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The question asks for the correct expanded ratio when the initial ratio of \( A : B : C = 2 : 3 : 4 \).

To expand the ratio, let's first understand that we need to find a form where each part of the ratio is scaled similarly. Let's examine each option:

1. **Option 1: \(8 : 9 : 16\)**  
   If we multiply the original ratio \(2 : 3 : 4\) by 4, we get:
   \[
   2 \times 4 : 3 \times 4 : 4 \times 4 = 8 : 12 : 16
   \]
   So, this option does not match because it has \(9\) as the middle term.

2. **Option 2: \(8 : 9 : 12\)**  
   Similar to above, scaling \(2 : 3 : 4\) by any factor will not yield \(8 : 9 : 12\), as the middle term remains 9, which is inconsistent.

3. **Option 3: \(8 : 9 : 24\)**  
   Once again, scaling cannot give us \(9\) as a term in the middle, so this is also incorrect.

4. **Option 4: \(4 : 9 : 16\)**  
   To see if this could be correct, we can try checking if each number in this ratio maintains the relation \(2 : 3 : 4\). Dividing each term by their common factors:
   \[
   4 : 9 : 16 \neq 2 : 3 : 4
   \]



If A:B:C = 2:3:4, then the ratio will be?

Learn how to solve and expand the ratio A:B:C = 2:3:4 by multiplying each term. This math problem teaches key concepts about ratios and proportions, ideal for students in Grades 6-8.

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