{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["247"],["60"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["frac"],"ques":"Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh: <br\/><br\/> $A = 1 : 0,25 . \\left( 1\\dfrac{1}{4} \\right)^2 + 25 . \\left[ 1 : \\left( \\dfrac{4}{3} \\right)^2 : \\left( \\dfrac{5}{4} \\right)^3 \\right] : \\left[ 1 : \\left( - \\dfrac{2}{3}\\right)^3 \\right] $ = <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\/> Kh\u00e9o l\u00e9o chuy\u1ec3n gi\u1eefa s\u1ed1 th\u1eadp ph\u00e2n v\u00e0 ph\u00e2n s\u1ed1 r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh theo th\u1ee9 t\u1ef1 th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $ \\begin{align*} & A = 1 : 0,25 . \\left( 1\\dfrac{1}{4} \\right)^2 + 25 . \\left[ 1 : \\left( \\dfrac{4}{3} \\right)^2 : \\left( \\dfrac{5}{4} \\right)^3 \\right] : \\left[ 1 : \\left( - \\dfrac{2}{3}\\right)^3 \\right] \\\\ &= 4 . \\left( \\dfrac{5}{4} \\right)^2 + 25 . \\left[ 1 : \\dfrac{16}{9} : \\dfrac{125}{64} \\right] : \\left[ 1 : \\dfrac{-8}{27} \\right] \\\\ &= 4 . \\dfrac{25}{16} + 25 . \\left[ 1 . \\dfrac{9}{16} . \\dfrac{64}{125} \\right] : \\left[ 1 . \\dfrac{-27}{8} \\right] \\\\ &= \\dfrac{25}{4} + 25 . \\dfrac{36}{125} : \\dfrac{-27}{8} \\\\ &= \\dfrac{25}{4} + \\dfrac{36}{5} . \\dfrac{-8}{27} \\\\ &= \\dfrac{25}{4} - \\dfrac{32}{15} \\\\ &= 4\\dfrac{7}{60} = \\dfrac{247}{60} \\end{align*} $"}]}],"id_ques":1791},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["20"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"B\u00e0i to\u00e1n Niu - t\u01a1n <br\/> B\u00f2 \u0103n c\u1ecf tr\u00ean m\u1ed9t c\u00e1nh \u0111\u1ed3ng. Gi\u1ea3 s\u1eed c\u1ecf m\u1ecdc d\u00e0y \u0111\u1eb7c v\u00e0 cao \u0111\u1ec1u nh\u01b0 nhau tr\u00ean to\u00e0n di\u1ec7n t\u00edch c\u00e1nh \u0111\u1ed3ng v\u00e0 b\u00f2 \u0103n c\u1ecf \u0111\u1ec1u nh\u01b0 nhau. Bi\u1ebft r\u1eb1ng 70 con b\u00f2 \u0103n h\u1ebft c\u1ecf c\u1ee7a c\u00e1nh \u0111\u1ed3ng trong 24 ng\u00e0y, n\u1ebfu c\u00f3 30 con b\u00f2 th\u00ec ch\u00fang s\u1ebd \u0103n h\u1ebft c\u1ecf c\u1ee7a c\u00e1nh \u0111\u1ed3ng trong 60 ng\u00e0y. H\u1ecfi bao nhi\u00eau con b\u00f2 s\u1ebd \u0103n h\u1ebft c\u1ecf c\u1ee7a c\u00e1nh \u0111\u1ed3ng trong 96 ng\u00e0y? <br\/> \u0110\u00e1p s\u1ed1: _input_ con b\u00f2 ","hint":"B\u00f2 \u0103n c\u1ecf \u0111\u1ec1u nh\u01b0 nhau, n\u00ean l\u01b0\u1ee3ng c\u1ecf m\u1ed7i con b\u00f2 \u0103n trong 1 ng\u00e0y l\u00e0 nh\u01b0 nhau, nh\u01b0ng c\u1ecf c\u0169ng ti\u1ebfp t\u1ee5c m\u1ecdc th\u00eam trong th\u1eddi gian t\u01b0\u01a1ng \u1ee9ng","explain":" <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> B\u00f2 \u0103n c\u1ecf \u0111\u1ec1u nh\u01b0 nhau, n\u00ean l\u01b0\u1ee3ng c\u1ecf m\u1ed7i con b\u00f2 \u0103n trong 1 ng\u00e0y l\u00e0 nh\u01b0 nhau. \u0110\u00f3 l\u00e0 \"su\u1ea5t c\u1ecf\" c\u1ee7a b\u00f2 trong 1 ng\u00e0y. C\u00f3 bao nhi\u00eau \"su\u1ea5t c\u1ecf\" th\u00ec c\u00f3 b\u1ea5y nhi\u00eau con b\u00f2. <br\/> B\u00f2 ti\u1ebfp t\u1ee5c \u0103n c\u1ecf nh\u01b0ng c\u1ecf c\u0169ng ti\u1ebfp t\u1ee5c m\u1ecdc th\u00eam trong th\u1eddi gian t\u01b0\u01a1ng \u1ee9ng <br\/> Do 70 con b\u00f2 \u0103n h\u1ebft ch\u1ed7 c\u1ecf trong 24 ng\u00e0y n\u00ean 70 . 24 = 1680 (su\u1ea5t c\u1ecf) ch\u00ednh l\u00e0 to\u00e0n th\u1ec3 s\u1ed1 c\u1ecf c\u1ee7a c\u00e1nh \u0111\u1ed3ng v\u00e0 s\u1ed1 c\u1ecf m\u1ecdc th\u00eam trong 24 ng\u00e0y <br\/> N\u1ebfu 30 con b\u00f2 \u0103n h\u1ebft s\u1ed1 c\u1ecf trong 60 ng\u00e0y th\u00ec ch\u00fang \u0103n h\u1ebft 30 . 60 = 1800 (su\u1ea5t c\u1ecf) <br\/> 1800 - 1680 = 120 (su\u1ea5t c\u1ecf) ch\u00ednh l\u00e0 l\u01b0\u1ee3ng c\u1ecf m\u1ecdc th\u00eam trong 60 - 24 = 36 (ng\u00e0y). Nh\u01b0 v\u1eady 24 ng\u00e0y c\u1ecf \u0111\u00e3 m\u1ecdc th\u00eam (120 . 24) : 36 = 80 (su\u1ea5t c\u1ecf) <br\/> Do \u0111\u00f3, s\u1ed1 l\u01b0\u1ee3ng c\u1ecf l\u00fac \u0111\u1ea7u c\u1ee7a c\u00e1nh \u0111\u1ed3ng l\u00e0: <br\/> 1680 - 80 = 1600 (su\u1ea5t c\u1ecf) <br\/> S\u1ed1 su\u1ea5t c\u1ecf m\u1ecdc th\u00eam trong 96 ng\u00e0y l\u00e0: <br\/> (120 . 96) : 36 = 320 (su\u1ea5t c\u1ecf) <br\/> S\u1ed1 c\u1ecf b\u00f2 \u0111\u00e3 \u0103n trong 96 ng\u00e0y l\u00e0: <br\/> 1600 + 320 = 1920 (su\u1ea5t c\u1ecf) <br\/> S\u1ed1 b\u00f2 ph\u1ea3i t\u00ecm l\u00e0: 1920 : 96 = 20 (con) <br\/> <br\/> <span class='basic_pink'> V\u1eady ph\u00e2n s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 20 <\/span> "}]}],"id_ques":1792},{"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":10,"width":50,"type_input":"","ques":"M\u1ed9t \u00f4 t\u00f4 du l\u1ecbch \u0111i t\u1eeb t\u1ec9nh A \u0111\u1ebfn t\u1ec9nh B trong 1 th\u1eddi gian nh\u1ea5t \u0111\u1ecbnh. Sau khi \u0111i $\\dfrac{1}{3}$ qu\u00e3ng \u0111\u01b0\u1eddng c\u00f2n l\u1ea1i \u00f4 t\u00f4 \u0111\u00e3 t\u0103ng v\u1eadn t\u1ed1c th\u00eam 20% so v\u1edbi v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh n\u00ean \u0111\u00e3 \u0111\u1ebfn B s\u1edbm h\u01a1n so v\u1edbi quy \u0111\u1ecbnh l\u00e0 20 ph\u00fat. T\u00ednh th\u1eddi gian d\u1ef1 \u0111\u1ecbnh \u0111i h\u1ebft qu\u00e3ng \u0111\u01b0\u1eddng AB. <br\/> \u0110\u00e1p s\u1ed1: _input_ gi\u1edd ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ecm ph\u00e2n s\u1ed1 ch\u1ec9 v\u1eadn t\u1ed1c c\u1ee7a xe sau khi t\u0103ng 20% so v\u1edbi v\u1eadn t\u1ed1c ban \u0111\u1ea7u <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm t\u1ec9 s\u1ed1 gi\u1eefa th\u1eddi gian \u0111i $\\dfrac{2}{3}$ qu\u00e3ng \u0111\u01b0\u1eddng c\u00f2n l\u1ea1i so v\u1edbi th\u1eddi gian d\u1ef1 \u0111\u1ecbnh <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ecm ph\u00e2n s\u1ed1 ch\u1ec9 20 ph\u00fat v\u1ec1 s\u1edbm h\u01a1n d\u1ef1 \u0111\u1ecbnh <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ednh th\u1eddi gian xe d\u1ef1 \u0111\u1ecbnh \u0111i c\u1ea3 qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00fac \u0111\u1ea7u <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>T\u1ef7 s\u1ed1 v\u1eadn t\u1ed1c c\u1ee7a xe sau khi t\u0103ng 20%, so v\u1edbi v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh ban \u0111\u1ea7u l\u00e0: <br\/> $1 + 20\\% = 1 + \\dfrac{1}{5} = \\dfrac{6}{5}$ (v\u1eadn t\u1ed1c ban \u0111\u1ea7u) <br\/> Suy ra, th\u1eddi gian \u0111i $1 - \\dfrac{1}{3} = \\dfrac{2}{3}$ qu\u00e3ng \u0111\u01b0\u1eddng AB b\u1eb1ng $\\dfrac{5}{6}$ th\u1eddi gian d\u1ef1 \u0111\u1ecbnh ban \u0111\u1ea7u \u0111i qu\u00e3ng \u0111\u01b0\u1eddng \u0111\u00f3 <br\/> Do \u0111\u00f3 20 ph\u00fat ch\u00ednh l\u00e0 $1 - \\dfrac{5}{6} = \\dfrac{1}{6}$ th\u1eddi gian d\u1ef1 \u0111\u1ecbnh <br\/> V\u1eady th\u1eddi gian d\u1ef1 \u0111\u1ecbnh \u0111i $\\dfrac{2}{3}$ qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0: <br\/> $20 : \\dfrac{1}{6} = 120$ (ph\u00fat) <br\/> Th\u1eddi gian d\u1ef1 \u0111\u1ecbnh \u0111i qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0: <br\/> $120 : \\dfrac{2}{3} = 180$ (ph\u00fat) = 3 gi\u1edd <br\/> \u0110\u00e1p s\u1ed1: 3 gi\u1edd <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 3 <\/span> "}]}],"id_ques":1793},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["24"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Trong ng\u00e0y h\u1ed9i To\u00e1n, \u0111\u1ed9i To\u00e1n c\u1ee7a m\u1ed9t kh\u1ed1i \u0111\u01b0\u1ee3c chia th\u00e0nh 4 t\u1ed1p. N\u1ea5u l\u1ea5y $\\dfrac{3}{5}$ s\u1ed1 h\u1ecdc sinh c\u1ee7a t\u1ed1p th\u1ee9 nh\u1ea5t chia \u0111\u1ec1u cho 3 t\u1ed1p kia th\u00ec s\u1ed1 h\u1ecdc sinh c\u1ee7a 4 t\u1ed1p b\u1eb1ng nhau. N\u1ebfu t\u1ed1p th\u1ee9 nh\u1ea5t b\u1edbt \u0111i 6 h\u1ecdc sinh th\u00ec s\u1ed1 h\u1ecdc sinh \u1edf t\u1ed1p th\u1ee9 nh\u1ea5t b\u1eb1ng t\u1ed5ng s\u1ed1 h\u1ecdc sinh c\u1ee7a 3 t\u1ed1p kia. H\u1ecfi \u0111\u1ed9i To\u00e1n c\u1ee7a kh\u1ed1i \u0111\u00f3 c\u00f3 bao nhi\u00eau h\u1ecdc sinh? <br\/> \u0110\u00e1p s\u1ed1: _input_ h\u1ecdc sinh","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u1ede ph\u00e2n s\u1ed1 tr\u00ean a c\u00f3 c\u1ea3 \u1edf t\u1eed v\u00e0 m\u1eabu, ta bi\u1ebfn \u0111\u1ed5i sao cho a ch\u1ec9 c\u00f3 \u1edf m\u1eabu <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo \u0111\u1ec1 b\u00e0i th\u00ec sau khi l\u1ea5y $\\dfrac{3}{5}$ s\u1ed1 h\u1ecdc sinh \u1edf t\u1ed1p th\u1ee9 nh\u1ea5t chia \u0111\u1ec1u cho 3 t\u1ed1p c\u00f2n l\u1ea1i th\u00ec s\u1ed1 h\u1ecdc sinh 4 t\u1ed1p b\u1eb1ng nhau v\u00e0 b\u1eb1ng $1 - \\dfrac{3}{5} = \\dfrac{2}{5}$ s\u1ed1 h\u1ecdc sinh c\u1ee7a t\u1ed1p th\u1ee9 nh\u1ea5t. <br\/> Khi b\u1edbp \u0111i 6 h\u1ecdc sinh th\u00ec s\u1ed1 h\u1ecdc sinh t\u1ed1p 1 b\u1eb1ng t\u1ed5ng s\u1ed1 h\u1ecdc sinh 3 t\u1ed1p c\u00f2n l\u1ea1i <br\/> Ta c\u00f3 s\u01a1 \u0111\u1ed3: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai37/lv3/img\/D639_K101.png' \/><\/center> <br\/> Nh\u00ecn v\u00e0o s\u01a1 \u0111\u1ed3, t\u1ed1p h\u1ecdc sinh th\u1ee9 nh\u1ea5t chia th\u00e0nh 5 ph\u1ea7n b\u1eb1ng nhau v\u00e0 b\u1edbt \u0111i 6 h\u1ecdc sinh, t\u1ee9c l\u00e0 b\u1edbt \u0111i hai ph\u1ea7n <br\/> S\u1ed1 h\u1ecdc sinh t\u1ed1p 1 l\u00e0: <br\/> $6 : \\dfrac{2}{5} = 15$ (h\u1ecdc sinh) <br\/> S\u1ed1 h\u1ecdc sinh 3 t\u1ed1p c\u00f2n l\u1ea1i l\u00e0: <br\/> 3 . (6 : 2) = 9 (h\u1ecdc sinh) <br\/> S\u1ed1 h\u1ecdc sinh \u0111\u1ed9i To\u00e1n c\u1ee7a kh\u1ed1i l\u00e0: <br\/> 15 + 9 = 24 (h\u1ecdc sinh) <br\/> \u0110\u00e1p s\u1ed1: 24 h\u1ecdc sinh <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 24 <\/span> "}]}],"id_ques":1794},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6","18","30"],["78","66","54"],["18","6","30"],["66","78","54"],["30","18","6"],["54","78","66"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean bi\u1ebft r\u1eb1ng t\u1ed5ng c\u1ee7a ch\u00fang b\u1eb1ng 84 (a < b) v\u00e0 \u01afCLN c\u1ee7a ch\u00fang b\u1eb1ng 6 <br\/> Hai s\u1ed1 \u0111\u00f3 l\u00e0: a = _input_; b = _input_ ho\u1eb7c a = _input_; b = _input_ ho\u1eb7c a = _input_; b = _input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> G\u1ecdi hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 a, b <br\/> V\u00ec a + b = 84 v\u00e0 (a, b) = 6, vi\u1ebft a = 6m, b = 6n sao cho (m, n) = 1 <br\/> T\u00ecm t\u1ed5ng m + n = $\\dfrac{a + b}{6}$ <br\/> sau \u0111\u00f3 t\u00ecm c\u00e1c gi\u00e1 tr\u1ecb m, n th\u1ecfa m\u00e3n m < n; (m, n) = 1 v\u00e0 c\u00f3 t\u1ed5ng nh\u01b0 tr\u00ean <br\/> Sau \u0111\u00f3 thay m v\u00e0o \u0111\u1ec3 t\u00ecm a, b <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 a v\u00e0 b (a < b) <br\/> Ta c\u00f3: \u01afCLN(a, b) = 6 n\u00ean a = 6m, b = 6n; (m, n) = 1 ($a, b, m, n \\in \\mathbb{N^*})$ <br\/> V\u00ec $a < b$ n\u00ean $m < n$ <br\/> Theo b\u00e0i ra: a + b = 84 $\\Rightarrow$ 6m + 6n = 84 <br\/> $\\Rightarrow$ m + n = 14 <br\/> V\u00ec m < n v\u00e0 (m, n) = 1 n\u00ean: <br\/> <table><tr><th>m<\/th><th>1<\/th><th>3<\/th><th>5<\/th><\/tr><tr><td>n<\/td><td>13<\/td><td>11<\/td><td>9<\/td><\/tr><\/table> <br\/> $\\Rightarrow$ <br\/> <table><tr><th>a<\/th><th>6<\/th><th>18<\/th><th>30<\/th><\/tr><tr><td>b<\/td><td>78<\/td><td>66<\/td><td>54<\/td><\/tr><\/table> <br\/> <span class='basic_pink'> V\u1eady a = 6; b = 78 v\u00e0 a = 18; b = 66 ho\u1eb7c a = 30, b = 54 <\/span> "}]}],"id_ques":1795},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["893"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn nh\u1ea5t c\u00f3 ba ch\u1eef s\u1ed1, bi\u1ebft r\u1eb1ng chia n\u00f3 cho 10 th\u00ec d\u01b0 3, chia n\u00f3 cho 12 th\u00ec d\u01b0 5, chia n\u00f3 cho 15 th\u00ec d\u01b0 8 v\u00e0 n\u00f3 chia h\u1ebft cho 19. <br\/> \u0110\u00e1p \u00e1n l\u00e0: _input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> G\u1ecdi s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 a (99 < a < 1000) <br\/> Ta c\u1ea7n t\u00ecm m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean n sao cho a + n chia h\u1ebft cho 10, 12 v\u00e0 15 <br\/> Khi \u0111\u00f3 a + n $\\in$ BC(10, 12, 15) <br\/> K\u1ebft h\u1ee3p \u0111i\u1ec1u ki\u1ec7n a $\\vdots$ 19 \u0111\u1ec3 t\u00ecm a <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 a (99 < a < 1000) <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: <br\/> a = 10b + 3 <br\/> a = 12c + 5 <br\/> a = 15d + 8 <br\/> Nh\u1eadn th\u1ea5y a + 7 = 10b + 10, (10b + 10) $\\vdots$ 10 <br\/> a + 7 = 12c + 12, (12c + 12) $\\vdots$ 12 <br\/> a + 7 = 15d + 15, (15d + 15) $\\vdots$ 15 <br\/> N\u00ean (a + 7) $\\in$ BC(10, 12, 15) <br\/> Ta c\u00f3: BCNN(10, 12, 15) = 60 <br\/> Do 99 < a < 1000 n\u00ean (a + 7) $\\in$ {960; 900; 840;....; 180; 120} <br\/> $\\Rightarrow$ a $\\in$ {953; 893; ...; 173; 113} <br\/> S\u1ed1 953 $\\not \\vdots$ 19 (lo\u1ea1i) <br\/> S\u1ed1 893 = 19 . 47 (th\u1ecfa m\u00e3n) <br\/> V\u1eady s\u1ed1 a l\u1edbn nh\u1ea5t c\u1ea7n t\u00ecm l\u00e0: 893 <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 893 <\/span> "}]}],"id_ques":1796},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6","24"],["120","30"],["24","6"],["30","120"]]],"list":[{"point":10,"width":80,"content":"","type_input":"","ques":"T\u00ecm c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean a, b (a < b) bi\u1ebft ab = 720; \u01afCLN(a; b) = 6 (a < b) <br\/> V\u1eady: a = _input_; b = _input_ ho\u1eb7c a = _input_; b = _input_","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> V\u00ec \u01afCLN(a, b) = 6 n\u00ean a = 6m; b = 6n ($m , n \\in \\mathbb{N}$); (m, n) = 1 <br\/> V\u00ec a < b $\\Rightarrow$ m < n <br\/> Ta \u0111i t\u00ecm m, n sao cho 6m . 6n = 720 v\u00e0 m < n <br\/> Sau \u0111\u00f3 thay ng\u01b0\u1ee3c tr\u1edf l\u1ea1i \u0111\u1ec3 t\u00ecm a, b <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> V\u00ec \u01afCLN(a , b) = 6 n\u00ean a = 6m; b = 6n ($m, n \\in \\mathbb{N}$); (m, n) = 1 <br\/> V\u00ec a < b $\\Rightarrow$ m < n <br\/> Theo b\u00e0i ra ta c\u00f3: ab = 720 $\\Rightarrow$ 6m . 6n = 720 <br\/> $\\Rightarrow$ mn = 20 <br\/> V\u00ec m < n v\u00e0 (m, n) = 1 ta c\u00f3: <br\/> <table><tr><th>m<\/th><th>1<\/th><th>4<\/th><\/tr><tr><td>n<\/td><td>20<\/td><td>5<\/td><\/tr><\/table> <br\/> $\\Rightarrow$ <br\/> <table><tr><th>a<\/th><th>6<\/th><th>24<\/th><\/tr><tr><td>b<\/td><td>120<\/td><td>30<\/td><\/tr><\/table> <br\/> <span class='basic_pink'> V\u1eady a = 6; b = 120 ho\u1eb7c a = 24; b = 30<\/span> "}]}],"id_ques":1797},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["4"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["frac"],"ques":"B\u1ed1n b\u1ea1n An, B\u00e1ch, C\u1ea3nh, D\u0169ng \u0111i ch\u01a1i nh\u01b0ng D\u0169ng kh\u00f4ng mang ti\u1ec1n. An cho D\u0169ng $\\dfrac{1}{5}$ s\u1ed1 ti\u1ec1n c\u1ee7a m\u00ecnh. B\u00e1ch cho D\u0169ng $\\dfrac{1}{4}$ s\u1ed1 ti\u1ec1n c\u1ee7a m\u00ecnh. C\u1ea3nh cho D\u0169ng $\\dfrac{1}{3}$ s\u1ed1 ti\u1ec1n c\u1ee7a m\u00ecnh. K\u1ebft qu\u1ea3 s\u1ed1 ti\u1ec1n D\u0169ng nh\u1eadn \u0111\u01b0\u1ee3c t\u1eeb ba b\u1ea1n \u0111\u1ec1u b\u1eb1ng nhau. Cu\u1ed1i c\u00f9ng D\u0169ng c\u00f3 s\u1ed1 ti\u1ec1n b\u1eb1ng bao nhi\u00eau ph\u1ea7n s\u1ed1 ti\u1ec1n c\u1ee7a c\u1ea3 nh\u00f3m. <br\/> \u0110\u00e1p \u00e1n l\u00e0: <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div> s\u1ed1 ti\u1ec1n c\u1ee7a c\u1ea3 nh\u00f3m ","hint":"L\u1ea5y s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch (l\u00fac \u0111\u1ea7u) l\u00e0m \u0111\u01a1n v\u1ecb \u0111\u1ec3 so s\u00e1nh","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> S\u1ed1 ti\u1ec1n m\u00e0 An, B\u00e1ch, C\u1ea3nh c\u00f3 l\u00fac \u0111\u1ea7u quan h\u1ec7 v\u1edbi nhau nh\u01b0 sau: <br\/> $\\dfrac{1}{5}$ s\u1ed1 ti\u1ec1n c\u1ee7a An = $\\dfrac{1}{4}$ s\u1ed1 ti\u1ec1n c\u1ee7a b\u00e1ch = $\\dfrac{1}{3}$ s\u1ed1 ti\u1ec1n c\u1ee7a C\u1ea3nh <br\/> Ta l\u1ea5y s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch l\u00e0m \u0111\u01a1n v\u1ecb so s\u00e1nh <br\/>V\u00ec s\u1ed1 ti\u1ec1n D\u0169ng nh\u1eadn \u0111\u01b0\u1ee3c t\u1eeb ba b\u1ea1n l\u00e0 b\u1eb1ng nhau <br\/> N\u00ean s\u1ed1 ti\u1ec1n D\u0169ng nh\u1eadn \u0111\u01b0\u1ee3c t\u1eeb ba b\u1ea1n b\u1eb1ng ba l\u1ea7n s\u1ed1 ti\u1ec1n B\u00e1ch cho D\u0169ng n\u00ean b\u1eb1ng: <br\/> $\\dfrac{1}{4} . 3 = \\dfrac{3}{4}$ (s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch) <br\/> S\u1ed1 ti\u1ec1n c\u1ee7a An b\u1eb1ng: <br\/> $\\dfrac{1}{4} : \\dfrac{1}{5} = \\dfrac{5}{4}$ (s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch) <br\/> S\u1ed1 ti\u1ec1n c\u1ee7a C\u1ea3nh b\u1eb1ng: <br\/> $\\dfrac{1}{4} : \\dfrac{1}{3} = \\dfrac{3}{4}$ (s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch) <br\/> S\u1ed1 ti\u1ec1n c\u1ee7a An, B\u00e1ch, C\u1ea3nh l\u00fac \u0111\u1ea7u b\u1eb1ng: <br\/> $\\dfrac{5}{4} + 1 + \\dfrac{3}{4} = 3$ (s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch) <br\/> S\u1ed1 ti\u1ec1n c\u1ee7a D\u0169ng nh\u1eadn \u0111\u01b0\u1ee3c so v\u1edbi s\u1ed1 ti\u1ec1n c\u1ee7a 3 b\u1ea1n An, B\u00e1ch, C\u1ea3nh c\u00f3 l\u00fac \u0111\u1ea7u l\u00e0: <br\/> $\\dfrac{3}{4} : 3 = \\dfrac{1}{4}$ <br\/> V\u1eady D\u0169ng nh\u1eadn \u0111\u01b0\u1ee3c s\u1ed1 ti\u1ec1n b\u1eb1ng $\\dfrac{1}{4}$ s\u1ed1 ti\u1ec1n c\u1ee7a c\u1ea3 nh\u00f3m <br\/> <span class='basic_left'><span class='basic_green'> <i> L\u01b0u \u00fd: Ta kh\u00f4ng t\u00ednh \u0111\u01b0\u1ee3c s\u1ed1 ti\u1ec1n c\u1ee5 th\u1ec3 m\u00e0 D\u0169ng nh\u1eadn \u0111\u01b0\u1ee3c, c\u0169ng kh\u00f4ng t\u00ednh \u0111\u01b0\u1ee3c s\u1ed1 ti\u1ec1n c\u1ee5 th\u1ec3 c\u1ee7a c\u1ea3 nh\u00f3m, nh\u01b0ng n\u1ebfu l\u1ea5y s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch (l\u00fac \u0111\u1ea7u) l\u00e0m \u0111\u01a1n v\u1ecb th\u00ec ta bi\u1ebft: <br\/> - S\u1ed1 ti\u1ec1n D\u0169ng nh\u1eadn b\u1eb1ng $\\dfrac{3}{4}$ s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch <br\/> - S\u1ed1 ti\u1ec1n c\u1ee7a c\u1ea3 nh\u00f3m b\u1eb1ng 3 s\u1ed1 ti\u1ec1n c\u1ee7a B\u00e1ch <br\/> Nh\u1edd \u0111\u00f3 ta t\u00ednh \u0111\u01b0\u1ee3c t\u1ec9 s\u1ed1 tr\u00ean <\/i> <\/span> "}]}],"id_ques":1798},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["25"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"M\u1ed9t c\u1eeda h\u00e0ng trong ng\u00e0y khai tr\u01b0\u01a1ng h\u1ea1 gi\u00e1 h\u00e0ng 12% so v\u1edbi gi\u00e1 b\u00e1n trong ng\u00e0y th\u01b0\u1eddng. Tuy v\u1eady, c\u1eeda h\u00e0ng v\u1eabn l\u00e3i 10% so v\u1edbi gi\u00e1 g\u1ed1c. H\u1ecfi n\u1ebfu kh\u00f4ng h\u1ea1 gi\u00e1 th\u00ec c\u1eeda h\u00e0ng l\u00e3i bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi gi\u00e1 g\u1ed1c? <br\/> \u0110\u00e1p S\u1ed1: _input_ % ","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 t\u1ec9 s\u1ed1 gi\u00e1 b\u00e1n trong ng\u00e0y khai tr\u01b0\u01a1ng so v\u1edbi gi\u00e1 ng\u00e0y th\u01b0\u1eddng (1) <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh t\u1ec9 s\u1ed1 gi\u00e1 b\u00e1n trong ng\u00e0y khai tr\u01b0\u01a1ng so v\u1edbi gi\u00e1 g\u1ed1c (coi gi\u00e1 g\u1ed1c l\u00e0 100%) (2) <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh t\u1ec9 s\u1ed1 gi\u00e1 b\u00e1n trong ng\u00e0y th\u01b0\u1eddng so v\u1edbi gi\u00e1 g\u1ed1c <br\/> L\u1ea5y (2) chia (1) <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ednh % l\u00e3i c\u1ee7a h\u00e0ng nh\u1eadn \u0111\u01b0\u1ee3c so v\u1edbi gi\u00e1 g\u1ed1c n\u1ebfu kh\u00f4ng h\u1ea1 gi\u00e1 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Gi\u00e1 b\u00e1n trong ng\u00e0y khai tr\u01b0\u01a1ng so v\u1edbi ng\u00e0y th\u01b0\u1eddng b\u1eb1ng: <br\/> 100% - 12% = 88% = 0,88 <br\/> Gi\u00e1 b\u00e1n trong ng\u00e0y khai tr\u01b0\u01a1ng so v\u1edbi gi\u00e1 g\u1ed1c b\u1eb1ng: <br\/> 100% + 10% = 110% = 1,1 <br\/> Nh\u01b0 v\u1eady 0,88 gi\u00e1 ng\u00e0y th\u01b0\u1eddng b\u1eb1ng 1,1 gi\u00e1 g\u1ed1c <br\/> Gi\u00e1 ng\u00e0y th\u01b0\u1eddng so v\u1edbi gi\u00e1 g\u1ed1c b\u1eb1ng: <br\/> 1,1 : 0,88 = 1,25 = 125% <br\/> N\u1ebfu kh\u00f4ng h\u1ea1 gi\u00e1 12% th\u00ec c\u1eeda h\u00e0ng l\u00e3i so v\u1edbi gi\u00e1 g\u1ed1c l\u00e0: <br\/> 125% - 100% = 25% <br\/> \u0110\u00e1p s\u1ed1: 25% <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 25<\/span>"}]}],"id_ques":1799},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2013"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["frac"],"ques":"T\u00ecm x bi\u1ebft: <br\/><br\/> $\\left( 1 + \\dfrac{1}{2} + \\dfrac{1}{3} + ... + \\dfrac{1}{2013} \\right) . x + 2013 = \\dfrac{2014}{1} + \\dfrac{2015}{2} + ... + \\dfrac{4025}{2012} + \\dfrac{4026}{2013}$ <br\/> <br\/> \u0110\u00e1p \u00e1n l\u00e0: $x$ = _input_ ","hint":"Chuy\u1ec3n 2013 sang v\u1ebf ph\u1ea3i, nh\u1eadn th\u1ea5y t\u1eeb $\\dfrac{2014}{1}$ \u0111\u1ebfn $\\dfrac{4026}{2013}$ c\u00f3 2013 s\u1ed1 h\u1ea1ng n\u00ean t\u00e1ch 2013 th\u00e0nh 2013 s\u1ed1 1 \u0111\u1ec3 c\u1ed9ng th\u00eam v\u00e0o m\u1ed7i ph\u00e2n s\u1ed1","explain":"<span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><br\/> Ta c\u00f3: <br\/> $\\left( 1 + \\dfrac{1}{2} + \\dfrac{1}{3} + ... + \\dfrac{1}{2013} \\right) . x + 2013 = \\dfrac{2014}{1} + \\dfrac{2015}{2} + ... + \\dfrac{4025}{2012} + \\dfrac{4026}{2013} \\\\ \\left( 1 + \\dfrac{1}{2} + \\dfrac{1}{3} + ... + \\dfrac{1}{2013} \\right) . x = \\dfrac{2014}{1} + \\dfrac{2015}{2} + ... + \\dfrac{4025}{2012} + \\dfrac{4026}{2013} - 2013$ <br\/> <br\/> X\u00e9t bi\u1ec3u th\u1ee9c: <br\/> $\\begin{align*} & \\dfrac{2014}{1} + \\dfrac{2015}{2} + ... + \\dfrac{4025}{2012} + \\dfrac{4026}{2013} - 2013 \\\\ &= \\left( \\dfrac{2014}{1} - 1 \\right) + \\left( \\dfrac{2015}{2} - 1 \\right) + \\left( \\dfrac{2016}{3} - 1 \\right) + ... + \\left( \\dfrac{4025}{2012} - 1 \\right) + \\left( \\dfrac{4026}{2013} - 1 \\right) \\\\ &= \\dfrac{2013}{1} + \\dfrac{2013}{2} + \\dfrac{2013}{3} + ... + \\dfrac{2013}{2012} + \\dfrac{2013}{2013} \\\\ &= 2013 . \\left( 1 + \\dfrac{1}{2} + \\dfrac{1}{3} + ... + \\dfrac{1}{2012} + \\dfrac{1}{2013} \\right) \\end{align*}$ <br\/> $\\Rightarrow$ $\\left( 1 + \\dfrac{1}{2} + \\dfrac{1}{3} + ... + \\dfrac{1}{2013} \\right) . x = 2013 . \\left( 1 + \\dfrac{1}{2} + \\dfrac{1}{3} + ... + \\dfrac{1}{2012} + \\dfrac{1}{2013} \\right) \\\\ x = 2013$ <br\/> <span class='basic_left'><span class='basic_green'> <i> Nh\u1eadn x\u00e9t: V\u1edbi b\u00e0i to\u00e1n t\u00ecm x m\u00e0 \u1edf c\u1ea3 hai v\u1ebf \u0111\u1ec1u c\u00f3 ch\u1ee9a 1 d\u00e3y c\u00e1c ph\u00e2n s\u1ed1 theo quy lu\u1eadt th\u00f4ng th\u01b0\u1eddng ta ch\u1ec9 c\u1ea7n bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c \u1edf v\u1ebf ph\u1ea3i sao cho c\u00f3 th\u1ec3 r\u00fat g\u1ecdn \u0111\u01b0\u1ee3c v\u1edbi bi\u1ec3u th\u1ee9c \u1edf v\u1ebf tr\u00e1i ch\u1ee9 kh\u00f4ng t\u00ednh gi\u00e1 tr\u1ecb t\u1eebng bi\u1ec3u th\u1ee9c \u0111\u00f3 <br\/> Nh\u01b0 \u1edf b\u00e0i to\u00e1n tr\u00ean nh\u1eadn th\u1ea5y d\u00e3y ph\u00e2n s\u1ed1 \u1edf c\u1ea3 hai v\u1ebf c\u00f3 m\u1eabu s\u1ed1 gi\u1ed1ng nhau, c\u00e1c ph\u00e2n s\u1ed1 \u1edf v\u1ebf ph\u1ea3i \u0111\u1ec1u l\u00e0 c\u00e1c ph\u00e2n s\u1ed1 l\u1edbn h\u01a1n 1, ta t\u00ecm c\u00e1ch \u0111\u01b0a ch\u00fang v\u1ec1 d\u1ea1ng t\u00edch c\u1ee7a 1 s\u1ed1 nguy\u00ean v\u00e0 m\u1ed9t d\u00e3y c\u00e1c ph\u00e2n s\u1ed1 gi\u1ed1ng \u1edf v\u1ebf tr\u00e1i r\u1ed3i r\u00fat g\u1ecdn <\/i> <\/span> "}]}],"id_ques":1800}],"lesson":{"save":0,"level":3}}