Question

Hacer ejercicios de operaciones combinadas con fracciones

Answer 1

Números reales

ejercicios de repaso:

1.- realiza las siguientes operaciones con fracciones:

$a) 1-(\frac{1}{3} +\frac{1}{6} )$

$\rightarrow 1-(\frac{(\bold{2})(1)+1}{6} )$

$\rightarrow 1-(\frac{2+1}{6} )$

$\rightarrow 1-(\frac{3}{6} )$

$\rightarrow 1-\frac{1}{2}$

$\rightarrow \frac{2}{2} -\frac{1}{2}$

$\rightarrow \bold{ \underline{\frac{1}{2} }}$

$b) \frac{7}{3} -(\frac{2}{6} + \frac{5}{9} )$

$\rightarrow \frac{7}{3} -(\frac{2}{6} +\frac{5}{9} )$

$\rightarrow \frac{7}{3} -(\frac{(\bold{9})(2)+(\bold{6})(5)}{54} )$

$\rightarrow \frac{7}{3} - (\frac{18+30}{54})$

$\rightarrow \frac{7}{3} - \frac{48}{54}$

$\rightarrow \frac{7}{3} - \frac{48 \bold{ \div 6 }}{54 \bold{ \div 6}}$

$\rightarrow \frac{7}{3} - \frac{8}{9}$

$\rightarrow \frac{(7)(3)-8}{9}$

$\rightarrow \frac{21-8}{9}$

$\rightarrow \bold{ \underline{\frac{13}{9} }}$

$c) (\frac{3}{5} -\frac{1}{4} + 2) - (\frac{3}{4} - \frac{2}{5} +1)$

$\rightarrow (\frac{(\bold{4})(3)-(\bold{5})(1)+(\bold{20})(2)}{20} )-(\frac{(\bold{5})(3)-(\bold{4})(2)+(\bold{20})(1)}{20} )$

$\rightarrow (\frac{12-5+40}{20} )-(\frac{15-8+20}{20} )$

$\rightarrow \frac{47}{20}-\frac{27}{20}$

$\rightarrow \frac{47-27}{20}$

$\rightarrow \frac{20}{20}$

$\rightarrow \bold{ \underline{ 1 }}$

$d)(1-\frac{5}{8}+\frac{7}{12} )-(\frac{3}{4}+\frac{5}{16} )$

$\rightarrow (\frac{(\bold{24})(1)-(\bold{3})(5)+(\bold{2})(7)}{24} )-(\frac{(\bold{4})(3)+5}{4} )$

$\rightarrow \frac{24-15+14}{24} - \frac{12+5}{16}$

$\rightarrow \frac{23}{24} - \frac{17}{16}$

$\rightarrow \frac{(\bold{2})(23)-(\bold{3})(17)}{(48)}$

$\rightarrow \frac{46-51}{48}$

$\rightarrow \bold{ \underline{ \frac{-5}{48} }}$

$e)(1+\frac{1}{3} ) - (\frac{3}{4} + \frac{1}{2} )+(\frac{1}{3} - \frac{1}{4} )$

$\rightarrow (\frac{(\bold{3})(1)+1}{3} )-(\frac{3+(\bold{2})(1)}{4} )+(\frac{(\bold{4})(1)-(\bold{3})(1)}{12} )$

$\rightarrow (\frac{3+1}{3} ) -(\frac{3+2}{4} ) + (\frac{4-3}{12} )$

$\rightarrow \frac{4}{3} -\frac{5}{4}+\frac{1}{12}$

$\rightarrow \frac{(\bold{4})(4)-(\bold{3})(5)+1}{12}$

$\rightarrow \frac{16-15+1}{12}$

$\rightarrow \frac{2}{12}$

$\rightarrow \bold{ \underline{ \frac{1}{6} }}$

2.- realiza las siguientes operaciones con fracciones:

$a)1+\frac{10}{9} \cdot (\frac{1}{5}+\frac{1}{4} )$

$\rightarrow 1 + \frac{10}{9} \cdot (\frac{(\bold{4})(1)+(\bold{5})(1)}{20} )$

$\rightarrow 1 +\frac{10}{9} \cdot (\frac{4+5}{20} )$

$\rightarrow 1 +\frac{10}{9} \cdot (\frac{9}{20} )$

$\rightarrow 1 +\frac{(10)(9)}{(9)(20)}$

$\rightarrow 1+ \frac{90}{180}$

$\rightarrow 1+ \frac{90 \bold{ \div 90}}{180 \bold{ \div 90}}$

$\rightarrow 1+ \frac{1}{2}$

$\rightarrow \frac{2}{2} + \frac{1}{2}$

$\rightarrow \bold{ \underline{ \frac{3}{2} }}$

$b) 1- (\frac{1}{2} +\frac{1}{3} -\frac{1}{4} ) \div \frac{3}{2}$

$\rightarrow 1- (\frac{(\bold{6})(1)+(\bold{4})(1)-(\bold{3})(1)}{12} ) \div \frac{3}{2}$

$\rightarrow 1 - (\frac{6+4-3}{12} ) \div \frac{3}{2}$

$\rightarrow 1 - \frac{7}{12} \div \frac{3}{2}$

$\rightarrow 1- \frac{(7)(2)}{(12)(3)}$

$\rightarrow 1-\frac{14}{36}$

$\rightarrow 1-\frac{14 \bold{ \div 2}}{36 \bold{ \div 2 }}$

$\rightarrow 1 - \frac{7}{18}$

$\rightarrow \frac{18}{18} - \frac{7}{18}$

$\rightarrow \bold{ \underline{ \frac{11}{18} }}$

$c) (1+\frac{1}{2}-\frac{1}{8} ) \div (3+\frac{1}{7} )$

$\rightarrow (\frac{(\bold{8})(1)+(\bold{4})(1)-1}{8} ) \div (\frac{(\bold{7})(3)+1}{7} )$

$\rightarrow (\frac{8+4-1}{8} ) \div (\frac{21+1}{7} )$

$\rightarrow \frac{11}{8} \div \frac{22}{7}$

$\rightarrow \frac{(11)(7)}{(8)(22)}$

$\rightarrow \frac{77}{176}$

$\rightarrow \frac{77 \bold{ \div 11} }{176 \bold{ \div 11}}$

$\rightarrow \bold{ \underline{ \frac{7}{16} }}$

$d) 2-(1-\frac{4}{7} \cdot \frac{14}{12} ) \cdot 21$

$\rightarrow 2-(1-\frac{(4)(14)}{(7)(12)} ) \cdot \frac{21}{1}$

$\rightarrow 2- (1-\frac{56}{84} ) \cdot \frac{21}{1}$

$\rightarrow 2- (1-\frac{56 \bold{ \div 28} }{84 \bold{ \div 28} } ) \cdot \frac{21}{1}$

$\rightarrow 2-(1-\frac{2}{3} ) \cdot \frac{21}{1}$

$\rightarrow 2-(\frac{3}{3} -\frac{2}{3} ) \cdot \frac{21}{1}$

$\rightarrow 2-\frac{1}{3} \cdot \frac{21}{1}$

$\rightarrow 2-\frac{(1) (21) }{(3) (1)}$

$\rightarrow 2 - \frac{21}{3}$

$\rightarrow 2 - \frac{21 \bold{ \div 3} }{3 \bold{ \div 3}}$

$\rightarrow 2-7$

$\rightarrow \bold{ \underline{ -5 }}$