{"segment":[{"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":"T\u00ecm s\u1ed1 nguy\u00ean x bi\u1ebft: <br\/> <br\/> $ \\dfrac{1}{3} + \\dfrac{-2}{5} + \\dfrac{1}{6} + \\dfrac{-1}{5} \\leq x < \\dfrac{-3}{4} + \\dfrac{2}{7} + \\dfrac{-1}{4} + \\dfrac{3}{5} + \\dfrac{5}{7} $ <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $x \\in \\left\\{ 1; 2; 3; 4; 5; 6; 7 \\right\\}$ ","B. $x \\in \\left\\{ 7; 6; 5; 4; 3 \\right\\}$ ","C. $x \\in \\left\\{ -1; 0; 1; 2; 3; 4; 5 \\right\\}$","D. $x \\in \\left\\{-6; -5; -4; -3; -2; -1 \\right\\}$ "],"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{1}{3} + \\dfrac{-2}{5} + \\dfrac{1}{6} + \\dfrac{-1}{5}$ b\u1eb1ng c\u00e1ch nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 m\u1ed9t c\u00e1ch th\u00edch h\u1ee3p <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $\\dfrac{-3}{4} + \\dfrac{2}{7} + \\dfrac{-1}{4} + \\dfrac{3}{5} + \\dfrac{5}{7} $ b\u1eb1ng c\u00e1ch nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 c\u00e1c ph\u00e2n s\u1ed1 v\u00e0 t\u00ecm s\u1ed1 nguy\u00ean x th\u1ecfa m\u00e3n y\u00eau c\u1ea7u c\u1ee7a b\u00e0i to\u00e1n <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} & \\dfrac{1}{3} + \\dfrac{-2}{5} + \\dfrac{1}{6} + \\dfrac{-1}{5} \\\\ &= \\left( \\dfrac{-2}{5} + \\dfrac{-1}{5} \\right) + \\dfrac{1}{3} + \\dfrac{1}{6} \\\\ &= \\dfrac{-2 + (-1)}{5} + \\dfrac{2}{6} + \\dfrac{1}{6} \\\\ &= \\dfrac{-3}{5} + \\dfrac{2 + 1}{6} \\\\ &= \\dfrac{-3}{5} + \\dfrac{1}{2} \\\\ &= \\dfrac{-3 . 2}{5 . 2} + \\dfrac{1 . 5}{2 . 5} \\\\ &= \\dfrac{-6 + 5}{10} \\\\ &= \\dfrac{-1}{10} \\end{align*}$ <br\/> $\\begin{align*} & \\dfrac{-3}{4} + \\dfrac{2}{7} + \\dfrac{-1}{4} + \\dfrac{3}{5} + \\dfrac{5}{7} \\\\ &=\\left( \\dfrac{-3}{4} + \\dfrac{-1}{4} \\right) + \\left( \\dfrac{2}{7} + \\dfrac{5}{7} \\right) + \\dfrac{3}{5} \\\\ &= \\dfrac{-1 + (-3)}{4} + \\dfrac{2 + 5}{7} + \\dfrac{3}{5} \\\\ &= -1 + 1 + \\dfrac{3}{5} \\\\ &= \\dfrac{3}{5} = \\dfrac{6}{10} \\end{align*}$ <br\/> $\\Rightarrow$ $\\dfrac{-1}{10} \\leq x < \\dfrac{6}{10}$ <br\/> $\\Rightarrow$ $x \\in$ {-1; 0; 1; 2; 3; 4; 5} <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C <\/span> ","column":2}]}],"id_ques":1591},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"T\u00ecm s\u1ed1 nguy\u00ean x bi\u1ebft: <br\/> <br\/> $ -1 + \\dfrac{1}{3} + \\dfrac{2}{9} < x < \\dfrac{-1}{3} + \\dfrac{-4}{9} + \\dfrac{8}{9}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $x \\in \\left\\{-4; -3; -2; -1; 0; 1 \\right\\}$ ","B. $x \\in \\left\\{ -3, -2, -1, 0, 1 \\right\\}$ ","C. $x \\in \\left\\{ -4, -3, -2, -1, 0 \\right\\}$","D. $x \\in \\left\\{-3, -2, -1, 0 \\right\\}$ "],"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 $ -1 + \\dfrac{1}{3} + \\dfrac{2}{9}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $\\dfrac{-1}{3} + \\dfrac{-4}{9} + \\dfrac{8}{9}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 c\u00e1c ph\u00e2n s\u1ed1 v\u00e0 t\u00ecm s\u1ed1 nguy\u00ean x th\u1ecfa m\u00e3n y\u00eau c\u1ea7u c\u1ee7a b\u00e0i to\u00e1n <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> $\\begin{align*} & -1 + \\dfrac{1}{3} + \\dfrac{2}{9} \\\\ &= \\dfrac{-9}{9} + \\dfrac{1 . 3}{3 . 3} + \\dfrac{2}{9} \\\\ &= \\dfrac{-9}{9} + \\dfrac{3}{9} + \\dfrac{2}{9} \\\\ &= \\dfrac{-9 + 3 + 2}{9} \\\\ &= \\dfrac{-4}{9} \\end{align*}$ <br\/> $\\begin{align*} & \\dfrac{-1}{3} + \\dfrac{-4}{9} + \\dfrac{8}{9} \\\\ &= \\dfrac{-1 . 3}{3 . 3} + \\dfrac{-4}{9} + \\dfrac{8}{9} \\\\ &= \\dfrac{-3}{9} + \\dfrac{-4}{9} + \\dfrac{8}{9} \\\\ &= \\dfrac{-3 + (-4) + 8}{9} \\\\ &= \\dfrac{1}{9} \\end{align*}$ <br\/> $\\Rightarrow$ $\\dfrac{-4}{9} < x < \\dfrac{1}{9}$ <br\/> $\\Rightarrow$ $x \\in$ {-3, -2, -1, 0} <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":1592},{"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":"Cho $A = \\dfrac{1}{10} + \\dfrac{1}{11} + \\dfrac{1}{12} + ... + \\dfrac{1}{18} + \\dfrac{1}{19}$ <br\/> <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?","select":["A. A > 1 ","B. A < 1 ","C. A = 1"],"hint":"So s\u00e1nh t\u1eebng ph\u00e2n s\u1ed1 trong t\u1ed5ng v\u1edbi $\\dfrac{1}{10}$ ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> So s\u00e1nh t\u1eebng s\u1ed1 h\u1ea1ng trong t\u1ed5ng v\u1edbi $\\dfrac{1}{10}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec t\u1ed5ng tr\u00ean c\u00f3 10 ph\u00e2n s\u1ed1 n\u00ean so s\u00e1nh <br\/> $\\dfrac{1}{10} + \\dfrac{1}{11} + \\dfrac{1}{12} + ... + \\dfrac{1}{18} + \\dfrac{1}{19}$ <br\/>V\u1edbi $\\underbrace{ \\dfrac{1}{10} + \\dfrac{1}{10} + \\dfrac{1}{10} + ... + \\dfrac{1}{10} + \\dfrac{1}{10}}_{10 \\text{s\u1ed1 h\u1ea1ng}} $ <br\/> <b> B\u01b0\u1edbc 3: <\/b> Bi\u1ebfn \u0111\u1ed5i v\u00e0 k\u1ebft lu\u1eadn <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: <br\/> $\\dfrac{1}{11} < \\dfrac{1}{10}$ <br\/> $\\dfrac{1}{12} < \\dfrac{1}{10}$ <br\/> ............... <br\/> $\\dfrac{1}{18} < \\dfrac{1}{10}$ <br\/> $\\dfrac{1}{19} < \\dfrac{1}{10}$ <br\/> V\u00ec t\u1ed5ng tr\u00ean c\u00f3 10 ph\u00e2n s\u1ed1 n\u00ean: <br\/> $\\dfrac{1}{10} + \\dfrac{1}{11} + \\dfrac{1}{12} + ... + \\dfrac{1}{18} + \\dfrac{1}{19} < \\underbrace{ \\dfrac{1}{10} + \\dfrac{1}{10} + \\dfrac{1}{10} + ... + \\dfrac{1}{10} + \\dfrac{1}{10}}_{10 \\text{s\u1ed1 h\u1ea1ng}} $ <br\/> M\u00e0 $\\underbrace{ \\dfrac{1}{10} + \\dfrac{1}{10} + \\dfrac{1}{10} + ... + \\dfrac{1}{10} + \\dfrac{1}{10}}_{10 \\text{s\u1ed1 h\u1ea1ng}} = \\dfrac{1 + 1 + ... + 1}{10} = \\dfrac{10}{10} = 1$ <br\/> $\\Rightarrow$ $\\dfrac{1}{10} + \\dfrac{1}{11} + \\dfrac{1}{12} + ... + \\dfrac{1}{18} + \\dfrac{1}{19}$ < 1 hay A < 1 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A < 1 <\/span> ","column":3}]}],"id_ques":1593},{"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":"Cho $D = \\dfrac{1}{11} + \\dfrac{1}{12} + \\dfrac{1}{13} + ... + \\dfrac{1}{19} + \\dfrac{1}{20}$ <br\/> <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?","select":["A. $D < \\dfrac{1}{2}$ ","B. $D = \\dfrac{1}{2}$ ","C. $D > \\dfrac{1}{2}$"],"hint":"So s\u00e1nh c\u00e1c ph\u00e2n s\u1ed1 trong t\u1ed5ng v\u1edbi $\\dfrac{1}{20}$ ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Nh\u1eadn th\u1ea5y t\u1ed5ng tr\u00ean c\u00f3 10 ph\u00e2n s\u1ed1 <br\/>N\u00ean vi\u1ebft $\\dfrac{1}{2}$ b\u1eb1ng t\u1ed5ng c\u1ee7a 10 ph\u00e2n s\u1ed1 r\u1ed3i so s\u00e1nh t\u1eebng ph\u00e2n s\u1ed1 trong D v\u1edbi c\u00e1c ph\u00e2n s\u1ed1 \u0111\u00f3 <br\/> $\\dfrac{1}{2} = \\dfrac{10}{20} = \\underbrace{ \\dfrac{1}{20} + \\dfrac{1}{20} + ... + \\dfrac{1}{20}}_{10 \\text{ph\u00e2n s\u1ed1}}$ <br\/> <b> B\u01b0\u1edbc 1: <\/b> So s\u00e1nh t\u1eebng ph\u00e2n s\u1ed1 trong t\u1ed5ng v\u1edbi $\\dfrac{1}{20}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh D v\u1edbi $\\dfrac{1}{2}$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> V\u00ec t\u1ed5ng D c\u00f3 (20 - 11) + 1 = 10 ph\u00e2n s\u1ed1 <br\/> N\u00ean vi\u1ebft $\\dfrac{1}{2}$ b\u1eb1ng t\u1ed5ng c\u1ee7a 10 ph\u00e2n s\u1ed1 r\u1ed3i so s\u00e1nh <br\/> $\\dfrac{1}{2} = \\dfrac{10}{20} = \\underbrace{ \\dfrac{1}{20} + \\dfrac{1}{20} + ... + \\dfrac{1}{20}}_{10 \\text{ph\u00e2n s\u1ed1}}$ <br\/> Ta c\u00f3: <br\/> $\\dfrac{1}{11} > \\dfrac{1}{20}$ <br\/> $\\dfrac{1}{12} > \\dfrac{1}{20}$ <br\/> $\\dfrac{1}{13} > \\dfrac{1}{20}$ <br\/> ............ <br\/> $\\dfrac{1}{19} > \\dfrac{1}{20}$ <br\/> $\\Rightarrow$ $\\dfrac{1}{11} + \\dfrac{1}{12} + \\dfrac{1}{13} + ... + \\dfrac{1}{19} + \\dfrac{1}{20} > \\underbrace{ \\dfrac{1}{20} + \\dfrac{1}{20} + ... + \\dfrac{1}{20}}_{10 \\text{ph\u00e2n s\u1ed1}} = \\dfrac{1}{2}$ <br\/> Hay $D > \\dfrac{1}{2}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: $D > \\dfrac{1}{2}$ <\/span> <br\/> <span class='basic_left'><span class='basic_green'> <i> Nh\u1eadn x\u00e9t: V\u1edbi nh\u1eefng b\u00e0i so s\u00e1nh t\u1ed5ng A g\u1ed3m n ph\u00e2n s\u1ed1 v\u1edbi 1 s\u1ed1 b th\u00f4ng th\u01b0\u1eddng ta l\u00e0m nh\u01b0 sau: <br\/> +) Vi\u1ebft s\u1ed1 b b\u1eb1ng t\u1ed5ng c\u1ee7a n ph\u00e2n s\u1ed1 <br\/> +) So s\u00e1nh t\u1eebng ph\u00e2n s\u1ed1 trong t\u1ed5ng A v\u1edbi m\u1ed9t ph\u00e2n s\u1ed1 v\u1eeba vi\u1ebft \u1edf tr\u00ean <br\/> +) So s\u00e1nh t\u1ed5ng A v\u1edbi b <\/i> <\/span> ","column":3}]}],"id_ques":1594},{"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":"An ngh\u0129 ra m\u1ed9t ph\u00e2n s\u1ed1. An nh\u00e2n t\u1eed s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 \u0111\u00f3 v\u1edbi 2 \u0111\u1ed3ng th\u1eddi chia m\u1eabu s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 \u0111\u00f3 cho 3 th\u00ec \u0111\u01b0\u1ee3c ph\u00e2n s\u1ed1 m\u1edbi. Bi\u1ebft t\u1ed5ng c\u1ee7a ph\u00e2n s\u1ed1 m\u1edbi v\u00e0 ph\u00e2n s\u1ed1 ban \u0111\u1ea7u l\u00e0 $\\dfrac{35}{9}$. T\u00ecm ph\u00e2n s\u1ed1 An ngh\u0129. <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $ \\dfrac{5}{9}$ ","B. $ \\dfrac{9}{5}$ ","C. $\\dfrac{10}{3}$","D. $\\dfrac{33}{9}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> G\u1ecdi ph\u00e2n s\u1ed1 ban \u0111\u1ea7u l\u00e0 $\\dfrac{a}{b}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Vi\u1ebft ph\u00e2n s\u1ed1 sau s\u1ed1 sau khi chia t\u1eed s\u1ed1 cho 2 v\u00e0 nh\u00e2n 3 v\u00e0o m\u1eabu s\u1ed1 <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh t\u1ed5ng c\u1ee7a ph\u00e2n s\u1ed1 ban \u0111\u1ea7u v\u00e0 ph\u00e2n s\u1ed1 sau khi nh\u00e2n 2 v\u00e0o t\u1eed s\u1ed1 v\u00e0 chia 3 \u1edf m\u1eabu s\u1ed1 <br\/> Bi\u1ebfn \u0111\u1ed5i v\u00e0 t\u00ecm a, b <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> G\u1ecdi ph\u00e2n s\u1ed1 An ngh\u0129 l\u00e0: $\\dfrac{a}{b}$ $(a, b \\in \\mathbb{Z}, b \\neq 0)$ <br\/> Khi nh\u00e2n t\u1eed s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ v\u1edbi 2 \u0111\u1ed3ng th\u1eddi chia m\u1eabu s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 \u0111\u00f3 cho 3 ta \u0111\u01b0\u1ee3c: <br\/> $\\dfrac{a . 2}{b : 3} = \\dfrac{2a}{\\dfrac{b}{3}} = 2a . \\dfrac{3}{b} = \\dfrac{6a}{b}$ <br\/> T\u1ed5ng c\u1ee7a ph\u00e2n s\u1ed1 ban \u0111\u1ea7u v\u00e0 ph\u00e2n s\u1ed1 m\u1edbi l\u00e0: <br\/> $\\dfrac{a}{b} + \\dfrac{6a}{b} = \\dfrac{7a}{b} = \\dfrac{35}{9}$ <br\/> $\\Rightarrow$ 7a . 9 = b . 35 <br\/> 63 . a = 35 . b <br\/> 9 . a = 5 . b <br\/> $\\Rightarrow$ a = 5, b = 9 <br\/> V\u1eady ph\u00e2n s\u1ed1 An ngh\u0129 l\u00e0: <span class='basic_pink'> $\\dfrac{5}{9}$ <\/span> ","column":2}]}],"id_ques":1595},{"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":"B\u1ea1n Lan v\u00e0 Mai ho\u00e0n th\u00e0nh m\u1ed9t c\u00f4ng vi\u1ec7c trong 3 gi\u1edd. Mai v\u00e0 An ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c \u0111\u00f3 trong 4 gi\u1edd. An v\u00e0 Lan ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c \u0111\u00f3 m\u1ea5t 2 gi\u1edd 30 ph\u00fat. H\u1ecfi c\u1ea3 3 b\u1ea1n c\u00f9ng l\u00e0m s\u1ebd ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c trong bao l\u00e2u? <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $ \\dfrac{59}{120}$ gi\u1edd ","B. $ \\dfrac{120}{59}$ gi\u1edd ","C. $\\dfrac{5}{2}$ gi\u1edd","D. $\\dfrac{59}{60}$ 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\u00ednh s\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c Lan v\u00e0 Mai l\u00e0m \u0111\u01b0\u1ee3c trong 1 gi\u1edd (1) <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c Mai v\u00e0 An l\u00e0m \u0111\u01b0\u1ee3c trong m\u1ed9t gi\u1edd (2) <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c An v\u00e0 Lan l\u00e0m \u0111\u01b0\u1ee3c trong 1 gi\u1edd (3) <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c c\u1ea3 3 b\u1ea1n l\u00e0m \u0111\u01b0\u1ee3c trong 1 gi\u1edd <br\/> [(1) + (2) + (3)] : 2 <br\/> <b> B\u01b0\u1edbc 5: <\/b> T\u00ednh th\u1eddi gian \u0111\u1ec3 c\u1ea3 3 b\u1ea1n ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> \u0110\u1ed5i 2 gi\u1edd 30 ph\u00fat = $\\dfrac{5}{2}$ gi\u1edd <br\/> S\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c Lan v\u00e0 Mai l\u00e0m \u0111\u01b0\u1ee3c trong 1 gi\u1edd l\u00e0: <br\/> 1 : 3 = $\\dfrac{1}{3}$ (c\u00f4ng vi\u1ec7c) <br\/> S\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c An v\u00e0 Lan l\u00e0m \u0111\u01b0\u1ee3c trong 1 gi\u1edd l\u00e0: <br\/> 1 : 4 = $\\dfrac{1}{4}$ (c\u00f4ng vi\u1ec7c) <br\/> S\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c An v\u00e0 Lan l\u00e0m \u0111\u01b0\u1ee3c trong 1 gi\u1edd l\u00e0: <br\/> $1 : \\dfrac{5}{2} = \\dfrac{2}{5}$ (c\u00f4ng vi\u1ec7c) <br\/> S\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c c\u1ea3 3 b\u1ea1n l\u00e0m \u0111\u01b0\u1ee3c trong 1 gi\u1edd l\u00e0: <br\/> $(\\dfrac{1}{3} + \\dfrac{1}{4} + \\dfrac{2}{5}) : 2 = \\dfrac{59}{120}$ (c\u00f4ng vi\u1ec7c) <br\/> C\u1ea3 3 b\u1ea1n c\u00f9ng l\u00e0m ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c h\u1ebft s\u1ed1 th\u1eddi gian l\u00e0: <br\/> $1 : \\dfrac{59}{120} = \\dfrac{120}{59}$ (gi\u1edd) <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'> B . $\\dfrac{120}{59}$ gi\u1edd <\/span> ","column":2}]}],"id_ques":1596},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["19"],["12"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"R\u00fat g\u1ecdn. <br\/> <br\/> $\\dfrac{3 . \\left( 1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)}{4 . \\left( \\dfrac{17}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)} + \\dfrac{5 . \\left( 1 + \\dfrac{-2}{26} + \\dfrac{3}{243} + \\dfrac{-1}{181} \\right)}{6 . \\left( 1 + \\dfrac{-2}{26} + \\dfrac{3}{243} + \\dfrac{-1}{181} \\right)}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"Bi\u1ebfn \u0111\u1ed5i $\\dfrac{17}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81}$ sao cho c\u00f3 th\u1ec3 r\u00fat g\u1ecdn v\u1edbi $1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81}$ ","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 $1 + \\dfrac{-2}{26} + \\dfrac{3}{243} + \\dfrac{-1}{181}$ \u1edf t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 $\\dfrac{5 . \\left( 1 + \\dfrac{-2}{26} + \\dfrac{3}{243} + \\dfrac{-1}{181} \\right)}{6 . \\left( 1 + \\dfrac{-2}{26} + \\dfrac{3}{243} + \\dfrac{-1}{181} \\right)}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Bi\u1ebfn \u0111\u1ed5i $\\dfrac{17}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81}$ sao cho c\u00f3 th\u1ec3 r\u00fat g\u1ecdn v\u1edbi $1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> Quy \u0111\u1ed3ng 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 . \\left( 1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)}{4 . \\left( \\dfrac{17}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)} + \\dfrac{5 . \\left( 1 + \\dfrac{-2}{26} + \\dfrac{3}{423} + \\dfrac{-1}{181} \\right)}{6 . \\left( 1 + \\dfrac{-2}{26} + \\dfrac{3}{243} + \\dfrac{-1}{181} \\right)} \\\\ &= \\dfrac{3 .\\left( 1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)}{4 . \\left( \\dfrac{19 - 2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)} + \\dfrac{5}{6} \\\\ &= \\dfrac{3 .\\left( 1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)}{4 . \\left( \\dfrac{19}{19} + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)} + \\dfrac{5}{6} \\\\ &= \\dfrac{3 .\\left( 1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)}{4 . \\left( 1 + \\dfrac{-2}{19} + \\dfrac{3}{143} + \\dfrac{-1}{81} \\right)} + \\dfrac{5}{6} \\\\ &= \\dfrac{3}{4} + \\dfrac{5}{6} \\\\ &= \\dfrac{19}{12} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 19; 12 <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: V\u1edbi nh\u1eefng b\u00e0i r\u00fat g\u1ecdn ph\u00e2n s\u1ed1 c\u00f3 bi\u1ec3u th\u1ee9c ch\u1ee9a ph\u00e2n s\u1ed1 \u1edf tr\u00ean t\u1eed v\u00e0 d\u01b0\u1edbi m\u1eabu th\u00f4ng th\u01b0\u1eddng ta bi\u1ebfn \u0111\u1ed5i t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 th\u00e0nh t\u00edch c\u1ee7a m\u1ed9t s\u1ed1 v\u00e0 m\u1ed9t bi\u1ec3u th\u1ee9c. Bi\u1ec3u th\u1ee9c n\u00e0y c\u00f3 th\u1ec3 r\u00fat g\u1ecdn \u0111\u01b0\u1ee3c \u1edf t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 <\/i> <\/span> "}]}],"id_ques":1597},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["31"],["20"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"R\u00fat g\u1ecdn. <br\/> <br\/> $\\dfrac{3 + \\dfrac{6}{12} + \\dfrac{9}{13} + \\dfrac{-12}{17}}{4 + \\dfrac{8}{12} + \\dfrac{12}{13} + \\dfrac{-16}{17} } + \\dfrac{4 + \\dfrac{16}{61} + \\dfrac{-24}{213} + \\dfrac{-32}{11}}{5 + \\dfrac{20}{61} + \\dfrac{-30}{213} + \\dfrac{-40}{11}} $= <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"T\u00ecm nh\u00e2n t\u1eed chung \u1edf t\u1eed s\u1ed1, m\u1eabu s\u1ed1 c\u1ee7a t\u1eebng ph\u00e2n s\u1ed1 sau \u0111\u00f3 nh\u00f3m ra ngo\u00e0i v\u00e0 r\u00fat g\u1ecdn ","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 ph\u00e2n s\u1ed1: $\\dfrac{3 + \\dfrac{6}{12} + \\dfrac{9}{13} + \\dfrac{-12}{17}}{4 + \\dfrac{8}{12} + \\dfrac{12}{13} + \\dfrac{-16}{17} }$ <br\/> Nh\u1eadn th\u1ea5y $3 + \\dfrac{6}{12} + \\dfrac{9}{13} + \\dfrac{-12}{17}$ c\u00f3 nh\u00e2n t\u1eed chung l\u00e0 3 <br\/> $4 + \\dfrac{8}{12} + \\dfrac{12}{13} + \\dfrac{-16}{17}$ c\u00f3 nh\u00e2n t\u1eed chung l\u00e0 4 <br\/> <b> B\u01b0\u1edbc 2: <\/b> R\u00fat g\u1ecdn ph\u00e2n s\u1ed1: $\\dfrac{4 + \\dfrac{16}{61} + \\dfrac{-24}{213} + \\dfrac{-32}{11}}{5 + \\dfrac{20}{61} + \\dfrac{-30}{213} + \\dfrac{-40}{11}}$ <br\/> $4 + \\dfrac{16}{61} + \\dfrac{-24}{213} + \\dfrac{-32}{11}$ c\u00f3 4 l\u00e0 nh\u00e2n t\u1eed chung <br\/> $5 + \\dfrac{20}{61} + \\dfrac{-30}{213} + \\dfrac{-40}{11}$ c\u00f3 5 l\u00e0 nh\u00e2n t\u1eed chung <br\/> <b> B\u01b0\u1edbc 3: <\/b> Quy \u0111\u1ed3ng 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 + \\dfrac{6}{12} + \\dfrac{9}{13} + \\dfrac{-12}{17}}{4 + \\dfrac{8}{12} + \\dfrac{12}{13} + \\dfrac{-16}{17} } + \\dfrac{4 + \\dfrac{16}{61} + \\dfrac{-24}{213} + \\dfrac{-32}{11}}{5 + \\dfrac{20}{61} + \\dfrac{-30}{213} + \\dfrac{-40}{11}} \\\\ &= \\dfrac{3 . \\left( 1 + \\dfrac{2}{12} + \\dfrac{3}{13} + \\dfrac{-4}{17} \\right)}{4 . \\left( 1 + \\dfrac{2}{12} + \\dfrac{3}{13} + \\dfrac{-4}{17} \\right)} + \\dfrac{4 . \\left( 1 + \\dfrac{4}{61} + \\dfrac{-6}{213} + \\dfrac{-8}{11} \\right)}{5 . \\left( 1 + \\dfrac{4}{61} + \\dfrac{-6}{213} + \\dfrac{-8}{11} \\right)} \\\\ &= \\dfrac{3}{4} + \\dfrac{4}{5} \\\\ &= \\dfrac{15}{20} + \\dfrac{16}{20} \\\\ &= \\dfrac{31}{20} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 31; 20 <\/span> "}]}],"id_ques":1598},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"K\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p t\u00ednh $\\left( \\dfrac{21}{31} + \\dfrac{-16}{7} \\right) + \\left( \\dfrac{44}{53} + \\dfrac{10}{31} \\right) + \\dfrac{9}{53}$ l\u00e0:","select":["A. $ \\dfrac{16}{7}$ ","B. $ \\dfrac{-16}{7}$ ","C. $\\dfrac{2}{7}$ ","D. $\\dfrac{-2}{7} $"],"hint":"Ph\u00e1 ngo\u1eb7c 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 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu v\u1edbi nhau <br\/> <b> B\u01b0\u1edbc 3: <\/b> C\u1ed9ng c\u00e1c ph\u00e2n s\u1ed1 trong ngo\u1eb7c, t\u00ecm k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> $\\begin{align*} & \\left( \\dfrac{21}{31} + \\dfrac{-16}{7} \\right) + \\left( \\dfrac{44}{53} + \\dfrac{10}{31} \\right) + \\dfrac{9}{53} \\\\ &= \\dfrac{21}{31} + \\dfrac{-16}{7} + \\dfrac{44}{53} + \\dfrac{10}{31} + \\dfrac{9}{53} \\\\ &= \\left( \\dfrac{21}{31} + \\dfrac{10}{31} \\right) + \\left( \\dfrac{44}{53} + \\dfrac{9}{53} \\right) + \\dfrac{-16}{7} \\\\ &= \\dfrac{21 + 10}{31} + \\dfrac{44 + 9}{53} + \\dfrac{-16}{7} \\\\ &= \\dfrac{31}{31} + \\dfrac{53}{53} + \\dfrac{-16}{7} \\\\ &= 2 + \\dfrac{-16}{7} \\\\ &= \\dfrac{14}{7} + \\dfrac{-16}{7} \\\\ &= \\dfrac{14 + (-16)}{7} \\\\ &= \\dfrac{-2}{7} \\end{align*} $ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $\\dfrac{-2}{7}$ <\/span> ","column":2}]}],"id_ques":1599},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"T\u00ecm x bi\u1ebft: $\\dfrac{x - 4}{12} = \\dfrac{3}{5} + \\dfrac{11}{7} + \\dfrac{-9}{35} + \\dfrac{-8}{7}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. $x = \\dfrac{-184}{35}$ ","B. $x = \\dfrac{184}{35}$ ","C. $x = \\dfrac{-464}{35}$ ","D. $x = \\dfrac{464}{35}$"],"hint":"S\u1eed d\u1ee5ng 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 gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c b\u00ean v\u1ebf ph\u1ea3i <br\/> <b> B\u01b0\u1edbc 2: <\/b> Theo kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau x\u00e9t t\u00edch ch\u00e9o \u0111\u1ec3 t\u00ecm x <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> $\\begin{align*} \\dfrac{x - 4}{12} &= \\dfrac{3}{5} + \\dfrac{11}{7} + \\dfrac{-9}{35} + \\dfrac{-8}{7} \\\\ \\dfrac{x - 4}{12} &= \\left( \\dfrac{3}{5} + \\dfrac{-9}{35} \\right) + \\left( \\dfrac{11}{7} + \\dfrac{-8}{7} \\right) \\\\ \\dfrac{x - 4}{12} &= \\left( \\dfrac{21}{35} + \\dfrac{-9}{35} \\right) + \\dfrac{11 + (-8)}{7} \\\\ \\dfrac{x - 4}{12} &= \\dfrac{21 + (-9)}{35} + \\dfrac{3}{7} \\\\ \\dfrac{x - 4}{12} &= \\dfrac{12}{35} + \\dfrac{15}{35} \\\\ \\dfrac{x - 4}{12} &= \\dfrac{12 + 15}{35} \\\\ \\dfrac{x - 4}{12} &= \\dfrac{27}{35} \\end{align*} $ <br\/> $\\begin{align*} \\Rightarrow (x - 4) . 35 &= 12 . 27 \\\\ 35x - 140 &= 324 \\\\ 35x &= 324 + 140 \\\\ 35x &= 464 \\\\ x &= \\dfrac{464}{35} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $x = \\dfrac{464}{35}$ <\/span> ","column":2}]}],"id_ques":1600}],"lesson":{"save":0,"level":3}}