1. **Problem a:** Simplify and solve \(\left(2 \frac{1}{3} + \frac{1}{2} - \frac{1}{12}\right) - 2 \left(\frac{1}{3} + \frac{1}{4}\right) - \sqrt{\frac{1}{9}}\). 2. Convert mixed number to improper fraction: \(2 \frac{1}{3} = \frac{7}{3}\). 3. Find common denominator for \(\frac{7}{3}, \frac{1}{2}, \frac{1}{12}\) which is 12. 4. Convert fractions: \(\frac{7}{3} = \frac{28}{12}, \frac{1}{2} = \frac{6}{12}, \frac{1}{12} = \frac{1}{12}\). 5. Calculate inside first parentheses: \(\frac{28}{12} + \frac{6}{12} - \frac{1}{12} = \frac{33}{12} = \frac{11}{4}\). 6. Calculate inside second parentheses: \(\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}\). 7. Multiply by 2: \(2 \times \frac{7}{12} = \frac{14}{12} = \frac{7}{6}\). 8. Calculate square root: \(\sqrt{\frac{1}{9}} = \frac{1}{3}\). 9. Combine all: \(\frac{11}{4} - \frac{7}{6} - \frac{1}{3}\). 10. Find common denominator 12: \(\frac{11}{4} = \frac{33}{12}, \frac{7}{6} = \frac{14}{12}, \frac{1}{3} = \frac{4}{12}\). 11. Calculate: \(\frac{33}{12} - \frac{14}{12} - \frac{4}{12} = \frac{15}{12} = \frac{5}{4} = 1.25\). --- 1. **Problem b:** Calculate \(-4.9(-12 + \sqrt{0.81}) - (2.2)^2 \times 1.59\). 2. Calculate square root: \(\sqrt{0.81} = 0.9\). 3. Sum inside parentheses: \(-12 + 0.9 = -11.1\). 4. Multiply: \(-4.9 \times -11.1 = 54.39\). 5. Square 2.2: \((2.2)^2 = 4.84\). 6. Multiply: \(4.84 \times 1.59 = 7.6956\). 7. Final calculation: \(54.39 - 7.6956 = 46.6944\). 8. Rounded to nearest hundredth: \(46.69\). --- 1. **Problem c:** Calculate \(\left[\left(-\frac{7}{10} - \frac{1}{2}\right) + 4\left(\frac{1}{5} + \frac{1}{4}\right)\right]^2\). 2. Find common denominator for \(-\frac{7}{10}\) and \(-\frac{1}{2}\) is 10. 3. Convert \(-\frac{1}{2} = -\frac{5}{10}\). 4. Sum: \(-\frac{7}{10} - \frac{5}{10} = -\frac{12}{10} = -\frac{6}{5}\). 5. Sum inside second parentheses: \(\frac{1}{5} + \frac{1}{4} = \frac{4}{20} + \frac{5}{20} = \frac{9}{20}\). 6. Multiply by 4: \(4 \times \frac{9}{20} = \frac{36}{20} = \frac{9}{5}\). 7. Sum both parts: \(-\frac{6}{5} + \frac{9}{5} = \frac{3}{5}\). 8. Square the result: \(\left(\frac{3}{5}\right)^2 = \frac{9}{25} = 0.36\). --- 1. **Problem d:** Calculate \(1 - \sqrt{6.35 - 5(1.44 - 0.78)}\). 2. Calculate inside parentheses: \(1.44 - 0.78 = 0.66\). 3. Multiply by 5: \(5 \times 0.66 = 3.3\). 4. Subtract: \(6.35 - 3.3 = 3.05\). 5. Calculate square root: \(\sqrt{3.05} \approx 1.746\). 6. Final calculation: \(1 - 1.746 = -0.746\). 7. Rounded to nearest hundredth: \(-0.75\).