https://file.aiquickdraw.com/mathbot/file/1729301601931fy3fesv4.jpg

The question asks to select all ratios equivalent to \(6:2\). To check if the given ratios are equivalent, we can simplify each ratio and compare it to the simplified form of \(6:2\).

1. **Simplify \(6:2\)**:
   \[
   \frac{6}{2} = 3:1
   \]
   So, the simplified form of \(6:2\) is \(3:1\).

2. **Check each ratio**:
   - **\(42:14\)**:
     \[
     \frac{42}{14} = 3:1
     \]
     So, \(42:14\) is equivalent to \(6:2\).
   
   - **\(9:3\)**:
     \[
     \frac{9}{3} = 3:1
     \]
     So, \(9:3\) is equivalent to \(6:2\).
   
   - **\(60:20\)**:
     \[
     \frac{60}{20} = 3:1
     \]
     So, \(60:20\) is equivalent to \(6:2\).

Therefore, all three ratios (\(42:14\), \(9:3\), and \(60:20\)) are equivalent to \(6:2\), and the selection in the image is correct.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How do you simplify ratios in general?
2. Can you explain why ratios are considered equivalent?
3. How can you verify if two ratios are proportional?
4. What are real-life examples of ratios that can be simplified similarly?
5. How do you find the greatest common divisor (GCD) for simplifying ratios?

**Tip**: Always simplify ratios by dividing both terms by their greatest common divisor (GCD) to ensure clarity and correctness.

Learn how to determine equivalent ratios by simplifying ratios. This example uses 6:2, showing how ratios like 42:14, 9:3, and 60:20 are equivalent by simplifying them to their lowest form. Perfect for students in Grades 5-7.

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