Question

{(1/2+1/3)+1/4-(1-5/8)}+2/3

Answer 1

$\left\{\left(\dfrac{1}{2}+\dfrac{1}{3} \right )+\dfrac{1}{4}-\left(1-\dfrac{5}{8} \right ) \right \}+\dfrac{2}{3}$


Resolvemos as expressões dos parênteses primeiro. Como estamos operando com frações de denominadores diferentes, devemos tirar o m.m.c. dos denominadores:

$\left\{\left(\dfrac{1}{2}+\dfrac{1}{3} \right )+\dfrac{1}{4}-\left(1-\dfrac{5}{8} \right ) \right \}+\dfrac{2}{3}\\ \\ =\left\{\left(\dfrac{6\div2 \times 1}{6}+\dfrac{6 \div 3 \times 1}{6} \right )+\dfrac{1}{4}-\left(\dfrac{8}{8}-\dfrac{5}{8} \right ) \right \}+\dfrac{2}{3}\\ \\ =\left\{\left(\dfrac{3 \times 1}{6}+\dfrac{2 \times 1}{6} \right )+\dfrac{1}{4}-\left(\dfrac{8-5}{8} \right ) \right \}+\dfrac{2}{3}\\ \\ =\left\{\left(\dfrac{3}{6}+\dfrac{2}{6} \right )+\dfrac{1}{4}-\left(\dfrac{3}{8} \right ) \right \}+\dfrac{2}{3}\\ \\ =\left\{\left(\dfrac{3+2}{6} \right )+\dfrac{1}{4}-\dfrac{3}{8} \right \}+\dfrac{2}{3}\\ \\ =\left\{\dfrac{5}{6}+\dfrac{1}{4}-\dfrac{3}{8} \right \}+\dfrac{2}{3}\\ \\ =\left\{\dfrac{24 \div 6 \times 5}{24}+\dfrac{24 \div 4 \times 1}{24}-\dfrac{24 \div 8 \times 3}{24} \right \}+\dfrac{2}{3}\\ \\ =\left\{\dfrac{4 \times 5}{24}+\dfrac{6 \times 1}{24}-\dfrac{3 \times 3}{24} \right \}+\dfrac{2}{3}$
$=\left\{\dfrac{4 \times 5}{24}+\dfrac{6 \times 1}{24}-\dfrac{3 \times 3}{24} \right \}+\dfrac{2}{3}\\ \\ =\left\{\dfrac{20}{24}+\dfrac{6}{24}-\dfrac{9}{24} \right \}+\dfrac{2}{3}\\ \\ =\left\{\dfrac{20+6-9}{24} \right \}+\dfrac{2}{3}\\ \\ =\dfrac{17}{24}+\dfrac{2}{3}\\ \\ =\dfrac{17}{24}+\dfrac{24 \div 3 \times 2}{24}\\ \\ =\dfrac{17}{24}+\dfrac{8 \times 2}{24}\\ \\ =\dfrac{17}{24}+\dfrac{16}{24}\\ \\ =\dfrac{17+16}{24}\\ \\ =\dfrac{33}{24}\\ \\ =\dfrac{33 \div 3}{24 \div 3}\\ \\ =\dfrac{11}{8}$

Answer 2

Oi,

Resolução

{(1/2+1/3)+1/4-(1-5/8)}+2/3
{(3/6 + 2/6)+1/4-(8/8 - 5/8)}+2/3
{5/6 + 1/4 - 3/8} + 2/3
{ 20/24 + 6/24 - 9/24 + 2/3 }
20/24 + 6/24 - 9/24 + 16/24 = 33/24 = 11/8

Espero ter ajudado e bons estudos !