{"segment":[{"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":[[["97"],["1560"]]],"list":[{"point":10,"width":50,"ques":"R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 sau: <br\/> $\\dfrac{5^2 . 6^{11} . 16^2 + 6^2 . 12^6 . 15^2}{2 . 6^{12} . 10^4 - 81^2 . 960^3}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u0110\u01b0a t\u1ea5t c\u1ea3 v\u1ec1 d\u1ea1ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 2, c\u01a1 s\u1ed1 3 v\u00e0 c\u01a1 s\u1ed1 5","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a t\u1ea5t c\u1ea3 v\u1ec1 d\u1ea1ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 2, c\u01a1 s\u1ed1 3 v\u00e0 c\u01a1 s\u1ed1 5 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Nh\u00f3m nh\u1eefng l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 ra ngo\u00e0i, m\u1ed7i l\u0169y th\u1eeba l\u1eaby v\u1edbi s\u1ed1 m\u0169 nh\u1ecf nh\u1ea5t c\u1ee7a n\u00f3 <br\/> <b> B\u01b0\u1edbc 3: <\/b> R\u00fat g\u1ecdn nh\u1eefng nh\u00e2n t\u1eed chung \u1edf t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ednh to\u00e1n 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*} & \\dfrac{5^2 . 6^{11} . 16^2 + 6^2 . 12^6 . 15^2}{2 . 6^{12} . 10^4 - 81^2 . 960^3}\\\\ &= \\dfrac{5^2 . (2 . 3)^{11} . (2^4)^2 + (3 . 2)^2 . (2^2 . 3)^{6} . (3 . 5)^{2}}{2 . (2 . 3)^{12} . (2 . 5)^4 - (3^4)^2 . (2^6 . 3 . 5)^3} \\\\ &= \\dfrac{5^2 . 2^{11} . 3^{11} . 2^8 + 3^2 . 2^2 . 2^{12} . 3^6 . 3^2 . 5^2}{2 . 2^{12} . 3^{12} . 2^4 . 5^4 - 3^8 . 2^{18} . 3^3 . 5^3} \\\\ &= \\dfrac{2^{19} . 3^{11} . 5^2 + 2^{14} . 3^{10} . 5^2}{2^{17} . 3^{12} . 5^4 - 2^{18} . 3^{11} . 5^3} \\\\ &= \\dfrac{2^{14} . 3^{10} . 5^2 . (2^5 . 3 + 1)}{2^{17} . 3^{11} . 5^3 . (3 . 5 - 2)} \\\\ &= \\dfrac{97}{2^3 . 3 . 5 . 13} \\\\ &= \\dfrac{97}{1560} \\end{align*}$<br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: Th\u00f4ng th\u01b0\u1eddng khi l\u00e0m c\u00e1c b\u00e0i to\u00e1n d\u1ea1ng l\u0169y th\u1eeba nh\u01b0 tr\u00ean ta th\u01b0\u1eddng \u0111\u01b0a t\u1ea5t c\u1ea3 c\u00e1c l\u0169y th\u1eeba v\u1ec1 c\u01a1 s\u1ed1 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 sau \u0111\u00f3 bi\u1ebfn \u0111\u1ed5i v\u00e0 r\u00fat g\u1ecdn <\/i><\/span> "}]}],"id_ques":1491},{"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"],["626"]]],"list":[{"point":10,"width":50,"ques":"R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 sau: <br\/> $\\dfrac{25^{28} + 25^{24} + .... + 25^4 + 1}{25^{30} + 25^{28} + ... + 25^2 + 1}$ = <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\/> Quan s\u00e1t \u0111\u1ec1 b\u00e0i ta th\u1ea5y: \u1ede tr\u00ean t\u1eed l\u00e0 d\u00e3y c\u00e1c l\u0169y th\u1eeba c\u01a1 s\u1ed1 25, c\u00e1ch nhau 4 b\u1eadc; d\u01b0\u1edbi m\u1eabu l\u00e0 d\u00e3y c\u00e1c l\u0169y th\u1eeba c\u01a1 s\u1ed1 25, c\u00e1ch nhau 2 b\u1eadc <br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00e1ch c\u00e1c s\u1ed1 h\u1ea1ng \u1edf d\u01b0\u1edbi m\u1eabu th\u00e0nh 2 nh\u00f3m l\u0169y th\u1eeba trong \u0111\u00f3 m\u1ed7i nh\u00f3m g\u1ed3m c\u00e1c l\u0169y th\u1eeba c\u00e1ch nhau 4 b\u1eadc <br\/> <b> B\u01b0\u1edbc 2: <\/b> Bi\u1ebfn \u0111\u1ed5i l\u00e0m xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung \u1edf m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> R\u00fat g\u1ecdn nh\u1eefng nh\u00e2n t\u1eed chung \u1edf t\u1eed \u1edf t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1, 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*} & \\dfrac{25^{28} + 25^{24} + .... + 25^4 + 1}{(25^{30} + 25^{26} + ... + 25^{6} + 25^2) + (25^{28} + 25^{24} + ... + 25^4 + 1)} \\\\ &= \\dfrac{25^{28} + 25^{24} + ... + 25^4 + 1}{25^2 . (25^{28} + 25^{24} + ... + 25^{4} + 1) + (25^{28} + 25^{24} + ... + 25^{4} + 1)} \\\\ &= \\dfrac{25^{28} + 25^{24} + ... + 25^{4} + 1}{(25^{28} + 25^{24} + ... + 25^{4} + 1) . (25^2 + 1)} \\\\ &= \\dfrac{1}{25^2 + 1} \\\\ &= \\dfrac{1}{626} \\end{align*}$"}]}],"id_ques":1492},{"time":14,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["60"],["72"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$, r\u00fat g\u1ecdn ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ ta \u0111\u01b0\u1ee3c ph\u00e2n s\u1ed1 $\\dfrac{5}{6}$. N\u1ebfu th\u00eam 8 \u0111\u01a1n v\u1ecb v\u00e0o m\u1eabu s\u1ed1 b v\u00e0 gi\u1eef nguy\u00ean t\u1eed s\u1ed1 a th\u00ec ta \u0111\u01b0\u1ee3c m\u1ed9t ph\u00e2n s\u1ed1 m\u1edbi. R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 m\u1edbi \u0111\u01b0\u1ee3c ph\u00e2n s\u1ed1 $\\dfrac{3}{4}$. T\u00ecm ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: $\\dfrac{a}{b} $ = <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> V\u00ec $\\dfrac{a}{b} = \\dfrac{5}{6}$ <br\/> N\u00ean ta t\u00ednh \u0111\u01b0\u1ee3c a theo b t\u1eeb \u0111\u1eb3ng th\u1ee9c tr\u00ean (1) <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec $\\dfrac{a}{b + 8} = \\dfrac{3}{4}$ <br\/> N\u00ean ta t\u00ednh \u0111\u01b0\u1ee3c a theo b t\u1eeb \u0111\u1eb3ng th\u1ee9c tr\u00ean (2) <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay (1) v\u00e0o (2) ta t\u00ecm \u0111\u01b0\u1ee3c b <br\/> <b> B\u01b0\u1edbc 4: <\/b> Thay b tr\u1edf l\u1ea1i (1) ho\u1eb7c (2) \u0111\u1ec3 t\u00ecm a <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: $\\dfrac{a}{b} = \\dfrac{5}{6}$ <br\/> $\\Rightarrow$ $a = \\dfrac{5b}{6}$ (1) <br\/> Khi c\u1ed9ng th\u00eam 8 v\u00e0o m\u1eabu s\u1ed1 v\u00e0 gi\u1eef nguy\u00ean t\u1eed s\u1ed1 ta \u0111\u01b0\u1ee3c: <br\/> $\\dfrac{a}{b + 8} = \\dfrac{3}{4}$ <br\/> $\\Rightarrow$ a . 4 = 3 . (b + 8) <br\/> 4a = 3b + 24 (2) <br\/> Thay a t\u1eeb (1) v\u00e0o (2) ta \u0111\u01b0\u1ee3c: <br\/> $\\begin{align*} 4.\\dfrac{5b}{6} & = 3b + 24 \\\\ \\dfrac{20b}{6}& = 3b + 24 \\\\ 20b &= 6 . (3b + 24) \\\\ 20b &= 18b + 144 \\\\ 2b &= 144 \\\\ b &= 72\\end{align*}$ <br\/> $\\Rightarrow$ $a = \\dfrac{5 . 72}{6} = \\dfrac{360}{6} = 60$ <br\/> <span class='basic_pink'> V\u1eady ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0: $\\dfrac{60}{72}$ <\/span> "}]}],"id_ques":1493},{"time":14,"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 m\u1ed9t ph\u00e2n s\u1ed1, bi\u1ebft ph\u00e2n s\u1ed1 \u0111\u00f3 b\u1eb1ng ph\u00e2n s\u1ed1 $\\dfrac{9}{20}$ v\u00e0 BCNN c\u1ee7a t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 l\u00e0 360. Ph\u00e2n s\u1ed1 \u0111\u00f3 l\u00e0:","select":["A. $\\dfrac{36}{80}$","B. $\\dfrac{18}{40}$","C. $\\dfrac{27}{60}$","D. $\\dfrac{9}{20}$ "],"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 BCNN(9, 20) = ? <br\/> <b> B\u01b0\u1edbc 2: <\/b> X\u00e9t xem BCNN(9, 20) g\u1ea5p, k\u00e9m 360 bao nhi\u00eau l\u1ea7n th\u00ec ph\u00e2n s\u1ed1 $\\dfrac{9}{20}$ \u0111\u00e3 \u0111\u01b0\u1ee3c g\u1ea5p, gi\u1ea3m \u0111i b\u1ea5y nhi\u00eau l\u1ea7n <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ecm ph\u00e2n s\u1ed1 ban \u0111\u1ea7u <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: <br\/> $BCNN(9, 20) = 2^2 . 3^2 . 5 = 180$ <br\/> V\u00ec 180 = 360 : 2 n\u00ean ph\u00e2n s\u1ed1 $\\dfrac{9}{20}$ \u0111\u00e3 \u0111\u01b0\u1ee3c r\u00fat g\u1ecdn cho 2 <br\/> V\u1eady ph\u00e2n s\u1ed1 ban \u0111\u1ea7u l\u00e0: $\\dfrac{9 . 2}{20 . 2} = \\dfrac{18}{40}$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. $\\dfrac{18}{40}$<\/span>","column":2}]}],"id_ques":1494},{"time":14,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["23"],["27"],["29"],["31"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm c\u00e1c s\u1ed1 nguy\u00ean b $(21 \\leq b \\leq 31)$ sao cho c\u00e1c ph\u00e2n s\u1ed1 $\\dfrac{7}{b}, \\dfrac{10}{b}; \\dfrac{11}{b}$ \u0111\u1ec1u l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n <br\/> \u0110\u00e1p \u00e1n l\u00e0: b $\\in$ {_input_; _input_; _input_; _input_}","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Lo\u1ea1i \u0111i c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ec3 t\u1eebng ph\u00e2n s\u1ed1 tr\u00ean kh\u00f4ng t\u1ed1i gi\u1ea3n <br\/> \u0110\u1ec3 $\\dfrac{7}{b}$ t\u1ed1i gi\u1ea3n th\u00ec b kh\u00f4ng nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb n\u00e0o <br\/> \u0110\u1ec3 $\\dfrac{10}{b}$ t\u1ed1i gi\u1ea3n th\u00ec b kh\u00f4ng nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb n\u00e0o <br\/> \u0110\u1ec3 $\\dfrac{11}{b}$ t\u1ed1i gi\u1ea3n th\u00ec b kh\u00f4ng nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb n\u00e0o <br\/> <b> B\u01b0\u1edbc 2: <\/b>K\u1ebft h\u1ee3p c\u00e1c \u0111i\u1ec1u ki\u1ec7n tr\u00ean \u0111\u1ec3 t\u00ecm c\u00e1c gi\u00e1 tr\u1ecb th\u00edch h\u1ee3p c\u1ee7a b \u0111\u1ec3 c\u1ea3 3 ph\u00e2n s\u1ed1 \u0111\u1ec1u t\u1ed1i gi\u1ea3n<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec c\u00e1c ph\u00e2n s\u1ed1 $\\dfrac{7}{b}, \\dfrac{10}{b}; \\dfrac{11}{b}$ \u0111\u1ec1u l\u00e0 t\u1ed1i gi\u1ea3n n\u00ean b $\\neq$ B(7), b $\\neq$ B(11) v\u00e0 b $\\neq$ B(2), b $\\neq$ B(5) (v\u00ec 10 = 2 . 5) <br\/> M\u1eb7t kh\u00e1c: $ 21 \\leq b \\leq 31$ <br\/> $\\Rightarrow$ $\\dfrac{7}{b}$ t\u1ed1i gi\u1ea3n khi b $\\neq$ 21, 28 <br\/> $\\dfrac{10}{b}$ t\u1ed1i gi\u1ea3n khi b $\\neq$ 20, 22, 24, 25, 26, 28, 30<br\/> $\\dfrac{11}{b}$ t\u1ed1i gi\u1ea3n khi b $\\neq$ 22 <br\/> V\u1eady \u0111\u1ec3 $\\dfrac{7}{b}, \\dfrac{10}{b}; \\dfrac{11}{b}$ t\u1ed1i gi\u1ea3n $\\Rightarrow$ b = 23, b = 27, b = 29, b = 31<br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 23, 27, 29, 31 <\/span> "}]}],"id_ques":1495},{"time":14,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["13"],["19"],["17"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm c\u00e1c s\u1ed1 nguy\u00ean a $(12 \\leq a \\leq 21)$ sao cho c\u00e1c ph\u00e2n s\u1ed1 $\\dfrac{5}{a}, \\dfrac{7}{a}; \\dfrac{8}{a}$ \u0111\u1ec1u l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n <br\/> \u0110\u00e1p \u00e1n l\u00e0: a $\\in$ {_input_; _input_; _input_}","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Lo\u1ea1i \u0111i c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ec3 t\u1eebng ph\u00e2n s\u1ed1 tr\u00ean kh\u00f4ng t\u1ed1i gi\u1ea3n <br\/> \u0110\u1ec3 $\\dfrac{5}{a}$ t\u1ed1i gi\u1ea3n th\u00ec a kh\u00f4ng nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb n\u00e0o <br\/> \u0110\u1ec3 $\\dfrac{7}{a}$ t\u1ed1i gi\u1ea3n th\u00ec a kh\u00f4ng nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb n\u00e0o <br\/> \u0110\u1ec3 $\\dfrac{8}{a}$ t\u1ed1i gi\u1ea3n th\u00ec a kh\u00f4ng nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb n\u00e0o <br\/> <b> B\u01b0\u1edbc 2: <\/b>K\u1ebft h\u1ee3p c\u00e1c \u0111i\u1ec1u ki\u1ec7n tr\u00ean \u0111\u1ec3 t\u00ecm c\u00e1c gi\u00e1 tr\u1ecb th\u00edch h\u1ee3p c\u1ee7a a \u0111\u1ec3 c\u1ea3 3 ph\u00e2n s\u1ed1 \u0111\u1ec1u t\u1ed1i gi\u1ea3n<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec c\u00e1c ph\u00e2n s\u1ed1 $\\dfrac{5}{a}, \\dfrac{7}{a}; \\dfrac{8}{a}$ \u0111\u1ec1u l\u00e0 t\u1ed1i gi\u1ea3n n\u00ean a $\\neq$ B(5), a $\\neq$ B(7) v\u00e0 a $\\neq$ B(2) (v\u00ec $8 = 2^3$) <br\/> M\u1eb7t kh\u00e1c: $ 12 \\leq a \\leq 21$ <br\/> $\\Rightarrow$ $\\dfrac{5}{a}$ t\u1ed1i gi\u1ea3n khi a $\\neq$ 15, 20 <br\/> $\\dfrac{7}{a}$ t\u1ed1i gi\u1ea3n khi a $\\neq$ 14, 21 <br\/> $\\dfrac{8}{a}$ t\u1ed1i gi\u1ea3n khi a $\\neq$ 12, 14, 16, 18, 20 <br\/> V\u1eady \u0111\u1ec3 $\\dfrac{5}{a}, \\dfrac{7}{a}; \\dfrac{8}{a}$ t\u1ed1i gi\u1ea3n $\\Rightarrow$ a = 13, a = 17, a = 19<br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 13, 17, 19 <\/span> "}]}],"id_ques":1496},{"time":14,"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 a, b bi\u1ebft $\\dfrac{42 : 6}{24 : a} = \\dfrac{7}{b}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. a = 6, b = 6","B. a = 4, b = 6","C. a = 4, b = 4","D. a = 6, b = 4 "],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1","explain":" <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: $\\dfrac{42 : 6}{24 : a} = \\dfrac{7}{b}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1 $\\Rightarrow$ a = 6 <br\/> Thay a = 6 v\u00e0o ta \u0111\u01b0\u1ee3c: $\\dfrac{42 : 6}{24 : 6} = \\dfrac{7}{4} = \\dfrac{7}{b}$ <br\/> $\\Rightarrow$ b = $\\dfrac{4 . 7}{7} = 4$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. a = 6, b = 4 <\/span>","column":2}]}],"id_ques":1497},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"T\u00ecm a, b bi\u1ebft $\\dfrac{54 : a}{45 : 9} = \\dfrac{6}{b}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. a = 9, b = 5","B. a = 5, b = 5","C. a = 5, b = 9","D. a = 9, b = 9 "],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1","explain":" <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: $\\dfrac{54 : a}{45 : 9} = \\dfrac{6}{b}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1 $\\Rightarrow$ a = 9 <br\/> Thay a = 9 v\u00e0o ta \u0111\u01b0\u1ee3c: $\\dfrac{54 : 9}{45 : 9} = \\dfrac{6}{5} = \\dfrac{6}{b}$ <br\/> $\\Rightarrow$ b = $\\dfrac{5 . 6}{6} = 5$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. a = 9, b = 5 <\/span>","column":2}]}],"id_ques":1498},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"T\u00ecm ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ bi\u1ebft a + b = 23, a - b = 5. <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $\\dfrac{a}{b} = \\dfrac{14}{9}$ ","B. $\\dfrac{a}{b} = \\dfrac{23}{5}$ ","C. $\\dfrac{a}{b} = \\dfrac{9}{14}$ ","D. $\\dfrac{a}{b} = \\dfrac{5}{23}$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> V\u00ec b\u00e0i to\u00e1n cho bi\u1ebfn t\u1ed5ng v\u00e0 hi\u1ec7u gi\u1eefa t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 <br\/> N\u00ean b\u00e0i to\u00e1n quy v\u1ec1 t\u00ecm hai s\u1ed1 khi bi\u1ebft t\u1ed5ng v\u00e0 hi\u1ec7u <br\/> S\u1ed1 b\u00e9 = (t\u1ed5ng - hi\u1ec7u) : 2 <br\/> S\u1ed1 l\u1edbn = (t\u1ed5ng + hi\u1ec7u) : 2 <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: a + b = 23, a - b = 5 <br\/> $\\Rightarrow$ a > b, a = $\\dfrac{23 + 5}{2} = 14$ <br\/> $b = \\dfrac{23 - 5}{2} = 9$ <br\/> V\u1eady ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0: $\\dfrac{14}{9}$ <br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. $\\dfrac{a}{b} = \\dfrac{14}{9}$ <\/span>","column":2}]}],"id_ques":1499},{"time":14,"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 ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ bi\u1ebft a + b = 40, a - b = 10. <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. $\\dfrac{a}{b} = \\dfrac{15}{25}$ ","B. $\\dfrac{a}{b} = \\dfrac{5}{15}$ ","C. $\\dfrac{a}{b} = \\dfrac{25}{15}$ ","D. $\\dfrac{a}{b} = \\dfrac{15}{5}$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> V\u00ec b\u00e0i to\u00e1n cho bi\u1ebfn t\u1ed5ng v\u00e0 hi\u1ec7u gi\u1eefa t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 <br\/> N\u00ean b\u00e0i to\u00e1n quy v\u1ec1 t\u00ecm hai s\u1ed1 khi bi\u1ebft t\u1ed5ng v\u00e0 hi\u1ec7u <br\/> S\u1ed1 b\u00e9 = (t\u1ed5ng - hi\u1ec7u) : 2 <br\/> S\u1ed1 l\u1edbn = (t\u1ed5ng + hi\u1ec7u) : 2 <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: a + b = 40, a - b = 10 <br\/> $\\Rightarrow$ a > b, a = $\\dfrac{40 + 10}{2} = 25$ <br\/> $b = \\dfrac{40 - 10}{2} = 15$ <br\/> V\u1eady ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0: $\\dfrac{25}{15}$ <br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $\\dfrac{a}{b} = \\dfrac{25}{15}$ <\/span>","column":2}]}],"id_ques":1500}],"lesson":{"save":0,"level":3}}