Find the HCF of several fractions Determine the highest common factor (HCF) of 1/2, 3/4, 5/6, 7/8, and 9/10 using the standard fraction-HCF rule.

Introduction / Context:
For fractions, the HCF (also called GCD) uses a reversed version of the LCM rule: take HCF of numerators and divide by LCM of denominators. This yields the greatest fraction that divides each given fraction exactly.

Given Data / Assumptions:

• Fractions: 1/2, 3/4, 5/6, 7/8, 9/10.
• Rule: HCF(fractions) = HCF(numerators) / LCM(denominators).

Concept / Approach:
Compute HCF(1, 3, 5, 7, 9) and LCM(2, 4, 6, 8, 10), then form the fraction HCF/LCM in lowest terms.

Step-by-Step Solution:
HCF of numerators: gcd(1, 3, 5, 7, 9) = 1.LCM of denominators: LCM(2, 4, 6, 8, 10) = 120.Therefore HCF of fractions = 1 / 120.

Verification / Alternative check:
Check that 1/120 divides each given fraction: e.g., (1/2) ÷ (1/120) = 60, (3/4) ÷ (1/120) = 90, etc. All quotients are integers, confirming correctness.

Why Other Options Are Wrong:
1/2 and 1/10 are too large to divide all given fractions exactly; 9/120 is not the greatest common factor by rule; 3/20 does not divide 1/2 an integer number of times when considered with all others.

Common Pitfalls:
Taking LCM of numerators and HCF of denominators (reversing the rule), or reducing early and losing track of the largest common divisor.

Final Answer:
1/120