Question

Find the value of  \(\frac{1}{1\space+\space\frac{1}{1\space+\space\frac{2}{3}}}\times \frac{1}{\frac{1}{5}\space of\space{45}\space \div\space 3}\space +\space\frac{1}{1\space+\space\frac{2}{2\space+\space\frac{1}{3}}}\)
1. 233/312
2. 240/311
3. 312/311
4. 233/234

Answer 1

Correct Answer - Option 1 : 233/312

Given:

\(\frac{1}{1\space+\space\frac{1}{1\space+\space\frac{2}{3}}}× \frac{1}{\frac{1}{5}\space of\space{45}\space \div\space 3}\space +\space\frac{1}{1\space+\space\frac{2}{2\space+\space\frac{1}{3}}}\)

Calculation:

\(\frac{1}{1\space+\space\frac{1}{1\space+\space\frac{2}{3}}}× \frac{1}{\frac{1}{5}\space of\space{45}\space \div\space 3}\space +\space\frac{1}{1\space+\space\frac{2}{2\space+\space\frac{1}{3}}}\)

⇒ 1/(1 + 3/5) × 1/3 + 1/(1 + 6/7)

⇒ 5/24 + 7/13

⇒ (65 + 168)/(24 × 13)

⇒ 233/312

∴ The required value is 233/312.