\(\frac{1}{3} \times \frac{5}{7} + \frac{2}{9} - \frac{3}{8} = \)...

\(\begin{array}{l}\frac{1}{3} \times \frac{5}{7} + \frac{2}{9} - \frac{3}{8}\\ = \frac{5}{{12}} + \frac{2}{9} - \frac{3}{8}\\ = \frac{{40}}{{168}} + \frac{{48}}{{168}} - \frac{{63}}{{168}} = \frac{{25}}{{168}}\end{array}\)

\(\begin{array}{l}\frac{1}{7} \times \frac{5}{9} + \frac{2}{{11}}\\ = \frac{5}{{63}} + \frac{2}{{11}}\\ = \frac{{55}}{{693}} + \frac{{126}}{{693}} = \frac{{181}}{{693}}\end{array}\)

\(\begin{array}{l}\frac{1}{9} \times \frac{5}{7} + \frac{2}{{13}}\\ = \frac{5}{{63}} + \frac{2}{{13}}\\ = \frac{{65}}{{819}} + \frac{{126}}{{819}} = \frac{{191}}{{819}}\end{array}\)

\(\begin{array}{l}\frac{4}{5} - \frac{2}{7}:\frac{3}{8} + \frac{1}{6}\\ = \frac{4}{5} - \frac{{16}}{{21}} + \frac{1}{6}\\ = \frac{{168}}{{210}} - \frac{{160}}{{210}} + \frac{{35}}{{210}} = \frac{{43}}{{210}}\end{array}\)

\(\begin{array}{l}\frac{3}{{10}}:\frac{1}{4} + \frac{5}{{13}}\\ = \frac{6}{5} + \frac{5}{{13}}\\ = \frac{{78}}{{65}} + \frac{{25}}{{65}} = \frac{{103}}{{65}}\end{array}\)

\(\begin{array}{l}\frac{3}{7} - \frac{1}{4} \times \frac{5}{9}\\ = \frac{3}{7} - \frac{5}{{36}}\\ = \frac{{108}}{{252}} - \frac{{35}}{{252}} = \frac{{73}}{{252}}\end{array}\)

\(\begin{array}{l}\frac{3}{{11}}:\frac{1}{4} \times \frac{5}{9} + \frac{2}{{13}}\\ = \frac{{12}}{{11}} \times \frac{5}{9} + \frac{2}{{13}}\\ = \frac{{20}}{{33}} + \frac{2}{{13}} = \frac{{260}}{{429}} + \frac{{66}}{{429}} = \frac{{326}}{{429}}\end{array}\)

\(\begin{array}{l}\frac{7}{{12}} + \frac{3}{8} \times \frac{5}{{11}}\\ = \frac{7}{{12}} + \frac{{15}}{{88}}\\ = \frac{{308}}{{528}} + \frac{{90}}{{528}} = \frac{{398}}{{528}} = \frac{{199}}{{264}}\end{array}\)

\(\begin{array}{l}\frac{7}{{13}} \times \frac{2}{5} + \frac{1}{8}\\ = \frac{{14}}{{65}} + \frac{1}{8}\\ = \frac{{112}}{{520}} + \frac{{65}}{{520}} = \frac{{177}}{{520}}\end{array}\)

\(\begin{array}{l}\frac{7}{{12}} + \frac{1}{5} \times \frac{3}{8} - \frac{2}{9}\\ = \frac{7}{{12}} + \frac{3}{{40}} - \frac{2}{9}\\ = \frac{{280}}{{480}} + \frac{{36}}{{480}} - \frac{{160}}{{480}} = \frac{{156}}{{480}} = \frac{{39}}{{120}}\end{array}\)

\(\begin{array}{l}\frac{2}{3} - \frac{1}{6} \times \frac{4}{7}\\ = \frac{2}{3} - \frac{4}{{42}}\\ = \frac{{28}}{{42}} - \frac{4}{{42}} = \frac{{24}}{{42}} = \frac{4}{7}\end{array}\)

\(\begin{array}{l}\frac{1}{6}:\frac{3}{8} - \frac{2}{{11}}\\ = \frac{4}{9} - \frac{2}{{11}}\\ = \frac{{44}}{{99}} - \frac{{18}}{{99}} = \frac{{26}}{{99}}\end{array}\)

\(\begin{array}{l}\frac{2}{3} - \frac{5}{6} \times \frac{1}{7} + \frac{4}{{11}}\\ = \frac{2}{3} - \frac{5}{{42}} + \frac{4}{{11}}\\ = \frac{{84}}{{126}} - \frac{{15}}{{126}} + \frac{{56}}{{126}} = \frac{{125}}{{126}}\end{array}\)

\(\begin{array}{l}\frac{5}{9} \times \frac{2}{7} + \frac{3}{{10}}\\ = \frac{{10}}{{63}} + \frac{3}{{10}}\\ = \frac{{100}}{{630}} + \frac{{189}}{{630}} = \frac{{289}}{{630}}\end{array}\)

\(\begin{array}{l}\frac{5}{9} + \frac{1}{7}:\frac{4}{5}\\ = \frac{5}{9} + \frac{5}{{28}}\\ = \frac{{140}}{{252}} + \frac{{45}}{{252}} = \frac{{185}}{{252}}\end{array}\)

\(\begin{array}{l}\frac{5}{9} \times \frac{3}{{10}} + \frac{1}{4}:\frac{2}{5}\\ = \frac{{15}}{{90}} + \frac{5}{8} = \frac{{60}}{{360}} + \frac{{225}}{{360}}\\ = \frac{{285}}{{360}} = \frac{{19}}{{24}}\end{array}\)

\(\begin{array}{l}\frac{6}{{11}} + \frac{1}{3}:\frac{5}{7}\\ = \frac{6}{{11}} + \frac{7}{{15}} = \frac{{90}}{{165}} + \frac{{77}}{{165}}\\ = \frac{{167}}{{165}}\end{array}\)

\(\begin{array}{l}\frac{2}{3} - \frac{5}{{12}} \times \frac{3}{7}\\ = \frac{2}{3} - \frac{{15}}{{84}} = \frac{{56}}{{84}} - \frac{{15}}{{84}}\\ = \frac{{41}}{{84}}\end{array}\)

\(\begin{array}{l}\frac{1}{8}:\frac{3}{7} - \frac{2}{5} \times \frac{4}{9}\\ = \frac{7}{{24}} - \frac{8}{{45}}\\ = \frac{{315}}{{1080}} - \frac{{192}}{{1080}} = \frac{{123}}{{1080}} = \frac{{41}}{{360}}\end{array}\)

\(\begin{array}{l}\frac{3}{4} - \frac{2}{5} \times \frac{7}{9}\\ = \frac{3}{4} - \frac{{14}}{{45}} = \frac{{135}}{{180}} - \frac{{56}}{{180}}\\ = \frac{{79}}{{180}}\end{array}\)

\(\begin{array}{l}\frac{3}{{10}} \times \frac{4}{7} + \frac{5}{{11}}\\ = \frac{{12}}{{70}} + \frac{5}{{11}}\\ = \frac{{66}}{{770}} + \frac{{350}}{{770}} = \frac{{416}}{{770}} = \frac{{208}}{{385}}\end{array}\)

\(\begin{array}{l}\frac{6}{{11}} + \frac{2}{9}:\frac{5}{7} - \frac{1}{3}\\ = \frac{6}{{11}} + \frac{{14}}{{45}} - \frac{1}{3}\\ = \frac{{270}}{{495}} + \frac{{154}}{{495}} - \frac{{165}}{{495}} = \frac{{259}}{{495}}\end{array}\)

\[\begin{array}{l}\frac{1}{8} \times \frac{3}{5} + \frac{7}{{12}}\\ = \frac{3}{{40}} + \frac{7}{{12}}\\ = \frac{9}{{120}} + \frac{{70}}{{120}} = \frac{{79}}{{120}}\end{array}\]

\(\begin{array}{l}\frac{7}{8}:\frac{2}{5} - \frac{1}{9}\\ = \frac{{35}}{{16}} - \frac{1}{9}\\ = \frac{{315}}{{144}} - \frac{{16}}{{144}} = \frac{{299}}{{144}}\end{array}\)

\(\begin{array}{l}\frac{3}{4} \times \frac{5}{8} - \frac{1}{6} + \frac{2}{7}\\ = \frac{{15}}{{32}} - \frac{1}{6} + \frac{2}{7}\\ = \frac{{315}}{{672}} - \frac{{112}}{{672}} + \frac{{192}}{{672}} = \frac{{395}}{{672}}\end{array}\)

\[\begin{array}{l}\frac{5}{{13}}:\frac{2}{7} - \frac{1}{4}\\ = \frac{{35}}{{26}} - \frac{1}{4}\\ = \frac{{70}}{{52}} - \frac{{13}}{{52}} = \frac{{57}}{{52}}\end{array}\]

\[\begin{array}{l}\frac{6}{7} - \frac{1}{3}:\frac{5}{8}\\ = \frac{6}{7} - \frac{8}{{15}}\\ = \frac{{90}}{{105}} - \frac{{56}}{{105}} = \frac{{34}}{{105}}\end{array}\]

\(\begin{array}{l}\frac{5}{{12}}:\frac{2}{7} \times \frac{3}{5} + \frac{1}{8}\\ = \frac{{35}}{{24}} \times \frac{3}{5} + \frac{1}{8}\\ = \frac{{21}}{8} + \frac{1}{8} = \frac{{22}}{8} = \frac{{11}}{4}\end{array}\)

\[\begin{array}{l}\frac{2}{3} \times \frac{4}{{11}} + \frac{5}{{12}}\\ = \frac{8}{{33}} + \frac{5}{{12}}\\ = \frac{{96}}{{396}} + \frac{{165}}{{396}} = \frac{{261}}{{396}} = \frac{{87}}{{132}}\end{array}\]

\(\begin{array}{l}\frac{2}{9} \times \frac{5}{6} + \frac{3}{{14}}\\ = \frac{{10}}{{54}} + \frac{3}{{14}}\\ = \frac{{70}}{{378}} + \frac{{81}}{{378}} = \frac{{151}}{{378}}\end{array}\)