Simplify the numerical expression exactly: (-21973) * (-1253) / 275123 What is the simplified exact value as a fraction in lowest terms?

Introduction / Context:
This question tests integer multiplication, sign handling, and fraction reduction. The main objective is to compute the exact rational value and reduce it to lowest terms (no common factor between numerator and denominator).

Given Data / Assumptions:

• Expression: (-21973) * (-1253) / 275123
• Exact simplification is required (no rounding).

Concept / Approach:
First handle the sign: negative times negative is positive. Then multiply the integers to get the numerator. Finally, reduce the resulting fraction by dividing numerator and denominator by their greatest common divisor (gcd), if any.

Step-by-Step Solution:

Verification / Alternative check:
A quick reasonableness check: 153811/1537 is about 100.07, so the value is a bit above 100. That is consistent with multiplying two ~2e4 and ~1e3 numbers then dividing by ~2.7e5, giving a result around 100.

Why Other Options Are Wrong:

Common Pitfalls:
Sign errors, skipping fraction reduction, and arithmetic slips in long multiplication. Also, cancelling without confirming a true common factor is a frequent mistake.

Final Answer:
153811/1537