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\(\frac{3}{4}+\frac{5}{9}:\frac{4}{5}=\frac{3}{4}+\frac{5}{9}\times\frac{5}{4}\)
\(=\frac{3}{4}+\frac{25}{36}=\frac{27}{36}+\frac{25}{36}=\frac{27+25}{36}=\frac{52}{36}=\frac{13}{9}\)
\(\frac{7}{19}\times\frac{4}{7}-\frac{7}{19}\times\frac{3}{7}=\frac{7}{19}\times\left(\frac{4}{7}-\frac{3}{7}\right)\)
\(=\frac{7}{19}\times\frac{1}{7}=\frac{1}{19}\)
\(\frac{3}{5}\times\frac{7}{9}+\frac{15}{18}\times\frac{2}{5}\)
\(=\frac{21}{45}+\frac{30}{90}\)
\(=\frac{4}{5}\)
#Hoktot#
\(\frac{7}{9}\)x\(\frac{3}{14}\):\(\frac{5}{8}\)
= \(\frac{21}{126} : \frac{5}{8}\)
= \(\frac{7}{42}:\frac{5}{8}\)
= \(\frac{56}{210}\)= \(\frac{4}{15}\)
\(S=\frac{3}{5.7}+\frac{3}{7.9}+.....+\frac{3}{59.61}\)
\(=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{7-5}{5.7}+\frac{9-7}{7.9}+......+\frac{61-59}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{7}{5.7}-\frac{5}{5.7}+\frac{9}{7.9}-\frac{7}{7.9}+.....+\frac{61}{59.61}-\frac{59}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{59}-\frac{1}{61}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)
=\(\frac{3}{2}.\frac{56}{305}\)
=\(\frac{84}{305}\)
19/14 x 3/7 + 3/7 x 5/14 - 3/7
= 3/7 x (19/14 + 5/14 - 1)
= 3/7 x 5/7
= 35/49
= 5/7