\(\frac{28}{700}\) = \(28\cdot\frac{28\cdot}{700\cdot}\)
Chọn dấu " "=", " \( \ne \) " thích hợp cho dấu “?” :
a) \(\frac{{28}}{9} \cdot 0,7 + \frac{{28}}{9} \cdot 0,5\) ? \(\frac{{28}}{9} \cdot (0,7 + 0,5)\);
b) \(\frac{{36}}{{13}}:4 + \frac{{36}}{{13}}:9\) ? \(\frac{{36}}{{13}}:(4 + 9)\).
a)
\(\frac{{28}}{9} \cdot 0,7 + \frac{{28}}{9} \cdot 0,5 = \frac{{28}}{9}.\left( {0,7 + 0,5} \right)\)
b)
\(\begin{array}{l}\frac{{36}}{{13}}:4 + \frac{{36}}{{13}}:9\\ = \frac{{36}}{{13}}.\frac{1}{4} + \frac{{36}}{{13}}.\frac{1}{9}\\ = \frac{{36}}{{13}}.\left( {\frac{1}{4} + \frac{1}{9}} \right)\\ = \frac{{36}}{{13}}.\frac{{13}}{{36}} = 1\end{array}\)
\(\begin{array}{l}\frac{{36}}{{13}}:(4 + 9)\\ = \frac{{36}}{{13}}:13\\ = \frac{{36}}{{13}}.\frac{1}{{13}}\\ = \frac{{36}}{{169}}\end{array}\)
Suy ra \(\frac{{36}}{{13}}:4 + \frac{{36}}{{13}}:9\) \( \ne \) \(\frac{{36}}{{13}}:(4 + 9)\).
\(\left[1-\frac{1}{21}\right]\cdot\left[1-\frac{1}{28}\right]\cdot\left[1-\frac{1}{36}\right]\cdot\cdot\cdot\cdot\cdot\cdot\left[1-\frac{1}{1326}\right]\)
bạn nào làm được cho link
\(\left[1-\frac{1}{21}\right]\times\left[1-\frac{1}{28}\right]\times\left[1-\frac{1}{36}\right]\times...\times\left[1-\frac{1}{1326}\right]\)
\(=\frac{20}{21}\times\frac{27}{28}\times\frac{35}{36}\times...\times\frac{1325}{1326}\)
\(=\frac{40}{42}\times\frac{54}{56}\times\frac{70}{72}\times...\times\frac{2650}{2652}\)
\(=\frac{5\times8}{6\times7}\times\frac{6\times9}{7\times8}\times\frac{7\times10}{8\times9}\times...\times\frac{50\times53}{51\times52}\)
\(=\frac{5\times6\times7\times...\times50}{6\times7\times8\times...\times51}\times\frac{8\times9\times10\times...\times53}{7\times8\times9\times...\times52}\)
\(=\frac{5}{51}\times\frac{53}{7}\)
\(=\frac{265}{357}\)
= 20/21 . 27/28 . 35/36 . ...... 1325/1326
= 2/2(20/21 . 27/28 . 35/36 . ...... 1325/1326)
= 40/42. 54/56 . 70/72 ......2650/2652
= 5.8 / 6.7 . 6.9/ 7.8 . 7.10/8.9 ..... 50.53/51.52
.......Sau đọc t cũng k hiểu nữa
Nguồn: của bn Thành :>>>>>
a) \(\left(-\frac{40}{51}\cdot0,32\cdot\frac{17}{20}\right):\frac{64}{75}\)
b) \(-\frac{10}{11}\cdot\frac{8}{9}+\frac{7}{18}\cdot\frac{10}{11}\)
c) \(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{11}{28}+\frac{29}{42}:\frac{1}{28}-8\)
a ) \(\left(-\frac{40}{51}.0,32.\frac{17}{20}\right):\frac{64}{75}\)
\(=\left(-\frac{40}{51}.\frac{8}{25}.\frac{17}{20}\right):\frac{64}{75}\)
\(=\left(\frac{-40.8.17}{51.25.20}\right):\frac{64}{75}\)
\(=\left(\frac{-16}{75}\right).\frac{75}{64}\)
\(=\frac{-1}{1}.\frac{1}{4}=-\frac{1}{4}\)
\(\left(1-\frac{1}{15}\right)\cdot\left(1-\frac{1}{21}\right)\cdot\left(1-\frac{1}{28}\right)\cdot......\cdot\left(1-\frac{1}{210}\right)\)
#)Giải :
\(\left(1-\frac{1}{15}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)...\left(1-\frac{1}{210}\right)=\frac{14}{15}\times\frac{20}{21}\times\frac{27}{28}\times...\times\frac{209}{210}\)
\(=\frac{28}{30}\times\frac{40}{42}\times\frac{54}{56}\times...\times\frac{418}{420}=\frac{4\times7}{5\times6}\times\frac{5\times8}{6\times7}\times\frac{6\times9}{7\times8}\times...\times\frac{19\times22}{20\times21}\)
\(=\frac{4\times5\times6\times...\times19}{5\times6\times7\times...\times20}\times\frac{7\times8\times9\times...\times22}{6\times7\times8\times...\times21}=\frac{4}{20}\times\frac{22}{6}=\frac{11}{15}\)
\(\left(1-\frac{1}{15}\right).\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right).....\left(1-\frac{1}{210}\right)\)
\(=\left(\frac{15}{15}-\frac{1}{15}\right).\left(\frac{21}{21}-\frac{1}{21}\right).\left(\frac{28}{28}-\frac{1}{28}\right).....\left(\frac{210}{210}-\frac{1}{210}\right)\)
\(=\frac{14}{15}.\frac{20}{21}.\frac{27}{28}....\frac{209}{210}\)
\(=\frac{2.7}{3.5}.\frac{5.4}{7.3}.\frac{3.9}{4.7}....\frac{11.19}{21.10}\)
\(=\frac{2}{3}.\frac{19}{10}\)
\(=\frac{19}{15}\)
Tính \(P=\left(1-\frac{1}{21}\right)\cdot\left(1-\frac{1}{28}\right)\cdot\left(1-\frac{1}{36}\right)\cdot...\cdot\left(1-\frac{1}{1326}\right)\)
\(=\frac{40}{a-20}=\frac{50}{b-68}=\frac{28}{c-21}a\cdot b\cdot c=22400\)
Tính
A=\(\left(1-\frac{1}{21}\right)\cdot\left(1-\frac{1}{28}\right)\cdot\left(1-\frac{1}{36}\right)\cdot....\cdot\left(1-\frac{1}{1326}\right)\)
B=\(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)\cdot....\cdot\left(1+\frac{1}{99\cdot101}\right)\)
Mình mong ai đo trả lời giúp mình:
Tinh bằng cách thuận tiện
\(\frac{9}{25}\cdot\frac{5}{7}+\frac{6}{25}\cdot\frac{20}{28}+2\cdot\frac{1}{5}:\frac{7}{5}-\frac{3}{7}-\frac{2}{7}\)
\(\frac{-15}{14}\cdot-\frac{28}{45}\)
\(\frac{-15}{14}.\frac{-28}{45}\)
\(=\frac{15.28}{14.15}=\frac{14.15.2}{14.15}=2\)
\(\frac{-15}{14}\).\(\frac{-28}{45}\)=\(\frac{-15.\left(-28\right)}{14.15}\)=\(\frac{-1.\left(-2\right)}{1.3}\)=\(\frac{3}{3}\)=1