Fractional composition of a number: Two-fifths of one-fourth of three-sevenths of a number equals 15. What is one-half of that number?

Introduction / Context:
This is a unit-fractions chaining problem that checks comfort with multiplying fractions and solving for an unknown. We are told that successive fractions of a number produce 15, and we are asked to find half of the original number.

Given Data / Assumptions:

• (2/5) * (1/4) * (3/7) * N = 15
• N is a real number
• Goal: compute (1/2) * N

Concept / Approach:
Combine the fractional multipliers first to avoid errors. Then solve for N by dividing 15 by the combined factor. Finally, take half of N as required.

Step-by-Step Solution:
Combined factor = (2 * 1 * 3) / (5 * 4 * 7) = 6 / 140 = 3 / 70(3/70) * N = 15 → N = 15 * (70/3) = 350Half of N = 350 / 2 = 175

Verification / Alternative check:
Back-substitute: (2/5)*(1/4)*(3/7)*350 = (3/70)*350 = 15, consistent. Half is then clearly 175.

Why Other Options Are Wrong:
168, 196, 210, 240 result from arithmetic slips such as inverting fractions incorrectly or mis-multiplying numerators/denominators.

Common Pitfalls:
Mixing the fraction order or canceling incorrectly. Keep numerators and denominators aligned and simplify only when safe.

Final Answer:
175