ᠵᠢᠭᠠᠨ ᠰᠣᠷᠭᠠᠬᠤ ᠲᠦᠰᠣᠪ .docx

︽ᠣᠷᠤᠨ ᠳᠠᠪ ᠰᠢᠬ ᠤ ᠦᠭᠡᠢ ᠨ ᠡᠮᠡᠬᠦ ︵ᠵᠢᠱᠢᠶ ᠡ 1︶ ︾ ᠵᠢᠭᠠᠨ ᠰ ᠤᠷᠭ ᠠᠬᠤ ᠲᠦᠰᠦᠪ ᠬᠢᠴᠢᠶᠡᠯ ᠲᠦ ᠷᠦᠯ ᠄ ᠪᠠᠭ ᠠ ᠰᠤᠷᠭᠠᠭ ᠤᠯᠢ ᠶᠢᠨ ᠲᠤᠭ ᠠᠨ ᠦ ᠤ ᠬᠠᠭᠠ ᠨ ᠬᠢᠴᠢᠶᠡᠯ ᠯᠡᠬᠦ ᠣ ᠨ᠄ ᠬᠤᠶᠠ ᠳᠤᠭ ᠠᠷ ᠣ ᠨ ᠦ ᠲᠡᠭᠡᠳᠦ ᠲᠡ ᠪᠳ ᠡᠷ ᠲᠦ ᠰᠦᠪᠯᠡᠭᠴ ᠢ᠄ ᠰᠠᠷ ᠠᠨ ᠠ ᠪᠠᠶᠢᠭᠤᠯ ᠭ ᠠ ᠨᠢᠭᠡᠴ ᠢ᠄ ᠲ ᠦᠩᠯᠢ ᠶᠣᠤ ᠬᠤᠳᠠ ᠶᠢᠨ ᠵᠠᠷ ᠤᠳ ᠬᠣᠰᠢᠭᠤᠨ ᠦ ᠴᠢᠪ ᠠᠭᠠᠳᠤ ᠰᠤᠷᠭᠠᠭ ᠤᠯᠢ ᠰᠡᠭᠦ ᠯᠴᠢ ᠶᠢᠨ ᠬᠢᠨᠠᠭ ᠴᠢ ᠄ ᠵᠢᠨ ᠷᠦ ᠩ ᠡᠴᠦᠰ ᠤᠨ ᠬᠢᠨᠠᠭ ᠴᠢ ᠄ ᠡ ᠭᠡᠷ ᠡᠯ ᠨᠢᠭᠡ᠂ ᠵᠢᠭᠠᠨ ᠰᠤ ᠷᠭᠠᠬᠤ ᠬᠠ ᠷᠠᠯᠲᠠ᠄ ︵ᠨᠢᠭ ᠡ ︶ ᠮᠡ ᠳᠡᠯ ᠭᠡ ᠪᠠ ᠮᠡ ᠷᠭᠡ ᠰᠢᠯ ⒈ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠲᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠶᠢ ᠨᠡᠮᠡ ᠬᠦ ᠶ ᠢᠨ ᠪᠣᠳᠤ ᠬᠤ ᠶᠤ ᠰᠤ ᠶ ᠢ ᠤ ᠬᠠᠬ ᠤ᠃ ⒉ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣᠭ ᠠ ᠲᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠶᠢ ᠨᠡᠮᠡ ᠬᠦ ᠶ ᠢᠨ ᠪᠢᠷ ᠢᠶᠡ ᠷ ᠪᠣᠳᠤ ᠬᠤ ᠠᠷ ᠭ ᠠ ᠶᠢ ᠡᠵᠡ ᠮᠰᠢᠵᠦ᠂ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠤ ᠭᠠᠨ ᠤ ᠣ ᠷᠣᠨ ᠲᠠᠪᠰᠢ ᠬᠤ ᠦ ᠭᠡᠢ ᠨᠡ ᠮᠡᠬᠦ ᠦ ᠢᠯᠡᠳᠦᠯ ᠢ ᠪᠣᠰᠤᠭ ᠠ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠢᠶᠡ ᠷ ᠵᠦᠪ ᠪᠣᠳᠤ ᠵᠤ ᠴᠢ ᠳᠠᠬ ᠤ᠃ ︵ ᠬᠤᠶᠠ ᠷ ︶ ᠶᠠᠪᠤᠴᠠ ᠪᠠ ᠠᠷ ᠭ ᠠ ⒈ ᠰᠤᠷᠤᠭᠴᠢ ᠳ ᠦ ᠷᠦᠬᠦ᠂ ᠵᠢᠷᠤᠬᠤ ᠣ ᠯᠠᠨ ᠤ ᠳᠠᠭᠠᠨ ᠤ ᠠᠵᠢᠯ ᠯᠠᠪᠤᠷᠢ ᠪᠠᠷ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠤ ᠭᠠᠨ ᠤ ᠣ ᠷᠣᠨ ᠲᠠ ᠪᠰᠢ ᠬᠤ ᠦ ᠭᠡᠢ ᠨᠡᠮᠡ ᠬᠦ ᠦ ᠢᠯᠡᠳᠦᠯ ᠢ ᠪᠢᠷ ᠢᠶᠡ ᠷ ᠪᠣᠳᠤ ᠬᠤ ᠠᠷ ᠭ ᠠ ᠶᠢ ᠰᠦᠪ ᠡᠭᠴᠢ ᠯᠡᠬᠦ ᠶᠠᠪᠤᠴᠠ ᠶ ᠢ ᠦ ᠩᠭᠡ ᠷᠡᠭᠦ ᠯᠵᠦ᠂ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠤ ᠭᠠᠨ ᠤ ᠣ ᠷᠣᠨ ᠲᠠ ᠪᠰᠢ ᠬᠤ ᠦ ᠭᠡᠢ ᠨᠡ ᠮᠡᠬᠦ ᠦ ᠢᠯᠡᠳᠦ ᠯ ᠤ ᠨ ᠪᠣᠳᠤ ᠬᠤ ᠠᠷ ᠭ ᠠ ᠶᠢᠨ ᠣ ᠯᠠᠨ ᠶᠠ ᠩᠵᠤᠳᠤ ᠴᠢᠨ ᠠᠷ ᠢ ᠪᠡᠶᠡ ᠴᠢᠯᠡᠨ ᠤ ᠬᠠᠬ ᠤ᠃ ︵ᠭᠤ ᠷᠪᠠ ︶ᠣ ᠪᠤᠷ ᠰᠡᠳ ᠬᠢᠯᠭᠡ ᠪᠠ ᠥ ᠷᠳᠡ ᠭ ᠦᠨ ᠦ ᠵᠡᠯᠳᠡ ⒈ ᠰᠤᠷᠤᠭᠴᠢ ᠳ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠤ ᠭᠠᠨ ᠤ ᠣ ᠷᠣᠨ ᠲᠠ ᠪᠰᠢ ᠬᠤ ᠦ ᠭᠡᠢ ᠨᠡᠮᠡ ᠬᠦ ᠦ ᠢᠯᠡᠳᠦᠯ ᠤᠨ ᠮᠡ ᠳᠡᠯ ᠭᠡ ᠪᠡᠷ ᠪᠣᠳᠠᠳᠠᠢ ᠠᠮᠢᠳᠤᠷᠠ ᠯ ᠳ᠋ᠡᠬᠢ ᠲᠦ ᠭᠦᠮ ᠠᠰᠠᠭ ᠤᠳᠠ ᠯ ᠢ ᠢᠯᠡᠷ ᠡᠭᠦᠯ ᠵᠦ᠂ ᠨᠠᠶᠢᠷᠠ ᠭᠤᠯ ᠵᠤ ᠴᠢᠳᠠᠬ ᠤ ᠪᠠ ᠪᠣᠳᠤᠵᠤ ᠬᠠ ᠷᠢᠭᠤᠯ ᠵᠤ ᠴᠢᠳᠠᠬ ᠤ᠃ ⒉ ᠲᠤ ᠭᠠᠨ ᠤ ᠤ ᠬᠠᠭᠠ ᠨ ᠤ ᠦ ᠨ ᠡ ᠥ ᠷᠳᠡᠭ ᠢ ᠪᠡᠶᠡ ᠴᠢᠯᠡᠨ ᠣ ᠶᠢᠯᠠᠭᠠᠵᠤ ᠂ ᠲᠤ ᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠ ᠨ ᠪᠠ ᠠᠮᠢᠳᠤᠷᠠ ᠯ ᠤᠨ ᠨᠢᠭᠲᠠ ᠬᠤᠯ ᠪᠤᠭᠳᠠᠯ ᠢ ᠰᠡ ᠷᠡᠵᠦ ᠮᠡᠳᠡᠬᠦ ᠃ ᠬᠤ ᠶᠠᠷ᠂ ᠵᠢᠭ ᠠᠬᠤ ᠠᠭᠤᠯ ᠭ ᠠ ᠶᠢ ᠨ ᠵᠠᠳᠠᠯᠤᠯ ᠳᠠ᠄ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠤ ᠭᠠᠨ ᠤ ᠣ ᠷᠣᠨ ᠲ ᠠᠪᠰᠢ ᠬᠤ ᠦ ᠭᠡᠢ ᠨᠡᠮᠡ ᠬᠦ ᠦ ᠢᠯᠡᠳ ᠦᠯ ᠤᠨ ᠪᠢᠷ ᠪᠣᠳ ᠤᠯᠭ ᠠ ᠨᠢ ᠨᠢᠭᠡᠨᠳᠡ ᠰᠤᠷᠤᠭ ᠰᠠᠨ ᠬᠣᠶᠠ ᠷ ᠤ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠲᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠪᠠ ᠪᠦᠬᠦᠯ ᠢ ᠠᠷ ᠪᠠ ᠶᠢᠨ ᠲᠣ ᠭ ᠠ ᠶᠢ ᠨᠡᠮᠡ ᠬᠦ ᠶ ᠢᠨ ᠪᠠᠳᠤᠳᠬ ᠠᠯ ᠪᠠ ᠬᠡᠷ ᠡᠭᠯᠡ ᠯᠲᠡ ᠪᠣᠯᠬ ᠤ ᠪᠦᠭᠡᠳ ᠣ ᠯᠠᠨ ᠣ ᠷᠤᠨᠳᠤ ᠲᠤ ᠭᠠᠨ ᠤ ᠨᠡᠮ ᠡᠬᠦ ᠦ ᠢᠯᠡᠳᠦᠯ ᠢ ᠰᠤᠷᠬᠤ ᠶᠢᠨ ᠰᠠᠭᠤᠷ ᠢ ᠪᠠᠶᠢᠵᠤ᠂ ᠠᠮᠠ ᠰᠡᠭᠡᠷ ᠢ ᠨᠢ ᠵᠣᠯᠭᠠ ᠭᠤᠯ ᠬᠤ ᠦ ᠢᠯᠡᠳᠦᠯ ᠲᠠᠢ᠃ ᠡᠶᠢᠮᠦ ᠡᠴᠡ ᠡᠨᠡ ᠬᠡᠰᠡᠭ ᠠᠭᠤᠯ ᠭ ᠠ ᠶᠢ ᠰᠠᠶᠢᠨ ᠰᠤᠷᠬᠤ ᠡᠰᠡᠭᠦ ᠨᠢ ᠰᠤᠷᠤᠭ ᠴᠢᠳ ᠤ ᠨ ᠪᠣᠳᠤ ᠯᠭ ᠠ ᠶᠢᠨ ᠵᠦᠪ ᠣ ᠨᠤᠪᠴ ᠢᠳᠤ ᠴᠢᠨ ᠠᠷ ᠪᠠ ᠬᠤᠷᠳᠤᠴᠠ ᠳ᠋ᠤ ᠰᠢᠭᠤᠳ ᠨ ᠦᠯᠦᠭᠡ ᠦ ᠵᠡᠭᠦᠯᠳᠡ ᠭ ᠪᠠᠶᠢᠨ ᠠ᠃ ᠭᠤ ᠷᠪᠠ᠂ ᠰᠤᠷᠤᠭᠴ ᠢ ᠶ ᠢᠨ ᠪᠠ ᠶᠢᠳᠠ ᠯ ᠤᠨ ᠵ ᠠᠳᠠᠯᠤᠯᠳ ᠠ᠄ ᠰᠤᠷᠤᠭᠴᠢᠳ ᠨ ᠢᠭᠡᠨᠳᠡ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠲᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠪᠠ ᠪᠦᠬᠦᠯ ᠢ ᠠᠷ ᠪᠠ ᠶᠢᠨ ᠲᠣ ᠭ ᠠ ᠶᠢ ᠨᠡᠮᠡ ᠬᠦ ᠶ ᠢᠨ ᠴᠡᠭᠡᠵᠢ ᠪᠣᠳᠤᠯᠭ ᠠ ᠶᠢᠨ ᠠᠷ ᠭ ᠠ᠂ ᠶᠣ ᠰᠤ ᠳ᠋ᠤ ᠴᠠᠭᠠᠷ ᠠᠭᠰᠠ ᠨ ᠪᠠᠶᠢᠨ ᠠ᠃ ᠳᠦᠷ ᠪᠡ᠂ ᠵᠢᠭᠠᠬᠤ ᠭᠣᠣ ᠯᠳᠠᠯᠭ ᠠ ᠬᠢᠭᠡᠳ ᠬᠦᠴᠢ ᠷᠳᠡ ᠯᠭᠡ᠄ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠲᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠶ ᠢ ᠨᠡᠮᠡ ᠬᠦ ᠶ ᠢᠨ ᠪᠣᠳᠤ ᠬᠤ ᠶᠤ ᠰᠤ ᠶ ᠢ ᠤ ᠬᠠᠵᠤ ᠂ ᠪᠢᠷ ᠢᠶᠡ ᠷ ᠪᠣᠳᠤ ᠬᠤ ᠠᠷ ᠭ ᠠ ᠶᠢ ᠡᠵᠡ ᠮᠰᠢᠨ ᠡ᠃ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠤ ᠭᠠᠨ ᠤ ᠣ ᠷᠣᠨ ᠲ ᠠᠪᠰᠢ ᠬᠤ ᠦ ᠭᠡᠢ ᠨᠡᠮᠡ ᠬᠦ ᠦ ᠢᠯᠡᠳᠦᠯ ᠢ ᠪᠣᠰᠤᠭ ᠠ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠢᠶᠡ ᠷ ᠪᠠᠶᠢᠭᠤᠯ ᠬᠤ ᠪᠠ ᠪᠣᠳᠤ ᠬᠤ ᠶᠢᠨ ᠲᠠ ᠷᠠᠭᠠ ᠯᠠᠯ ᠢ ᠤ ᠬᠠᠵᠤ ᠂ ᠵᠦᠪ ᠣ ᠨᠤᠪᠴᠢᠳᠠ ᠢ ᠪᠣᠳᠤ ᠵᠤ ᠴᠢᠳᠠᠬ ᠤ᠃ ᠲᠠᠪᠤ᠂ ᠵᠢᠭᠠᠨ ᠰᠤ ᠷᠭᠠᠬᠤ ᠠᠷ ᠭ ᠠ᠄ ᠦ ᠷᠦᠬᠦ ᠂ ᠵᠢᠷᠤᠬᠤ ᠂ ᠪᠢᠴᠢᠬ ᠦ ᠂᠂᠂᠂ ᠵᠡᠷ ᠭᠡ ᠣ ᠯᠠᠨ ᠵᠦᠢ ᠯ ᠦ ᠨ ᠠᠵᠢᠯ ᠯᠠᠬᠤ ᠬᠦᠳᠡ ᠯᠪᠦᠷᠢ ᠪ ᠡᠷ ᠡᠵᠡ ᠨ ᠮᠡᠳᠡᠨ ᠰᠦᠪ ᠡᠭᠴ ᠢᠯᠡᠵᠦ ᠰᠤᠷᠤᠯᠴᠠᠬ ᠤ᠂ ᠬᠣᠷᠰᠢᠨ ᠰᠤᠷᠤᠯᠴᠠᠬ ᠤ᠃ ᠵᠢᠷᠭᠤᠭ ᠠ᠂ ᠵᠢᠭᠠ ᠨ ᠰᠤᠷᠭᠠᠬᠤ ᠡᠬᠢ ᠰᠤ ᠷᠪᠤ ᠯᠵᠢ ᠄ ᠰᠤᠷᠬᠤ ᠪᠢᠴᠢᠭ᠂ ᠬᠢᠴᠢᠶᠡᠯ ᠦᠨ ᠪᠠᠷᠢᠮᠵᠢᠶ ᠠ᠂ ᠰᠠᠪᠠᠭ ᠠ ᠂ ᠠᠵᠢᠯ ᠯᠠᠪᠤᠷᠢ ᠶᠢᠨ ᠬᠠ ᠭᠤᠳᠠᠰᠤ᠂ ᠺᠣᠣᠷᠰ ᠸᠠᠶᠢᠷ ᠲᠤᠯᠤᠭ ᠠ᠂ ᠵᠢᠭ ᠠᠨ ᠰᠤ ᠷᠭᠠᠬᠤ ᠶᠠᠪ ᠤᠴᠠ᠄ ᠠᠬᠤᠢ ᠣ ᠷᠴᠢᠨ ᠪᠦᠳᠦᠭ ᠡᠬᠦ᠄ ᠨᠠᠮ ᠤᠷ ᠪᠤᠯᠤᠯ ᠠ ᠂ ᠬᠤᠸ ᠠᠷ ᠴᠡᠴᠡᠭ ᠲᠡᠯᠭᠡᠷ ᠡᠭᠡᠳ ᠰᠤᠷᠭᠠᠭ ᠤᠯᠢ ᠶᠢᠨ ᠬᠦᠷᠢ ᠶ ᠡ ᠮᠠᠨ ᠢ ᠴᠡ ᠴᠡᠷᠯᠢᠭ ᠰᠢᠭ ᠭᠣ ᠶᠤ ᠬᠠᠷᠠ ᠭᠳᠠ ᠨ ᠠ᠃ ᠠᠩᠭ ᠢ ᠶᠢᠨ ᠡᠷᠬᠢ ᠯᠡᠭᠴᠢ ᠪᠣᠤ ᠪᠠᠭᠰᠢ ᠲᠠᠢ ᠴᠢᠨ ᠢ ᠪᠢᠳᠡ ᠬᠤᠶᠠ ᠭᠤᠯᠠ ᠲᠠ ᠨᠤᠰ ᠲᠠ ᠢ ᠬᠠᠮ ᠳᠤ ᠶᠢᠨ ᠰᠡᠭᠦ ᠳᠡᠷ ᠲᠠᠲ ᠠᠵᠤ᠂ ᠦ ᠰᠦᠨ ᠪᠣᠶᠢ ᠵᠢᠯᠳᠠ ᠶᠢᠨ ᠲᠡᠮᠳᠡ ᠭᠯᠡᠯ ᠦ ᠯᠡᠳᠡ ᠭᠡᠬᠦ ᠪᠡᠷ ᠪᠠᠶᠢᠨ ᠠ᠃ ⒈ ᠣ ᠷᠤᠯ ᠳᠤᠯᠭ ᠠ 1. ⑴ ᠲᠣ ᠭᠠᠨ ᠤ ᠤ ᠬᠠᠭᠠ ᠨ ᠤ ᠮᠡ ᠳᠡᠭᠡ ᠵᠠ ᠩᠭᠢ ᠡᠷᠢ ᠨ ᠡ ︵2 ᠪᠠᠭᠰᠢ᠂ 2 5 ᠰᠤᠷᠤᠭᠴᠢ ︶᠃ ⑵ ᠨᠡ ᠮᠡᠬᠦ ᠦ ᠢᠯᠡᠳᠦᠯ ᠢᠶᠡ ᠷ ᠪᠣᠳᠤ ᠬᠤ ᠠᠰᠠᠭ ᠤᠯᠲᠠ ᠲᠤ ᠷᠠᠳᠤᠨ ᠠ᠄ ᠨᠡᠶᠢᠲᠡ ᠬᠡᠳᠦᠢ ᠬᠦᠮ ᠦᠨ ᠪᠠᠶᠢᠬᠤ ᠪᠣᠢ ︖ ⑶ ᠪᠣᠳᠤ ᠬᠤ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠪᠠᠶᠢᠭᠤᠯ ᠤᠨ ᠠ᠄ 25 +2 = ⒉ ᠣ ᠷᠤᠯ ᠳᠤᠯᠭ ᠠ 2. ⑴ ᠪᠣᠳᠤ ᠬᠤ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠢ ᠴᠡ ᠭᠡᠵᠢ ᠪ ᠡᠷ ᠪ ᠣᠳᠤᠬᠤ ᠶᠠᠪᠤᠴᠠ ᠪᠠᠨ ᠵᠢᠷᠤᠭᠴᠢᠯ ᠠ᠃ ⑵ ᠵᠢᠷᠤᠭᠴᠢᠯᠠᠭᠰᠠ ᠨ ᠶᠠᠪᠤᠴᠠ ᠪᠠᠨ ᠪᠣᠳᠤ ᠬᠤ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠪᠤᠯᠭᠠ ᠨ ᠪᠢᠴᠢ ᠃ ⑶ ᠵᠢᠷᠤᠭᠰᠠᠨ ᠰᠡᠳ ᠬᠢᠮᠵ ᠢ ᠪᠠᠨ ᠶᠠᠷᠢᠶ ᠠ᠃ ⒊ ᠣ ᠷᠤᠯ ᠳᠤᠯᠭ ᠠ 3. ⑴ ᠪᠣᠰ ᠤᠭ ᠠ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯ ᠡᠯ ᠢᠶᠡᠷ ᠲᠤ ᠷᠰᠢᠨ ᠪᠣᠳᠤᠭ ᠠᠷᠠᠢ ᠃ ⑵ ᠪᠢᠷ ᠢᠶᠡ ᠷ ᠪᠣᠳᠤ ᠭᠰᠠ ᠨ ᠰᠡᠳ ᠬᠢᠮᠵᠢ ᠪᠠᠨ ᠶᠠᠷᠢ ᠶ ᠠ᠃ ⒋ ᠰᠤᠷᠤᠭᠴᠢ ᠳ ᠤ ᠨ ᠬᠠᠷᠢ ᠭᠤ ᠮᠡᠳᠡᠭᠦᠯᠦᠯ ᠳᠡ ᠶᠢ ᠪᠠᠭᠰᠢ ᠠᠴᠠ ᠦ ᠨᠡᠯᠡᠨ ᠬᠤᠷᠢᠶᠠᠩᠭᠤᠶᠢᠯ ᠠᠵᠤ᠂ ᠰᠠᠮ ᠪᠠᠷ ᠠ ᠳ᠋ᠤ ᠳᠦᠷᠢᠮᠴᠢᠯᠡ ᠨ ᠪᠣᠳᠤ ᠭᠠᠳ᠂ ᠬᠡᠦᠬ ᠡᠳ ᠲᠦ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠲᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣᠭ ᠠ ᠶᠢ ᠨᠡᠮᠡ ᠬᠦ ᠶ ᠢᠨ ᠪᠣᠳᠤ ᠬᠤ ᠶᠤ ᠰᠤ ᠶ ᠢ ᠤ ᠬᠠᠭᠠ ᠷᠠᠭᠤᠯ ᠬᠤ ᠶᠢᠨ ᠬᠠ ᠮᠳᠤ ᠬᠤᠶᠠ ᠷ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠲᠡᠭᠡᠷ ᠡ ᠨᠢᠭᠡ ᠣ ᠷᠤᠨᠳᠤ ᠲᠣ ᠭ ᠠ ᠶᠢ ᠨᠡ ᠮᠡᠬᠦ ᠶ ᠢᠨ ᠪᠢᠷ ᠢᠶᠡ ᠷ ᠪᠣᠳᠤ ᠬᠤ ᠠᠷ ᠭ ᠠ ᠶᠢ ᠵᠦᠪ ᠂ ᠭᠦᠨᠵᠡ ᠭᠡᠢ ᠡᠵᠡ ᠮᠰᠢᠭ ᠦᠯᠦᠨ ᠡ᠃ ︵ ᠭᠤ ᠷᠪᠠ ︶ᠪᠣᠯᠪᠠᠰᠤᠷᠠ ᠯ ᠬᠢ ᠵᠦ᠂ ᠦ ᠪᠡᠷ ᠢ ᠪᠠᠨ ᠪᠠᠶᠢᠴ ᠠᠭᠠᠨ ᠠ᠄ ︽ ᠬᠢᠵᠦ ᠦ ᠵᠡ ︾ ᠶᠢᠨ ᠰᠡᠳᠦᠪ ᠃ ⑴ ᠡᠵᠡ ᠨ ᠮᠡᠳᠡ ᠨ ᠰᠦᠪ ᠡᠭᠴ ᠢᠯᠡᠨ ᠡ᠃ ⑵ ᠦ ᠪᠡᠷ ᠦ ᠪᠡᠷ ᠦᠨ ᠰᠡᠳ ᠬᠢᠮᠵ ᠢ ᠪᠠᠨ ᠣ ᠯᠠᠨ ᠳ᠋ᠤ ᠲᠡᠯ ᠭᠡᠨ ᠡ᠃ ︵ ᠳᠦᠷ ᠪᠡ ︶ᠦ ᠷᠭᠡ ᠳᠬᠡᠯ ᠪᠣᠯᠪᠠᠰᠤᠷᠠ ᠯ ᠡᠨᠡ ᠬᠢ ᠴᠢᠶᠡ ᠯ ᠦᠨ ᠰᠤᠷᠤ ᠭᠰᠠ ᠨ ᠮᠡᠳᠡᠯ ᠭᠡ ᠪᠡᠷ ᠢᠶᠡ ᠨ ᠠᠰᠠᠭ ᠤᠳᠠᠯ ᠨ ᠠᠶᠢᠷ ᠠᠭᠤᠯᠤᠭᠠᠳ᠂ ᠪᠠᠰᠠ ᠪᠣᠳ ᠤᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯ ᠤᠶ ᠠ ᠃ ︵ ᠲᠠ ᠪᠤ ︶ᠰᠤᠷᠤᠭᠴᠢ ᠳ ᠤ ᠨ ᠣ ᠯᠤᠯᠳᠠ ᠲᠦ ᠷᠦᠭ ᠳᠡᠯ ᠢ ᠶᠠ ᠷᠢᠭᠤᠯ ᠤᠨ ᠠ᠄ ᠲᠤ ᠰ ᠬᠢᠴᠢᠶᠡᠯ ᠢ ᠰᠤᠷᠤᠭᠠ ᠳ ᠶᠠ ᠭᠤ ᠶᠠᠷᠢᠮᠠ ᠷ ᠪᠠ ᠶᠢᠨ ᠠ ︖ ᠨᠠᠢ ᠮᠠ ᠂ ᠲ ᠠᠰᠬᠠ ᠯ ᠪᠣᠯᠪᠠᠰᠤ ᠷᠠᠯ ᠦᠯᠡ ᠳᠡᠭᠡ ᠨ ᠡ᠄ ⒈ ︽ᠰᠤᠷᠬᠤ ᠪᠢᠴᠢᠭ ︾ ᠡᠴᠡ ᠰᠤᠷᠤᠭᠰᠠᠨ ᠠᠭᠤᠯ ᠭ ᠠ ᠪᠠᠨ ᠨᠢᠭᠡ ᠤ ᠳᠠᠭ ᠠ ᠦ ᠵᠡᠬᠦ᠃ ⒉ ︽ᠪᠣᠯᠪᠠᠰᠤᠷᠠ ᠯ ᠤᠨ ᠦ ᠷᠦᠭᠡ ︾ ᠶᠢᠨ ᠬᠠ ᠷᠠᠭᠠᠯ ᠵᠠᠭᠰᠠ ᠨ ᠰᠡᠳᠦᠪ ᠦᠳ ᠢ ᠬᠢᠬᠦ ᠃ ᠶᠢᠰᠦ ᠂ ᠰᠠᠮ ᠪᠠᠷᠠᠴᠢᠯᠠ ᠯ᠄ ᠣ ᠷᠤᠨ ᠳᠠ ᠪᠰᠢ ᠬᠤ ᠦ ᠭᠡᠢ ᠨᠡ ᠮᠡᠬᠦ 25+2=27 ( ) 2 5 + 2 2 7 ᠬᠦᠮᠦᠨ ᠬᠠᠷ ᠢᠭᠤᠯᠲ ᠠ᠄ ᠨᠡᠶᠢᠲᠡ 27 ᠬᠦᠮᠦ ᠨ ᠪᠠᠶᠢ ᠨ ᠠ᠃ ᠠᠵᠢᠯ ᠯᠠᠪᠤᠷᠢ ᠶᠢᠨ ᠬᠠᠭᠤᠳᠠᠰᠤ ᠨᠡᠷ ᠡ᠄ ᠣ ᠷᠤᠯ ᠳᠤᠯᠭ ᠠ 1. ⑴ ᠲᠣ ᠭᠠᠨ ᠤ ᠤ ᠬᠠᠭᠠ ᠨ ᠤ ᠮᠡ ᠳᠡᠭᠡ ᠵᠠᠩᠭ ᠢ ᠶ ᠢ ᠡᠷ ᠢᠵᠦ ᠭᠠ ᠷᠭ ᠠ᠃ ⑵ ᠨᠡ ᠮᠡᠬᠦ ᠦ ᠢᠯᠡᠳᠦᠯ ᠢᠶᠡ ᠷ ᠪᠣᠳᠤ ᠬᠤ ᠠᠰᠠᠭ ᠤᠯᠲᠠ ᠳᠤᠷᠠ ᠳ᠃ ⑶ ᠪᠣᠳᠤ ᠬᠤ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠪᠠᠶᠢᠭᠤᠯ᠃ ᠣ ᠷᠤᠯ ᠳᠤᠯᠭ ᠠ 2. ⑴ ᠪᠣᠳᠤ ᠬᠤ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯ ᠡᠯ ᠢ ᠴᠡ ᠭᠡᠵᠢ ᠪᠡᠷ ᠪᠣᠳ ᠤᠬᠤ ᠶᠠᠪᠤᠴᠠ ᠪᠠᠨ ᠵᠢᠷᠤᠭᠴ ᠢᠯᠠ᠃ ⑵ ᠵᠢᠷᠤᠭᠴᠢᠯᠠᠭᠰᠠ ᠨ ᠶᠠᠪᠤᠴᠠ ᠪᠠᠨ ᠪᠣᠳᠤ ᠬᠤ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯᠡᠯ ᠪᠤᠯᠭ ᠠᠨ ᠪᠢᠴᠢ ᠃ ⑶ ᠵᠢᠷᠤᠭᠰᠠᠨ ᠰᠡᠳ ᠬᠢᠮᠵᠢ ᠪᠠᠨ ᠶᠠᠷᠢᠬᠤ ᠪᠠ ᠷ ᠪᠡ ᠯᠡᠳ ᠬᠡᠨ ᠡ᠃ ᠣ ᠷᠤᠯ ᠳᠤᠯᠭ ᠠ 3. ⑴ ᠪᠣᠰ ᠤᠭ ᠠ ᠢᠯᠡᠷ ᠬᠡᠶᠢᠯ ᠡᠯ ᠢᠶᠡᠷ ᠲᠤ ᠷᠰᠢᠨ ᠪᠣᠳ ᠤᠭᠠᠷ ᠠᠢ᠃ ⑵ ᠪᠢᠷ ᠢᠶᠡ ᠷ ᠪᠣᠳ ᠤᠭᠰᠠ ᠨ ᠰᠡᠳ ᠬᠢᠮᠵᠢ ᠪᠠᠨ ᠶᠠᠷᠢᠬᠤ ᠪᠠ ᠷ ᠪᠡ ᠯᠡᠳ ᠬᠡᠨ ᠡ᠃ ᠦᠷ ᠭᠡᠳ ᠬᠡᠯ ᠪᠣᠯᠪᠠᠰᠤ ᠷᠠᠯ᠄ ᠰᠤᠷᠤᠭᠰᠠᠨ ᠮᠡ ᠳᠡᠯ ᠭᠡ ᠪᠡᠷ ᠢᠶᠡ ᠨ ᠠᠰᠠᠭ ᠤᠳᠠᠯ ᠨᠠᠶᠢᠷᠠ ᠭᠤᠯ ᠤᠭᠠ ᠳ᠂ ᠪᠠᠰᠠ ᠪᠣᠳᠤ ᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯ ᠤᠶ ᠠ᠃