{"id":1384,"date":"2020-08-19T20:55:11","date_gmt":"2020-08-19T18:55:11","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1384"},"modified":"2020-08-26T22:46:10","modified_gmt":"2020-08-26T20:46:10","slug":"proporcja","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1384","title":{"rendered":"Proporcja"},"content":{"rendered":"<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Je\u015bli przyr\u00f3wnamy do siebie dwa ilorazy, kt\u00f3rych wynik jest taki sam<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{12}{4}=3=\\frac{27}{9}\" alt=\"\\frac{12}{4}=3=\\frac{27}{9}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">to otrzymamy<span style=\"color: #4472c4;\"><strong> proporcj\u0119<\/strong><\/span>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Je\u015bli ilorazy <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{a}{b}\" alt=\"\\frac{a}{b}\" align=\"absmiddle\" \/>\u00a0 i <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{c}{d}\" alt=\"\\frac{c}{d}\" align=\"absmiddle\" \/>\u00a0 dla\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?b\\neq&amp;space;0,\\;&amp;space;d\\neq&amp;space;0\" alt=\"b\\neq 0,\\; d\\neq 0\" align=\"absmiddle\" \/> s\u0105 sobie r\u00f3wne, to \u00a0 <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{a}{b}=\\frac{c}{d}\" alt=\"\\frac{a}{b}=\\frac{c}{d}\" align=\"absmiddle\" \/>\u00a0 nazywamy <strong><span style=\"color: #4472c4;\">proporcj\u0105<\/span><\/strong>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1393 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/proporcja-300x155.png\" alt=\"\" width=\"288\" height=\"149\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/proporcja-300x155.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/proporcja.png 448w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Iloczyn wyraz\u00f3w skrajnych jest r\u00f3wny iloczynowi wyraz\u00f3w \u015brodkowych.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1394 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/proporcje.png\" alt=\"\" width=\"128\" height=\"62\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Je\u015bli jeden odcinek <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;|&amp;space;AB&amp;space;\\right&amp;space;|\" alt=\"\\left | AB \\right |\" align=\"absmiddle\" \/> mie\u015bci si\u0119 kilka razy w drugim odcinku <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;|&amp;space;CD&amp;space;\\right&amp;space;|\" alt=\"\\left | CD \\right |\" align=\"absmiddle\" \/> to ich iloraz <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{\\left&amp;space;|&amp;space;AB&amp;space;\\right&amp;space;|}{\\left&amp;space;|&amp;space;CD&amp;space;\\right&amp;space;|}\" alt=\"\\frac{\\left | AB \\right |}{\\left | CD \\right |}\" align=\"absmiddle\" \/> jest <strong><span style=\"color: #4472c4;\">stosunkiem d\u0142ugo\u015bci odcink\u00f3w<\/span><\/strong> <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;|&amp;space;AB&amp;space;\\right&amp;space;|\" alt=\"\\left | AB \\right |\" align=\"absmiddle\" \/> i <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;|&amp;space;CD&amp;space;\\right&amp;space;|\" alt=\"\\left | CD \\right |\" align=\"absmiddle\" \/>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Najlepiej zobrazuje to przyk\u0142ad.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Dana jest rurka d\u0142ugo\u015bci 100 cm chcemy j\u0105 rozci\u0105\u0107 na dwie cz\u0119\u015bci w stosunku 1:4. Jak to zrobi\u0107? Po ile centymetr\u00f3w b\u0119d\u0105 mia\u0142y obie cz\u0119\u015bci naszej rurki?<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Za\u0142\u00f3\u017cmy, \u017ce <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1x\" alt=\"1x\" align=\"absmiddle\" \/> to b\u0119dzie pierwsza cz\u0119\u015b\u0107 naszej rurki, a <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?4x\" alt=\"4x\" align=\"absmiddle\" \/> to druga cz\u0119\u015b\u0107. Nast\u0119pnie dodajmy nasze dwie cz\u0119\u015bci do siebie i przyr\u00f3wnajmy do d\u0142ugo\u015bci rurki.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1x+4x=100\\;&amp;space;cm\" alt=\"1x+4x=100\\; cm\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?5x=100\\;&amp;space;cm&amp;space;\\;&amp;space;\\;&amp;space;\/:5\" alt=\"5x=100\\; cm \\; \\; \/:5\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x=20&amp;space;\\;&amp;space;cm\" alt=\"x=20 \\; cm\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Czyli pierwsza cz\u0119\u015b\u0107 rurki b\u0119dzie mia\u0142a <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x=20&amp;space;cm\" alt=\"x=20 cm\" align=\"absmiddle\" \/> a druga <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?4x=4\\cdot&amp;space;20\\;&amp;space;cm=80\\;&amp;space;cm\" alt=\"4x=4\\cdot 20\\; cm=80\\; cm\" align=\"absmiddle\" \/>.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Je\u015bli przyr\u00f3wnamy do siebie dwa ilorazy, kt\u00f3rych wynik jest taki sam to otrzymamy proporcj\u0119. Je\u015bli ilorazy \u00a0 i \u00a0 dla\u00a0 s\u0105 sobie r\u00f3wne, to \u00a0 \u00a0 nazywamy proporcj\u0105. Iloczyn wyraz\u00f3w skrajnych jest r\u00f3wny iloczynowi wyraz\u00f3w \u015brodkowych. Je\u015bli jeden odcinek mie\u015bci si\u0119 kilka razy w drugim odcinku to ich iloraz jest stosunkiem d\u0142ugo\u015bci odcink\u00f3w i . [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,14],"tags":[],"class_list":["post-1384","post","type-post","status-publish","format-standard","hentry","category-baza-wiedzy","category-klasa-vii"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Proporcja - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/matma.com.pl\/?p=1384\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Proporcja - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Je\u015bli przyr\u00f3wnamy do siebie dwa ilorazy, kt\u00f3rych wynik jest taki sam to otrzymamy proporcj\u0119. 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