Find the original fraction given: the numerator is 4 less than the denominator. If the numerator is decreased by 2 and the denominator increased by 1, the new denominator becomes eight times the new numerator. Determine the fraction.

Introduction / Context: This question involves building equations from a word description of a fraction and solving for numerator and denominator using simple algebra.

Given Data / Assumptions:

• Let the fraction be n/d.
• n = d - 4.
• After changes: (n - 2) and (d + 1) satisfy (d + 1) = 8 * (n - 2).

Concept / Approach: Translate the statements into algebraic equations, then substitute n = d - 4 into the second condition to solve for d and n. Ensure the fraction is in simplest terms at the end if needed.

Step-by-Step Solution:

Verification / Alternative check: New numerator = 1, new denominator = 8; indeed 8 = 8 * 1 holds. Original condition n = d - 4 also holds (3 = 7 - 4).

Why Other Options Are Wrong: 4/8 simplifies to 1/2 and fails the transformed condition; 2/7 and 3/8 do not satisfy d + 1 = 8(n - 2).

Common Pitfalls: Misreading “becomes eight times” or forgetting to adjust both numerator and denominator as specified; mixing up original and transformed values; not simplifying relationships before solving.

Final Answer: 3/7