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To check if the given ratios are equivalent to \(2:3\), we can reduce each ratio to its simplest form or compare the cross products of each ratio with \(2:3\).

### Step-by-step breakdown:

1. **18:12**  
   To simplify, divide both numbers by their greatest common divisor (GCD), which is 6:  
   \[
   \frac{18}{12} = \frac{18 \div 6}{12 \div 6} = \frac{3}{2}
   \]
   This simplifies to \(3:2\), which is **not equivalent** to \(2:3\).

2. **12:18**  
   Simplify by dividing both numbers by their GCD, which is 6:  
   \[
   \frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}
   \]
   This simplifies to \(2:3\), which is **equivalent** to \(2:3\).

3. **28:27**  
   Simplify by dividing both numbers by their GCD, which is 1 (as 28 and 27 are coprime):  
   \[
   \frac{28}{27} = \frac{28}{27}
   \]
   This is already in its simplest form and is **not equivalent** to \(2:3\).

### Correct Equivalent Ratio:
- **12:18** is the only ratio equivalent to \(2:3\).

Would you like more details, or do you have any questions?

Here are some follow-up questions for further exploration:
1. How can you quickly check if two ratios are equivalent?
2. What does the GCD represent, and how is it useful in simplifying ratios?
3. Can two ratios with different numbers still be equivalent? Why?
4. How do cross products help in comparing ratios?
5. How could you visualize equivalent ratios on a graph?

**Tip:** When simplifying ratios, always find the greatest common divisor (GCD) of the two numbers to reduce them efficiently.

Learn how to identify which ratios are equivalent to 2:3 by using simplification and GCD methods. This problem involves simplifying ratios like 18:12, 12:18, and 28:27, comparing them to 2:3. Ideal for students in Grades 6-8.

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