Equal fractional forms: If a/7 = b/9 = c/11, determine the simplified ratio a : b : c.

Introduction / Context:
When several fractions are equal, each numerator is proportional to its denominator. This is a standard method to derive direct ratios from equal fractional relationships.

Given Data / Assumptions:
a/7 = b/9 = c/11 = k (say), with positive quantities for ratio interpretation.

Concept / Approach:
Express a, b, c in terms of k and their denominators. Then form the ratio and simplify if needed.

Step-by-Step Solution:
Let a/7 = b/9 = c/11 = k. Then a = 7k, b = 9k, c = 11k. Therefore, a : b : c = 7 : 9 : 11.

Verification / Alternative check:
Substitute sample k = 1 to see a = 7, b = 9, c = 11, which obviously satisfy the original equal fractions.

Why Other Options Are Wrong:

• Any permutation that does not keep denominators aligned with numerators will be incorrect.
• 14 : 18 : 22 is a correct multiple but not the simplest form the question expects.

Common Pitfalls:
Inverting denominators or mixing the order. Keep a aligned with 7, b with 9, and c with 11.

Final Answer:
7 : 9 : 11