Among the ratios 7 : 15, 15 : 23, 17 : 25, and 21 : 29, which is the smallest?

Introduction / Context:
To compare fractions a:b, compute a/b (or cross-multiply pairwise). The smallest fraction corresponds to the smallest decimal value. We compare the four given ratios by converting to decimals or by quick cross-multiplications.

Given Data / Assumptions:

• Ratios: 7:15, 15:23, 17:25, 21:29
• All positive, so direct comparison of decimals is valid.

Concept / Approach:
Compute approximate decimals: 7/15 ≈ 0.4667; 15/23 ≈ 0.6522; 17/25 = 0.68; 21/29 ≈ 0.724. The smallest is the least decimal value.

Step-by-Step Solution:
7/15 ≈ 0.466715/23 ≈ 0.652217/25 = 0.6821/29 ≈ 0.724Smallest = 7 : 15

Verification / Alternative check:
Cross-multiply 7/15 vs. each other ratio to confirm 7/15 is smaller in each comparison.

Why Other Options Are Wrong:
Each corresponds to a larger decimal value and hence a larger ratio.

Common Pitfalls:
Assuming larger denominators always mean smaller fractions without considering numerators; rounding too coarsely.

Final Answer:
7 : 15