Operaciones combinadas con valor absoluto

$$ \left ( 5 \div 2 \right ) – \left | 9 \cdot 4 – 15 \right | + \left | 21 \div 7 \right | $$

$$ 2,5 – \left | 36 – 15 \right | + \left | 3 \right | $$

$$ 2,5 – \left | 21 \right | + \left | 3 \right | $$

$$ 2,5 – 21 + 3 $$

$$ -18,5 + 3 $$

$$ \boxed{-15,5} $$

$$ -956 + \left | 63 – \left ( -12 \right )\right | – \left | 11 \cdot \left ( -5 \right )\right | $$

$$ -956 + \left | 63 + 12 \right | – \left | -55 \right | $$

$$ -956 + \left | 75 \right | – \left | -55 \right | $$

$$ -956 + 75 – 55 $$

$$ -881 – 55 $$

$$ \boxed{-936} $$

$$ \left | 3-7 \right |+ 2 \cdot \left ( 4 + 1 \right ) $$

$$ \left | -4 \right |+ 2 \cdot 5 $$

$$ 4 + 10 $$

$$ \boxed{14} $$

$$ \left | -16 \right | + \left | 2 \cdot 9 \right | – 5 $$

$$ 16 + \left | 18 \right | – 5 $$

$$ 16 + 18 – 5 $$

$$ 34 – 5 $$

$$ \boxed{29} $$

$$ \left | -2,6 + 7,8 \right | \cdot \left | 121 \div 11 + (-5,7) \right | + \left | 54 \div 12 \right | $$

$$ \left | 5,2 \right | \cdot \left | 11 + (-5,7) \right | + \left | 4,5 \right | $$

$$  5,2 \cdot \left | 5,3 \right | + \left | 4,5 \right | $$

$$  5,2 \cdot  5,3 + 4,5  $$

$$  27,56 + 4,5  $$

$$  \boxed{32,06} $$

$$ \left | (-1,3) – (-5,1) + 2 \right | \div (-4) + \left | 9 \cdot 0,2 \right | – 3,5 $$

$$ \left | (-1,3) + 5,1 + 2 \right | \div (-4) + \left | 1,8 \right | – 3,5 $$

$$ \left | 3,8 + 2 \right | \div (-4) + 1,8 – 3,5 $$

$$ \left | 5,8 \right | \div (-4) + 1,8 – 3,5 $$

$$ 5,8 \div (-4) + 1,8 – 3,5 $$

$$ (-1,45) + 1,8 – 3,5 $$

$$ 0,35 – 3,5 $$

$$ \boxed{-3,15} $$

$$ 6 + \left | 2 \cdot \left ( 5 – 9 \right )\right | – 3 $$

$$ 6 + \left | 2 \cdot -4 \right | – 3 $$

$$ 6 + \left | -8 \right | – 3 $$

$$ 6 + 8 – 3 $$

$$ 14 – 3 $$

$$ \boxed{11} $$

$$ \frac{1}{2} + \left | \frac{4}{5} – \frac{11}{5} \right | – \left | – \frac{7}{10} \right | $$

$$ \frac{1}{2} + \left | – \frac{7}{5} \right | – \left | – \frac{7}{10} \right | $$

$$ \frac{1}{2} + \frac{7}{5} – \frac{7}{10} $$

Se calcula el m.c.m entre los denominadores para calcular fracciones equivalentes.

• \( M_{2} = \left\{2, 4, 6, 8, \boxed{10}, 12, …\right\} \)
• \( M_{5} = \left\{5, \boxed{10}, 15, 20, …\right\} \)
• \( M_{10} = \left\{\boxed{10}, 20, 30, 40, …\right\} \)

$$ M.C.M._{\left (2, 5, 10 \right )} = 10 $$

Se amplifica la primera fracción por 5 y segunda fracción por 2 para obtener en ambas denominador 10.

• \( \frac{1 {\color{Blue}\cdot 5}}{2 {\color{Blue}\cdot 5}} = \frac{5}{10} \)
• \( \frac{7 {\color{Blue}\cdot 2}}{5 {\color{Blue}\cdot 2}} = \frac{14}{10} \)

Reemplazo de las fracciones equivalentes.

$$ \frac{5}{10} + \frac{14}{10} – \frac{7}{10} $$

$$ \frac{5 + 14 – 7}{10} $$

$$ \frac{12}{10} $$

Se simplifica por 2 para obtener la fracción irreductible.

$$ \frac{12 {\color{Blue} \div 2}}{10 {\color{Blue} \div 2}} $$

$$ \boxed{\frac{6}{5}} $$

$$ \left | 54 – 23 \right | \cdot \left | 32 \div 8 \right | + 562 $$

$$ \left | 31 \right | \cdot \left | 4 \right | + 562 $$

$$ 31 \cdot 4 + 562 $$

$$ 124 + 562 $$

$$ \boxed{686} $$

$$ \left | -\frac{3}{2} \cdot -\frac{1}{4} \right | \cdot \left | \frac{4}{7} \div \frac{2}{3} \right |  $$

$$ \left | \frac{3}{8} \right | \cdot \left | \frac{4}{7} \cdot \frac{3}{2} \right |  $$

$$ \frac{3}{8} \cdot \left | \frac{12}{14}\right |  $$

$$ \frac{3}{8} \cdot \frac{12}{14}  $$

$$ \frac{36}{112}  $$

Se calcula el M.C.D entre el numerador y denominador para simplificar.

• \( D_{36} = \left\{1, 2, 3, \boxed{4}, 6, 9, 12, 18, 36\right\} \)
• \( D_{112} = \left\{1, 2, \boxed{4}, 7, 8, 14, 16, 28, 56, 112\right\} \)

$$ M.C.D._{\left (36, 112 \right )} = 4 $$

Se simplifica para obtener una fracción irreductible.

$$ \frac{36 {\color{Blue} \div 4}}{112 {\color{Blue} \div 4}}  $$

$$ \boxed{\frac{9}{28}}  $$