a)
[tex]12 \frac{1}{2} \div \frac{1}{5} \times 2.5 = \frac{25}{2} \times 5 \times 2.5 = \frac{125}{2} \times 2.5 = \frac{125}{2} \times 2 \frac{1}{2} = \frac{125}{2} \times \frac{5}{2} = \frac{625}{4} = 156 \frac{1}{4} [/tex]
[tex]3 \frac{3}{4} + 0.28 \times 1 \frac{11}{14} = \frac{15}{4} + \frac{28}{100} \times \frac{25}{14} = \frac{15}{4} + \frac{1}{2} = \frac{15}{8} = 1 \frac{7}{8} [/tex]
b)
[tex]5.7 \div (5 \frac{3}{7} - 3.8 )= 5.7 \div ( \frac{38}{7} - \frac{38}{10} ) = 5.7 \div ( \frac{380}{70} - \frac{266}{70}) = 5.7 \div \frac{114}{70} = 5.7 \div 1 \frac{44}{70} = 5 \frac{7}{10} \div 1 \frac{22}{35} = \frac{57}{10} \times \frac{35}{57} = \frac{35}{10} = 3.5[/tex]
[tex]4.08 - 2.08 \div \frac{13}{25} = 4 \frac{8}{100} - 2 \frac{8}{100} \div \frac{13}{25} = 4 \frac{2}{25} - 2 \frac{2}{25} \div \frac{13}{25} = \frac{102}{25} - \frac{52}{25} \times \frac{25}{13} = \frac{102}{25} - \frac{52}{13} = \frac{102}{25} - \frac{4}{1} = \frac{102}{25} - \frac{100}{25} = \frac{2}{25} [/tex]
c)
[tex]2.5 \times 4 \frac{1}{2} - 5 \frac{17}{20} \div 0.9 = \frac{5}{2} \times \frac{9}{2} - \frac{117}{20} \times \frac{10}{9} = \frac{45}{4} - \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 1 \frac{1}{4} = \frac{13}{4} + \frac{39}{8} \times \frac{4}{5} = \frac{13}{4} + \frac{39}{10} = 3.25 + 3.9 = 7.15[/tex]
d)
[tex]3 \times ( {1 \frac{2}{3} )}^{2} - 2 \times ( {0.5)}^{3} = 3 \times \frac{25}{9} - 2 \times \frac{125}{1000} = \frac{25}{3} - \frac{125}{500} = \frac{25}{3} - \frac{1}{4} = \frac{100}{12} - \frac{3}{12} = \frac{97}{12} = 8 \frac{1}{12} [/tex]
[tex] {(5 \frac{1}{4} - 5.05)}^{2} - \frac{1}{25} = {(5.25 - 5.05)}^{2} - \frac{1}{25} = {(0.2)}^{2} - \frac{1}{25} = \frac{4}{100} - \frac{1}{25} = \frac{1}{25} - \frac{1}{25} = 0[/tex]
