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b ) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}=\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
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) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
a,
\(x+\frac{7}{15}=1\frac{1}{20}\)
\(x+\frac{7}{15}=\frac{21}{20}\)
\(x=\frac{21}{20}-\frac{7}{15}=\frac{63}{60}-\frac{28}{60}\)
\(x=\frac{35}{60}=\frac{7}{12}\)
b,
\(\left[3\frac{1}{2}-x\right]\cdot1\frac{1}{4}=\frac{15}{16}\)
\(\left[\frac{7}{2}-x\right]\cdot\frac{5}{4}=\frac{15}{16}\)
\(\frac{7}{2}-x=\frac{15}{16}:\frac{5}{4}=\frac{3}{4}\)
\(\frac{7}{2}-x=\frac{3}{4}\Rightarrow x=\frac{7}{2}-\frac{3}{4}\)
\(x=\frac{11}{4}\)
c,
\(1\frac{1}{5}x+\frac{2}{3}x=\frac{56}{125}\Leftrightarrow\frac{6}{5}x+\frac{2}{3}x=\frac{56}{125}\)
\(\frac{28}{15}x=\frac{56}{125}\Rightarrow x=\frac{6}{25}\)
d,
\(60\%x+0,4x+x:3=2\)
\(\frac{3}{5}x+\frac{2}{5}x+\frac{1}{3}x=2\)
\(\frac{4}{3}x=2\Rightarrow x=\frac{3}{2}\)
Nguyễn Anh Thiện
a)
x + \(\frac{7}{15}\) = \(1\frac{1}{20}\)
X + \(\frac{7}{15}=\frac{21}{20}\)
X \(=\frac{21}{20}-\frac{7}{15}\)
X \(=\frac{63}{60}-\frac{28}{60}=\frac{35}{60}=\frac{7}{12}\)
^^ Học tốt !
\(\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{2\text{x}3+4\text{x}6+6\text{x}9+8\text{x}12}\)
\(\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{2\text{x}3+4\text{x}6+6\text{x}9+8\text{x}12}\)
\(=\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{\text{1x}2\text{x}3+2\text{x}4\text{x}3+3\text{x}6\text{x}3+4\text{x}8\text{x}3}\)
\(=\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{3\left(1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8\right)}\)
\(=\frac{1}{3}\)
Ta có: \(\frac{1.2+2.4+3.6+4.8}{2.3+4.6+6.9+8.12}=\frac{1.2}{2.3}+\frac{2.4}{4.6}+\frac{3.6}{6.9}+\frac{4.8}{8.12}.\)
\(=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{1}{3}.4=\frac{4}{3}\)
\(\frac{2}{3\times5}\times a+\frac{2}{5\times7}\times a+...+\frac{2}{13\times15}\times a=\frac{28}{15}\)
=> \(\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}\right)\times x=\frac{28}{15}\)
=> \(\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\times x=\frac{28}{15}\)
=> \(\left(\frac{1}{3}-\frac{1}{15}\right)\times x=\frac{28}{15}\)
=> \(\frac{4}{15}\times x=\frac{28}{15}\)
=> \(x=\frac{28}{15}:\frac{4}{15}\)
-> \(x=7\)
\(\frac{2}{3\times5}\times a+\frac{2}{5\times7}\times a+...+\frac{2}{13\times15}\times a=\frac{28}{15}\)
\(a\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}\right)=\frac{28}{15}\)
\(a\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)=\frac{28}{15}\)
\(a\times\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{28}{15}\)
\(a\times\frac{4}{15}=\frac{28}{15}\)
\(a=\frac{28}{15}:\frac{4}{15}\)
\(a=\frac{28}{15}\times\frac{25}{4}\)
\(a=\frac{28}{4}=7\)