{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" T\u00ecm s\u1ed1 nguy\u00ean $m$ th\u1ecfa m\u00e3n: <br\/> $\\dfrac{1}{3} + \\left( \\dfrac{3}{4} - 1\\dfrac{2}{5} \\right) < m < 2\\dfrac{1}{7} + \\left( -\\dfrac{2}{5} - \\dfrac{1}{4} \\right) $","select":["A. $m \\in \\lbrace -1; 0; 1 \\rbrace$ ","B. $m \\in \\lbrace 0; 1 \\rbrace$ ","C. $m = 1$","D. $m \\in \\lbrace -1; 0; 1; 2 \\rbrace$ "],"hint":"T\u00ednh t\u1eebng v\u1ebf r\u1ed3i t\u00ecm m.","explain":" Ta c\u00f3: $\\dfrac{1}{3} + \\left( \\dfrac{3}{4} - 1\\dfrac{2}{5} \\right) < m < 2\\dfrac{1}{7} + \\left( -\\dfrac{2}{5} - \\dfrac{1}{4} \\right)$ <br\/>V\u1ebf tr\u00e1i = $\\dfrac{1}{3} + \\dfrac{15-28}{20} = \\dfrac{1}{3} + \\dfrac{-13}{20} = \\dfrac{20-39}{60} = \\dfrac{-19}{60} $ <br\/> V\u1ebf ph\u1ea3i = $ 2 + \\dfrac{1}{7} + \\dfrac{-8-5}{20} = 2 + \\dfrac{1}{7} + \\dfrac{-13}{20} = 2 +\\dfrac{20-91}{140} = 2 + \\dfrac{-71}{140} = 1\\dfrac{69}{140} $ <br\/> Suy ra $\\dfrac{-19}{60} < m < 1\\dfrac{69}{30} $ <br\/> M\u00e0 s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 s\u1ed1 nguy\u00ean n\u00ean $m \\in \\lbrace 0; 1 \\rbrace$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span> <br\/>","column":2}]}],"id_ques":91},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai2/lv3/img\/4.jpg' \/><\/center>Ch\u1ecdn k\u1ebft qu\u1ea3 \u0111\u00fang c\u1ee7a bi\u1ec3u th\u1ee9c $ N = \\left( \\dfrac{2}{3} - 4 \\right) + \\left( \\dfrac{-1}{2} + 5 \\right) - \\dfrac{3}{4} $ ","select":["A. $-\\dfrac{5}{12}$","B. $\\dfrac{5}{12}$","C. $1\\dfrac{5}{12}$","D. $-1\\dfrac{5}{12}$"],"explain":" Ta c\u00f3: $ N = \\left( \\dfrac{2}{3} - 4 \\right) + \\left( \\dfrac{-1}{2} + 5 \\right) - \\dfrac{3}{4} \\\\ = \\left( \\dfrac{2}{3} - \\dfrac{12}{3} \\right) + \\left( \\dfrac{-1}{2} + \\dfrac{10}{2} \\right) - \\dfrac{3}{4} \\\\ = \\dfrac{-10}{3} + \\dfrac{9}{2} - \\dfrac{3}{4} \\\\ = \\dfrac{-40}{12} + \\dfrac{54}{12} - \\dfrac{9}{12} \\\\ = \\dfrac{5}{12} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span> <br\/>","column":2}]}],"id_ques":92},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 c\u1ee7a bi\u1ec3u th\u1ee9c P v\u00e0o \u00f4 tr\u1ed1ng <br\/>$P = \\left( 7 + \\dfrac{7}{5} - \\dfrac{2}{3} \\right) - \\left( 4 + \\dfrac{4}{5} + \\dfrac{3}{8} \\right) + \\left( 3 - \\dfrac{3}{5} + \\dfrac{2}{3} + \\dfrac{3}{8} \\right) $= _input_","explain":" Ta c\u00f3: $ P = \\left( 7 + \\dfrac{7}{5} - \\dfrac{2}{3} \\right) - \\left( 4 + \\dfrac{4}{5} + \\dfrac{3}{8} \\right) + \\left( 3 - \\dfrac{3}{5} + \\dfrac{2}{3} + \\dfrac{3}{8} \\right) \\\\ = 7 + \\dfrac{7}{5} - \\dfrac{2}{3} - 4 - \\dfrac{4}{5} - \\dfrac{3}{8} + 3 - \\dfrac{3}{5} + \\dfrac{2}{3} + \\dfrac{3}{8} \\\\ = \\left( 7 -4 + 3 \\right) + \\left( \\dfrac{7}{5} - \\dfrac{4}{5} - \\dfrac{3}{5} \\right) + \\left( \\dfrac{-2}{3} + \\dfrac{2}{3} \\right) + \\left( \\dfrac{-3}{8} + \\dfrac{3}{8} \\right) \\\\ = 6 + 0 + 0 + 0 = 6 $<br\/> <br\/> <span class='basic_pink'> Gi\u00e1 tr\u1ecb c\u1ee7a P l\u00e0 $6$ <\/span><\/span> <br\/>"}]}],"id_ques":93},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: <br\/>$B = 2\\dfrac{2}{3} - 1\\dfrac{2}{5} + 1\\dfrac{3}{10} - \\left( \\dfrac{2}{5} - \\dfrac{5}{6} \\right) + \\dfrac{4}{5} - 1\\dfrac{1}{3} $= _input_$\\dfrac{7}{15}$ (Nh\u1eadp v\u00e0o ph\u1ea7n nguy\u00ean c\u1ee7a h\u1ed7n s\u1ed1)","explain":"Nh\u00f3m c\u00e1c s\u1ed1 h\u1ea1ng th\u00edch h\u1ee3p r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh <br\/> <br\/> $ B = 2\\dfrac{2}{3} - 1\\dfrac{2}{5} + 1\\dfrac{3}{10} - \\left( \\dfrac{2}{5} - \\dfrac{5}{6} \\right) + \\dfrac{4}{5} - 1\\dfrac{1}{3} \\\\ = 2\\dfrac{2}{3} - 1\\dfrac{2}{5} + 1\\dfrac{3}{10} - \\dfrac{2}{5} + \\dfrac{5}{6} + \\dfrac{4}{5} - 1\\dfrac{1}{3} \\\\ = \\left( 2\\dfrac{2}{3} + \\dfrac{5}{6} - 1\\dfrac{1}{3} \\right) + \\left( -1\\dfrac{2}{5} + 1\\dfrac{3}{10} - \\dfrac{2}{5} + \\dfrac{4}{5} \\right) \\\\ = \\left( 2 + \\dfrac{2}{3} + \\dfrac{5}{6} - 1 - \\dfrac{1}{3} \\right) + \\left( -1 - \\dfrac{2}{5} + 1 + \\dfrac{3}{10} - \\dfrac{2}{5} + \\dfrac{4}{5} \\right) \\\\ = \\left( 1 + \\dfrac{4+5-2}{6} \\right) + \\dfrac{3}{10} \\\\ = 1 + \\dfrac{7}{6} + \\dfrac{3}{10} \\\\ = \\dfrac{30+35+9}{30} \\\\ = \\dfrac{74}{30} = \\dfrac{37}{15} = 2\\dfrac{7}{15}$ <br\/> <br\/> <span class='basic_pink'>S\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 2. <\/span><\/span> <br\/>"}]}],"id_ques":94},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" T\u00ecm $x \\in \\mathbb{Q}$ bi\u1ebft: <br\/> $ \\dfrac{x+2016}{2} + \\dfrac{2x+4032}{7} = \\dfrac{x+2016}{5} + \\dfrac{x+2016}{6} $ ","select":["A. $ x = 2016$","B. $x = -2016$","C. $x = \\dfrac{1}{2016}$","D. $ x = \\dfrac{-1}{2016} $"],"explain":" $\\dfrac{x+2016}{2} + \\dfrac{2x+4032}{7} = \\dfrac{x+2016}{5} + \\dfrac{x+2016}{6} \\\\ \\Rightarrow \\dfrac{x+2016}{2} + \\dfrac{2(x+2016)}{7} = \\dfrac{x+2016}{5} + \\dfrac{x+2016}{6} \\\\ \\Rightarrow \\left( x + 2016 \\right) \\left( \\dfrac{1}{2} + \\dfrac{2}{7} - \\dfrac{1}{5} - \\dfrac{1}{6} \\right) = 0 $ <br\/> M\u00e0 $\\left( \\dfrac{1}{2} + \\dfrac{2}{7} - \\dfrac{1}{5} - \\dfrac{1}{6} \\right) \\neq 0 $ <br\/> Suy ra: $x + 2016 = 0 \\Rightarrow x = -2016 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span> <br\/>","column":2}]}],"id_ques":95},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"Ch\u1ecdn k\u1ebft qu\u1ea3 \u0111\u00fang c\u1ee7a bi\u1ec3u th\u1ee9c $ E = \\dfrac{15}{34} + \\dfrac{7}{21} + \\dfrac{19}{34} - \\dfrac{20}{15} + \\dfrac{3}{7} $ ","select":["A. $\\dfrac{3}{7}$","B. $\\dfrac{-23}{21}$","C. $\\dfrac{11}{7}$","D. $-1\\dfrac{23}{21}$"],"hint":" Nh\u00f3m c\u00e1c s\u1ed1 h\u1ea1ng th\u00edch h\u1ee3p r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh. ","explain":" Ta c\u00f3: $ E = \\dfrac{15}{34} + \\dfrac{7}{21} + \\dfrac{19}{34} - \\dfrac{20}{15} + \\dfrac{3}{7} \\\\ = \\left( \\dfrac{15}{34} + \\dfrac{19}{34} \\right) + \\left( \\dfrac{7}{21} + \\dfrac{3}{7} \\right) - \\dfrac{20}{15} \\\\ = 1 + \\left( \\dfrac{7}{21} + \\dfrac{9}{21} \\right) - \\dfrac{20}{15} \\\\ = 1 + \\dfrac{16}{21} - \\dfrac{20}{15} \\\\ = \\dfrac{105}{105}+ \\dfrac{80}{105} - \\dfrac{140}{105} \\\\ = \\dfrac{45}{105} \\\\ = \\dfrac{3}{7} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span><\/span> <br\/>","column":2}]}],"id_ques":96},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["26"],["35"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c: <br\/> $ F = \\dfrac{\\dfrac{3}{7} - \\dfrac{3}{17} + \\dfrac{3}{37}}{\\dfrac{5}{7} - \\dfrac{5}{17} + \\dfrac{5}{37}} + \\dfrac{\\dfrac{1}{2} - \\dfrac{1}{3} + \\dfrac{1}{4} - \\dfrac{1}{5}}{\\dfrac{7}{5} - \\dfrac{7}{4} + \\dfrac{7}{3} - \\dfrac{7}{2}} $=<div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":" \u0110\u1eb7t nh\u00e2n t\u1eed chung r\u1ed3i r\u00fat g\u1ecdn.","explain":" Ta c\u00f3: $ F = \\dfrac{\\dfrac{3}{7} - \\dfrac{3}{17} + \\dfrac{3}{37}}{\\dfrac{5}{7} - \\dfrac{5}{17} + \\dfrac{5}{37}} + \\dfrac{\\dfrac{1}{2} - \\dfrac{1}{3} + \\dfrac{1}{4} - \\dfrac{1}{5}}{\\dfrac{7}{5} - \\dfrac{7}{4} + \\dfrac{7}{3} - \\dfrac{7}{2}} \\\\ = \\dfrac{3.\\left( \\dfrac{1}{7}-\\dfrac{1}{17}+\\dfrac{1}{37} \\right)}{5.\\left( \\dfrac{1}{7}-\\dfrac{1}{17}+\\dfrac{1}{37} \\right)}+\\dfrac{\\dfrac{1}{2}-\\dfrac{1}{3}+\\dfrac{1}{4}-\\dfrac{1}{5}}{7.\\left( \\dfrac{1}{2}-\\dfrac{1}{3}+\\dfrac{1}{4}-\\dfrac{1}{5} \\right)} \\\\ =\\dfrac{3}{5}+\\dfrac{1}{7} \\\\ =\\dfrac{21+5}{35}=\\dfrac{26}{35} $ <br\/> <br\/> <span class='basic_pink'> Gi\u00e1 tr\u1ecb c\u1ee7a F l\u00e0 $\\dfrac{26}{35}$ <\/span><\/span> <br\/>"}]}],"id_ques":97},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":" Cho ba s\u1ed1 $a, b, c$ th\u1ecfa m\u00e3n $abc = 1$. Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $G = \\dfrac{1}{ab + a + 1} + \\dfrac{b}{bc + b + 1} + \\dfrac{1}{abc + bc + b} $= _input_","hint":" Thay 1 = abc v\u00e0o ph\u00e2n s\u1ed1 \u0111\u1ea7u ti\u00ean trong G <br\/> Thay abc = 1 v\u00e0o ph\u00e2n s\u1ed1 th\u1ee9 ba trong G ","explain":" V\u1edbi $abc = 1$ ta c\u00f3: <br\/> $ G = \\dfrac{1}{ab + a + 1} + \\dfrac{b}{bc + b + 1} + \\dfrac{1}{abc + bc + b} \\\\ = \\dfrac{abc}{ab + a + abc} + \\dfrac{b}{bc + b + 1} + \\dfrac{1}{1 + bc + b} \\\\ = \\dfrac{abc}{a(bc + b + 1)} + \\dfrac{b}{bc + b + 1} + \\dfrac{1}{bc + b + 1} \\\\ = \\dfrac{bc}{bc + c + 1} + \\dfrac{b}{bc + b + 1} + \\dfrac{1}{bc + b + 1} \\\\ = \\dfrac{bc + b + 1}{bc + b + 1} = 1. $ <br\/> <br\/> <span class='basic_pink'> Gi\u00e1 tr\u1ecb c\u1ee7a G l\u00e0 $1$ <\/span><\/span> <br\/>"}]}],"id_ques":98},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"Ch\u1ecdn k\u1ebft qu\u1ea3 \u0111\u00fang c\u1ee7a bi\u1ec3u th\u1ee9c $ S = -\\dfrac{1}{1.2} - \\dfrac{1}{2.3} - \\dfrac{1}{3.4} - ... \\dfrac{1}{(n-1)n} \\\\ ( n \\in \\mathbb{N^{*}}, n \\neq 1). $ ","select":["A. $ 1 - \\dfrac{1}{n}$","B. $1$","C. $ \\dfrac{1}{n} - 1$","D. $ \\dfrac{1}{n}$"],"explain":" Ta c\u00f3: $ S = -\\dfrac{1}{1.2} - \\dfrac{1}{2.3} - \\dfrac{1}{3.4} - ... \\dfrac{1}{(n-1)n} ( n \\in \\mathbb{N}) \\\\ = - \\left( \\dfrac{1}{1.2} + \\dfrac{1}{2.3} + \\dfrac{1}{3.4} + ...+ \\dfrac{1}{(n-1)n} \\right) \\\\ = - \\left( 1 - \\dfrac{1}{2} + \\dfrac{1}{2} - \\dfrac{1}{3} + \\dfrac{1}{3} - \\dfrac{1}{4} + ...+ \\dfrac{1}{(n-1)} - \\dfrac{1}{n} \\right) \\\\ = - \\left( 1 - \\dfrac{1}{n} \\right) \\\\ = \\dfrac{1}{n} - 1. $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span><\/span> <br\/> <span class='basic_left'> <u> <b> Nh\u1eadn x\u00e9t: <\/b> <\/u> <br\/> Ta th\u1ea5y c\u00e1c gi\u00e1 tr\u1ecb \u1edf t\u1eed kh\u00f4ng thay \u0111\u1ed5i v\u00e0 ch\u00fang \u0111\u00fang b\u1eb1ng hi\u1ec7u hai th\u1eeba s\u1ed1 \u1edf m\u1eabu. <br\/> M\u1ed7i s\u1ed1 h\u1ea1ng \u0111\u1ec1u c\u00f3 d\u1ea1ng: $\\dfrac{m}{b(b+m)} = \\dfrac{1}{b} - \\dfrac{1}{b+m}$ <br\/> N\u00ean ta c\u00f3 m\u1ed9t t\u1ed5ng v\u1edbi c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m: c\u00e1c s\u1ed1 h\u1ea1ng li\u00ean ti\u1ebfp lu\u00f4n \u0111\u1ed1i nhau, n\u00ean c\u00e1c s\u1ed1 h\u1ea1ng trong t\u1ed5ng \u0111\u01b0\u1ee3c kh\u1eed li\u00ean ti\u1ebfp \u0111\u1ebfn khi trong t\u1ed5ng ch\u1ec9 c\u00f2n s\u1ed1 h\u1ea1ng \u0111\u1ea7u v\u00e0 s\u1ed1 h\u1ea1ng cu\u1ed1i, l\u00fac \u0111\u00f3 th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh s\u1ebd d\u1ec5 d\u00e0ng h\u01a1n.<\/span>","column":2}]}],"id_ques":99},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["27"],["4"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> T\u00ecm m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9, bi\u1ebft r\u1eb1ng khi ta c\u1ed9ng s\u1ed1 \u0111\u00f3 v\u1edbi $2\\dfrac{3}{4}$ \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 bao nhi\u00eau \u0111em tr\u1eeb cho $\\dfrac{22}{5}$ th\u00ec \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0 $5,1$. <\/span> <br\/> <br\/> K\u1ebft qu\u1ea3: <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","explain":" <span class='basic_left'> G\u1ecdi s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 $x \\in \\mathbb{Q}$ <br\/> Theo b\u00e0i ta c\u00f3: $ x + 2\\dfrac{3}{4} - \\dfrac{22}{5} = 5,1 $ <br\/> Suy ra $x + \\dfrac{11}{4} - \\dfrac{22}{5} = \\dfrac{51}{10} $ <br\/> $ x - \\dfrac{33}{20} = \\dfrac{51}{10} $ <br\/> $x = \\dfrac{51}{10} + \\dfrac{33}{20} $ <br\/> $ x = \\dfrac{27}{4}$ <br\/> <br\/> <span class='basic_pink'> S\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 $\\dfrac{27}{4}$ <\/span><\/span> <br\/>"}]}],"id_ques":100}],"lesson":{"save":0,"level":3}}