| Directions: What should come at the place of question mark (?) in the following questions? |
| \[1-\frac{5}{7+\frac{1}{4+\frac{1}{2+\frac{1}{3}}}}=?\] |
A) \[\frac{39}{127}\]
B) \[\frac{69}{224}\]
C) \[\frac{42}{247}\]
D) \[\frac{63}{771}\]
Correct Answer: B
Solution :
| \[1-\frac{5}{7+\frac{1}{4+\frac{1}{2\frac{1}{3}}}}=1-\frac{5}{7+\frac{1}{4+\frac{1}{3}}}=1-\frac{5}{7+\frac{1}{4+\frac{3}{7}}}\] |
| \[=1-\frac{5}{7+\frac{1}{\frac{31}{7}}}=1-\frac{5}{7+\frac{7}{31}}=1-\frac{5}{\frac{7\times 31+7}{31}}\] |
| \[=1-\frac{5\times 31}{217+7}=1\frac{155}{224}\] |
| \[=\frac{224-155}{224}=\frac{69}{224}\] |
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