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\(\frac{\left(\frac{3}{15}+\frac{1}{4}+\frac{7}{20}\right)\times\frac{17}{49}}{5\frac{1}{3}+\frac{2}{5}}=\frac{\left(\frac{1}{5}+\frac{1}{4}+\frac{7}{20}\right)\times\frac{17}{49}}{\frac{16}{3}+\frac{2}{5}}\)
=\(\frac{\left(\frac{4}{20}+\frac{5}{20}+\frac{7}{20}\right)\times\frac{17}{49}}{\frac{80}{15}+\frac{6}{15}}=\frac{\frac{16}{20}\times\frac{17}{49}}{\frac{86}{15}}=\frac{\frac{4}{5}\times\frac{17}{49}}{\frac{86}{15}}\)
=\(\frac{68}{245}\times\frac{15}{86}=\frac{102}{2107}\)
Bài 2:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2003}{2004}\)
\(=\frac{1}{2004}\)
P = \(\left(\frac{13}{84}\times1\frac{2}{5}-2\frac{1}{2}\times\frac{7}{180}\right):2\frac{7}{18}+4\frac{1}{2}\times\frac{1}{10}\)
P = ( 13/84 x 7/5 - 5/2 x 7/180 ) : 43/18 + 9/2 x 1/10
P = ( 13/60 - 7/72 ) : 43/18 + 9/20
P = 43/360 : 43/18 + 9/20
P = 43/360 x 18/43 + 9/20
P = 1/20 + 9/20
P = 1/2
\(\frac{6:\frac{3}{5}-1\frac{1}{6}\times\frac{6}{7}}{4\frac{1}{5}\times\frac{10}{11}+5\frac{2}{11}}\)
\(=\frac{\frac{6}{1}:\frac{3}{5}-\frac{7}{6}\times\frac{6}{7}}{\frac{21}{5}\times\frac{10}{11}\times\frac{57}{11}}\)
\(=\frac{\frac{6}{1}\times\frac{5}{3}-1}{\frac{210}{55}+\frac{57}{11}}\)
\(=\frac{\frac{30}{3}-1}{\frac{42}{11}+\frac{57}{11}}\)
\(=\frac{10-1}{\frac{99}{11}}\)
\(=\frac{9}{9}\)
\(=1\)
\(6:\frac{3}{5}-1\frac{1}{6}\)X \(\frac{6}{7}\) \(4\frac{1}{5}\)X \(\frac{10}{11}+5\frac{2}{11}\)
\(=\frac{33}{5}-\frac{7}{6}\)X \(\frac{6}{7}\) \(=\) \(\frac{21}{5}\)X \(\frac{10}{11}+\frac{57}{11}\)
\(=\frac{33}{5}-1\) \(=\frac{42}{11}+\frac{57}{11}\)
\(=\frac{28}{5}\) \(=\frac{99}{11}=9\)
\(\frac{\left(\frac{3}{15}+\frac{1}{4}+\frac{7}{20}\right)\times\frac{17}{49}}{5\frac{1}{3}+\frac{2}{5}}\)
\(=\frac{\left(\frac{12}{60}+\frac{15}{60}+\frac{21}{60}\right)\times\frac{17}{49}}{\frac{16}{3}\times\frac{2}{5}}\)
\(=\frac{\frac{48}{60}\times\frac{17}{49}}{\frac{80}{15}+\frac{6}{15}}\)
\(=\frac{\frac{816}{2940}}{\frac{86}{15}}\)
\(=\frac{816}{2940}:\frac{86}{15}\)
\(=\frac{816}{2940}\times\frac{15}{86}\)
\(=\frac{68}{245}\times\frac{15}{86}\)
\(=\frac{102}{2107}\)