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\(-2\dfrac{1}{4}.\)\(\left(3\dfrac{5}{12}-1\dfrac{2}{9}\right)\)
=\(\dfrac{-9}{4}\).\(\left(\dfrac{41}{12}-\dfrac{11}{9}\right)\)
=\(\dfrac{-9}{4}.\dfrac{41}{12}-\dfrac{-9}{4}.\dfrac{11}{9}\)
=\(\dfrac{-123}{16}-\dfrac{-11}{4}\)
=\(\dfrac{-123}{16}-\dfrac{-44}{16}\)
=\(\dfrac{-79}{16}\)
\(\left(-25\%+0,75+\dfrac{7}{12}\right)\div\left(-2\dfrac{1}{8}\right)\)
=\(\left(\dfrac{-1}{4}+\dfrac{3}{4}+\dfrac{7}{12}\right)\div\left(\dfrac{-17}{8}\right)\)
=\(\left(\dfrac{-3}{12}+\dfrac{9}{12}+\dfrac{7}{12}\right).\dfrac{-8}{17}\)
=\(\dfrac{13}{12}.\dfrac{-8}{17}=\dfrac{-26}{51}\)
\(C=\dfrac{-5}{7}+\dfrac{-2}{7}+\dfrac{3}{4}+\dfrac{1}{4}+\dfrac{-1}{5}=-1+1-\dfrac{1}{5}=\dfrac{-1}{5}\)
A,
\(\left(7\dfrac{4}{9}+3\dfrac{7}{11}\right)-3\dfrac{4}{9}=7\dfrac{4}{9}+3\dfrac{7}{11}-3\dfrac{4}{9}\)
\(=7\dfrac{4}{9}-3\dfrac{4}{9}+3\dfrac{7}{11}=4+3\dfrac{7}{11}=7\dfrac{7}{11}\)
B,
\(5\dfrac{2}{7}.\dfrac{8}{11}+5\dfrac{2}{7}.\dfrac{5}{11}-5\dfrac{2}{7}.\dfrac{2}{11}=5\dfrac{2}{7}.\left(\dfrac{8}{11}+\dfrac{5}{11}-\dfrac{2}{11}\right)\)
\(=5\dfrac{2}{7}.1=5\dfrac{2}{7}\)
a) x.(\(\dfrac{6}{7}\)+\(\dfrac{5}{6}\))=\(\dfrac{3}{4}\)
x.\(\dfrac{71}{42}\)=\(\dfrac{3}{4}\)
x=\(\dfrac{3}{4}\):\(\dfrac{71}{42}\)
x=\(\dfrac{63}{142}\)
a.\(\dfrac{6}{7}x+\dfrac{5}{6}x=\dfrac{3}{4}\)
\(x.\left(\dfrac{6}{7}+\dfrac{5}{6}\right)=\dfrac{3}{4}\)
\(x.\dfrac{71}{42}=\dfrac{3}{4}\)
\(x=\dfrac{3}{4}:\dfrac{71}{42}\)
\(x=\dfrac{63}{142}\)
b\(\dfrac{5}{4}-\dfrac{3}{5}:x=1\dfrac{1}{3}\)
\(\dfrac{3}{5}:x=\dfrac{5}{4}-1\dfrac{1}{3}\)
\(\dfrac{3}{5}:x=\dfrac{-1}{12}\)
\(x=\dfrac{3}{5}:\dfrac{-1}{12}\)
\(x=\dfrac{-36}{5}\)
c. \(\left(\dfrac{4}{7}x-\dfrac{1}{3}\right):3\dfrac{1}{2}=0,5\)
\(\left(\dfrac{4}{7}x-\dfrac{1}{3}\right)=0,5:3\dfrac{1}{2}\)
\(\dfrac{4}{7}x-\dfrac{1}{3}=\dfrac{1}{7}\)
\(\dfrac{4}{7}x=\dfrac{1}{7}+\dfrac{1}{3}\)
\(\dfrac{4}{7}x=\dfrac{10}{21}\)
\(x=\dfrac{10}{21}:\dfrac{4}{7}\)
\(x=\dfrac{5}{6}\)
d.\(\dfrac{4}{5}-\dfrac{2}{3}x=1\dfrac{1}{4}+2,5x\)
\(\dfrac{4}{5}-\left(\dfrac{2}{3}x-2,5x\right)=1\dfrac{1}{4}\)
\(\dfrac{4}{5}-\dfrac{-11}{6}x=1\dfrac{1}{4}\)
\(\dfrac{-11}{6}x=\dfrac{4}{5}-1\dfrac{1}{4}\)
\(\dfrac{-11}{6}x=\dfrac{-9}{20}\)
\(x=\dfrac{-9}{20}:\dfrac{-11}{6}\)
\(x=\dfrac{27}{110}\)
có sai sót j xin bn thông cảm !
câu a
\(\left(5\dfrac{7}{9}+2\dfrac{3}{11}\right)-\left(-1\dfrac{8}{11}+3\dfrac{7}{9}\right)\)
= \(5\dfrac{7}{9}+2\dfrac{3}{11}+1\dfrac{8}{11}-3\dfrac{7}{9}\)
= \(\left(5\dfrac{7}{9}-3\dfrac{7}{9}\right)+\left(2\dfrac{3}{11}+1\dfrac{8}{11}\right)\)
= \(2+3\dfrac{11}{11}\)
= \(2+3+1\)
= \(6\)
câu b
\(\left(2\dfrac{7}{19}-3\dfrac{8}{9}\right)-\left(1\dfrac{7}{19}-2\dfrac{1}{9}\right)\)
= \(2\dfrac{7}{19}-3\dfrac{8}{9}-1\dfrac{7}{19}+2\dfrac{1}{9}\)
= \(\left(2\dfrac{7}{19}-1\dfrac{7}{19}\right)-\left(3\dfrac{8}{9}-2\dfrac{1}{9}\right)\)
= \(1-1\dfrac{7}{9}\)
= \(\dfrac{-7}{9}\)
\(\dfrac{-1}{12},\dfrac{-3}{4},\dfrac{2}{9},\dfrac{7}{6}\)
`1/5 . 4/7 + 3/7 . 1/5 -1/5`
`=1/5 . 4/7 + 3/7 . 1/5 -1/5 . 1`
`=1/5 . ( 4/7+3/7-1)`
`=1/5 . ( 7/7-1)`
`= 1/5 . 0`
`=0`
\(\dfrac{1}{5}\times\dfrac{4}{7}+\dfrac{3}{7}\times\dfrac{1}{5}-\dfrac{1}{5}=\dfrac{1}{5}\times\left(\dfrac{4}{7}+\dfrac{3}{7}-1\right)=\dfrac{1}{5}\times0=0\)
Lời giải:
$S=\frac{1}{7^2}+\frac{2}{7^3}+\frac{3}{7^4}+...+\frac{69}{7^{70}}$
$7S=\frac{1}{7}+\frac{2}{7^2}+\frac{3}{7^3}+...+\frac{69}{7^{69}}$
$6S=7S-S=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+....+\frac{1}{7^{69}}-\frac{69}{7^{70}}$
$42S=1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{68}}-\frac{69}{7^{69}}$
$\Rightarrow 42S-6S=(1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{68}}-\frac{69}{7^{69}})-(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+....+\frac{1}{7^{69}}-\frac{69}{7^{70}})$
$\Rightarrow 36S=1-\frac{69}{7^{69}}-\frac{1}{7^{69}}+\frac{69}{7^{70}}$
Hay $36S=1-\frac{69.7-7-69}{7^{70}}=1-\frac{407}{7^{70}}$
$\Rightarrow S=\frac{1}{36}(1-\frac{407}{7^{70}})$