\n\n\n<p>[smartslider3 slider=&#8220;7&#8243;]<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#ffb8dd\">Sollte es zu <strong>Kollisionen*<\/strong> in der Rechnung kommen, so sind diese immer zu beseitigen!<br><em><strong>Kollisionen*<\/strong> sind H\u00e4ufungen von Vorzeichen und Operatoren!<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#ffdada\"><strong>Es gelten die Kollisionsregeln:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln.jpg\" alt=\"\" class=\"wp-image-3239\" width=\"508\" height=\"159\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln.jpg 800w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln-300x94.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln-768x240.jpg 768w\" sizes=\"auto, (max-width: 508px) 100vw, 508px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#ffedde\"><strong>2 gleiche Vorzeichen ergeben immer ein Plus!<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#d8ffc3\"><strong><em>Erkl\u00e4rungsversuch zu <span style=\"color:#ff0004\" class=\"has-inline-color\">-(- <\/span>ist immer Plus&#8230;<\/em><\/strong><br><br>Nehmen wir die  Zahl 3, so ist die Gegenzahl von 3 &#8230;die  &#8211; 3 <br>und die Gegenzahl von  &#8211; 3  ist -(- 3) ..aber eigentlich +3.<br>Alles klar? <br>Weiter &#8230;  <\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Addieren und Subtrahieren von rationalen Zahlen\" width=\"860\" height=\"484\" src=\"https:\/\/www.youtube.com\/embed\/l552ncawl_A?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background has-medium-font-size\">Multiplikation und Division<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#ff60ad\"><strong>Auch f\u00fcr die Punktrechnung und das Potenzieren gelten die Kollisionsregeln!<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln.jpg\" alt=\"\" class=\"wp-image-3239\" width=\"390\" height=\"122\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln.jpg 800w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln-300x94.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/kollisionsregeln-768x240.jpg 768w\" sizes=\"auto, (max-width: 390px) 100vw, 390px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Jeder hat gelernt:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/viermaldrei.jpg\" alt=\"\" class=\"wp-image-3240\" width=\"388\" height=\"81\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/viermaldrei.jpg 512w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/viermaldrei-300x63.jpg 300w\" sizes=\"auto, (max-width: 388px) 100vw, 388px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\"> Multipliziert man aber <strong>mit der GEGENZAHL von 3<\/strong>, so gilt&#8230; <\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/viermal_minus_drei-1.jpg\" alt=\"\" class=\"wp-image-3242\" width=\"368\" height=\"77\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/viermal_minus_drei-1.jpg 512w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2021\/10\/viermal_minus_drei-1-300x63.jpg 300w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Es entsteht so also auch die Gegenzahl des Ergebnisses der ersten Aufgabe! <\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-text-color has-background\" style=\"background-color:#ff0004\"><strong>Weiterdenken!<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size\">5<strong>\u22c5<\/strong> 6 = 30 aber  5<strong>\u22c5<\/strong> (<span style=\"color:#ff0004\" class=\"has-inline-color\">-6<\/span>) = -30   <\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size\"><em>und auch<\/em>  <\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size\">7<strong>\u22c5<\/strong> 4 = 28 aber  (<span style=\"color:#ff0004\" class=\"has-inline-color\">-7<\/span>) <strong>\u22c5<\/strong> 4 = -28  <\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\"><strong>Und was w\u00e4re bei &#8230; <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-background has-medium-font-size\" style=\"background-color:#e9f8ff\"><strong>4 \u22c5  3 = 12<\/strong><br><em>aber<\/em><br><span style=\"color:#ff0004\" class=\"has-inline-color\"> &#8211; 4<\/span> <strong>\u22c5<\/strong> (<span style=\"color:#ff0004\" class=\"has-inline-color\">-3<\/span>) = <strong><span style=\"color:#fe0548\" class=\"has-inline-color\">&#8211;<\/span>(<span style=\"color:#ff0004\" class=\"has-inline-color\">&#8211;<\/span><\/strong> 12) = <span style=\"color:#ff0004\" class=\"has-inline-color\">?  ?  ?<\/span><\/p>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_59\" class=\"pvc_stats all  \" data-element-id=\"59\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>Addition und Subtraktion Jede Additions- und Subtraktionsaufgabe besteht aus 3 Teilen ! Sollte es zu Kollisionen* in der Rechnung kommen, so sind diese immer zu beseitigen!Kollisionen* sind H\u00e4ufungen von Vorzeichen und Operatoren! Es gelten die Kollisionsregeln: 2 gleiche Vorzeichen ergeben immer ein Plus! Erkl\u00e4rungsversuch zu -(- ist immer Plus&#8230; Nehmen wir die Zahl 3, so ist die Gegenzahl von 3<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_59\" class=\"pvc_stats all  \" data-element-id=\"59\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[970,38],"tags":[268,561,647,3,89],"class_list":["post-59","post","type-post","status-publish","format-standard","hentry","category-ganze-rationale-zahlen","category-rationale-zahlen","tag-zahlengerade","tag-division","tag-multiplikation","tag-addition","tag-subtraktion"],"a3_pvc":{"activated":true,"total_views":503,"today_views":0},"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/59","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=59"}],"version-history":[{"count":0,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/59\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=59"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=59"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=59"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}