The simplified value of `((3 1/5-3/5)div 8/5)/ (1 1/7 div {6/7-(1/7 div 1/5)})` :
`((3 1/5-3/5)div 8/5)/ (1 1/7 div {6/7-(1/7 div 1/5)})` का सरलीकृत मान है

Options

A. `13/64`
B. `13/16`
C. `13/8`
D. `13/7`

Answer

To simplify the expression \(\frac{(3 \frac{1}{5} - \frac{3}{5}) \div \frac{8}{5}}{(1 \frac{1}{7} \div ( \frac{6}{7} - (\frac{1}{7} \div \frac{1}{5} )))}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert \(3 \frac{1}{5}\) and \(1 \frac{1}{7}\) to improper fractions.

\[ 3 \frac{1}{5} = \frac{16}{5} \]
\[ 1 \frac{1}{7} = \frac{8}{7} \]

### Step 2: Substitute the Improper Fractions
Now substitute these values into the expression:

\[ \frac{(\frac{16}{5} - \frac{3}{5}) \div \frac{8}{5}}{(\frac{8}{7} \div (\frac{6}{7} - (\frac{1}{7} \div \frac{1}{5})) )} \]

### Step 3: Simplify the Numerator
In the numerator, simplify \(\frac{16}{5} - \frac{3}{5}\):

\[ \frac{16}{5} - \frac{3}{5} = \frac{16 - 3}{5} = \frac{13}{5} \]

Now the expression becomes:

\[ \frac{(\frac{13}{5}) \div \frac{8}{5}}{(\frac{8}{7} \div (\frac{6}{7} - (\frac{1}{7} \div \frac{1}{5})))} \]

### Step 4: Simplify the Division in the Numerator
Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \frac{13}{5} \div \frac{8}{5} = \frac{13}{5} \times \frac{5}{8} = \frac{13}{8} \]

### Step 5: Simplify the Denominator
Now, simplify the denominator:

First, calculate \(\frac{1}{7} \div \frac{1}{5}\):

\[ \frac{1}{7} \div \frac{1}{5} = \frac{1}{7} \times 5 = \frac{5}{7} \]

Now substitute this back into the denominator:

\[ \frac{6}{7} - \frac{5}{7} = \frac{1}{7} \]

So, the denominator now looks like:

\[ \frac{8}{7} \div \frac{1}{7} \]

### Step 6: Simplify the Division in the Denominator
Again, divide by a fraction:

\[ \frac{8}{7} \div \frac{1}{7} = \frac{8}{7} \times 7 = 8 \]

### Step 7: Combine the Results
Now we have:

\[ \frac{\frac{13}{8}}{8} \]

This can be simplified as follows:

\[ \frac{13}{8} \div 8 = \frac{13}{8} \times \frac{1}{8} = \frac{13}{64} \]

### Final Result
Thus, the simplified value of the expression is:

\[ \frac{13}{64} \]