a)\(\frac{16x25+44\text{x}100}{29\text{x}96+142\text{x}48}\)

=\(\frac{4\text{x}4\text{x}25+11\text{x}4\text{x}4\text{x}25}{29\text{x}2\text{x}48+71\text{x}\text{ }2\text{x}48}\)

=\(\frac{\left(1+11\right)x4\text{x}4\text{x}25}{\left(29+71\right)x2\text{x}48}\)

=\(\frac{12\text{x}4\text{x}100}{100\text{x}2\text{x}48}\)

=\(\frac{48\text{x}100}{48\text{x}100\text{x}2}\)

=\(\frac{1}{2}\)

\(\frac{369}{656}\)

\(\frac{64\times50+44\times100}{27\times38+146\times19}\)

\(=\frac{32\times2\times50+44\times100}{27\times38+73\times2\times19}\)

\(=\frac{32\times100+44\times100}{27\times38+73\times38}\)

\(=\frac{\left(32+44\right)\times100}{\left(27+73\right)\times38}\)

\(=\frac{76\times100}{100\times38}\)

\(=\frac{38\times2\times100}{100\times38}\)

\(=2\)

đó là cách thuận tiện nhất

      \(\frac{64\times50+44\times100}{27\times38+146\times19}\)

\(=\frac{32\times2\times50+44\times100}{27\times38+73\times2\times19}\)

\(=\frac{32\times100+44\times100}{27\times38+73\times38}\)

\(=\frac{\left(32+44\right)\times100}{\left(27+73\right)\times38}\)

\(=\frac{76\times100}{100\times38}\)

\(=\frac{76}{38}\)

\(=2\)

       \(\frac{64\times50+44\times100}{27\times38+146\times19}\)

\(=\frac{64\times50+44\times50\times2}{27\times38+73\times2\times19}\)

\(=\frac{\left(64+44\right)\times50\times2}{27\times38+73\times38}\)

\(=\frac{108\times100}{\left(27+73\right)\times38}\)

\(=\frac{108\times100}{100\times38}\)

\(=\frac{108}{38}\)

\(=\frac{27}{8}\)

\(\frac{64.50+44.100}{27.38+146.19}\)

= \(\frac{32.2.50+44.100}{27.38+73.2.19}\)

= \(\frac{32.100+44.100}{27.38+73.38}\)

= \(\frac{\left(32+44\right).100}{\left(27+73\right).38}\)

= \(\frac{76.100}{100.38}\)

= \(2\)

Đặt \(A=\frac{3}{1\cdot4}+\frac{5}{4\cdot9}+\frac{7}{9\cdot16}+\frac{9}{16\cdot25}+\frac{11}{25\cdot36}\)

\(A=\frac{4-1}{1\cdot4}+\frac{9-4}{4\cdot9}+\frac{16-9}{9\cdot16}+\frac{25-16}{16\cdot25}+\frac{36-25}{25\cdot36}\)

\(A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{25}+\frac{1}{25}-\frac{1}{36}\)

\(\Rightarrow A=1-\frac{1}{36}=\frac{35}{36}\)

= 1-\(\frac{1}{4}\)+ \(\frac{1}{4}\)-\(\frac{1}{9}\)+\(\frac{1}{9}\)-\(\frac{1}{16}\)+\(\frac{1}{16}\)-\(\frac{1}{25}\)+\(\frac{1}{25}\)-\(\frac{1}{36}\)=1-\(\frac{1}{36}\)=35/36

12166,59259

lấy máy tính

kết quả =12216,59259