Find the H.C.F. (greatest common divisor) of the fractions 4/5 and 7/15.

Introduction / Context:
For fractions, the HCF (also called GCD) is computed using a specific rule that involves the numerators and denominators separately. This problem checks knowledge of that rule and careful simplification.

Given Data / Assumptions:

• Fractions: 4/5 and 7/15.
• All values are positive rational numbers.

Concept / Approach:
The HCF of fractions a/b and c/d is given by HCF(numerators) / LCM(denominators). Thus compute HCF(4, 7) and LCM(5, 15). Since 4 and 7 are coprime, their HCF is 1. For 5 and 15, LCM is 15.

Step-by-Step Solution:

Verification / Alternative check:
Any common fractional divisor must be at most 1/15 because 1/15 times an integer must divide both fractions cleanly; testing confirms 1/15 is feasible and larger fractional candidates fail simultaneously for both fractions.

Why Other Options Are Wrong:

• 1/5 and 1/25: Do not satisfy the fraction HCF rule here.
• 1/13 and 2/15: Not derived from HCF(4, 7) and LCM(5, 15); these are distractors.

Common Pitfalls:

• Using LCM of numerators over HCF of denominators (that is for LCM of fractions, not HCF).

Final Answer:
1/15