The simplified value of \[ \left(\frac{\frac{17}{21}}{\frac{17}{3}}\right) \div \left(\frac{2}{6}\times\frac{12}{6}+\frac{2}{7}\right) +\frac{3}{7}\div\frac{20}{12}\text{ of }\frac{12}{7} \] is:
\(\frac{3}{10}\)
Given:
\[ \left(\frac{\frac{17}{21}}{\frac{17}{3}}\right) \div \left(\frac{2}{6}\times\frac{12}{6}+\frac{2}{7}\right) +\frac{3}{7}\div\left(\frac{20}{12}\text{ of }\frac{12}{7}\right) \]
Step 1: Simplify the first fraction
\[ \frac{\frac{17}{21}}{\frac{17}{3}} =\frac{17}{21}\times\frac{3}{17} =\frac{1}{7} \]
Step 2: Simplify the bracket
\[ \frac{2}{6}\times\frac{12}{6}+\frac{2}{7} =\frac{1}{3}\times2+\frac{2}{7} \]
\[ =\frac{2}{3}+\frac{2}{7} =\frac{14+6}{21} =\frac{20}{21} \]
Therefore,
\[ \frac{1}{7}\div\frac{20}{21} =\frac{1}{7}\times\frac{21}{20} =\frac{3}{20} \]
Step 3: Simplify the second part
\[ \frac{20}{12}\text{ of }\frac{12}{7} =\frac{20}{12}\times\frac{12}{7} =\frac{20}{7} \]
Thus,
\[ \frac{3}{7}\div\frac{20}{7} =\frac{3}{7}\times\frac{7}{20} =\frac{3}{20} \]
Step 4: Add both parts
\[ \frac{3}{20}+\frac{3}{20} =\frac{6}{20} =\frac{3}{10} \]
Hence, \(\boxed{\frac{3}{10}}\)
Important Questions from Fractions
The value of $\frac{5}{3} + (\frac{1}{1+\frac{5}{6}}) - \frac{5}{3}$ is
The value of $\frac{4}{5} + (\frac{1}{1+\frac{5}{6}}) - \frac{2}{5}$ is
- The value of $\frac{5}{2} + \frac{1}{(1 + \frac{3}{8})} - \frac{3}{5}$ is
- Ritik and Sanjay together invested ₹62,400 in a business. At the end of the year, out of a total profit of ₹15,600, Sanjay's share was ₹1,900. What was the difference between their investments?
- The value of $\frac{3}{4} + \frac{1}{\left(1+\frac{3}{7}\right)} - \frac{3}{4}$ is
