\(\frac{2}{9} \times \frac{3}{4} + \frac{5}{6} = \)...

\(\begin{array}{l}\frac{2}{9} \times \frac{3}{4} + \frac{5}{6}\\ = \frac{6}{{36}} + \frac{5}{6}\\ = \frac{6}{{36}} + \frac{{30}}{{36}} = \frac{{36}}{{36}} = 1\end{array}\)

\(\begin{array}{l}\frac{7}{8} - \frac{1}{3}:\frac{4}{5}\\ = \frac{7}{8} - \frac{5}{{12}}\\ = \frac{{21}}{{24}} - \frac{{10}}{{24}} = \frac{{11}}{{24}}\end{array}\)

\(\begin{array}{l}\frac{3}{7}:\frac{2}{5} + \frac{1}{9}\\ = \frac{{15}}{{14}} + \frac{1}{9}\\ = \frac{{135}}{{126}} + \frac{{14}}{{126}} = \frac{{149}}{{126}}\end{array}\)

\(\begin{array}{l}\frac{5}{9}:\frac{1}{3} - \frac{2}{{11}}\\ = \frac{5}{3} - \frac{2}{{11}}\\ = \frac{{55}}{{33}} - \frac{6}{{33}} = \frac{{49}}{{33}}\end{array}\)

\(\begin{array}{l}\frac{3}{4} + \frac{1}{8} \times \frac{5}{6}\\ = \frac{3}{4} + \frac{5}{{48}}\\ = \frac{{36}}{{48}} + \frac{5}{{48}} = \frac{{41}}{{48}}\end{array}\)

\(\begin{array}{l}\frac{2}{7} \times \frac{6}{{11}} + \frac{4}{9}\\ = \frac{{12}}{{77}} + \frac{4}{9}\\ = \frac{{108}}{{693}} + \frac{{308}}{{693}} = \frac{{416}}{{693}} = \frac{{64}}{{99}}\end{array}\)

\(\begin{array}{l}\frac{{11}}{{12}}:\frac{5}{6} - \frac{1}{4}\\ = \frac{{11}}{{10}} - \frac{1}{4}\\ = \frac{{44}}{{40}} - \frac{{10}}{{40}} = \frac{{34}}{{40}} = \frac{{17}}{{20}}\end{array}\)

\(\begin{array}{l}\frac{1}{5} + \frac{7}{9} \times \frac{3}{8}\\ = \frac{1}{5} + \frac{{21}}{{72}}\\ = \frac{{72}}{{360}} + \frac{{105}}{{360}} = \frac{{177}}{{360}} = \frac{{59}}{{120}}\end{array}\)

\(\begin{array}{l}\frac{3}{{10}} \times \frac{5}{8} + \frac{7}{{12}}\\ = \frac{{15}}{{80}} + \frac{7}{{12}}\\ = \frac{{45}}{{240}} + \frac{{140}}{{240}} = \frac{{185}}{{240}} = \frac{{37}}{{48}}\end{array}\)

\(\begin{array}{l}\frac{9}{{11}}:\frac{3}{4} - \frac{2}{5}\\ = \frac{{36}}{{33}} - \frac{2}{5}\\ = \frac{{180}}{{165}} - \frac{{66}}{{165}} = \frac{{114}}{{165}} = \frac{{38}}{{55}}\end{array}\)

\(\begin{array}{l}\frac{1}{3} + \frac{4}{7} \times \frac{5}{9}\\ = \frac{1}{3} + \frac{{20}}{{63}}\\ = \frac{{21}}{{63}} + \frac{{20}}{{63}} = \frac{{41}}{{63}}\end{array}\)

\(\begin{array}{l}\frac{5}{6} - \frac{1}{4} \times \frac{3}{5}\\ = \frac{5}{6} - \frac{3}{{20}}\\ = \frac{{50}}{{60}} - \frac{9}{{60}} = \frac{{41}}{{60}}\end{array}\)

\(\begin{array}{l}\frac{2}{9}:\frac{1}{6} + \frac{7}{8}\\ = \frac{4}{3} + \frac{7}{8}\\ = \frac{{32}}{{24}} + \frac{{21}}{{24}} = \frac{{53}}{{24}}\end{array}\)

\(\begin{array}{l}\frac{3}{8} + \frac{5}{{12}} \times \frac{2}{7}\\ = \frac{3}{8} + \frac{{10}}{{84}}\\ = \frac{{126}}{{336}} + \frac{{40}}{{336}} = \frac{{166}}{{336}} = \frac{{83}}{{168}}\end{array}\)

\(\begin{array}{l}\frac{7}{{10}} - (\frac{4}{9}:\frac{2}{3})\\ = \frac{7}{{10}} - \frac{4}{6}\\ = \frac{{21}}{{30}} - \frac{{20}}{{30}} = \frac{1}{{30}}\end{array}\)

\(\begin{array}{l}\frac{1}{7} \times \frac{6}{4} + \frac{3}{{10}}\\ = \frac{6}{{35}} + \frac{3}{{10}} = \frac{{60}}{{350}} + \frac{{105}}{{350}} = \frac{{165}}{{350}} = \frac{{33}}{{70}}\end{array}\)

\(\begin{array}{l}\frac{5}{8}:\frac{2}{9} - \frac{1}{6}\\ = \frac{{45}}{{16}} - \frac{1}{6} = \frac{{135}}{{48}} - \frac{8}{{48}} = \frac{{127}}{{48}}\end{array}\)

\(\begin{array}{l}\frac{4}{{11}} + \frac{3}{5} \times \frac{7}{8}\\ = \frac{4}{{11}} + \frac{{21}}{{40}} = \frac{{160}}{{440}} + \frac{{231}}{{440}} = \frac{{391}}{{440}}\end{array}\)

\(\begin{array}{l}\frac{9}{{14}} - \frac{1}{7}:\frac{3}{4}\\ = \frac{9}{{14}} - \frac{4}{{21}}\\ = \frac{{27}}{{42}} - \frac{8}{{42}} = \frac{{19}}{{42}}\end{array}\)

\(\begin{array}{l}\frac{2}{5} \times \frac{3}{{10}} + \frac{{11}}{{12}}\\ = \frac{6}{{50}} + \frac{{11}}{{12}} = \frac{{36}}{{300}} + \frac{{275}}{{300}} = \frac{{311}}{{300}}\end{array}\)

\(\begin{array}{l}\frac{7}{9}:\frac{5}{6} - \frac{2}{7}\\ = \frac{{42}}{{45}} - \frac{2}{7}\\ = \frac{{294}}{{315}} - \frac{{90}}{{315}} = \frac{{204}}{{315}} = \frac{{68}}{{105}}\end{array}\)

\(\begin{array}{l}\frac{1}{8} + \frac{4}{9} \times \frac{5}{7}\\ = \frac{1}{8} + \frac{{20}}{{63}} = \frac{{63}}{{504}} + \frac{{160}}{{504}} = \frac{{223}}{{504}}\end{array}\)

\[\begin{array}{l}\frac{3}{5} - \frac{2}{{11}}:\frac{4}{7}\\ = \frac{3}{5} - \frac{7}{{22}}\\ = \frac{{66}}{{110}} - \frac{{35}}{{110}} = \frac{{31}}{{110}}\end{array}\]

\(\begin{array}{l}\frac{3}{5} - \frac{2}{{11}}:\frac{4}{7}\\ = \frac{3}{5} - \frac{7}{{22}}\\ = \frac{{66}}{{110}} - \frac{{35}}{{110}} = \frac{{31}}{{110}}\end{array}\)

\(\begin{array}{l}\frac{5}{{12}} \times \frac{3}{8} + \frac{1}{9}\\ = \frac{{15}}{{96}} + \frac{1}{9}\\ = \frac{{45}}{{288}} + \frac{{32}}{{288}} = \frac{{77}}{{288}}\end{array}\)

\[\begin{array}{l}\frac{8}{{15}}:\frac{2}{5} - \frac{3}{{10}}\\ = \frac{4}{3} - \frac{3}{{10}}\\ = \frac{{40}}{{30}} - \frac{9}{{30}} = \frac{{31}}{{30}}\end{array}\]

\(\begin{array}{l}\frac{1}{4} + \frac{7}{{10}} \times \frac{2}{9}\\ = \frac{1}{4} + \frac{{14}}{{90}}\\ = \frac{{45}}{{180}} + \frac{{28}}{{180}} = \frac{{73}}{{180}}\end{array}\)

\(\begin{array}{l}\frac{6}{7} - \frac{3}{8} \times \frac{5}{9}\\ = \frac{6}{7} - \frac{5}{{24}}\\ = \frac{{144}}{{168}} - \frac{{35}}{{168}} = \frac{{109}}{{168}}\end{array}\)

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

\(\begin{array}{l}\frac{9}{{10}}:\frac{3}{5} - \frac{1}{8}\\ = \frac{3}{2} - \frac{1}{8}\\ = \frac{{24}}{{16}} - \frac{2}{{16}} = \frac{{22}}{{16}} = \frac{{11}}{8}\end{array}\)

\[\begin{array}{l}\frac{1}{6} + \frac{5}{7} \times \frac{3}{{10}}\\ = \frac{1}{6} + \frac{{15}}{{70}}\\ = \frac{{70}}{{420}} + \frac{{90}}{{420}} = \frac{{160}}{{420}} = \frac{8}{{21}}\end{array}\]

\(\begin{array}{l}\frac{3}{8} \times \frac{5}{9} + \frac{7}{{12}}\\ = \frac{{15}}{{72}} + \frac{7}{{12}}\\ = \frac{{15}}{{72}} + \frac{{42}}{{72}} = \frac{{57}}{{72}} = \frac{{19}}{{24}}\end{array}\)

\(\begin{array}{l}\frac{{11}}{{15}}:\frac{4}{5} - \frac{2}{9}\\ = \frac{{11}}{{12}} - \frac{2}{9}\\ = \frac{{99}}{{108}} - \frac{{24}}{{108}} = \frac{{75}}{{108}} = \frac{{25}}{{36}}\end{array}\)

\(\begin{array}{l}\frac{1}{7} + \frac{3}{{10}} \times \frac{4}{9}\\ = \frac{1}{7} + \frac{{12}}{{90}}\\ = \frac{1}{7} + \frac{2}{{15}} = \frac{{14}}{{105}} + \frac{{14}}{{105}} = \frac{{29}}{{105}}\end{array}\)

\(\begin{array}{l}\frac{2}{5} \times \frac{7}{8} + \frac{3}{{11}}\\ = \frac{{14}}{{40}} + \frac{3}{{11}}\\ = \frac{{154}}{{440}} + \frac{{120}}{{440}} = \frac{{274}}{{440}} = \frac{{137}}{{120}}\end{array}\)

\(\begin{array}{l}\frac{8}{5}:\frac{5}{6} - \frac{1}{7}\\ = \frac{{16}}{{15}} - \frac{1}{7}\\ = \frac{{112}}{{105}} - \frac{{15}}{{105}} = \frac{{97}}{{105}}\end{array}\)

\(\begin{array}{l}\frac{4}{5}:\frac{2}{3} - \frac{7}{{10}}\\ = \frac{6}{5} - \frac{7}{{10}}\\ = \frac{{12}}{{10}} - \frac{7}{{10}} = \frac{5}{{10}} = \frac{1}{2}\end{array}\)

\(\begin{array}{l}\frac{2}{9} \times \frac{3}{7} + \frac{5}{8}\\ = \frac{6}{{63}} + \frac{5}{8}\\ = \frac{{48}}{{504}} + \frac{{315}}{{504}} = \frac{{363}}{{504}} = \frac{{121}}{{168}}\end{array}\)

\(\begin{array}{l}\frac{7}{{12}} - \frac{3}{8} \times \frac{5}{9}\\ = \frac{7}{{12}} - \frac{{15}}{{72}}\\ = \frac{{42}}{{72}} - \frac{{15}}{{72}} = \frac{{27}}{{72}} = \frac{3}{8}\end{array}\)

\(\begin{array}{l}\frac{5}{7} - \frac{1}{4}:\frac{3}{5}\\ = \frac{5}{7} - \frac{5}{{12}}\\ = \frac{{60}}{{84}} - \frac{{35}}{{84}} = \frac{{25}}{{84}}\end{array}\)

\(\begin{array}{l}\frac{3}{5} \times \frac{2}{3} + \frac{1}{4}\\ = \frac{6}{{15}} + \frac{1}{4}\\ = \frac{{24}}{{60}} + \frac{{15}}{{60}} = \frac{{39}}{{60}} = \frac{{13}}{{20}}\end{array}\)

\(\begin{array}{l}\frac{2}{3}:\frac{1}{5} - \frac{3}{7}\\ = \frac{{10}}{3} - \frac{3}{7}\\ = \frac{{70}}{{21}} - \frac{9}{{21}} = \frac{{61}}{{21}}\end{array}\)

\(\begin{array}{l}\frac{5}{{13}} \times \frac{2}{7} + \frac{3}{8}\\ = \frac{{10}}{{91}} + \frac{3}{8}\\ = \frac{{80}}{{728}} + \frac{{273}}{{728}} = \frac{{353}}{{728}}\end{array}\)

\[\begin{array}{l}\frac{1}{5} \times \frac{3}{7} + \frac{2}{9}\\ = \frac{3}{{35}} + \frac{2}{9}\\ = \frac{{27}}{{315}} + \frac{{70}}{{315}} = \frac{{97}}{{315}}\end{array}\]

\(\begin{array}{l}\frac{4}{7} - \frac{1}{3}:\frac{5}{8}\\ = \frac{4}{7} - \frac{8}{{15}}\\ = \frac{{60}}{{105}} - \frac{{56}}{{105}} = \frac{4}{{105}}\end{array}\)