18. \( \frac{8}{9} \div \frac{1}{3} \) 19. \( \sqrt{\frac{3}{4} \cdot \frac{1}{2}+\frac{3}{16}} \) 20. \( \sqrt{\frac{150}{6}}-\sqrt{\frac{3}{4}-\frac{1}{2}} \)

To tackle the first problem, when dividing fractions like \( \frac{8}{9} \div \frac{1}{3} \), you multiply the first fraction by the reciprocal of the second. So, it becomes \( \frac{8}{9} \times \frac{3}{1} = \frac{24}{9} \), which simplifies down to \( \frac{8}{3} \). In the second expression, \(\sqrt{\frac{3}{4} \cdot \frac{1}{2}+\frac{3}{16}}\), start by calculating \(\frac{3}{4} \cdot \frac{1}{2} = \frac{3}{8}\). Next, add \(\frac{3}{8} + \frac{3}{16}\). To combine these, convert \(\frac{3}{8}\) to its sixteenths equivalent, giving \(\frac{6}{16}\), and now you can add them to get \(\frac{9}{16}\). Finally, take the square root: \(\sqrt{\frac{9}{16}} = \frac{3}{4}\). Lastly, in the third problem, \(\sqrt{\frac{150}{6}} - \sqrt{\frac{3}{4} - \frac{1}{2}}\) simplifies to \(\sqrt{25} - \sqrt{\frac{1}{4}}\). So, that becomes \(5 - \frac{1}{2} = \frac{10}{2} - \frac{1}{2} = \frac{9}{2}\).