Evaluate: f. `3 xx 7 (3)/(7) x 3 (3)/( 13)`

Answer

To evaluate the expression \( 3 \times 7 \frac{3}{7} \times 3 \frac{3}{13} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers \( 7 \frac{3}{7} \) and \( 3 \frac{3}{13} \) into improper fractions.

- For \( 7 \frac{3}{7} \):
\[ 7 \frac{3}{7} = 7 + \frac{3}{7} = \frac{7 \times 7 + 3}{7} = \frac{49 + 3}{7} = \frac{52}{7} \]

- For \( 3 \frac{3}{13} \):
\[ 3 \frac{3}{13} = 3 + \frac{3}{13} = \frac{3 \times 13 + 3}{13} = \frac{39 + 3}{13} = \frac{42}{13} \]

### Step 2: Rewrite the Expression
Now we can rewrite the original expression using the improper fractions:
\[ 3 \times \frac{52}{7} \times \frac{42}{13} \]

### Step 3: Multiply the Fractions
Next, we will multiply the fractions together:
\[ = 3 \times \frac{52 \times 42}{7 \times 13} \]

### Step 4: Simplify the Expression
Now we can simplify the multiplication:
- First, calculate \( 52 \times 42 \):
\[ 52 \times 42 = 2184 \]

- Next, calculate \( 7 \times 13 \):
\[ 7 \times 13 = 91 \]

So, we have:
\[ = 3 \times \frac{2184}{91} \]

### Step 5: Divide and Multiply
Now we will divide \( 2184 \) by \( 91 \):
\[ 2184 \div 91 = 24 \]

Now multiply by \( 3 \):
\[ 3 \times 24 = 72 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{72} \]

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