If four-fifths (4/5) of a certain number is 64, what is half of that number?

Introduction / Context:
Scaling numbers using fractions is a frequent aptitude task. Given a fractional value of an unknown, you can recover the whole and then compute any other required fraction, such as one-half in this problem.

Given Data / Assumptions:

• (4/5) * N = 64.
• We need (1/2) * N.
• N is positive.

Concept / Approach:
Solve for N directly by multiplying both sides by the reciprocal of 4/5, which is 5/4. Once N is known, take half to answer the question. Always keep operations symbolic to avoid arithmetic mistakes, then substitute numbers.

Step-by-Step Solution:

Verification / Alternative check:
Check the given: (4/5) * 80 = 64; correct. The requested half is 40; consistent.

Why Other Options Are Wrong:
32 and 16 are smaller fractions (1/2 of 64 or 1/4 of 64) misapplied; 80 is the full number, not half; 64 merely restates the given 4/5 value.

Common Pitfalls:
Multiplying by 4/5 instead of its reciprocal; halving 64 directly (confusing the target with the given part).

Final Answer:
40