Question

Calcule o valor das expresões numéricas

 

a) -{[2-(5-10-6)-5+20-(-17+13)]-1}+13=

 

b){3-[5/9-(7/6-4)+7/12]}dividido{3/4-[1/8+5/6-2)-1/2]}=

Answer 1

a)

 

$- \left \{ \left [ 2 - \left ( 5 - 10 - 6 \right ) - 5 + 20 - \left ( - 17 + 13 \right ) \right ] - 1 \right \} + 13 = \\ - \left \{ \left [ 2 - \left ( - 11 \right ) + 15 - \left ( - 4 \right ) \right ] - 1 \right \} + 13 = \\ - \left \{ \left [ 2 + 11 + 15 + 4 \right ] - 1 \right \} + 13 = \\ - \left \{ \left [ 32 \right ] - 1 \right \} + 13 = \\ - \left \{ 32 - 1 \right \} + 13 = \\ - \left \{ 31 \right \} + 13 = \\ - 31 + 13 = \\ \boxed{- 18}$

 

 

b)

 

$\frac{\left \{ 3 - \left [ \frac{5}{9} - \left ( \frac{7}{6} - 4 \right ) + \frac{7}{12} \right ] \right \}}{\left \{ \frac{3}{4} - \left [ \frac{1}{8} + \frac{5}{6} - 2 \right ] - \frac{1}{2} \right \}} = \\\\\\ \frac{\left \{ 3 - \left [ \frac{5}{9} - \frac{7}{6} + 4 + \frac{7}{12} \right ] \right \}}{\left \{ \frac{3}{4} - \frac{1}{8} - \frac{5}{6} + 2 - \frac{1}{2} \right \}} =$

 

$\frac{\left \{ 3 - \frac{5}{9} + \frac{7}{6} - 4 - \frac{7}{12} \right \}}{\left \{ \frac{3}{4} - \frac{1}{8} - \frac{5}{6} + 2 - \frac{1}{2} \right \}} =$

 

$\frac{\frac{3 \cdot 36 - 5 \cdot 4 + 7 \cdot 6 - 4 \cdot 36 - 7 \cdot 3}{36}}{\frac{3 \cdot 6 - 1 \cdot 3 - 5 \cdot 4 + 2 \cdot 24 - 1 \cdot 12}{24}} = \\\\\\ \frac{108 - 20 + 42 - 144 - 21}{36} \div \frac{18 - 3 - 20 + 42 - 12}{24} = \\\\\\ \frac{- 35}{36} \times \frac{24}{25} =$

 

$\frac{- 35^{\div 5}}{36^{\div 12}} \times \frac{24^{\div 12}}{25^{\div 5}} = \\\\ \frac{- 7 \cdot 2}{3 \cdot 5} = \\\\ \boxed{\frac{- 14}{15}}$