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a: =8/15x1/4=2/15
b: \(=\dfrac{5}{3}\cdot\dfrac{4}{5}\cdot\dfrac{6}{7}=\dfrac{24}{21}=\dfrac{8}{7}\)
c: \(=\dfrac{2}{5}\left(\dfrac{3}{7}+\dfrac{4}{7}\right)=\dfrac{2}{5}\)
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\(\frac{1}{2}\cdot\frac{18}{14}+\frac{1}{2}\cdot\frac{3}{14}-\frac{1}{2}\cdot\frac{7}{14}\)
\(=\frac{1}{2}\left(\frac{18}{14}+\frac{3}{14}-\frac{7}{14}\right)\)
\(=\frac{1}{2}\cdot1=\frac{1}{2}\)
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\(a.60\times\left(\frac{7}{12}+\frac{4}{15}\right)\)
\(=60\times\left(\frac{35}{60}+\frac{16}{60}\right)\)
\(=60\times\frac{51}{60}\)
\(=51\)
\(b.\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times\frac{8}{9}\)
\(=\frac{1\times2\times3\times4\times5\times6\times7\times8}{2\times3\times4\times5\times6\times7\times8\times9}\)
\(=\frac{1}{9}\)
1/2 x 1/3 x 1/7 + 1/2 x 1/3 x 2/7 + 1/2 x 1/3 x 4/7
= 1/2 x 1/3 x (1/7 + 2/7 + 4/7)
= 1/6 x 1
= 1/6
\(\dfrac{1}{2}\times\dfrac{1}{3}\times\dfrac{1}{7}+\dfrac{1}{2}\times\dfrac{1}{3}\times\dfrac{2}{7}+\dfrac{1}{2}\times\dfrac{1}{3}\times\dfrac{4}{7}\)
\(=\dfrac{1}{2}\times\dfrac{1}{3}\times\left(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{4}{7}\right)\)
\(=\dfrac{1}{2}\times\dfrac{1}{3}\times1=\dfrac{1}{6}\)