Question

Resolva a expressão (0,3636...) : (0,1212...) + (0,25) : (0,5) - 1/2 + 6

Answer 1

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Cálculos preliminares:
$0,3636...= \frac{36^{:9}}{99_{:9}} = \frac{4}{11} \\ \\0,1212...= \frac{12^{:3}}{99_{:3}} = \frac{4}{33} \\ \\ 0,25=\frac{25^{:25}}{100_{:25}} = \frac{1}{4} \\ \\ 0,5=\frac{5^{:5}}{10_{:5}} = \frac{1}{2}$
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$(0,3636...) : (0,1212...) + (0,25) : (0,5) - 1/2 + 6\\ \\= \frac{4}{11} : \frac{4}{33} +\frac{1}{4} : \frac{1}{2} - \frac{1}{2} + 6\\ \\= \frac{4}{11} \cdot \frac{33}{4} +\frac{1}{4} \cdot \frac{2}{1} - \frac{1}{2} + 6\\ \\= \frac{33}{11} +\frac{2}{4} - \frac{1}{2} + 6\\ \\= 3 +\frac{2^{:2}}{4_{:2}} - \frac{1}{2} + 6\\ \\= 3 +\frac{1}{2} - \frac{1}{2} + 6\\ \\= 3 + 6\\ \\= 9$