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\(\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+...+\frac{1}{8}\times\frac{1}{9}=\frac{1}{2\times3}+\frac{1}{3\times4}+....+\frac{1}{8\times9}\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)
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a) \(\dfrac{11}{3}-\dfrac{2}{3}\times\dfrac{5}{6}\)
\(=\dfrac{11}{3}-\dfrac{10}{18}\)
\(=\dfrac{11}{3}-\dfrac{5}{9}\)
\(=\dfrac{33}{9}-\dfrac{5}{9}\)
\(=\dfrac{28}{9}\)
b) \(\dfrac{13}{2}+\dfrac{7}{6}:\dfrac{2}{3}\)
\(=\dfrac{13}{2}+\dfrac{7}{6}\cdot\dfrac{3}{2}\)
\(=\dfrac{13}{2}+\dfrac{7}{4}\)
\(=\dfrac{26}{4}+\dfrac{7}{4}\)
\(=\dfrac{33}{4}\)
c) \(\dfrac{28}{9}-\dfrac{3}{4}+\dfrac{1}{3}\)
\(=\dfrac{28}{9}+\dfrac{3}{9}-\dfrac{3}{4}\)
\(=\dfrac{31}{9}-\dfrac{3}{4}\)
\(=\dfrac{124}{36}-\dfrac{27}{36}\)
\(=\dfrac{97}{36}\)
d) \(\dfrac{5}{8}:\dfrac{2}{3}\times\dfrac{1}{5}\)
\(=\dfrac{5}{8}\times\dfrac{3}{2}\times\dfrac{1}{5}\)
\(=\dfrac{15}{80}\)
\(=\dfrac{3}{16}\)
a) \(\dfrac{11}{3}-\dfrac{2}{3}\times\dfrac{5}{6}=\dfrac{11}{3}-\dfrac{5}{9}=\dfrac{28}{9}\)
b) \(\dfrac{13}{2}+\dfrac{7}{6}:\dfrac{2}{3}=\dfrac{13}{2}+\dfrac{7}{6}\times\dfrac{3}{2}=\dfrac{13}{2}+\dfrac{7}{4}=\dfrac{33}{4}\)
c) \(\dfrac{28}{9}-\dfrac{3}{4}+\dfrac{1}{3}=\dfrac{97}{36}\)
d) \(\dfrac{5}{8}:\dfrac{2}{3}\times\dfrac{1}{5}=\dfrac{5}{8}\times\dfrac{3}{2}\times\dfrac{1}{5}=\dfrac{3}{16}\)
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x- \(\dfrac{1}{2}\) = 6 x \(\dfrac{1}{24}\)
x- 0,5 = 6 x \(\dfrac{1}{24}\)
x- 0,5 = \(\dfrac{1}{4}\)
x- 0,5 = 0,25
x = 0,25+0,5
x =0,3
x - 1/2 = 6 x 1/24
x - 0,5 = 1/4
x - 0,5 = 0,25
x = 0,25 + 0,5
x = 0,3
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\(1\frac{1}{3}.1\frac{1}{4}.1\frac{1}{5}.1\frac{1}{6}.1\frac{1}{7}.1\frac{1}{8}=\frac{4}{3}.\frac{5}{4}.\frac{6}{5}.\frac{7}{6}.\frac{8}{7}.\frac{9}{8}=\frac{9}{3}=3\)
\(\frac{1}{3}\times\frac{1}{6}\times\frac{1}{9}=\frac{1\times1\times1}{3\times6\times9}=\frac{1}{162}\)
\(\frac{1}{3}\times\frac{1}{6}:\frac{1}{9}=\frac{1}{3}\times\frac{1}{6}\times\frac{9}{1}=\frac{1\times1\times9}{3\times6\times1}=\frac{9}{18}=\frac{1}{2}\)
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