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a) \(19\times\left(52+38\right)-9\times\left(52+38\right)=\)
\(=\) \(19\times90-9\times90\)
\(=90\times\left(19-9\right)\)
\(=90\times10\)
\(=900\)
b) \(\dfrac{2}{5}\div\dfrac{3}{7}\times\dfrac{3}{7}\div\dfrac{2}{5}+2019=\)
\(=\left(\dfrac{2}{5}\div\dfrac{2}{5}\right)\times\left(\dfrac{3}{7}\div\dfrac{3}{7}\right)+2019\)
\(=1\times1+2019\)
\(=2019\)
\(a)\frac{3}{5}\times\frac{2}{5}+\frac{3}{4}\times\frac{3}{5}\)
\(=\frac{3}{5}\times\left(\frac{2}{5}+\frac{3}{4}\right)\)
\(=\frac{3}{5}\times\left(\frac{8}{20}+\frac{15}{20}\right)\)
\(=\frac{3}{5}\times\frac{23}{20}\)
\(=\frac{69}{100}\)
\(b)\frac{5}{9}\times\frac{7}{3}\times\frac{9}{5}\)
\(=\left(\frac{5}{9}\times\frac{9}{5}\right)\times\frac{7}{3}\)
\(=1\times\frac{7}{3}\)
\(=\frac{7}{3}\)
`( 9 xx 6 xx 5 xx 7 )/( 19 xx 7 xx 2 xx 3 )`
`= ( 9 xx 2 xx 3 xx 7 xx 5 )/( 19 xx 7 xx 2 xx 3 )`
`= (9xx5)/19`
`= 45/19`
\(a.60\times\left(\frac{7}{12}+\frac{4}{15}\right)\)
\(=60\times\left(\frac{35}{60}+\frac{16}{60}\right)\)
\(=60\times\frac{51}{60}\)
\(=51\)
\(b.\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times\frac{8}{9}\)
\(=\frac{1\times2\times3\times4\times5\times6\times7\times8}{2\times3\times4\times5\times6\times7\times8\times9}\)
\(=\frac{1}{9}\)
2/5 x 2/7 x 2/5 x 5/7 x 9
= 2/5 x (2/7 x 5/7) x 9
= 2/5 x 10/49 x 9
= 2 x 2/49 x 9
= 4/49 x 9
= 36/49
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