The simplified value of (`7/5 divide 7/10` of `3/4` ) `divide 4/9` - (`7/16 divide 10 1/2 xx 7 1/5)xx 5/12` is

Options

A. `47/8`
B. `39/4`
C. `49/8`
D. `41/4`

Answer

To solve the expression step by step, we will break it down into manageable parts.

### Step 1: Write the Expression
The expression we need to simplify is:
\[ \left( \frac{7}{5} \div \frac{7}{10} \times \frac{3}{4} \right) \div \frac{4}{9} - \left( \frac{7}{16} \div 10 \frac{1}{2} \times 7 \frac{1}{5} \times \frac{5}{12} \right) \]

### Step 2: Convert Mixed Numbers to Improper Fractions
Convert the mixed numbers into improper fractions:
- \(10 \frac{1}{2} = \frac{21}{2}\)
- \(7 \frac{1}{5} = \frac{36}{5}\)

Now, the expression becomes:
\[ \left( \frac{7}{5} \div \frac{7}{10} \times \frac{3}{4} \right) \div \frac{4}{9} - \left( \frac{7}{16} \div \frac{21}{2} \times \frac{36}{5} \times \frac{5}{12} \right) \]

### Step 3: Simplify the First Part
First, simplify the left part:
\[ \frac{7}{5} \div \frac{7}{10} = \frac{7}{5} \times \frac{10}{7} = \frac{10}{5} = 2 \]
Now multiply by \(\frac{3}{4}\):
\[ 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \]
Now divide by \(\frac{4}{9}\):
\[ \frac{3}{2} \div \frac{4}{9} = \frac{3}{2} \times \frac{9}{4} = \frac{27}{8} \]

### Step 4: Simplify the Second Part
Now simplify the right part:
\[ \frac{7}{16} \div \frac{21}{2} = \frac{7}{16} \times \frac{2}{21} = \frac{14}{336} = \frac{1}{24} \]
Now multiply by \(\frac{36}{5}\):
\[ \frac{1}{24} \times \frac{36}{5} = \frac{36}{120} = \frac{3}{10} \]
Now multiply by \(\frac{5}{12}\):
\[ \frac{3}{10} \times \frac{5}{12} = \frac{15}{120} = \frac{1}{8} \]

### Step 5: Combine Both Parts
Now we have:
\[ \frac{27}{8} - \frac{1}{8} = \frac{27 - 1}{8} = \frac{26}{8} = \frac{13}{4} \]

### Final Answer
The simplified value is:
\[ \frac{13}{4} \]