This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the fraction. The problem asks for the actual value of the expression (882)/(922). This means simplifying the fraction to its lowest terms. Step 2: Find the greatest common divisor (GCD) of the numerator and the denominator. First, find the prime factorization of the numerator, 882: 882 = 2 × 441 441 = 3 × 147 147 = 3 × 49 49 = 7 × 7 So, the prime factorization of 882 is 2 × 3^2 × 7^2. Next, find the prime factorization of the denominator, 922: 922 = 2 × 461 To check if 461 is prime, we test divisibility by prime numbers up to sqrt(461) ≈ 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 ÷ 7 = 65 with a remainder of 6. • 461 ÷ 11 = 41 with a remainder of 10. • 461 ÷ 13 = 35 with a remainder of 6. • 461 ÷ 17 = 27 with a remainder of 2. • 461 ÷ 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 × 461. The common factor between 882 and 922 is 2. Therefore, the GCD(882, 922) = 2. Step 3: Divide both the numerator and the denominator by their GCD. (882)/(922) = (882 ÷ 2)/(922 ÷ 2) (882)/(922) = (441)/(461) The fraction is now in its simplest form because 441 and 461 have no common factors other than 1. The actual value of (882)/(922) is (441)/(461).