Question

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[tex] \frac{13}{9} + \frac{5}{6} * \frac{8}{3}

[tex] \frac{21}{5} - \frac{1}{10} : \frac{1}{2}

[tex] \frac{33}{16} - \frac{5}{16} : \frac{5}{8} - \frac{3}{4} * \frac{3}{4}

Answer 1

13 / 9 + 5 /6 ×8 /3  =13 / 9  + 5×4 / 3×3 = 13 / 9  + 20 /9 = 33 / 9 = 11 /3 
21 / 5 - 1 /10 × 2 /1 = 21 /5 - 2 /10 = 21 /5 -  1 /5 = (21 -1 ) / 5 =20 /5 =4 
33 /16 - 5 /16 ×8 /5 - 3 /4×3 /4  = 33 / 16  - 8 /16  - 9 /16 = 
 = ( 33 - 8 - 9 ) /16 = 16 / 16 =1 

Answer 2

$\displaystyle a). \frac{13}{9} + \frac{5}{6} \cdot \frac{8}{3} = \frac{13}{9} + \frac{40}{18} = \frac{26}{18} + \frac{40}{18} = \frac{66}{18} = \frac{22}{6} = \frac{11}{3} \\ \\ b).\frac{21}{5} - \frac{1}{10} : \frac{1}{2} = \frac{21}{5} - \frac{1}{10} \cdot 2= \frac{21}{5} - \frac{2}{10} = \frac{42}{10} - \frac{2}{10} = \frac{40}{10} =4$

$\displaystyle c).\frac{33}{16} - \frac{5}{16} : \frac{5}{8} - \frac{3}{4} * \frac{3}{4} = \frac{33}{16} - \frac{5}{16} \cdot \frac{8}{5} - \frac{9}{16} = \frac{33}{16} - \frac{40}{80} - \frac{9}{16} = \\ \\ = \frac{165}{80} - \frac{40}{80} - \frac{45}{80} = \frac{125}{80} - \frac{45}{80} = \frac{80}{80} =1$