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1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200
a) MC :24
\(\frac{1}{3}+\frac{3}{8}-\frac{7}{12}=\frac{1\times8+3\times3-7\times2}{24}=\frac{3}{24}=\frac{1}{8}\)
b)MC : 56
\(\frac{3}{14}+\frac{5}{8}-\frac{1}{2}=\frac{3\times4+5\times7-1\times28}{56}=\frac{19}{56}\)
c) MC: 36
\(\frac{1}{4}-\frac{2}{3}-\frac{11}{18}=\frac{1\times9-2\times12-11\times2}{36}=\frac{-37}{36}\)
d) MC: 312
\(\frac{1}{4}+\frac{5}{12}-\frac{1}{13}-\frac{7}{8}=\frac{1\times78+5\times26-1\times24-7\times39}{312}=\frac{-89}{312}\)
\(\hept{\begin{cases}\frac{x}{3}+\frac{y}{5}=12\\\frac{x}{5}+\frac{y}{7}=8\end{cases}\Rightarrow\hept{\begin{cases}\frac{x}{15}+\frac{y}{25}=\frac{12}{5}\\\frac{x}{15}+\frac{y}{21}=\frac{8}{3}\end{cases}}}\)
\(\Rightarrow\left(\frac{x}{15}+\frac{y}{21}\right)-\left(\frac{x}{15}+\frac{y}{25}\right)=\frac{12}{5}-\frac{8}{3}\)
\(\Rightarrow\frac{y}{21}-\frac{y}{25}=\frac{-4}{15}\)
\(\Rightarrow\frac{4y}{525}=-\frac{4}{15}\Rightarrow\frac{4y}{525}=\frac{-140}{525}\)
\(\Rightarrow y=-35\Rightarrow x=65\)
a) (1,5 . 1,9 - x - 0,5) : 0,25 = 7,5 : 0,125
=> (2,85 - x - 0,5) : 0,25 = 60
=> (2,85 - 0,5) - x = 60 . 0,25
=> 2,35 - x = 15
=> x = 2,35 - 15
=> x = -12,65
Vậy x = -12,65
b) \(1-\left(5\frac{2}{9}+x-7\frac{7}{18}\right)\div2\frac{1}{6}=0\)
\(\Rightarrow\left(5\frac{2}{9}-7\frac{7}{18}+x\right)\div2\frac{1}{6}=1-0\)
\(\Rightarrow\left(\frac{47}{9}-\frac{133}{18}+x\right)\div2\frac{1}{6}=1\)
\(\Rightarrow\frac{-13}{6}+x=2\frac{1}{6}\)
\(\Rightarrow x=2\frac{1}{6}-\frac{-13}{6}\)
\(\Rightarrow x=\frac{13}{6}+\frac{13}{6}\)
\(\Rightarrow x=\frac{26}{6}\)
\(\Rightarrow x=\frac{13}{3}\)
Vậy \(x=\frac{13}{3}\)
c) \(35\left(2\frac{1}{5}-x\right)=32\)
\(\Rightarrow2\frac{1}{5}-x=32\div35\)
\(\Rightarrow\frac{11}{5}-x=\frac{32}{35}\)
\(\Rightarrow x=\frac{11}{5}-\frac{32}{35}\)
\(\Rightarrow x=\frac{9}{7}\)
Vậy \(x=\frac{9}{7}\)
d) \(\frac{4}{3}+\left(x\div2\frac{2}{3}-0,5\right).1\frac{35}{55}=0,6\)
\(\Rightarrow\left(x\div\frac{8}{3}-\frac{1}{2}\right).\frac{18}{11}=\frac{3}{5}-\frac{4}{3}\)
\(\Rightarrow\left(x\div\frac{8}{3}-\frac{1}{2}\right).\frac{18}{11}=\frac{-11}{15}\)
\(\Rightarrow x\div\frac{8}{3}-\frac{1}{2}=\frac{-11}{15}\div\frac{18}{11}\)
\(\Rightarrow x\div\frac{8}{3}-\frac{1}{2}=\frac{-121}{270}\)
\(\Rightarrow x\div\frac{8}{3}=\frac{-121}{270}+\frac{1}{2}\)
\(\Rightarrow x\div\frac{8}{3}=\frac{7}{135}\)
\(\Rightarrow x=\frac{7}{135}.\frac{8}{3}\)
\(\Rightarrow x=\frac{56}{405}\)
Vậy \(x=\frac{56}{405}\)
e) \(1\frac{1}{3}.2\frac{2}{4}\div\frac{5}{6}.1\frac{1}{11}=11-5\div x\)
\(\Rightarrow\frac{4}{3}.\frac{5}{2}\div\frac{5}{6}.\frac{12}{11}=11-5\div x\)
\(\Rightarrow\frac{10}{3}\div\frac{5}{6}.\frac{12}{11}=11-5\div x\)
\(\Rightarrow4.\frac{12}{11}=11-5\div x\)
\(\Rightarrow11-5\div x=\frac{48}{11}\)
\(\Rightarrow5\div x=11-\frac{48}{11}\)
\(\Rightarrow5\div x=\frac{73}{11}\)
\(\Rightarrow x=5\div\frac{73}{11}\)
\(\Rightarrow x=\frac{55}{73}\)
Vậy \(x=\frac{55}{73}\)
a) (1,5 * 1,9 - x - 0,5) : 0,25 = 7,5 : 0,125
(2,85 - x - 0,5) : 0,25 = 60
(2,85 - x - 0,5) = 60 x 0,25
(2,85 - x - 0,5) = 15
2,35 - x = 15
x = 2,35 - 15
x = -12,65
\(\frac{12}{7}:x+\frac{2}{3}=\frac{7}{5}\)
\(\frac{12}{7}:x=\frac{7}{5}-\frac{2}{3}\)
\(\frac{12}{7}:x=\frac{11}{15}\)
\(x=\frac{12}{7}:\frac{11}{15}\)
\(x=\frac{12}{7}x\frac{15}{11}\)
\(x=\frac{180}{77}\)
\(\frac{12}{7}:x+\frac{2}{3}=\frac{7}{5}\)
\(\frac{12}{7}:x=\frac{7}{5}-\frac{2}{3}\)
\(\frac{12}{7}:x=\frac{21}{15}-\frac{10}{15}\)
\(\frac{12}{7}:x=\frac{11}{15}\)
\(x=\frac{12}{7}:\frac{11}{15}\)
\(x=\frac{12}{7}\cdot\frac{15}{11}\)
\(x=\frac{180}{77}\)
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