Approximation using complements: Compute 98743 ÷ 198 and express it as 800 − ?, then determine the missing value (closest option).

Introduction / Context:This problem reframes a division as a complement-to-800 calculation. By first approximating or computing 98743 ÷ 198, we can subtract the quotient from 800 to obtain the required missing amount. This is a common trick to make mental computation easier when the target figure is a round number like 800.

Given Data / Assumptions:

• N = 98743
• D = 198
• We want 800 − (N ÷ D)

Concept / Approach:Compute or estimate the quotient Q = N / D. Then the answer is 800 − Q. Because 198 is very close to 200, we can use 98743/200 as a quick ballpark and refine slightly since dividing by 198 gives a slightly larger quotient than dividing by 200.

Step-by-Step Solution:

Verification / Alternative check:Use back-multiplication: if the answer were exactly 300, then the quotient would be 800 − 300 = 500. That is very close to 498.7, and 300 is the nearest given option to 301.3.

Why Other Options Are Wrong:

• 200: Implies quotient 600, too high.
• 250: Implies quotient 550, too high.
• 350: Implies quotient 450, too low.
• 275: Implies quotient 525, still too high.

Common Pitfalls:Forgetting that a smaller divisor (198 vs. 200) increases the quotient; also, rounding too coarsely can push the complement far away from the true value.

Final Answer:300