Question

Calcule o valor da expressão
abaixo:
1,969696... - (0,333... -0,5)
0,454545... +0,4666...

Answer 1

Explicação passo-a-passo:

• $\sf 1,9696\dots=\dfrac{196-1}{99}=\dfrac{195}{99}=\dfrac{65}{33}$

• $\sf 0,333\dots=\dfrac{3}{9}=\dfrac{1}{3}$

• $\sf 0,5=\dfrac{5}{10}=\dfrac{1}{2}$

• $\sf 0,4545\dots=\dfrac{45}{99}=\dfrac{5}{11}$

• $\sf 0,4666\dots=\dfrac{46-4}{90}=\dfrac{42}{90}=\dfrac{14}{30}$

Temos:

$\sf \dfrac{1,9696\dots-(0,333\dots-0,5)}{0,4545\dots+0,4666\dots}$

$\sf =\dfrac{\frac{65}{33}-\Big(\frac{1}{3}-\frac{1}{2}\Big)}{\frac{5}{11}+\frac{14}{30}}$

$\sf =\dfrac{\frac{65}{33}-\Big(\frac{2-3}{6}\Big)}{\frac{150+154}{330}}$

$\sf =\dfrac{\frac{65}{33}-\Big(-\frac{1}{6}\Big)}{\frac{150+154}{330}}$

$\sf =\dfrac{\frac{65}{33}+\frac{1}{6}}{\frac{304}{330}}$

$\sf =\dfrac{\frac{130+11}{66}}{\frac{152}{165}}$

$\sf =\dfrac{\frac{47}{22}}{\frac{152}{165}}$

$\sf =\dfrac{47}{22}\cdot\dfrac{165}{152}$

$\sf =\dfrac{7755}{3344}$

$\sf =\red{\dfrac{705}{304}}$