[tex]a) (\frac{5}{6}+ \frac{3}{4})\cdot \frac{24}{19}= \frac{(4\cdot5+6\cdot3)}{19}= \frac{20+18}{24}\cdot \frac{24}{19}= \frac{38}{24}\cdot \frac{24}{19}=2 \\ \\ \\b)(\frac{1}{6}+ \frac{7}{9})\cdot \frac{18}{17}= \frac{(3+14)}{18}\cdot \frac{18}{17} = \frac{17}{18}\cdot \frac{18}{17}=1 [/tex]
[tex]c)( \frac{5}{6}+ \frac{7}{8})\cdot \frac{18}{41} + \frac{1}{4}=( \frac{20+21}{24})\cdot \frac{18}{41}+ \frac{1}{4} = \frac{41}{24}\cdot\frac{18}{41}+ \frac{1}{4} = \frac{3}{4}+ \frac{1}{4}= \frac{4}{4} =1[/tex]
[tex]d)( \frac{5}{12}- \frac{3}{18})\cdot 4 = \frac{15-6}{36}\cdot 4= \frac{9}{36}\cdot 4=1[/tex]
[tex]e)( \frac{11}{45}- \frac{1}{30})\cdot \frac{18}{19} = \frac{22-3}{90}\cdot \frac{18}{19}= \frac{19}{90}\cdot \frac{18}{19}= \frac{1}{5} [/tex]
[tex]f) ( \frac{11}{12}- \frac{7}{15})\cdot \frac{10}{9}+ \frac{1}{2} = \frac{55-28}{60}\cdot \frac{10}{9}+ \frac{1}{2} = \frac{27}{60}\cdot \frac{10}{9}+ \frac{1}{2} = \frac{1}{2}+ \frac{1}{2} = \frac{2}{2}=1 [/tex]
