14/17 •34/63

To multiply the fractions \( \frac{14}{17} \) and \( \frac{34}{63} \), you can follow these steps:

1. Multiply the numerators: \[ 14 \times 34 = 476 \]
2. Multiply the denominators: \[ 17 \times 63 = 1071 \]
3. Combine the results: \[ \frac{476}{1071} \]

Now, let's check if this fraction can be simplified.

Both 476 and 1071 can be divided by their greatest common divisor (GCD). Let's find the GCD.

• The factors of 476 are 1, 2, 4, 7, 14, 19, 28, 38, 68, 119, 238, and 476.
• The factors of 1071 are 1, 3, 11, 33, 37, 99, 333, and 1071.

The GCD is 1, meaning \( \frac{476}{1071} \) cannot be simplified further.

Therefore, the final answer is: \[ \frac{476}{1071} \]