Scale a known quotient to a new one: Given 2805 ÷ 2.55 = 1100, evaluate 280.5 ÷ 25.5 by using proportional scaling rather than long division.

Introduction / Context:When a related quotient is known, you can exploit scaling to find a new quotient quickly. This avoids redundant long division and is a powerful test shortcut in decimal-fraction topics.

Given Data / Assumptions:

• Known: 2805 ÷ 2.55 = 1100
• Find: 280.5 ÷ 25.5

Concept / Approach:Observe that the new numerator is 1/10 of 2805 and the new denominator is 10 times 2.55. Since division is multiplicative, (a/10) ÷ (10b) = (a/b) ÷ 100. Thus the new quotient equals the old quotient divided by 100.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1.01, 1.1, 0.11: These represent dividing by 1000, 10, or 10,000 incorrectly; the correct scaling factor is 100.

Common Pitfalls:

• Not applying equal decimal shifts to numerator and denominator.
• Mishandling powers of 10 while rescaling.

Final Answer: