Among the fractions 1/2, 3/7, 3/5, and 4/9, which is the smallest in value?

Introduction / Context:
Comparing fractions can be done by converting to decimal, using cross-multiplication, or reducing them to a common denominator. We are to identify the smallest fraction among the given set.

Given Data / Assumptions:

• Fractions: 1/2, 3/7, 3/5, 4/9.
• All are positive proper fractions.

Concept / Approach:
Multiple quick methods exist. Decimal approximation: 1/2 = 0.5; 3/5 = 0.6; 4/9 ≈ 0.444…; 3/7 ≈ 0.42857…. The smallest decimal corresponds to the smallest fraction. Alternatively, compare via cross-multiplication pairwise if decimals are not desired.

Step-by-Step Solution:

Verification / Alternative check:
Use common denominator 630 (LCM of 2, 5, 7, 9): 1/2 = 315/630; 3/5 = 378/630; 4/9 = 280/630; 3/7 = 270/630. The smallest numerator is 270 for 3/7, confirming the result.

Why Other Options Are Wrong:

• 4/9 and 1/2 are larger than 3/7 but close.
• 3/5 equals 0.6, clearly the largest here among the listed fractions.

Common Pitfalls:

• Mistakenly comparing only denominators for proper fractions without considering numerators.
• Rounding too coarsely when using decimals.

Final Answer:
3/7