Simplify : f. `(13)/(7) + 4 (4)/(5) xx (3)/(4) div (7)/(15)`

Answer

To simplify the expression \( \frac{13}{7} + 4 \frac{4}{5} \times \frac{3}{4} \div \frac{7}{15} \), we will follow the order of operations (BODMAS/BIDMAS). Here are the steps:

### Step 1: Convert the mixed fraction to an improper fraction
First, we convert the mixed fraction \( 4 \frac{4}{5} \) into an improper fraction.
\[ 4 \frac{4}{5} = 4 \times 5 + 4 = 20 + 4 = \frac{24}{5} \]

### Step 2: Rewrite the expression
Now, rewrite the expression with the improper fraction:
\[ \frac{13}{7} + \frac{24}{5} \times \frac{3}{4} \div \frac{7}{15} \]

### Step 3: Perform the division
Next, we handle the division \( \frac{3}{4} \div \frac{7}{15} \). To divide fractions, we multiply by the reciprocal:
\[ \frac{3}{4} \div \frac{7}{15} = \frac{3}{4} \times \frac{15}{7} = \frac{3 \times 15}{4 \times 7} = \frac{45}{28} \]

### Step 4: Substitute back into the expression
Now substitute this back into the expression:
\[ \frac{13}{7} + \frac{24}{5} \times \frac{45}{28} \]

### Step 5: Perform the multiplication
Now, multiply \( \frac{24}{5} \) by \( \frac{45}{28} \):
\[ \frac{24 \times 45}{5 \times 28} = \frac{1080}{140} \]

### Step 6: Simplify the fraction
Now simplify \( \frac{1080}{140} \):
\[ \frac{1080 \div 20}{140 \div 20} = \frac{54}{7} \]

### Step 7: Rewrite the expression
Now we have:
\[ \frac{13}{7} + \frac{54}{7} \]

### Step 8: Combine the fractions
Since both fractions have the same denominator, we can add them directly:
\[ \frac{13 + 54}{7} = \frac{67}{7} \]

### Step 9: Convert to a mixed number
To convert \( \frac{67}{7} \) into a mixed number, divide 67 by 7:
\[ 67 \div 7 = 9 \quad \text{(remainder 4)} \]
So, \( \frac{67}{7} = 9 \frac{4}{7} \).

### Final Answer
Thus, the simplified form of the expression is:
\[ 9 \frac{4}{7} \]