To find the actual value (वास्तविक मान) of the fraction (882)/(922). This means simplifying the fraction to its lowest terms.

The problem asks to find the actual value (वास्तविक मान) of the fraction $\frac{882}{922}$. This means simplifying the fraction to its lowest terms.

The numerator is 882.

So, the prime factorization of 882 is $2 \times 3^2 \times 7^2$.

The denominator is 922.

To determine if 461 is a prime number, we test for divisibility by prime numbers up to $\sqrt{461} \approx 21.47$. The prime numbers to check are 2, 3, 5, 7, 11, 13, 17, 19.

• 461 is not divisible by 2 (it is an odd number).
• The sum of its digits $4+6+1=11$, which is not divisible by 3.
• It does not end in 0 or 5, so it is not divisible by 5.
• $461 \div 7 = 65$ with a remainder of 6.
• $461 \div 11 = 41$ with a remainder of 10.
• $461 \div 13 = 35$ with a remainder of 6.
• $461 \div 17 = 27$ with a remainder of 2.
• $461 \div 19 = 24$ with a remainder of 5. Since 461 is not divisible by any prime number up to its square root, 461 is a prime number. So, the prime factorization of 922 is $2 \times 461$.

Comparing the prime factorizations:
$882 = 2 \times 3^2 \times 7^2$
$922 = 2 \times 461$
The only common prime factor is 2.
Therefore, the GCD of 882 and 922 is 2.

Divide both the numerator and the denominator by their GCD.

The fraction $\frac{441}{461}$ is in its simplest form because 441 and 461 have no common factors other than 1.

The actual value of $\frac{882}{922}$ is $\boxed{\frac{441}{461}}$.