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10 tháng 7 2019
\(\frac{3}{2}\cdot\frac{17}{5}+\frac{19}{5}\cdot\frac{3}{2}+\frac{3}{2}\cdot\frac{1}{5}\)
\(=\frac{3}{2}\left[\frac{17}{5}+\frac{19}{5}+\frac{1}{5}\right]\)
\(=\frac{3}{2}\cdot\frac{37}{5}=\frac{111}{10}\)
27 tháng 7 2015
b ) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}=\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
N
11 tháng 6 2018
215 - 15 x { 25 - 15 : [ 3 x 45 - 3 x ( 50 - 2 x 3 ) ] }
= 215 - 15 x { 25 - 15 : [ 3 x 45 - 3 x 44 ] }
= 215 - 15 x { 25 - 15 : 3 }
= 215 - 15 x 20
= 215 - 300
= -85
b) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
MA
14 tháng 10 2016
a ) \(1\frac{1}{2}+2\frac{1}{3}+3\frac{1}{6}-5\)
\(=\frac{3}{2}+\frac{7}{3}+\frac{19}{6}-\frac{5}{1}\)
\(=\frac{9}{6}+\frac{14}{6}+\frac{19}{6}-\frac{30}{6}\)
\(=\frac{23}{6}+\frac{19}{6}-\frac{30}{6}\)
\(=\frac{42}{6}-\frac{30}{6}\)
\(=\frac{12}{6}=2\)
b ) \(2\frac{2}{3}\times3\frac{3}{4}\div4\frac{4}{5}\)
\(=\frac{8}{3}\times\frac{15}{4}\div\frac{24}{5}\)
\(=\frac{120}{12}\div\frac{24}{5}\)
\(=\frac{120}{12}\times\frac{5}{24}\)
\(=\frac{600}{288}=\frac{25}{12}\)
c ) \(4\frac{1}{5}+5\frac{1}{3}-2\frac{2}{3}\times3\frac{1}{5}+\frac{9}{25}\div\frac{9}{20}\)
\(=\frac{21}{5}+\frac{16}{3}-\frac{8}{3}\times\frac{16}{5}+\frac{9}{25}\div\frac{9}{20}\)
\(=\frac{63}{15}+\frac{80}{15}-\frac{128}{15}+\frac{9}{25}\times\frac{20}{9}\)
\(=\frac{143}{15}-\frac{128}{15}+\frac{180}{225}\)
\(=\frac{15}{15}+\frac{12}{15}\)
\(=\frac{27}{15}=\frac{9}{5}\)
30 tháng 8 2020
1.Chuyển các hỗn số sau thành phân số:
\(2\frac{1}{3}\)= \(\frac{7}{3}\)
\(4\frac{2}{5}=\frac{22}{5}\)
\(3\frac{1}{4}=\frac{12}{4}\)
\(9\frac{5}{7}=\frac{68}{7}\)
\(10\frac{3}{10}=\frac{103}{10}\)
30 tháng 8 2020
2.Chuyển các hỗn số thành phân số rồi thực hiện phép tính:
\(\alpha.\)\(2\frac{1}{3}+4\frac{1}{3}=\frac{7}{3}+\frac{13}{3}=\frac{20}{3}\)
b. \(9\frac{2}{7}+5\frac{3}{7}=\frac{65}{7}+\frac{38}{7}=\frac{103}{7}\)
c. \(10\frac{3}{10}+4\frac{7}{10}=\frac{103}{10}+\frac{47}{10}=\frac{150}{10}\)=\(15\)
d. \(2\frac{1}{3}+5\frac{1}{4}=\frac{7}{3}+\frac{21}{4}=\frac{21}{12}+\frac{63}{12}=\frac{84}{12}\)= 7
e. \(3\frac{2}{5}+2\frac{1}{7}=\frac{17}{5}+\frac{15}{7}=\frac{119}{35}+\frac{75}{35}=\frac{194}{35}\)
g. \(8\frac{1}{6}+2\frac{1}{7}=\frac{49}{6}+\frac{15}{7}=\frac{342}{42}+\frac{90}{42}=\frac{432}{42}\)
8 tháng 6 2015
\(3\frac{2}{5}=\frac{3\cdot5+2}{5}=\frac{17}{5}\)
\(2\frac{1}{7}=\frac{2\cdot7+1}{7}=\frac{15}{7}\)
\(8\frac{1}{6}=\frac{8\cdot6+1}{6}=\frac{49}{6}\)
\(2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}\)
\(3\frac{2}{5}\cdot2\frac{1}{7}=\frac{17}{5}\cdot\frac{15}{7}=\frac{51}{7}\)
\(8\frac{1}{6}:2\frac{1}{2}=\frac{49}{6}:\frac{5}{2}=\frac{49}{6}\cdot\frac{2}{5}=\frac{49}{15}\)
8 tháng 6 2015
3/2+5/3
=19/6
8/3-11/7
=23/21
8/3*21/4
=168/12=14
7/2:9/4
=7/2*4/9
=28/18=10//9
8 tháng 6 2015
\(1\frac{1}{2}+1\frac{1}{3}=\frac{3}{2}+\frac{4}{3}=\frac{9}{6}+\frac{8}{6}=\frac{17}{6}\)
\(2\frac{2}{3}-1\frac{4}{7}=\frac{8}{3}-\frac{11}{7}=\frac{56}{21}-\frac{33}{21}=\frac{23}{21}\)
\(2\frac{2}{3}\cdot5\frac{1}{4}=\frac{8}{3}.\frac{21}{4}=14\)
\(3\frac{1}{2}:2\frac{1}{4}=\frac{7}{2}:\frac{9}{4}=\frac{7}{2}.\frac{4}{9}=\frac{14}{9}\)
AK
1 tháng 6 2018
Dấu \(.\)là dấu nhân
\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{2}.\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}+\frac{2}{195}\right)\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{7}{15}\)
~ Ủng hộ nhé
1 tháng 6 2018
Đặt \(A=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
Suy ra ; \(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{13}-\frac{1}{15}\)
\(=1-\frac{1}{15}=\frac{14}{15}\)
=> A = \(\frac{14}{15}:2=\frac{14}{15}.\frac{1}{2}=\frac{7}{15}\)
\(1+\frac{1+\frac{2}{2}}{1+\frac{2}{3}}=1+\frac{2}{1+\frac{2}{\frac{5}{3}}}=1+\frac{2}{1+2\cdot\frac{3}{5}}\)
\(=1+\frac{2}{1+\frac{6}{5}}=1+\frac{2}{\frac{11}{5}}=1+2\cdot\frac{5}{11}=1+\frac{10}{11}\)
\(=\frac{21}{11}\)
\(1+\frac{1+\frac{2}{2}}{1+\frac{2}{3}}\)
\(=1+\frac{2}{\frac{5}{3}}\)
\(=1+\frac{6}{5}\)
\(=\frac{11}{5}\)