Calculate the value of the expression: (22 × 495 + 891 × 44) divided by (33 × 176 + 55 × 264). What is the result?

Explanation

First, rewrite the terms with common factors: (22 × 495 + 891 × 44) = (22 × 33 × 15 + 9 × 99 × 2 × 22) and (33 × 176 + 55 × 264) = (33 × 22 × 8 + 5 × 11 × 22 × 12). Simplifying both numerator and denominator gives (22 × 33 × 15 + 22 × 33 × 54) over (33 × 22 × 8 + 33 × 22 × 20). Factoring out common terms results in (22 × 33)(15 + 54) divided by (33 × 22)(8 + 20), which simplifies to 69/28. Thus, the value of the expression is 2.