Find the H.C.F. (greatest common divisor) of the fractions 1/2, 3/4, and 4/5.

Introduction / Context:
The HCF of multiple fractions is computed via the same rule as for two fractions: HCF of numerators divided by LCM of denominators. This problem applies that rule to three fractions simultaneously.

Given Data / Assumptions:

• Fractions: 1/2, 3/4, 4/5.
• All are positive rationals.

Concept / Approach:
For fractions a/b, c/d, e/f: HCF = HCF(a, c, e) / LCM(b, d, f). Compute the integer HCF of the numerators and the integer LCM of the denominators, then form the fraction.

Step-by-Step Solution:

Verification / Alternative check:
Check that 1/20 is a common fractional divisor: (1/2) ÷ (1/20) = 10; (3/4) ÷ (1/20) = 15; (4/5) ÷ (1/20) = 16. All quotients are integers, confirming 1/20 works; any larger fractional divisor would require a smaller denominator than 20, which would fail at least one fraction.

Why Other Options Are Wrong:

• 1/40: Too small; not the greatest possible.
• 20, 15: These are integers, not fractional HCFs here.
• 1/10: Larger than the true HCF; it does not divide all three fractions exactly.

Common Pitfalls:

• Confusing the rules for HCF and LCM of fractions.
• Forgetting to take HCF of numerators and LCM of denominators in the correct places.

Final Answer:
1/20