Find the compound ratio (product of ratios) of 2 : 7, 5 : 3, and 4 : 7. Express your answer as a : b in simplest terms.

Introduction / Context:
The compound ratio of several ratios is obtained by multiplying them termwise: (a1 : b1) × (a2 : b2) × (a3 : b3) = (a1*a2*a3) : (b1*b2*b3).

Given Data / Assumptions:
Ratios: 2 : 7, 5 : 3, and 4 : 7.

Concept / Approach:
Multiply numerators together and denominators together, then simplify if needed.

Step-by-Step Solution:
Numerators: 2 * 5 * 4 = 40. Denominators: 7 * 3 * 7 = 147. Compound ratio = 40 : 147.

Verification / Alternative check:
Consider fractions: (2/7) * (5/3) * (4/7) = 40/147, matching the ratio.

Why Other Options Are Wrong:
147 : 40 swaps order; 147 : 30 and 30 : 147 arise from incorrect multiplication.

Common Pitfalls:
Forgetting to multiply all numerators together and denominators together, or simplifying prematurely.

Final Answer:
40 : 147