{"id":1495,"date":"2024-09-22T10:42:20","date_gmt":"2024-09-22T10:42:20","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=1495"},"modified":"2024-09-24T18:40:00","modified_gmt":"2024-09-24T18:40:00","slug":"%ce%b1-7-6-%ce%b4%ce%b9%ce%b1%ce%af%cf%81%ce%b5%cf%83%ce%b7-%cf%81%ce%b7%cf%84%cf%8e%ce%bd-%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%cf%8e%ce%bd","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=1495","title":{"rendered":"\u0391.7.6. \u0394\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7 \u03c1\u03b7\u03c4\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd"},"content":{"rendered":"

<\/i> \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2<\/i><\/b><\/span><\/h4>\n

\u0397 \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7 \u03b4\u03cd\u03bf \u03c1\u03b7\u03c4\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c5\u03c0\u03b1\u03ba\u03bf\u03cd\u03b5\u03b9 \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf\u03c5\u03c2 \u03ba\u03b1\u03bd\u03cc\u03bd\u03b5\u03c2 \u03c0\u03bf\u03c5 \u03ba\u03b1\u03b8\u03bf\u03c1\u03af\u03b6\u03bf\u03c5\u03bd \u03c4\u03bf \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf \u03c4\u03bf\u03c5 \u03c0\u03b7\u03bb\u03af\u03ba\u03bf\u03c5. \u0391\u03c5\u03c4\u03bf\u03af \u03bf\u03b9 \u03ba\u03b1\u03bd\u03cc\u03bd\u03b5\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf \u03c4\u03b7\u03c2 \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03cc\u03bc\u03bf\u03b9\u03bf\u03b9 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03ba\u03b1\u03bd\u03cc\u03bd\u03b5\u03c2 \u03c0\u03bf\u03c5 \u03b9\u03c3\u03c7\u03cd\u03bf\u03c5\u03bd \u03c3\u03c4\u03bf\u03bd \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03b1\u03c3\u03bc\u03cc \u03c1\u03b7\u03c4\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd. \u0394\u03b7\u03bb\u03b1\u03b4\u03ae<\/p>\n

\u0394\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7 \u03c1\u03b7\u03c4\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd (\u03bc\u03b5 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2)<\/strong><\/span><\/em><\/p>\n

\u0393\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c3\u03bf\u03c5\u03bc\u03b5 \u03b4\u03cd\u03bf \u03c1\u03b7\u03c4\u03bf\u03cd\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9, \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b1 \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03b2\u03ae\u03bc\u03b1\u03c4\u03b1:<\/p>\n

    \n
  1. \u0394\u03b9\u03b1\u03b9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b5\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2<\/strong> \u03c4\u03c9\u03bd \u03b4\u03cd\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd.<\/li>\n
  2. \u03a3\u03c4\u03bf \u03c0\u03b7\u03bb\u03af\u03ba\u03bf \u03b2\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5:\n
      \n
    • \u03a4\u03bf \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf +<\/strong> \u03b1\u03bd \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03bc\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9<\/strong> (\u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03bf \u03af\u03b4\u03b9\u03bf \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf).<\/li>\n
    • \u03a4\u03bf \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf –<\/strong> \u03b1\u03bd \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c4\u03b5\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9<\/strong> (\u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03ad\u03c7\u03bf\u03c5\u03bd \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03cc \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf).<\/li>\n<\/ul>\n<\/li>\n
    • \u0391\u03bd \u03bf \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03c4\u03ad\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 0<\/strong>, \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03ac\u03bd\u03c4\u03b1 0<\/strong>.<\/li>\n<\/ol>\n

      \u039a\u03b1\u03bd\u03cc\u03bd\u03b5\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf:<\/strong><\/em><\/span><\/p>\n

        \n
      • \"+ : + = +\"<\/li>\n
      • \"- : - = +\"<\/li>\n
      • \"+ : - = -\"<\/li>\n
      • \"- : + = -\"<\/li>\n<\/ul>\n

        \u039d\u03b1 \u03b8\u03c5\u03bc\u03af\u03c3\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b5\u03ba\u03c6\u03c1\u03b1\u03c3\u03c4\u03b5\u03af \u03c9\u03c2 \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1, \u03cc\u03c0\u03bf\u03c5 \u03bf \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03c4\u03ad\u03bf\u03c2 (\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03af\u03c4\u03b1\u03b9) \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03ae \u03ba\u03b1\u03b9 \u03bf \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c4\u03b7\u03c2 (\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03b4\u03b9\u03b1\u03b9\u03c1\u03bf\u03cd\u03bc\u03b5) \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af \u03c4\u03bf\u03bd \u03c0\u03b1\u03c1\u03bf\u03bd\u03bf\u03bc\u03b1\u03c3\u03c4\u03ae. \u03a3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2, \u03b7 \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7 \u03b4\u03cd\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \"\alpha:\beta\" \u03b9\u03c3\u03bf\u03b4\u03c5\u03bd\u03b1\u03bc\u03b5\u03af \u03bc\u03b5 \u03c4\u03bf \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1 \"\dfrac{\alpha}{\beta},\" \u03cc\u03c0\u03bf\u03c5 \"\beta \neq 0\". \u039c\u03b5 \u03b1\u03c5\u03c4\u03cc\u03bd \u03c4\u03bf\u03bd \u03c4\u03c1\u03cc\u03c0 \u03b8\u03b1 \u03bb\u03c5\u03b8\u03bf\u03cd\u03bd \u03c4\u03b1 \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03c0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1.<\/p>\n

        \n

        <\/i> \u039c\u03b5\u03b8\u03bf\u03b4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1<\/i><\/b><\/span><\/h4>\n

        \u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 1: \u039f\u03bc\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af (\u03b8\u03b5\u03c4\u03b9\u03ba\u03bf\u03af)<\/strong><\/em><\/span><\/p>\n

          <\/span>   <\/span>\"\[\dfrac{24}{6} = 4\]\"<\/p>\n

        \u039a\u03b1\u03b9 \u03bf\u03b9 \u03b4\u03cd\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03bf\u03af, \u03ac\u03c1\u03b1 \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc: \"4\".<\/p>\n

        \u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 2: \u039f\u03bc\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af (\u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03bf\u03af)<\/span><\/strong><\/em><\/p>\n

          <\/span>   <\/span>\"\[\dfrac{-48}{-12} = 4\]\"<\/p>\n

        \u0391\u03c6\u03bf\u03cd \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03b4\u03cd\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03bf\u03af, \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc: \"4\".<\/p>\n

        \u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 3: \u0395\u03c4\u03b5\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af (\u03b8\u03b5\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03c4\u03ad\u03bf\u03c2, \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c4\u03b7\u03c2)<\/span><\/strong><\/em><\/p>\n

          <\/span>   <\/span>\"\[\dfrac{35}{-7} = -5\]\"<\/p>\n

        \u0395\u03c0\u03b5\u03b9\u03b4\u03ae \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c4\u03b5\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9, \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03cc: \"-5\".<\/p>\n

        \u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 4: \u0395\u03c4\u03b5\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af (\u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03c4\u03ad\u03bf\u03c2, \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c4\u03b7\u03c2)<\/strong><\/em><\/span><\/p>\n

          <\/span>   <\/span>\"\[\dfrac{-56}{8} = -7\]\"<\/p>\n

        \u0395\u03c0\u03b5\u03b9\u03b4\u03ae \u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c4\u03b5\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf\u03b9, \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03cc: \"-7\".<\/p>\n

        \u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 5: \u0391\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03bc\u03b5 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03bc\u03b7\u03b4\u03ad\u03bd<\/strong><\/em><\/span><\/p>\n

          <\/span>   <\/span>\"\[\dfrac{0}{9} = 0\]\"<\/p>\n

        \u038c\u03c4\u03b1\u03bd \u03b4\u03b9\u03b1\u03b9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03bf \u03bc\u03b7\u03b4\u03ad\u03bd \u03bc\u03b5 \u03bf\u03c0\u03bf\u03b9\u03bf\u03bd\u03b4\u03ae\u03c0\u03bf\u03c4\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc, \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03ac\u03bd\u03c4\u03b1 \u03bc\u03b7\u03b4\u03ad\u03bd: \"0\".<\/p>\n

        \n

        <\/i> <\/i>Let’s Practise<\/b><\/span><\/h4>\n

        1. \u0391\u03c0\u03bb\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03c4\u03b5 \u03c4\u03b1 \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1\u03c4\u03b1<\/strong><\/p>\n

        \u03b1.<\/strong> \"\dfrac{6}{-8}\"<\/p>\n

        \u03b2.<\/strong> \"\dfrac{-9}{12}\"<\/p>\n

        \u03b3.<\/strong> \"\dfrac{10}{-15}\"<\/p>\n

        \u03b4.<\/strong> \"\dfrac{-16}{20}\"<\/p>\n

        \u03b5.<\/strong> \"\dfrac{18}{-24}\"<\/p>\n

        \u03c3\u03c4.<\/strong> \"\dfrac{-14}{21}\"<\/p>\n

        \u03b6.<\/strong> \"\dfrac{-8}{6}\"<\/p>\n

        \u03b7.<\/strong> \"\dfrac{12}{-9}\"<\/p>\n

        \u03b8.<\/strong> \"\dfrac{-15}{10}\"<\/p>\n

        \u03b9.<\/strong> \"\dfrac{-9}{-12}\"<\/p>\n

        \n

        \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1:<\/strong> \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u0391 \u0393\u03c5\u03bc\u03bd\u03b1\u03c3\u03af\u03bf\u03c5 (\u0399\u03c9\u03ac\u03bd\u03bd\u03b7\u03c2 \u0392\u03b1\u03bd\u03b4\u03bf\u03c5\u03bb\u03ac\u03ba\u03b7\u03c2,\u00a0\u03a7\u03b1\u03c1\u03ac\u03bb\u03b1\u03bc\u03c0\u03bf\u03c2 \u039a\u03b1\u03bb\u03bb\u03b9\u03b3\u03ac\u03c2,\u00a0\u039d\u03b9\u03ba\u03b7\u03c6\u03cc\u03c1\u03bf\u03c2 \u039c\u03b1\u03c1\u03ba\u03ac\u03ba\u03b7\u03c2,\u00a0\u03a3\u03c0\u03cd\u03c1\u03bf\u03c2 \u03a6\u03b5\u03c1\u03b5\u03bd\u03c4\u03af\u03bd\u03bf\u03c2, \u03a5.\u03a0\u0391\u0399.\u0398.)<\/p>\n

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