{"id":100,"date":"2024-08-23T12:47:58","date_gmt":"2024-08-23T12:47:58","guid":{"rendered":"https:\/\/kierunekmatura.pl\/blog\/?p=100"},"modified":"2025-08-01T20:32:52","modified_gmt":"2025-08-01T20:32:52","slug":"example-post-2","status":"publish","type":"post","link":"https:\/\/kierunekmatura.pl\/blog\/example-post-2\/","title":{"rendered":"Liczby odwrotne"},"content":{"rendered":"\n<p>Liczby odwrotne<\/p>\n\n\n<div class=\"box-definition2\">\r\n<h3 class=\"box-legend2\"><span>\r\nLiczba odwrotna<\/span><\/h3>\r\n<p>Je\u015bli \\(a\\) jest niezerow\u0105 liczb\u0105 rzeczywist\u0105, to liczb\u0105 odwrotn\u0105 do niej jest liczba \\(\\frac{1}{a}\\).<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>Przyk\u0142ady liczb odwrotnych:<br \/>\n&#8211; Dla liczby 4, liczb\u0105 odwrotn\u0105 jest \\(\\frac{1}{4}\\)<br \/>\n&#8211; Dla liczby \\(\\frac{5}{8}\\), liczb\u0105 odwrotn\u0105 jest \\(\\frac{8}{5}\\)<br \/>\n&#8211; Dla liczby \\(-\\frac{2}{3}\\), liczb\u0105 odwrotn\u0105 jest \\(-\\frac{3}{2}\\)<br \/>\n&#8211; Dla liczby \\(\\sqrt{5}\\), liczb\u0105 odwrotn\u0105 jest \\(\\frac{1}{\\sqrt{5}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nW\u0142a\u015bciwo\u015bci<\/span><\/h3>\r\n<p>1. Iloczyn liczby niezerowej i jej liczby odwrotnej zawsze r\u00f3wna si\u0119 1.<br \/>\n2. Liczba odwrotna do liczby odwrotnej to liczba wyj\u015bciowa.<br \/>\n3. Liczba odwrotna do 1 to 1.<\/p>\n\r\n<\/div>\n\n\n<p>Wyznaczanie liczby odwrotnej<\/p>\n\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nWa\u017cne<\/span><\/h3>\r\n<p>Aby wyznaczy\u0107 liczb\u0119 odwrotn\u0105:<br \/>\n1. Dla liczby ca\u0142kowitej: zapisz j\u0105 jako u\u0142amek z mianownikiem 1, a nast\u0119pnie odwr\u00f3\u0107 licznik z mianownikiem.<br \/>\n2. Dla u\u0142amka: zamie\u0144 miejscami licznik z mianownikiem, zachowuj\u0105c znak.<br \/>\n3. Dla liczby mieszanej: najpierw zapisz j\u0105 jako u\u0142amek niew\u0142a\u015bciwy, a nast\u0119pnie odwr\u00f3\u0107 licznik z mianownikiem.<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>Przyk\u0142ad dla liczby mieszanej:<br \/>\n\\(3\\frac{1}{2} = \\frac{7}{2}\\), wi\u0119c liczb\u0105 odwrotn\u0105 b\u0119dzie \\(\\frac{2}{7}\\)<\/p>\n\r\n<\/div>\n\n\n<p>Zastosowanie liczb odwrotnych<\/p>\n\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nWa\u017cne<\/span><\/h3>\r\n<p>Liczby odwrotne s\u0105 przydatne w wielu obliczeniach matematycznych, na przyk\u0142ad:<br \/>\n1. Przy dzieleniu u\u0142amk\u00f3w (mno\u017cenie przez liczb\u0119 odwrotn\u0105)<br \/>\n2. W algebrze przy rozwi\u0105zywaniu r\u00f3wna\u0144<br \/>\n3. W fizyce i in\u017cynierii przy obliczaniu odwrotno\u015bci wielko\u015bci fizycznych<\/p>\n\r\n<\/div>\n\n<div class=\"box-important\">\r\n<h3 class=\"box-legend\"><span>\r\nWa\u017cne<\/span><\/h3>\r\n<p>Iloczyn niezerowej liczby rzeczywistej i liczby do niej odwrotnej jest zawsze r\u00f3wny 1. Ta w\u0142a\u015bciwo\u015b\u0107 jest kluczowa w wielu matematycznych operacjach i dowodach.<\/p>\n\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Liczby odwrotne Wyznaczanie liczby odwrotnej Zastosowanie liczb odwrotnych<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[106],"tags":[],"class_list":["post-100","post","type-post","status-publish","format-standard","hentry","category-matematyka"],"_links":{"self":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts\/100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/comments?post=100"}],"version-history":[{"count":2,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts\/100\/revisions"}],"predecessor-version":[{"id":532,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts\/100\/revisions\/532"}],"wp:attachment":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/media?parent=100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/categories?post=100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/tags?post=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}