2.b)
[tex]5.7 \div (5 \frac{3}{7} - 3.8) = \frac{57}{10} \div ( \frac{38}{7} - \frac{38}{10} ) = \frac{57}{10} \div ( \frac{380}{70} - \frac{266}{70} ) = \frac{57}{10} \div \frac{114}{70} = \frac{57}{10} \times \frac{70}{114} = \frac{7}{2} = 3 \frac{1}{2} [/tex]
[tex]4.08 - 2.08 \div \frac{13}{25} = \frac{408}{100} - \frac{208}{100} \times \frac{25}{13} = \frac{408}{100} - \frac{16}{4} = 4.08 - 4 = 0.08[/tex]
c)
[tex]2.5 \times 4 \frac{1}{2} - 5 \frac{17}{20} \div 0.9 = \frac{25}{10} \times \frac{9}{2} - \frac{117}{20} \times \frac{10}{9} = \frac{5}{2} \times \frac{9}{2} - \frac{13}{2} = \frac{45}{4} - \frac{26}{4} = \frac{19}{4} = 4 \frac{3}{4} [/tex]
[tex]2 \frac{1}{2} \times 1.3 + 4 \frac{7}{8} \div 1.25 = \frac{5}{2} \times \frac{13}{10} + \frac{39}{8} \div \frac{125}{100} = \frac{1}{2} \times \frac{13}{2} + \frac{39}{8} \times \frac{100}{125} = \frac{13}{4} + \frac{3900}{1000} = \frac{13}{4} + \frac{39}{10} = \frac{65}{20} + \frac{78}{20} = \frac{143}{20} = 7 \frac{3}{20} = 7 \frac{15}{100} = 7.15[/tex]
d)
[tex]3 \times (1 \frac{2}{3} )^{2} - 2 \times (0.5)^{2} = 3 \times ( \frac{5}{3} )^{2} - 2 \times ( \frac{5}{10} )^{2} = 3 \times \frac{25}{9} - 2 \times \frac{25}{100} = \frac{25}{3} - \frac{25}{50} = \frac{1250}{150} - \frac{75}{150} = \frac{1175}{150} = 7 \frac{125}{150} = 7 \frac{5}{6} [/tex]
[tex](5 \frac{1}{4} - 5.05)^{2} - \frac{1}{25} = (5.25 - 5.05)^{2} - \frac{4}{100} = (0.2)^{2} - 0.04 = 0.04 - 0.04 = 0[/tex]
