Simplify the fraction 882/922.

The problem asks for the actual value of the expression $\frac{882}{922}$. This means simplifying the fraction to its lowest terms.

First, find the prime factorization of the numerator, 882:

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

Next, find the prime factorization of the denominator, 922:

To check if 461 is prime, we test divisibility by prime numbers up to $\sqrt{461} \approx 21.47$.
Prime numbers to check: 2, 3, 5, 7, 11, 13, 17, 19.

• 461 is not divisible by 2 (it's odd).
• $4+6+1=11$, which is not divisible by 3.
• 461 does not end in 0 or 5, so it's 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 $2 \times 461$.

The common factor between 882 and 922 is 2. Therefore, the GCD(882, 922) = 2.

The fraction is now in its simplest form because 441 and 461 have no common factors other than 1.

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