[tex]a. \frac{5}{9} - ( \frac{1}{3} - \frac{7}{90} ) + (\frac{4}{3} - \frac{7}{45} ) + \frac{5}{4} = \\ \\ = \frac{5}{9} - ( \frac{30}{90} - \frac{7}{90} ) + ( \frac{60}{45} - \frac{7}{45} ) + \frac{5}{4} = \\ \\ = \frac{5}{9} - \frac{23}{90} + \frac{53}{45} + \frac{5}{4} = \\ \\ = \frac{5 \times 20}{180} - \frac{23 \times 2}{90 \times 2} + \frac{53 \times 4}{45 \times 4} + \frac{5 \times 45}{4 \times 45} = \\ \\ = \frac{100 - 46 + 212 + 225}{180} \\ \\ = \frac{491}{180} = 2.72(7) \\ \\ \\ \\ \\ [/tex]
[tex]b. \: \: \frac{25}{32} - ( \frac{2}{3} - \frac{3}{8} ) + ( \frac{5}{12} - \frac{1}{4} ) - \frac{1}{96} = \\ \\ = \frac{25}{32} -( \frac{16}{24} - \frac{9}{24} ) + ( \frac{10}{24} - \frac{6}{24} ) - \frac{1}{96} = \\ \\ = \frac{25}{32} - \frac{7}{24} + \frac{4}{24} - \frac{1}{96} = \\ \\ = \frac{25 \times 3 - 7 \times 4 + 4 \times 4 - 1 \times 1}{96} = \\ \\ = \frac{62}{96} = 0.6458(3)[/tex]
[tex]c. \: \: \frac{2}{3} - ( \frac{5}{10} - \frac{1}{2} ) = \\ \\ = \frac{2}{3} -( \frac{5}{10} - \frac{5}{10} ) = \\ \\ = \frac{2}{3} = 0.(7)[/tex]
[tex]d. \: \: \frac{104}{11} - \frac{3}{2} - \frac{5}{22} = \\ \\ = \frac{104 \times 2 - 3 \times 11 - 5}{22} = \\ \\ = \frac{208 - 33 - 5}{22} = \\ \\ = \frac{170}{22} = 7.(72)[/tex]
