{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $\\dfrac{-7}{21} + \\left( 1 + \\dfrac{1}{3} \\right)$ l\u00e0: ","select":["A. 1 ","B. -1 ","C. $\\dfrac{1}{21}$","D. $\\dfrac{-1}{21}$ "],"hint":"Quy \u0111\u1ed3ng r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b>Quy \u0111\u1ed3ng c\u00e1c ph\u00e2n s\u1ed1 tr\u00ean v\u1edbi m\u1eabu s\u1ed1 chung l\u00e0 21 <br\/> <b> B\u01b0\u1edbc 2: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} \\dfrac{-7}{21} + \\left( 1 + \\dfrac{1}{3} \\right) &= \\dfrac{-7}{21} + \\left( \\dfrac{1 . 21}{1 . 21} + \\dfrac{1 . 7}{3 . 7} \\right) \\\\ &= \\dfrac{-7}{21} + \\dfrac{21}{21} + \\dfrac{7}{21} \\\\ &= \\dfrac{-7 + 21 + 7}{21} \\\\ &= \\dfrac{21}{21} \\\\ &= 1 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A <\/span> ","column":2}]}],"id_ques":1571},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $\\dfrac{5}{12} + \\left( \\dfrac{5}{9} + \\dfrac{-6}{9} \\right)$ l\u00e0: ","select":["A. $\\dfrac{-11}{36}$ ","B. $\\dfrac{11}{36}$ ","C. $\\dfrac{-19}{36}$","D. $\\dfrac{-4}{9}$ "],"hint":"Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh trong ngo\u1eb7c tr\u01b0\u1edbc","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b>Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh trong ngo\u1eb7c tr\u01b0\u1edbc <br\/> <b> B\u01b0\u1edbc 2: <\/b> Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 <br\/> <b> B\u01b0\u1edbc 3: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} \\dfrac{5}{12} + \\left( \\dfrac{5}{9} + \\dfrac{-6}{9} \\right) &= \\dfrac{5}{12} + \\dfrac{5 + (-6)}{9} \\\\ &= \\dfrac{5}{12} + \\dfrac{-1}{9} \\\\ &= \\dfrac{5 . 3}{12 . 3} + \\dfrac{-1 . 4}{9 . 4} \\\\ &= \\dfrac{15}{36} + \\dfrac{-4}{36} \\\\ &= \\dfrac{15 + (-4)}{36} \\\\ &= \\dfrac{11}{36} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B <\/span> ","column":2}]}],"id_ques":1572},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $ \\left( \\dfrac{-1}{5} + \\dfrac{3}{12} \\right) + \\dfrac{-3}{4}$ l\u00e0: ","select":["A. $\\dfrac{-6}{5}$ ","B. $\\dfrac{6}{5}$ ","C. $\\dfrac{7}{10}$","D. $\\dfrac{-7}{10}$ "],"hint":"R\u00fat g\u1ecdn r\u1ed3i quy \u0111\u1ed3ng v\u00e0 th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b>B\u1ecf ngo\u1eb7c, r\u00fat g\u1ecdn ph\u00e2n s\u1ed1 n\u00e0o ch\u01b0a t\u1ed1i gi\u1ea3n <br\/> <b> B\u01b0\u1edbc 2: <\/b> Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 c\u00e1c ph\u00e2n s\u1ed1 <br\/> <b> B\u01b0\u1edbc 3: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} \\left( \\dfrac{-1}{5} + \\dfrac{3}{12} \\right) + \\dfrac{-3}{4} &= \\dfrac{-1}{5} + \\dfrac{3 : 3}{12 : 3} + \\dfrac{-3}{4} \\\\ &= \\dfrac{-1}{5} + \\dfrac{1}{4} + \\dfrac{-3}{4} \\\\ &= \\dfrac{-1 . 4}{5 . 4} + \\dfrac{1 . 5}{4 . 5} + \\dfrac{-3 . 5}{4 . 5} \\\\ &= \\dfrac{-4}{20} + \\dfrac{5}{20} + \\dfrac{-15}{20} \\\\ &= \\dfrac{-4 + 5 + (-15)}{20} \\\\ &= \\dfrac{-14}{20} \\\\ &= \\dfrac{-7}{10} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":1573},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"H\u00e3y \u0111i\u1ec1n d\u1ea5u (>, < ho\u1eb7c =) th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng. <br\/> $\\dfrac{7}{3} + \\dfrac{-5}{4} $ _input_ $\\dfrac{-3}{4} + \\dfrac{18}{3}$ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Ngo\u00e0i c\u00e1ch th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh v\u00e0 so s\u00e1nh nh\u01b0 th\u00f4ng th\u01b0\u1eddng ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00e1ch sau <br\/> <b> B\u01b0\u1edbc 1: <\/b> So s\u00e1nh $\\dfrac{-5}{4}$ v\u1edbi $\\dfrac{-3}{4}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh $\\dfrac{7}{3}$ v\u1edbi $\\dfrac{18}{3}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> K\u1ebft lu\u1eadn <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $\\dfrac{7}{3} < \\dfrac{18}{3}$ (1) <br\/> $\\dfrac{-5}{4} < \\dfrac{-3}{4}$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $\\dfrac{7}{3} + \\dfrac{-5}{4} < \\dfrac{-3}{4} + \\dfrac{18}{3}$ <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0: < <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: V\u1edbi nhi\u1ec1u b\u00e0i so s\u00e1nh hai bi\u1ec3u th\u1ee9c A, B ch\u1ee9a ph\u00e2n s\u1ed1 kh\u00f4ng nh\u1ea5t thi\u1ebft ph\u1ea3i t\u00ednh ra k\u1ebft qu\u1ea3 r\u1ed3i m\u1edbi so s\u00e1nh m\u00e0 ta so s\u00e1nh t\u1eebng ph\u00e2n s\u1ed1 c\u1ee7a A v\u1edbi m\u1ed9t ph\u00e2n s\u1ed1 t\u01b0\u01a1ng \u1ee9ng c\u1ee7a B r\u1ed3i k\u1ebft lu\u1eadn <\/i> <\/span> "}]}],"id_ques":1574},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"H\u00e3y \u0111i\u1ec1n d\u1ea5u (>, < ho\u1eb7c =) th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng. <br\/> $\\dfrac{-8}{5} + \\dfrac{7}{-3} $ _input_ $\\dfrac{-8}{5} + \\dfrac{1}{3}$ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>V\u00ec $\\dfrac{-8}{5}$ = $\\dfrac{-8}{5}$ n\u00ean ch\u1ec9 c\u1ea7n so s\u00e1nh $\\dfrac{7}{-3}$ v\u1edbi $\\dfrac{1}{3}$ v\u00e0 k\u1ebft lu\u1eadn <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec $\\dfrac{-8}{5} = \\dfrac{-8}{5}$ n\u00ean ch\u1ec9 c\u1ea7n so s\u00e1nh $\\dfrac{7}{-3}$ v\u1edbi $\\dfrac{1}{3}$ <br\/> $\\dfrac{7}{-3} = \\dfrac{-7}{3}$ m\u00e0 $\\dfrac{-7}{3} < \\dfrac{1}{3}$ <br\/> $\\Rightarrow$ $\\dfrac{-8}{5} + \\dfrac{7}{-3} < \\dfrac{-8}{5} + \\dfrac{1}{3}$ <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0: < <\/span> "}]}],"id_ques":1575},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"H\u00e3y \u0111i\u1ec1n d\u1ea5u (>, < ho\u1eb7c =) th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng. <br\/> $\\dfrac{-7}{3} + \\dfrac{-8}{30} $ _input_ $\\dfrac{-9}{6} + \\dfrac{-7}{5}$ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh \u1edf v\u1ebf tr\u00e1i v\u00e0 v\u1ebf ph\u1ea3i r\u1ed3i so s\u00e1nh <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec $\\dfrac{-7}{3} + \\dfrac{-8}{30} = \\dfrac{-7 . 10}{3 . 10} + \\dfrac{-8}{30} = \\dfrac{-70 + (-8)}{30} = \\dfrac{-78}{30}$ <br\/> $\\dfrac{-9}{6} + \\dfrac{-7}{5} = \\dfrac{-9 . 5}{6 . 5} + \\dfrac{-7 . 6}{5 . 6} = \\dfrac{-45}{30} + \\dfrac{-42}{30} = \\dfrac{-45 + (-42)}{30} = \\dfrac{-87}{30}$ <br\/> V\u00ec $\\dfrac{-78}{30} > \\dfrac{-87}{30}$ <br\/> $\\Rightarrow$ $\\dfrac{-7}{3} + \\dfrac{-8}{30} > \\dfrac{-9}{6} + \\dfrac{-7}{5}$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0: > <\/span> "}]}],"id_ques":1576},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00ecm x bi\u1ebft $ \\dfrac{x - 2}{8} = \\dfrac{1}{2} + \\dfrac{3}{4}$ l\u00e0: ","select":["A. x = 12 ","B. x = 10 ","C. x = 8 ","D. x = -10"],"hint":"D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} \\dfrac{x - 2}{8} &= \\dfrac{1}{2} + \\dfrac{3}{4} \\\\ \\dfrac{x - 2}{8} &= \\dfrac{2}{4} + \\dfrac{3}{4} \\\\ \\dfrac{x - 2}{8} &= \\dfrac{2 + 3}{4} \\\\ \\dfrac{x - 2}{8} &= \\dfrac{5}{4} \\end{align*}$ <br\/> $\\begin{align*} \\Rightarrow (x - 2). 4 &= 8 . 5 \\\\ 4x - 8 &= 40 \\\\ 4x &= 40 + 8 \\\\ 4x &= 48 \\\\ x &= 12 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. x = 12 <\/span> ","column":2}]}],"id_ques":1577},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"T\u00ecm x bi\u1ebft $ \\dfrac{4 + x}{8} = \\dfrac{-7}{8} + \\dfrac{1}{4}$ l\u00e0: ","select":["A. x = -1 ","B. x = -9 ","C. x = 9 ","D. x = 1"],"hint":"D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1 <\/b> T\u00ednh $\\dfrac{-7}{8} + \\dfrac{1}{4}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau x\u00e9t t\u00edch ch\u00e9o r\u1ed3i t\u00ecm x <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} \\dfrac{4 + x}{8} &= \\dfrac{-7}{8} + \\dfrac{1}{4} \\\\ \\dfrac{x + 4}{8} &= \\dfrac{-7}{8} + \\dfrac{2}{8} \\\\ \\dfrac{x + 4}{8} &= \\dfrac{-7 + 2}{8} \\\\ \\dfrac{x + 4}{8} &= \\dfrac{-5}{8} \\end{align*}$ <br\/> $\\begin{align*} \\Rightarrow (x + 4). 8 &= 8 . (-5) \\\\ x + 4 &= -5 \\\\ x &= -5 - 4 \\\\ x &= -9 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. x = -9 <\/span> ","column":2}]}],"id_ques":1578},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"T\u00ecm x bi\u1ebft $ \\dfrac{x + 1}{12} = \\dfrac{-2}{3} + \\dfrac{1}{4}$ l\u00e0: ","select":["A. x = -5 ","B. x = 4 ","C. x = -4 ","D. x = -6"],"hint":"D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1 <\/b> T\u00ednh $\\dfrac{-2}{3} + \\dfrac{1}{4}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau x\u00e9t t\u00edch ch\u00e9o r\u1ed3i t\u00ecm x <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} \\dfrac{x + 1}{12} &= \\dfrac{-2}{3} + \\dfrac{1}{4} \\\\ \\dfrac{x + 1}{12} &= \\dfrac{-2 . 4}{3 . 4} + \\dfrac{1 . 3}{4 . 3} \\\\ \\dfrac{x + 1}{12} &= \\dfrac{-8 + 3}{12} \\\\ \\dfrac{x + 1}{12} &= \\dfrac{-5}{12} \\end{align*}$ <br\/> $\\begin{align*} \\Rightarrow (x + 1). 12 &= -5 . 12 \\\\ x + 1 &= -5 \\\\ x &= -5 - 1 \\\\ x &= -6 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. x = -6 <\/span> ","column":2}]}],"id_ques":1579},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"],["5"]]],"list":[{"point":5,"width":50,"ques":"T\u00ednh b\u1eb1ng c\u00e1ch thu\u1eadn ti\u1ec7n <br\/> $\\dfrac{-3}{4} + \\dfrac{2}{7} + \\dfrac{-1}{4} + \\dfrac{3}{5} + \\dfrac{5}{7}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu v\u1edbi nhau <br\/> <b> B\u01b0\u1edbc 2: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> Bi\u1ebfn \u0111\u1ed5i v\u00e0 t\u00ednh k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} & \\dfrac{-3}{4} + \\dfrac{2}{7} + \\dfrac{-1}{4} + \\dfrac{3}{5} + \\dfrac{5}{7} \\\\ &= \\left( \\dfrac{-3}{4} + \\dfrac{-1}{4} \\right) + \\left( \\dfrac{2}{7} + \\dfrac{5}{7} \\right) + \\dfrac{3}{5} \\\\ &= \\dfrac{-3 + (-1)}{4} + \\dfrac{2 + 5}{7} + \\dfrac{3}{5} \\\\ &= -1 + 1 + \\dfrac{3}{5} \\\\ &= \\dfrac{3}{5} \\end{align*}$ "}]}],"id_ques":1580},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"],["19"]]],"list":[{"point":5,"width":50,"ques":"T\u00ednh b\u1eb1ng c\u00e1ch thu\u1eadn ti\u1ec7n <br\/> $\\dfrac{-2}{17} + \\dfrac{15}{23} + \\dfrac{-15}{17} + \\dfrac{4}{19} + \\dfrac{8}{23}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu v\u1edbi nhau <br\/> <b> B\u01b0\u1edbc 2: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> Bi\u1ebfn \u0111\u1ed5i v\u00e0 t\u00ednh k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} & \\dfrac{-2}{17} + \\dfrac{15}{23} + \\dfrac{-15}{17} + \\dfrac{4}{19} + \\dfrac{8}{23} \\\\ &= \\left( \\dfrac{-2}{17} + \\dfrac{-15}{17} \\right) + \\left( \\dfrac{15}{23} + \\dfrac{8}{23} \\right) + \\dfrac{4}{19} \\\\ &= \\dfrac{-2 + (-15)}{17} + \\dfrac{15 + 8}{23} + \\dfrac{4}{19} \\\\ &= -1 + 1 + \\dfrac{4}{19} \\\\ &= \\dfrac{4}{19} \\end{align*}$<br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: V\u1edbi nh\u1eefng b\u00e0i t\u00ednh b\u1eb1ng c\u00e1ch thu\u1eadn ti\u1ec7n th\u00f4ng th\u01b0\u1eddng ta hay nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u1ed9ng v\u1edbi nhau khi r\u00fat g\u1ecdn \u0111\u01b0\u1ee3c s\u1ed1 nguy\u00ean, ho\u1eb7c c\u00e1c ph\u00e2n s\u1ed1 khi c\u1ed9ng v\u1edbi nhau \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0 0 <\/i><\/span> "}]}],"id_ques":1581},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-6"],["7"]]],"list":[{"point":5,"width":50,"ques":"T\u00ednh b\u1eb1ng c\u00e1ch thu\u1eadn ti\u1ec7n <br\/> $\\dfrac{-1}{2} + \\dfrac{3}{21} + \\dfrac{-2}{6} + \\dfrac{-5}{30}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> R\u00fat g\u1ecdn c\u00e1c ph\u00e2n s\u1ed1 \u0111\u1ebfn t\u1ed1i gi\u1ea3n <br\/> <b> B\u01b0\u1edbc 2: <\/b> Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 \u0111\u1ec3 t\u00ednh thu\u1eadn ti\u1ec7n nh\u1ea5t <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} & \\dfrac{-1}{2} + \\dfrac{3}{21} + \\dfrac{-2}{6} + \\dfrac{-5}{30} \\\\ &= \\dfrac{-1}{2} + \\dfrac{3 : 3}{21 : 3} + \\dfrac{-2 : 2}{6 : 2} + \\dfrac{-5 : 5}{30 : 5} \\\\ &= \\dfrac{-1}{2} + \\dfrac{1}{7} + \\dfrac{-1}{3} + \\dfrac{-1}{6} \\\\ &= \\left( \\dfrac{-1}{2} + \\dfrac{-1}{3} + \\dfrac{-1}{6} \\right) + \\dfrac{1}{7} \\\\ &= \\left( \\dfrac{-1 . 3}{2 . 3} + \\dfrac{-1 . 2}{3 . 2} + \\dfrac{-1}{6} \\right) + \\dfrac{1}{7} \\\\ &= \\left( \\dfrac{-3}{6} + \\dfrac{-2}{6} + \\dfrac{-1}{6} \\right) + \\dfrac{1}{7} \\\\ &= \\dfrac{-3 + (-2) + (-1)}{6} + \\dfrac{1}{7} \\\\ &= \\dfrac{-6}{6} + \\dfrac{1}{7} \\\\ &= -1 + \\dfrac{1}{7} \\\\ &= \\dfrac{-7}{7} + \\dfrac{1}{7} \\\\ &= \\dfrac{-7 + 1}{6} \\\\ &= \\dfrac{-6}{7} \\end{align*}$"}]}],"id_ques":1582},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["frac"],"ques":" $\\dfrac{5}{8}$ = $\\dfrac{1}{8} +$ <div class=\"frac123\" style=\"margin-top: -11px;\"><div class=\"ts\">1<\/div><div class=\"ms\">_input_<\/div><\/div> ","hint":"Vi\u1ebft $\\dfrac{5}{8} = $\\dfrac{a}{8}$ + \\dfrac{b}{8}$ r\u1ed3i r\u00fat g\u1ecdn","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Vi\u1ebft $\\dfrac{5}{8} = \\dfrac{a + b}{8} = \\dfrac{a}{8} + \\dfrac{b}{8}$ r\u1ed3i r\u00fat g\u1ecdn <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $\\dfrac{5}{8} = \\dfrac{1 + 4}{8} = \\dfrac{1}{8} + \\dfrac{4}{8} = \\dfrac{1}{8} + \\dfrac{1}{2}$"}]}],"id_ques":1583},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"]]],"list":[{"point":5,"width":50,"ques":"<div class=\"frac123\"><div class=\"ts\">5<\/div><div class=\"ms\">6<\/div><\/div> = <div class=\"frac123\"><div class=\"ts\">1<\/div><div class=\"ms\">2<\/div><\/div>+<div class=\"frac123\"><div class=\"ts\">1<\/div><div class=\"ms\">_input_<\/div><\/div> ","hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/>Vi\u1ebft $\\dfrac{5}{6} = \\dfrac{1}{2} + \\dfrac{1}{a}$<br\/> $\\dfrac{1}{a} = \\dfrac{5}{6} - \\dfrac{1}{2} = \\dfrac{2}{6} = \\dfrac{1}{3}$. S\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 <strong>3<\/strong>."}]}],"id_ques":1584},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ecm s\u1ed1 nguy\u00ean x bi\u1ebft $ \\dfrac{1}{5} + \\dfrac{2}{11} < \\dfrac{x}{55} < \\dfrac{2}{5} + \\dfrac{1}{55}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. x = 21 ","B. x = 23 ","C. x = 22 ","D. x = 24"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1 <\/b> T\u00ednh $\\dfrac{1}{5} + \\dfrac{2}{11} = \\dfrac{a}{b}$; $\\dfrac{2}{5} + \\dfrac{1}{55} = \\dfrac{c}{d}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm x th\u1ecfa m\u00e3n $\\dfrac{a}{b} < \\dfrac{x}{55} < \\dfrac{c}{d}$ <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: <br\/> $\\dfrac{1}{5} + \\dfrac{2}{11} = \\dfrac{1 . 11}{5 . 11} + \\dfrac{2 . 5}{11 . 5} = \\dfrac{11}{55} + \\dfrac{10}{55} = \\dfrac{21}{55}$ <br\/> $\\dfrac{2}{5} + \\dfrac{1}{55} = \\dfrac{2 . 11}{5 . 11} + \\dfrac{1}{55} = \\dfrac{22}{55} + \\dfrac{1}{55} = \\dfrac{23}{55}$ <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3 $\\dfrac{21}{55} < \\dfrac{x}{55} < \\dfrac{23}{55}$ <br\/> $\\Rightarrow$ 21 < x < 23 n\u00ean x = 22 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. x = 22 <\/span> ","column":2}]}],"id_ques":1585},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"T\u00ecm s\u1ed1 nguy\u00ean x bi\u1ebft $ \\dfrac{11}{3} + \\dfrac{-19}{6} + \\dfrac{-15}{2} \\leq x \\leq \\dfrac{19}{12} + \\dfrac{-5}{4} + \\dfrac{-10}{3}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. $x \\in \\left\\{ -7; -6; -5; -4; -3; -2 \\right\\}$","B. $x \\in \\left\\{ -2; -3; -4; -5; -6 \\right\\}$ ","C. $x \\in \\left\\{ -7; -5; -2; -1; -4 \\right\\}$ ","D. $x \\in \\left\\{ -7; -6; -5; -4; -3 \\right\\}$"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1 <\/b> T\u00ednh $\\dfrac{11}{3} + \\dfrac{-19}{6} + \\dfrac{-15}{2} = a$; $\\dfrac{19}{12} + \\dfrac{-5}{4} + \\dfrac{-10}{3} = b$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm x th\u1ecfa m\u00e3n $a \\leq x \\leq b$ <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: <br\/> $\\begin{align*} \\dfrac{11}{3} + \\dfrac{-19}{6} + \\dfrac{-15}{2} &= \\dfrac{11 . 2}{3 . 2} + \\dfrac{-19}{6} + \\dfrac{-15 . 3}{2 . 3} \\\\ &= \\dfrac{22}{6} + \\dfrac{-19}{6} + \\dfrac{-45}{6} \\\\ &= \\dfrac{22 + (-19) + (-45)}{6} \\\\ &= \\dfrac{-42}{6} \\\\ &= -7 \\end{align*}$ <br\/> $\\begin{align*} \\dfrac{19}{12} + \\dfrac{-5}{4} + \\dfrac{-10}{3} &= \\dfrac{19}{12} + \\dfrac{-5 . 3}{4 . 3} + \\dfrac{-10 . 4}{3 . 4} \\\\ &= \\dfrac{19}{12} + \\dfrac{-15}{12} + \\dfrac{-40}{12} \\\\ &= \\dfrac{19 + (-15) + (-40)}{12} \\\\ &= \\dfrac{-36}{12} \\\\ &= -3 \\end{align*}$ <br\/> $\\Rightarrow$ $-7 \\leq x \\leq -3$ <br\/> $\\Rightarrow$ $x \\in \\left\\{ -7; -6; -5; -4; -3 \\right\\}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":1586},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["8"]]],"list":[{"point":5,"width":50,"ques":"T\u00ednh nhanh. <br\/> $\\dfrac{1}{2} + \\dfrac{-1}{3} + \\dfrac{1}{4} + \\dfrac{-1}{5} + \\dfrac{1}{6} + \\dfrac{-1}{7} + \\dfrac{1}{8} + \\dfrac{1}{7} + \\dfrac{-1}{6} + \\dfrac{1}{5} + \\dfrac{-1}{4} + \\dfrac{1}{3} + \\dfrac{-1}{2}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu v\u1edbi nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 2: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} & \\dfrac{1}{2} + \\dfrac{-1}{3} + \\dfrac{1}{4} + \\dfrac{-1}{5} + \\dfrac{1}{6} + \\dfrac{-1}{7} + \\dfrac{1}{8} + \\dfrac{1}{7} + \\dfrac{-1}{6} + \\dfrac{1}{5} + \\dfrac{-1}{4} + \\dfrac{1}{3} + \\dfrac{-1}{2} \\\\ &= \\left( \\dfrac{1}{2} + \\dfrac{-1}{2} \\right) + \\left( \\dfrac{1}{3} + \\dfrac{-1}{3} \\right) + \\left( \\dfrac{1}{4} + \\dfrac{-1}{4} \\right) + \\left( \\dfrac{1}{5} + \\dfrac{-1}{5} \\right) + \\left( \\dfrac{1}{6} + \\dfrac{-1}{6} \\right) + \\left( \\dfrac{1}{7} + \\dfrac{-1}{7} \\right) + \\dfrac{1}{8} \\\\ &= \\dfrac{-1 + 1}{2} + \\dfrac{-1 + 1}{3} + \\dfrac{-1 + 1}{4} + \\dfrac{-1 + 1}{5} + \\dfrac{-1 + 1}{6} + \\dfrac{-1 + 1}{7} + \\dfrac{1}{8} \\\\ &= \\dfrac{0}{2} + \\dfrac{0}{3} + \\dfrac{0}{4} + \\dfrac{0}{5} + \\dfrac{0}{6} + \\dfrac{0}{7} + \\dfrac{1}{8} \\\\ &= \\dfrac{1}{8} \\end{align*}$ "}]}],"id_ques":1587},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-5"],["7"]]],"list":[{"point":5,"width":50,"ques":"T\u00ednh nhanh. <br\/> $\\dfrac{5}{13} + \\dfrac{-5}{7} + \\dfrac{-20}{41} + \\dfrac{8}{13} + \\dfrac{-21}{41} $ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu v\u1edbi nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 2: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} & \\dfrac{5}{13} + \\dfrac{-5}{7} + \\dfrac{-20}{41} + \\dfrac{8}{13} + \\dfrac{-21}{41} \\\\ &= \\left( \\dfrac{5}{13} + \\dfrac{8}{13} \\right) + \\left( \\dfrac{-20}{41} + \\dfrac{-21}{41} \\right) + \\dfrac{-5}{7} \\\\ &= \\dfrac{5 + 8}{13} + \\dfrac{-20 + (-21)}{41} \\\\ &= \\dfrac{13}{13} + \\dfrac{-41}{41} + \\dfrac{-5}{7} \\\\ &= 1 + (-1) + \\dfrac{-5}{7} \\\\ &= \\dfrac{-5}{7} \\end{align*}$ "}]}],"id_ques":1588},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-2"],["11"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["frac"],"ques":"T\u00ednh nhanh. <br\/> $\\dfrac{-5}{9} + \\dfrac{8}{15} + \\dfrac{-2}{11} + \\dfrac{4}{-9} + \\dfrac{7}{15} $ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu v\u1edbi nhau","explain":" <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} &\\dfrac{-5}{9} + \\dfrac{8}{15} + \\dfrac{-2}{11} + \\dfrac{4}{-9} + \\dfrac{7}{15} \\\\ &= \\left( \\dfrac{-5}{9} + \\dfrac{4}{-9} \\right) + \\left( \\dfrac{8}{15} + \\dfrac{7}{15} \\right) + \\dfrac{-2}{11} \\\\ &= \\dfrac{-5 + (-4)}{9} + \\dfrac{8 + 7}{15} + \\dfrac{-2}{11} \\\\ &= \\dfrac{-9}{9} + \\dfrac{15}{15} + \\dfrac{-2}{11} \\\\ &= -1 + 1 + \\dfrac{-2}{11} \\\\ &= \\dfrac{-2}{11} \\end{align*}$ "}]}],"id_ques":1589},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"],["3"]]],"list":[{"point":5,"width":50,"ques":"T\u00ednh nhanh. <br\/> $ \\left( \\dfrac{1}{9} + \\dfrac{-5}{17} \\right) + \\dfrac{3}{6} + \\left( \\dfrac{-12}{17} + \\dfrac{-1}{2} \\right) + \\dfrac{5}{9} $ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"Ph\u00e1 ngo\u1eb7c, r\u00fat g\u1ecdn v\u00e0 nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ph\u00e1 ngo\u1eb7c v\u00e0 r\u00fat g\u1ecdn ph\u00e2n s\u1ed1 n\u00e0o ch\u01b0a t\u1ed1i gi\u1ea3n <br\/> <b> B\u01b0\u1edbc 2: <\/b> Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> Bi\u1ebfn \u0111\u1ed5i t\u00ecm k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} &\\left( \\dfrac{1}{9} + \\dfrac{-5}{17} \\right) + \\dfrac{3}{6} + \\left( \\dfrac{-12}{17} + \\dfrac{-1}{2} \\right) + \\dfrac{5}{9} \\\\ &= \\dfrac{1}{9} + \\dfrac{-5}{17} + \\dfrac{1}{2} + \\dfrac{-12}{17} + \\dfrac{-1}{2} + \\dfrac{5}{9} \\\\ &= \\left( \\dfrac{1}{9} + \\dfrac{5}{9} \\right) + \\left( \\dfrac{1}{2} + \\dfrac{-1}{2} \\right) + \\left( \\dfrac{-5}{17} + \\dfrac{-12}{17} \\right) \\\\ &= \\dfrac{1 + 5}{9} + \\dfrac{1 + (-1)}{9} + \\dfrac{-5 + (-12)}{17} \\\\ &= \\dfrac{2}{3} + 0 + -1 \\\\ &= \\dfrac{2}{3} + \\dfrac{-3}{3} \\\\ &= \\dfrac{-1}{3} \\end{align*}$"}]}],"id_ques":1590}],"lesson":{"save":0,"level":2}}