Question : The value of $0.4 \overline{6}+0.7 \overline{23}-0.3 \overline{9} \times 0. \overline{7}$ is:
Option 1: $0.\overline{97}$
Option 2: $0.\overline{57}$
Option 3: $0.\overline{77}$
Option 4: $0.\overline{87}$
Correct Answer: $0.\overline{87}$
Solution :
$0.4 \overline{6}+0.7 \overline{23}-0.3 \overline{9} \times 0. \overline{7}$
= $\frac{46-4}{90} + \frac{723-7}{990} - \frac{39-3}{90} × \frac{7}{9}$
= $\frac{42}{90} + \frac{716}{990} - (\frac{36}{90} × \frac{7}{9})$
= $\frac{42}{90} + \frac{716}{990} - \frac{28}{90}$
= $\frac{14}{90} + \frac{716}{990}$
= $\frac{154+716}{990}$
= $\frac{870}{990}$
= 0.878787....
= $0.\overline{87}$
Hence, the correct answer is $0.\overline{87}$.
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