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Вычислим:

1. \[ \frac{11}{16}-\frac{9}{10}\cdot\frac{5}{24} =\frac{11}{16}-\frac{3}{16} =\frac{8}{16}=\boxed{\frac12} \]

2. \[ \frac{18}{25}:\frac{9}{10}+\frac{4}{15} =\frac{18}{25}\cdot\frac{10}{9}+\frac{4}{15} =\frac45+\frac4{15} =\frac{12}{15}+\frac4{15} =\boxed{\frac{16}{15}} \]

3. \[ \frac{3}{16}\cdot\left(\frac49-\frac8{27}\right) =\frac{3}{16}\cdot\left(\frac{12}{27}-\frac8{27}\right) =\frac{3}{16}\cdot\frac4{27} =\boxed{\frac1{36}} \]

4. \[ \left(\frac78-\frac5{24}\right)\cdot\frac3{14} =\left(\frac{21}{24}-\frac5{24}\right)\cdot\frac3{14} =\frac23\cdot\frac3{14} =\boxed{\frac17} \]

5. \[ 1-\frac4{11}:\frac{20}{33} =1-\frac4{11}\cdot\frac{33}{20} =1-\frac35 =\boxed{\frac25} \]

6. \[ \frac38:\left(\frac76+\frac{15}{24}\right) =\frac38:\left(\frac{28}{24}+\frac{15}{24}\right) =\frac38:\frac{43}{24} =\frac38\cdot\frac{24}{43} =\boxed{\frac9{43}} \]

Ответы:
\[ \boxed{\frac12;\ \frac{16}{15};\ \frac1{36};\ \frac17;\ \frac25;\ \frac9{43}} \]